From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Dec 1 21:33:44 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB23Xg913403 for reliable_computing-outgoing; Sun, 1 Dec 2002 21:33:42 -0600 (CST) Received: from mail.comset.net (mail.comset.net [213.172.0.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB23XYi13394 for ; Sun, 1 Dec 2002 21:33:35 -0600 (CST) Received: from 8-124.dialup.comset.net ([213.172.8.124] helo=e0gumi46) by mail.comset.net with smtp (Exim 3.33 #1) id 18IhNo-0002lP-00 for reliable_computing [at] interval [dot] louisiana.edu; Mon, 02 Dec 2002 06:36:32 +0300 Message-ID: <001f01c299b3$0ad7b660$710bfea9 [at] wplus [dot] net> From: "Vyacheslav Nesterov" To: "RC mailing list" Subject: be careful !! Date: Mon, 2 Dec 2002 06:28:56 +0300 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_001C_01C299CC.175C53A0" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------=_NextPart_000_001C_01C299CC.175C53A0 Content-Type: text/plain; charset="koi8-r" Content-Transfer-Encoding: quoted-printable Colleagues, I just received a message from the address=20 nest [at] tiscali [dot] fr The received message is the exact copy of my message which I sent to the Reliable Computing mailing list on March 12, 2000. The subject is "special issues". The recently received message is infected by a virus. I am not sure but I guess that other members of the mailing list will receive the same infected message. Please don't open the attachment and delete the message. Best regards, Slava ------=_NextPart_000_001C_01C299CC.175C53A0 Content-Type: text/html; charset="koi8-r" Content-Transfer-Encoding: quoted-printable
Colleagues,
 
I just received a message from = the address=20

nest [at] tiscali [dot] fr

The received message is the exact copy of my message

which I sent to the Reliable Computing mailing list on March 12, = 2000.

The subject is "special issues".

The recently received message is infected by a = virus.

I am not sure but I guess that other members of the = mailing=20 list

will receive the same infected message.

Please don't open the attachment and delete the=20 message.

 

Best regards,

Slava

 

------=_NextPart_000_001C_01C299CC.175C53A0-- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 2 06:54:09 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB2Cs9Q14848 for reliable_computing-outgoing; Mon, 2 Dec 2002 06:54:09 -0600 (CST) Received: from mailbox.univie.ac.at (mailbox.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB2Cs2i14843 for ; Mon, 2 Dec 2002 06:54:03 -0600 (CST) Received: from univie.ac.at (hektor.mat.univie.ac.at [131.130.16.21]) by mailbox.univie.ac.at (8.12.2/8.12.2) with ESMTP id gB2Crkhu310458; Mon, 2 Dec 2002 13:53:48 +0100 Message-ID: <3DEB57DA.D98E07AD [at] univie [dot] ac.at> Date: Mon, 02 Dec 2002 13:53:46 +0100 From: Arnold Neumaier Organization: University of Vienna X-Mailer: Mozilla 4.79 [en] (X11; U; Linux 2.4.18-18.7.x i686) X-Accept-Language: en, de MIME-Version: 1.0 To: interval , coconut , alexandre goldsztejn Subject: New paper: Exclusion regions for systems of equations Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk The following paper is now available on the WWW: H. Schichl and A. Neumaier, Exclusion regions for systems of equations http://www.mat.univie.ac.at/~neum/papers.html#excl Branch and bound methods for finding all zeros of a nonlinear system of equations in a box frequently have the difficulty that subboxes containing no solution cannot be easily eliminated if there is a nearby zero outside the box. This has the effect that near each zero, many small boxes are created by repeated splitting, whose processing may dominate the total work spent on the global search. This paper discusses the reasons for the occurrence of this so-called cluster effect, and how to reduce the cluster effect by defining exclusion regions around each zero found, that are guaranteed to contain no other zero and hence can safely be discarded. Such exclusion regions are traditionally constructed using uniqueness tests based on the Krawczyk operator or the Kantorovich theorem. These results are reviewed; moreover, refinements are proved that significantly enlarge the size of the exclusion region. Existence and uniqueness tests are also given. From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 2 12:42:43 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB2Iggc15654 for reliable_computing-outgoing; Mon, 2 Dec 2002 12:42:42 -0600 (CST) Received: from wrath.cs.utah.edu (wrath.cs.utah.edu [155.99.198.100]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB2Igai15650 for ; Mon, 2 Dec 2002 12:42:37 -0600 (CST) Received: from faith.cs.utah.edu (faith.cs.utah.edu [155.99.198.108]) by wrath.cs.utah.edu (8.11.6/8.11.6) with ESMTP id gB2IgTT29641; Mon, 2 Dec 2002 11:42:29 -0700 (MST) Received: from localhost (sikorski@localhost) by faith.cs.utah.edu (8.11.6+Sun/8.11.1) with ESMTP id gB2IgS711788; Mon, 2 Dec 2002 11:42:28 -0700 (MST) Date: Mon, 2 Dec 2002 11:42:28 -0700 (MST) From: Kris Sikorski To: Richard Smith - Systems Engineer - Melbourne cc: reliable_computing [at] interval [dot] louisiana.edu Subject: Re: Solutions of systems of equations In-Reply-To: <200211270845.gAR8j2Ex005236 [at] vic [dot] Aus.Sun.COM> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Richard: some of the complexity issues + bibilography on this problem are given in my book: Optimal Solution of Nonlinear Equations, Oxford 2001. chris for example: the interior ellipsoid algorithm is optimal in the worst case for fixed points of nonexpanding mappings (with respect to second norm and the residual error criterion.); 1999 paper with Huang and Khachiyan in J. Complexity; circumscribed ellipsoid algorithm is "almost" optimal (modulo exponent 2 not 1); etc. --------------------------------------- Christopher Sikorski, Ph.D. Professor Director of the CES Program (www.ces.utah.edu) School of Computing 50 S Central Campus Drive Rm 3190 University of Utah Salt Lake City, UT 84112-9205 e-mail: sikorski [at] cs [dot] utah.edu Tel: 801-5818579 Fax: 801-5815843 www.cs.utah.edu/~sikorski --------------------------------------- On Wed, 27 Nov 2002, Richard Smith - Systems Engineer - Melbourne wrote: > Reading through the original problem and subsequent responses left me just > a bit uneasy. It seemed that the original statement exposes the limits of > computing with sets. We may be able to shrink these sets, but not indefinitely > given finite precision. Algorithms that apply contractive mappings and stop > when the set no longer shrinks will terminate in finite time, but possibly > leave unanswered the question re existence of a [single] zero. > > However if we can assume [or know apriori] continuity and differentiability then > we might be able to make stronger statements, with the strength of a theorem, > about a [small] box/region/subpaving/set. > > In some sense I think of interval arithmetic as being like probing atomic > structure with [high-energy] particles displaying wave-like behaviour. This > places fundamental limits on the ability to explore a region of space. Sure, > use higher energy particles [greater precision], but run into the same limit. > > What does the solution to a set of non-linear equations really "look like"? > And with finite precision, what is the smallest possible collection of > subpavings that enclose the solution set? I imagine a whole string of boxes > possibly 1 ULP wide. Without further knowledge about properties so as to > invoke Mean Value Theorem, where next? > > ============================================================================ > ,-_|\ Richard Smith - SE Melbourne > / \ Sun Microsystems Australia Phone : +61 3 9869 6200 > richard.smith [at] Sun [dot] COM Direct : +61 3 9869 6224 > \_,-._/ 476 St Kilda Road Fax : +61 3 9869 6290 > v Melbourne Vic 3004 Australia > =========================================================================== > From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 3 07:21:18 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB3DLI317947 for reliable_computing-outgoing; Tue, 3 Dec 2002 07:21:18 -0600 (CST) Received: from mailbox.univie.ac.at (mail.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB3DLCi17943 for ; Tue, 3 Dec 2002 07:21:12 -0600 (CST) Received: from univie.ac.at (hektor.mat.univie.ac.at [131.130.16.21]) by mailbox.univie.ac.at (8.12.2/8.12.2) with ESMTP id gB3DL1TH336382; Tue, 3 Dec 2002 14:21:02 +0100 Message-ID: <3DECAFBD.5430C87E [at] univie [dot] ac.at> Date: Tue, 03 Dec 2002 14:21:01 +0100 From: Arnold Neumaier Organization: University of Vienna X-Mailer: Mozilla 4.79 [en] (X11; U; Linux 2.4.18-18.7.x i686) X-Accept-Language: en, de MIME-Version: 1.0 To: interval , coconut , alexandre goldsztejn Subject: Re: New paper: Exclusion regions for systems of equations References: <3DEB57DA.D98E07AD [at] univie [dot] ac.at> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Arnold Neumaier wrote: > > The following paper is now available on the WWW: > > H. Schichl and A. Neumaier, > Exclusion regions for systems of equations > http://www.mat.univie.ac.at/~neum/papers.html#excl Alexander Semenov pointed out that our Example 3 was stated inconsistently; indeed, we had forgotten a term in one of the equations. This error is now corrected, and the link now points to the corrected version. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 3 13:36:00 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB3Ja0d18799 for reliable_computing-outgoing; Tue, 3 Dec 2002 13:36:00 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB3JZtd18794 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 3 Dec 2002 13:35:55 -0600 (CST) Received: from lcyoung.math.wisc.edu (lcyoung.math.wisc.edu [144.92.166.90]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gAUJr7i08899 for ; Sat, 30 Nov 2002 13:53:08 -0600 (CST) Received: from ultra10.math.wisc.edu (ultra10.math.wisc.edu [144.92.166.180]) by lcyoung.math.wisc.edu (8.11.6/8.11.6) with ESMTP id gAUJpiX16180; Sat, 30 Nov 2002 13:51:44 -0600 (CST) Date: Sat, 30 Nov 2002 13:51:42 -0600 (CST) From: Hans Schneider To: NETS -- at-net , E-LETTER , Pradeep Misra , Shaun Fallat , "na.digest" , ipnet-digest [at] math [dot] msu.edu, wim@bell-labs.com, hjt [at] eos [dot] ncsu.edu, SMBnet [at] smb [dot] org, vkm [at] eedsp [dot] gatech.edu, reliable_computing [at] interval [dot] louisiana.edu Subject: LAA contents Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-MailScanner: Found to be clean Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Net Organizer: Please circulate the attached LAA contents over your net. Thanks hans ********************************************************************* Hans Schneider Office: Home: Mathematics Department 910 S. Midvale Blvd. Van Vleck Hall Madison, WI 53711 USA University of Wisconsin 608-271-7252 480 Lincoln Drive Madison, WI 53706-1313 USA Email: hans [at] math [dot] wisc.edu Office Phone: 608-262-1402 WWW: http://www.math.wisc.edu/~hans Math Dept Phone: 608-263-3054 Math Dept Fax: 608-263-8891 ********************************************************************* Journal: Linear Algebra and its Applications ISSN : 0024-3795 Volume : 359 Issue : 1-3 Date : 15-Jan-2003 For more information about this journal visit: http://www.elsevier.com/locate/jnlnr/07738 ______________________________________________________ Table of Contents: List of Editors pp ii-iii Caratheodory-Fejer interpolation in the ball D. Alpay, C. Dubi pp 1-19 Necessary conditions of Hurwitz polynomials X. Yang pp 21-27 Two-dimensional representations of the free group with two generators over a finite field Z. Yan, H. You pp 29-36 Continued fraction expansion of the geometric matrix mean and applications M. Rassouli, F. Leazizi pp 37-57 Some norm inequalities for completely monotone functions-II J.S. Aujla pp 59-65 Spectral variation under congruence for a nonsingular matrix with 0 on the boundary of its field of values S. Furtado, C.R. Johnson pp 67-78 Generalized oscillatory matrices S.M. Fallat, M. Fiedler, T.L. Markham pp 79-90 On nonsingular sign regular matrices J.M. Pena pp 91-100 Translations in simply transitive affine actions of Heisenberg type Lie groups T. De Cat, K. Dekimpe, P. Igodt pp 101-111 Sign patterns that allow diagonalizability Y. Shao, Y. Gao pp 113-119 Equitable switching and spectra of graphs Y. Teranishi pp 121-131 Nonsingularity/singularity criteria for nonstrictly block diagonally dominant matrices L.Y. Kolotilina pp 133-159 Linear transformations preserving log-concavity Y. Wang pp 161-167 On the operator equation e^A=e^B C. Schmoeger pp 169-179 A matrix approach to polynomials T. Arponen pp 181-196 Perturbation bounds for coupled matrix Riccati equations M. Konstantinov, V. Angelova, P. Petkov, D. Gu, V. Tsachouridis pp 197-218 Additive maps on standard operator algebras preserving invertibilities or zero divisors J. Hou, J. Cui pp 219-233 Unextendible product bases and the construction of inseparable states A.O. Pittenger pp 235-248 On the eigenvalues of Jordan products E.A. Martins, F.C. Silva pp 249-262 A sin2@Q theorem for graded indefinite Hermitian matrices N. Truhar, R.-C. Li pp 263-276 A class of atomic positive linear maps in matrix algebras K.-C. Ha pp 277-290 Call for Papers: Special Issue on Positivity in Linear Algebra pp 291-292 Author index pp 293 ----------------------------------------------------------------- Information on eleven LAA special issues currently accepting papers for consideration is available at http://www.math.wisc.edu/~hans/speciss.html . From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Dec 5 02:53:47 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB58rlk23144 for reliable_computing-outgoing; Thu, 5 Dec 2002 02:53:47 -0600 (CST) Received: from pop0.greatbasin.net (pop0.greatbasin.net [207.228.35.2]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB58rdi23140 for ; Thu, 5 Dec 2002 02:53:40 -0600 (CST) Received: from D3HN8211 (66-214-108-73.nlt-cres.charterpipeline.net [66.214.108.73]) by pop0.greatbasin.net (8.12.1/8.12.1) with SMTP id gB58rXcW029242; Thu, 5 Dec 2002 00:53:35 -0800 From: "Daniel H. Fylstra" To: "interval" , "coconut" Subject: Interval Solver for Microsoft Excel Date: Thu, 5 Dec 2002 00:55:28 -0800 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook IMO, Build 9.0.2416 (9.0.2911.0) In-Reply-To: <3DEB57DA.D98E07AD [at] univie [dot] ac.at> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Importance: Normal Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk A commercial optimization software package that includes a new Interval Solver as a featured component was released in November. The Premium Solver Platform Version V5.0 is available from Frontline Systems, Inc., developers of the Solver bundled with every copy of Microsoft Excel (though that bundled Solver doesn't include the interval methods) and is described at www.solver.com. A talk describing the methods in this Interval Solver was presented at the SIAM Workshop on Validated Computing in Toronto, May 2002; the full paper is to appear in Reliable Computing. The abstract of the talk is available at http://www.cs.utep.edu/interval-comp/interval.02/neno.pdf and PowerPoint slides at www.solver.com/VC02_Solver.htm. A specific summary of the Interval Solver's capabilities is at www.solver.com/xlsplatform9.htm, and there is quite a bit of detail about this Solver in the Premium Solver Platform User Guide, which can be downloaded in PDF form from the Support section of www.solver.com (free, but you must register on the site). Some notes on what this Interval Solver is and is not: (1) This software is not intended to allow users to work with intervals and interval arithmetic etc. on an Excel spreadsheet. Rather, it is intended to solve smooth global optimization problems, and find all real solutions to systems of nonlinear equations, using interval methods internally. Problems are defined in terms of the usual floating point values found in Excel spreadsheet cells. On the other hand, it is quite easy to define and solve problems, and this software does implement interval extensions and gradients for nearly all of Excel's 300+ built-in functions. (2) The methods implemented in this software are "complete" but "non-rigorous". That is, it uses a systematic search for the global optimum and for all real zeroes of a system of equations, rather than a "sampling" approach, but it does not use intervals and directed rounding in all of its algorithms, so it can potentially lose solutions due to roundoff error. Also, its normal mode is to accept problem parameters as "reals" (thin intervals) and present "reals" as solutions (midpoints of the enclosing intervals). A rigorous mode and/or interval input/output may be added in the future; however the focus of this software is on fast solution of global optimization and equation solving problems on standard PC hardware. We believe this software implements most of the best currently available methods from the interval analysis and constraint propagation literature, and is highly competitive in terms of performance. (3) The Interval Solver is one component of a [much] larger software package that includes linear, mixed-integer, and classic nonlinear programming, as well as multistart methods, an Evolutionary Solver, and other optimization tools. And it depends upon an "interpreter" for Excel formulas that is part of the Premium Solver Platform. Hence, it's not currently possible to obtain or use this Interval Solver separately from the Platform or from Excel. Also, as part of a commercial package, this Solver is not "free". But academic pricing is available, and a special discount is available in the month of December, as described on the solver.com Website. While I am co-author of the paper to appear in Reliable Computing, and president of the company offering the software, I have endeavored above to provide a straightforward and hopefully objective "user's view" of the software. Of course, we look forward to independent evaluations by other people, both expert and non-expert (since the software is designed to be easy to use by non-experts). I would like to credit Ivo P. Nenov for many innovations and most of the software design and implementation in this Interval Solver. Daniel H. Fylstra, President Frontline Systems, Inc. P.O. Box 4288 Incline Village, NV 89450 Tel (775) 831-0300 Fax (775) 831-0314 Web http://www.solver.com Email dfylstra [at] frontsys [dot] com From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Dec 5 10:42:37 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB5GgaK24325 for reliable_computing-outgoing; Thu, 5 Dec 2002 10:42:36 -0600 (CST) Received: from mailbox.univie.ac.at (mailbox.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB5GgUi24320 for ; Thu, 5 Dec 2002 10:42:31 -0600 (CST) Received: from univie.ac.at (lisa.mat.univie.ac.at [131.130.16.25]) by mailbox.univie.ac.at (8.12.2/8.12.2) with ESMTP id gB5GgDSe026258; Thu, 5 Dec 2002 17:42:17 +0100 Message-ID: <3DEF81E5.2DA96846 [at] univie [dot] ac.at> Date: Thu, 05 Dec 2002 17:42:13 +0100 From: Arnold Neumaier Organization: University of Vienna X-Mailer: Mozilla 4.79 [en] (X11; U; Linux 2.4.18-17.7.x i686) X-Accept-Language: en, de MIME-Version: 1.0 To: William Walster CC: reliable_computing [at] interval [dot] louisiana.edu, coconut [at] ilog [dot] fr, dfylstra [at] frontsys [dot] com Subject: Re: Interval Solver for Microsoft Excel References: <200212051613.IAA12519 [at] heliopolis [dot] eng.sun.com> Content-Type: text/plain; charset=iso-8859-15 Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk William Walster wrote: > > I continue to believe that calling any software or algorithms that fail to > produce rigorous interval bounds as "interval" will cause great confusion in > the future. If such methods can be described as being "interval" then from > now on those of us who care about computing what used to be called "interval > bounds" must now be careful to write and say the words "*rigorous* interval" > whenever we want to distinguish what we are doing from *approximate* interval > methods that do *not* produce rigorous mathematical bounds. I don't think there will be confusion. People in optimization used intervals for many many years (long before Hansen wrote his first global optimization paper) in the traditional way mathematicians use them, simply to denote lower and upper bounds - which in approximate computations naturally means approximate upper and lower bounds. And it is still being used in this way in 2002 by those having the most powerful global optimization systems (alphaBB and BARON) - those that the industrial users that the interval community wants to win will be likely to use *before* they are interested in 'rigorous' interval products. Mathematical concepts are not trademarks of a particular philosophy such as that espoused by Bill Walster, but are social agreements, and to be effective, the agreement must be on a much wider scale than just the interval analysis camp. I don't think that such an agreement would be achievable; in fact I don't think it is even desirable. It is not a good idea to try to force the restricted use of the interval concepts upon others. The notions of 'validated' or 'rigorous' do have the desired connotation already, and have often be used by interval people to emphasize the rigor if they wanted to emphasize it, and this is all needed. It is only on this mailing list that the traditional usage may cause confusion. Fylstra and others have at least *my* full support if they use intervals in the approximate sense they do, with a few words of caution (as they do) that full rigor is not guaranteed. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Dec 8 16:59:07 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gB8Mx6803502 for reliable_computing-outgoing; Sun, 8 Dec 2002 16:59:06 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB8Mx1i03498 for ; Sun, 8 Dec 2002 16:59:02 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gB8Mwik01737 for ; Sun, 8 Dec 2002 15:58:48 -0700 (MST) Message-Id: <200212082258.gB8Mwik01737 [at] cs [dot] utep.edu> Date: Sun, 8 Dec 2002 15:58:43 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: from NA Digest To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: GOsGtBJpYSbsdSjPgauD/Q== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk From: RNC5 Date: Wed, 4 Dec 2002 13:24:14 +0100 (MET) Subject: Conference in Lyon on Real Numbers and Computers 5th CONFERENCE ON REAL NUMBERS AND COMPUTERS (RNC5) September 3-5, 2003 Ecole Normale Superieure de Lyon Lyon, France Web site: http://www.ens-lyon.fr/LIP/Arenaire/RNC5 Dates: Submission of manuscripts: 17 Mar 2003 Notification of acceptance: 15 May 2003 Revised Papers required by: 1 Jul 2003 Conference: 3-5 Sep 2003 Objective: The aim of the symposia on "Real Numbers and Computers" is to bring together specialists from various research areas, all concerned with problems related to computations based on real numbers. These computations may use any number system implemented by a software package or in hardware, including floating and fixed point, serial, on line, continued fractions, exact, multiple precision, interval and stochastic arithmetic. Results are sought on both applied and fundamental questions. Important topics discussed during these conferences include but are not limited to: * Foundation and properties of number systems * Computability and complexity * Formal aspects and automatic proof checking * Links with number theory and automata theory * Basic arithmetic operations * Implementation of the standard and special functions * Engineering of floating and fixed point algorithms * Symbolic manipulation of numbers * Accuracy and reliability for applications and industry * Robust geometric algorithms and exact geometric computation * Hardware design support and implementations The conference will feature invited lectures and contributed talks. Original research results and insightful analyses of current concerns are solicited for submission. Survey and tutorial articles may be suitable for submission if clearly identified as such. Proceedings and special issue: Instructions for how to submit will be posted on the website of the conference. The proceedings will be distributed at the conference. They will be published electronically by the INRIA. A special issue on real numbers and computers of Elsevier's journal Theoretical Computer Science is to follow the conference. Authors of the conferences will be strongly encouraged to propose expanded work for review and inclusion. Steering Committee: Jean Claude Bajard, Montpellier, France Jean Marie Chesneaux, Paris, France Christiane Frougny, Paris, France Peter Kornerup, Odense, Denmark (chair) Dominique Michelucci, Dijon, France Jean Michel Muller, Lyon, France Program Committee: Jean Paul Allouche, Orsay, France Jean Claude Bajard, Montpellier, France Vasco Brattka, Hagen, Germany Jean Marie Chesneaux, Paris, France Marc Daumas, Lyon, France (chair) James Demmel, Berkeley, United States Milos Ercegovac, Los Angeles, United States Martin Escardo, Birmingham, United Kingdom Christiane Frougny, Paris, France Peter Kornerup, Odense, Denmark Philippe Langlois, Perpignan, France Dominique Michelucci, Dijon, France Michael Parks, Sun, United States Siegfried Rump, Hamburg, Germany David Russinoff, AMD, United States Laurent Thery, Sophia Antipolis, France Chee Yap, New York, United States Organizing Committee: Nicolas Brisebarre, Lyon, France Claude-Pierre Jeannerod, Lyon, France Nathalie Revol, Lyon, France Gilles Villard, Lyon, France (chair) From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 10 22:05:55 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBB45tB09716 for reliable_computing-outgoing; Tue, 10 Dec 2002 22:05:55 -0600 (CST) Received: from smtp2.usinternet.com (smtp2.usinternet.com [216.17.3.40]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBB45mi09712 for ; Tue, 10 Dec 2002 22:05:49 -0600 (CST) Received: from carmen ([216.17.66.184]) by smtp2.usinternet.com (VisNetic.MailServer.v5.0.2.3) with ESMTP id Y5YNPW for ; Tue, 10 Dec 2002 22:05:01 -0600 From: "Nate Hayes" To: Subject: Radiance Measurements Date: Tue, 10 Dec 2002 22:05:41 -0600 Message-ID: <000901c2a0ca$9251af60$6f01a8c0@carmen> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_000A_01C2A098.47B73F60" X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook, Build 10.0.2627 Importance: Normal X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------=_NextPart_000_000A_01C2A098.47B73F60 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Hello All, I am currently in need of white papers and/or reference material on basic radiometry. In particular, I am looking to model the way a CCD element measures incoming flux and/or radiance. Any reference that contains intervals as part of the model would especially be helpful to me. Sincerely, Nate Hayes Sunfish Studio ------=_NextPart_000_000A_01C2A098.47B73F60 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

 

Hello All,

 

I am currently in need of white papers and/or = reference material on basic radiometry. In particular, I am looking to model the = way a CCD element measures incoming flux and/or = radiance.

 

Any reference that contains intervals as part of = the model would especially be helpful to me.

 

Sincerely,

 

Nate Hayes

Sunfish = Studio<= /p>

 

------=_NextPart_000_000A_01C2A098.47B73F60-- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Dec 12 10:42:15 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBCGgE614176 for reliable_computing-outgoing; Thu, 12 Dec 2002 10:42:14 -0600 (CST) Received: from isis.lip6.fr (IDENT:root [at] isis [dot] lip6.fr [132.227.60.2]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBCGg7i14172 for ; Thu, 12 Dec 2002 10:42:08 -0600 (CST) Received: from tibre.lip6.fr (tibre.lip6.fr [132.227.74.2]) by isis.lip6.fr (8.12.4/jtpda-5.4+victor) with ESMTP id gBCGfx3q031948 (version=TLSv1/SSLv3 cipher=EDH-RSA-DES-CBC3-SHA bits=168 verify=NO) for ; Thu, 12 Dec 2002 17:42:00 +0100 X-pt: isis.lip6.fr Received: from lip6.fr (sphinx [132.227.74.253]) by tibre.lip6.fr (8.11.6/8.11.3) with ESMTP id gBCGfxE08605 for ; Thu, 12 Dec 2002 17:41:59 +0100 (MET) Message-ID: <3DF8AA25.875ECFB6 [at] lip6 [dot] fr> Date: Thu, 12 Dec 2002 16:24:21 +0100 From: Jean-Luc Lamotte Reply-To: cadna-team [at] lip6 [dot] fr X-Mailer: Mozilla 4.76 [en] (X11; U; Linux 2.4.2 i686) X-Accept-Language: French, fr, en MIME-Version: 1.0 To: "reliable_computing [at] interval [dot] louisiana.edu" Subject: CADNA Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Scanned-By: isis.lip6.fr Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Colleagues, A freeware version of the CADNA library is now avalaible on the new web site of CADNA at http://www.lip6.fr/cadna The tools, examples, documentations and references you will find in this site deal with the round-off error propagation which appears at each time one performes numerical computations using the finite precision floating point arithmetic on computers. The main tool is the CADNA library which allows to estimate the round-off error propagation on every scientific code written in FORTRAN or C language. You will find in this site a complete descrition with examples and documentation of the ACADEMIC non-commercial version of CADNA. The library itself may be downloaded directly from the site Others tools deals with the four different rounding modes for the floating point arithmetic defined by the IEEE 754 norm. Generally, they are avalaible on computers but there is no somple way to use it. Very short assembler codes are presented which allows to change dynamically the rounding mode in every scientific codes under Unix systems. All comments and suggestions are welcome and have to be sent to cadna-team [at] lip6 [dot] fr Best regards, The CADNA TEAM -- ------------------------------------------------------------------------- Jean-Luc Lamotte Theme Algorithmique Numerique et Parallelisme Tel:+33 1 44 27 58 78 Laboratoire LIP6 Tel:+33 1 44 27 73 63 Universite Paris VI Tel:+33 1 44 27 71 34 4, place Jussieu Fax:+33 1 44 27 53 53 F-75252 PARIS CEDEX 05 FRANCE E-mail : Jean-Luc.Lamotte [at] lip6 [dot] fr -------------------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Dec 12 22:34:36 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBD4YZY15586 for reliable_computing-outgoing; Thu, 12 Dec 2002 22:34:35 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBD4YPi15582 for ; Thu, 12 Dec 2002 22:34:26 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBD4YLR19655 for ; Thu, 12 Dec 2002 21:34:21 -0700 (MST) Message-Id: <200212130434.gBD4YLR19655 [at] cs [dot] utep.edu> Date: Thu, 12 Dec 2002 21:34:21 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: East Coast Computer Algebra Day 2003 To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: pbu4ZfMdUUGovwxWmmeQ5Q== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk ------------- Begin Forwarded Message ------------- From: Xuhong Gao Date: Thu, 12 Dec 2002 14:50:16 -0500 (EST) To: vladik [at] cs [dot] utep.edu Subject: East Coast Computer Algebra Day 2003 ANNOUNCEMENT AND CALL FOR PARTICIPATION EAST COAST COMPUTER ALGEBRA DAY 2003 Saturday, April 5, 2003 Clemson University The 10th annual East Coast Computer Algebra Day (ECCAD'2003) will be held on Saturday, April 5, 2003, at Clemson University, South Carolina, USA. THEMES * Algebraic Algorithms * Hybrid Symbolic-Numeric Computation * Computer Algebra Systems and Generic Programming * Mathematical Communication * Complexity of Algebraic Problems INVITED SPEAKERS * Professor Richard Brent Oxford University, England Title: Primitive and almost primitive trinomials over GF(2) * Professor Jeremy Johnson Drexel University, USA Title: TBA * Professor Wolfgang Schreiner Johannes Kepler University, Austria Title: Distributed Maple - Lessons Learned on Parallel Computer Algebra in Distributed Environments POSTER SESSIONS In keeping with tradition, there will be two poster sessions offering all participants an opportunity to present timely research in an informal environment. The conference auditorium is well equipped with video projectors, computers and internet access. Software demos are welcome. TRAVEL SUPPORT Subject to successful funding, a limited number of participants will be supported to attend ECCAD 2003. Support may cover partially your travel expenses and lodging for up to two nights. Graduate students and junior faculty are particularly encouraged to apply. REGISTRATION There is no registration fee for the conference. You can register and get more information at the conference website: http://www.math.clemson.edu/~sgao/ECCAD03/ LOCAL and TRAVEL INFORMATION Up-to-date information regarding accommodations, directions, area restaurants, registration, etc. can be found at the conference website. Important Dates: ECCAD03 April 5, 2003 Deadline for room reservations February 19, 2003 Deadline for submitting poster abstracts March 22, 2003 Deadline for travel support February 19, 2003 Registration begins February 1, 2003 Questions about the conference may be addressed to the organizing committee: Shuhong Gao, sgao [at] math [dot] clemson.edu David Jacobs, dpj [at] cs [dot] clemson.edu PLEASE HELP COMMUNICATE THIS ANNOUNCEMENT TO ALL INTERESTED PARTIES. ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Dec 12 22:47:50 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBD4lm815715 for reliable_computing-outgoing; Thu, 12 Dec 2002 22:47:48 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBD4lci15711 for ; Thu, 12 Dec 2002 22:47:39 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBD4lZH19762 for ; Thu, 12 Dec 2002 21:47:35 -0700 (MST) Message-Id: <200212130447.gBD4lZH19762 [at] cs [dot] utep.edu> Date: Thu, 12 Dec 2002 21:47:35 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: 2-nd Announcement To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: MULTIPART/mixed; BOUNDARY=Sounder_of_Swine_004_000 X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk --Sounder_of_Swine_004_000 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: hpBOYUbH5Olxq5dMqvKapg== of International Federation of Automatic Control (IFAC) Workshop Modelling and Analysis of Logic Controlled Dynamic Systems where our own Lakeyev is one of the organizers; a link to the 1st announcement is placed on the forthocming conference part of the 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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAByZERvYwAQAAAAV29yZC5Eb2N1bWVu dC44APQ5snEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA== --Sounder_of_Swine_004_000-- From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Dec 13 10:55:40 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBDGtdC00730 for reliable_computing-outgoing; Fri, 13 Dec 2002 10:55:39 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBDGtWq00725 for ; Fri, 13 Dec 2002 10:55:33 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBDGtR624516; Fri, 13 Dec 2002 09:55:27 -0700 (MST) Message-Id: <200212131655.gBDGtR624516 [at] cs [dot] utep.edu> Date: Fri, 13 Dec 2002 09:55:27 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: interval-related position in El Paso To: reliable_computing [at] interval [dot] louisiana.edu Cc: vladik [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: wTxtSSqcyiUXCXATPoUxkQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, I have just learned that our department's webpage erroneosuly states that we are not hiring; the webmaster will make changes shortly, meanwhile, please apply. We plan to start interviewing in January, so please apply ASAP. My apologies for the webpage confusion. Vladik P.S. Our announcement has been posted on the UTEP Web site on October 18. To find it, go to http://www.utep.edu/hresourc/job/search.html and push the obvious buttons. Please note that although the announcement's title says "Assistant/Associate Professor," the text indicates correctly that we're considering applicants at all ranks. From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 16 08:39:27 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBGEdQw06460 for reliable_computing-outgoing; Mon, 16 Dec 2002 08:39:26 -0600 (CST) Received: from ccsmta1.resource.rmcs.cranfield.ac.uk (ccsmta1.resource.rmcs.cranfield.ac.uk [193.63.243.9]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBGEdJ606456 for ; Mon, 16 Dec 2002 08:39:20 -0600 (CST) Message-ID: <55360F67A4EAD611B38F00B0D0D1AC6B242674 [at] UXSTAFF [dot] resource.rmcs.cranfield.ac.uk> From: Ashokaraj Mr IA To: "'reliable_computing [at] interval [dot] louisiana.edu'" Subject: INTLAB - any function for finding determinent or adjoint in inter val matrix? Date: Mon, 16 Dec 2002 14:37:41 -0000 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2653.19) Content-Type: text/plain; charset="iso-8859-1" Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Sirs, I am an user of the INTLAB toolbox for MATLAB. Just wondering is there any function to find the "determinent" and also the "adjoint" of an interval matrix in the INTLAB tool box already as i couldnt find any? Hope to hear from you soon. Regards, Immanuel. From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 16 09:31:29 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBGFVTn06657 for reliable_computing-outgoing; Mon, 16 Dec 2002 09:31:29 -0600 (CST) Received: from ccsmta1.resource.rmcs.cranfield.ac.uk (ccsmta1.resource.rmcs.cranfield.ac.uk [193.63.243.9]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBGFVO606653 for ; Mon, 16 Dec 2002 09:31:24 -0600 (CST) Message-ID: <55360F67A4EAD611B38F00B0D0D1AC6B242675 [at] UXSTAFF [dot] resource.rmcs.cranfield.ac.uk> From: Ashokaraj Mr IA To: "'reliable_computing [at] interval [dot] louisiana.edu'" Subject: Regarding INTLAB - inv (interval matrix inverse function) gives d ifferent answer!!!!! Date: Mon, 16 Dec 2002 15:29:47 -0000 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2653.19) Content-Type: text/plain; charset="iso-8859-1" Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Sirs, My name is Immanuel and i am a Post Graduate student. I have already sent an email regarding a related problem (regarding functions for finding the determinent and adjoint of interval matrices in INTLAB). Actually i tried to find the inverse of an interval matrix using the "inv" function in INTLAB but it seems to be giving a different answer from the one it should actually give. I have give the example below from my matlab workspace: >> intvalinit('DisplayInfSup') ===> Default display of intervals by infimum/supremum (e.g. [ 3.14 , 3.15 ]) >> intvalinit('SharpIVmult','true') ===> Slow but sharp interval matrix multiplication in use >> a1 = intval('[2,3]'); >> a2 = intval('[0,1]'); >> a3 = intval('[1,2]'); >> a4 = intval('[2,3]'); >> a = [a1 a2; a3 a4] intval a = [ 2.0000, 3.0000] [ 0.0000, 1.0000] [ 1.0000, 2.0000] [ 2.0000, 3.0000] >> b = inv(a) intval b = [ -0.1003, 1.0094] [ -0.5071, 0.3252] [ -1.0125, 0.4671] [ -0.1003, 1.0094] >> Infact it should give an answer as given below which i got when i did it by hand: a = [ 2.0000, 3.0000] [ 0.0000, 1.0000] [ 1.0000, 2.0000] [ 2.0000, 3.0000] inv a = adjoint(a)/determinent(a) adjoint(a) = [a1 -a2; -a3 a4] adjoint(a) = [ 2.0000, 3.0000] - [ 0.0000, 1.0000] - [ 1.0000, 2.0000] [ 2.0000, 3.0000] determinent(a) = [2,3] [2,3] - [0,1] [1,2] = [2,9] inv(a) = [ 0.2222, 1.5000] [ -0.5000, 0.0000] [ -1.0000, -0.1111] [ 0.2222, 1.5000] When i compare both the results i think the "inv" function in the INTLAB toolbox may be giving an incorrect answer. This may be due to the function "verifylss" which it calls. So can anyone please give me any suggestion regarding this! Hope to hear from you soon. Sincerely, Immanuel. From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 16 11:27:42 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBGHRge06985 for reliable_computing-outgoing; Mon, 16 Dec 2002 11:27:42 -0600 (CST) Received: from mailbox.univie.ac.at (mail.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBGHRZ606980 for ; Mon, 16 Dec 2002 11:27:36 -0600 (CST) Received: from univie.ac.at (edoras.mat.univie.ac.at [131.130.16.104]) by mailbox.univie.ac.at (8.12.2/8.12.2) with ESMTP id gBGHRRh0124664; Mon, 16 Dec 2002 18:27:28 +0100 Message-ID: <3DFE0CFF.BE46D3EA [at] univie [dot] ac.at> Date: Mon, 16 Dec 2002 18:27:27 +0100 From: Arnold Neumaier Organization: University of Vienna X-Mailer: Mozilla 4.79 [en] (X11; U; Linux 2.4.18-18.7.x i686) X-Accept-Language: en, de MIME-Version: 1.0 To: Ashokaraj Mr IA CC: "'reliable_computing [at] interval [dot] louisiana.edu'" Subject: Re: Regarding INTLAB - inv (interval matrix inverse function) gives different answer!!!!! References: <55360F67A4EAD611B38F00B0D0D1AC6B242675 [at] UXSTAFF [dot] resource.rmcs.cranfield.ac.uk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Ashokaraj Mr IA wrote: > > Sirs, > My name is Immanuel and i am a Post Graduate student. I have > already sent an email regarding a related problem (regarding functions for > finding the determinent and adjoint of interval matrices in INTLAB). > > Actually i tried to find the inverse of an interval matrix using > the "inv" function in INTLAB but it seems to be giving a different answer > from the one it should actually give. I have give the example below from my > matlab workspace: > > >> intvalinit('DisplayInfSup') > ===> Default display of intervals by infimum/supremum (e.g. [ 3.14 , 3.15 ]) > >> intvalinit('SharpIVmult','true') > ===> Slow but sharp interval matrix multiplication in use > >> a1 = intval('[2,3]'); > >> a2 = intval('[0,1]'); > >> a3 = intval('[1,2]'); > >> a4 = intval('[2,3]'); > >> a = [a1 a2; a3 a4] > intval a = > [ 2.0000, 3.0000] [ 0.0000, 1.0000] > [ 1.0000, 2.0000] [ 2.0000, 3.0000] > >> b = inv(a) > intval b = > [ -0.1003, 1.0094] [ -0.5071, 0.3252] > [ -1.0125, 0.4671] [ -0.1003, 1.0094] > >> > > Infact it should give an answer as given below which i got when i did it by > hand: > > a = [ 2.0000, 3.0000] [ 0.0000, 1.0000] > [ 1.0000, 2.0000] [ 2.0000, 3.0000] > > inv a = adjoint(a)/determinent(a) > > adjoint(a) = [a1 -a2; -a3 a4] > > adjoint(a) = [ 2.0000, 3.0000] - [ 0.0000, 1.0000] > - [ 1.0000, 2.0000] [ 2.0000, 3.0000] > > determinent(a) = [2,3] [2,3] - [0,1] [1,2] > > = [2,9] > > inv(a) = [ 0.2222, 1.5000] [ -0.5000, 0.0000] > [ -1.0000, -0.1111] [ 0.2222, 1.5000] > > When i compare both the results i think the "inv" function in the INTLAB > toolbox may be giving an incorrect answer. This may be due to the function > "verifylss" which it calls. So can anyone please give me any suggestion > regarding this! Compound interval operations usually don't give the ideal result, but only enclosures. Both methods mentioned overestimate the true interval hull [a b;c d]^{-1}= [A B;C D], where A=[1/3,1], B=[-1/2,0], C=[-1,-1/9], D=[1/3,1], which can be computed from A=1/(a-bc/d), B=1/(c-ad/b), C=1/(b-ad/c), D=1/(d-bc/a), and Kahan's extension of interval arithmetic is used if one of a,b,c,d contains 0. This is optimal since in each expression, each variable occurs only once. The above methods suffer from dependence and yield wider intervals. But both are correct since they enclose the hull. Now if you try to compute inv(A)*b, don't be surprised that you dont get the optimal result for the solution of the linear equation Ax=b, even when you use the ideal inverse! Cf. Example 3.4.2 in my book 'Intterval methods for systems of equations'. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 16 14:57:59 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBGKvwu07403 for reliable_computing-outgoing; Mon, 16 Dec 2002 14:57:58 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBGKvr607399 for ; Mon, 16 Dec 2002 14:57:54 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBGKvnb18835 for ; Mon, 16 Dec 2002 13:57:49 -0700 (MST) Message-Id: <200212162057.gBGKvnb18835 [at] cs [dot] utep.edu> Date: Mon, 16 Dec 2002 13:57:48 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: ACA2003: Announcement and Call for Sessions To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: YLjcj7SjxvvHg2HkpC/Bgw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk ------------- Begin Forwarded Message ------------- To: vladik [at] cs [dot] utep.edu Subject: ACA2003: Announcement and Call for Sessions From: Conference on Applied Computer Algebra Date: Mon, 16 Dec 2002 12:01:56 -0700 FIRST ANNOUNCEMENT AND CALL FOR SESSIONS ACA'2003 July 28-31, 2003 9th International Conference on Applications of Computer Algebra North Carolina State University Raleigh, North Carolina, USA ACA'2003 will be held from July 28 to July 31, 2003 at North Carolina State University in Raleigh, North Carolina, USA General Chairs: Hoon Hong, Erich Kaltofen, Agnes Szanto Program Chair: Mark Giesbrecht Organizing Committee: Stanly Steinberg, Michael Wester. ACA'2003 conference e-mail: aca2003 [at] math [dot] unm.edu ACA'2003 conference web site: http://math.unm.edu/ACA/2003 ACA Conferences main web site: http://math.unm.edu/aca.html Call for Sessions ----------------- The Scientific Committee is soliciting proposals to organize sessions at the conference. Session chairs are expected to organize 4 or more speakers on a theme consistent with that of the conference. Proposals for organizing a session should be directed to the Program Chair: Mark Giesbrecht: mwg [at] uwaterloo [dot] ca While there is a target date of March 1 for session proposals, organizing earlier will help guarantee your choice of session date and time in the ACA schedule. Please see http://math.unm.edu/ACA/2003/Sessions.html for details. Important Dates --------------- March 1, 2003 Target to submit a Session proposal (see above) May 1, 2003 Target date for submission of speaker list and abstracts May 15, 2003 Deadline to submit an application for financial support June 15, 2003 Notification of decisions for financial support June 15, 2003 Deadline for early registration July 15, 2003 Deadline for regular registration July 28-31, 2003 Conference Scientific Committee: ACA WORKING GROUP --------------------------------------- Alkiviadis G. Akritas Greece Jacques Calmet Germany Victor Edneral Russia Victor Ganzha Germany Vladimir Gerdt Russia Mark Giesbrecht Canada Hoon Hong USA Erich Kaltofen USA Ilias S. Kotsireas Canada Bernard Kutzler Austria Richard Liska Czech Republic Bill Pletsch USA Eugenio Roanes-Lozano Spain Stanly Steinberg USA Quoc-Nam Tran USA Nikolay Vassiliev Russia Michael Wester USA ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 17 13:15:12 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBHJFCo10181 for reliable_computing-outgoing; Tue, 17 Dec 2002 13:15:12 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBHJF7610177 for ; Tue, 17 Dec 2002 13:15:07 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBHFddw25841 for ; Tue, 17 Dec 2002 08:39:40 -0700 (MST) Message-Id: <200212171539.gBHFddw25841 [at] cs [dot] utep.edu> Date: Tue, 17 Dec 2002 08:39:38 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: database: forwarding To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: uyxmCaw50jWNFf1KU2JYMw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Date: Tue, 17 Dec 2002 08:17:54 -0200 (BRST) From: Renata Maria Cardoso Rodrigues de Souza I am looking for a database that is related to telecomunications or engineering where the data are intervals. The idea is to obtain a table where the columns are variables (intervals) and rows are objects. Do you know where I can find it? Thanks Renata ___________________________________________ "Every home is built by somebody but who build everything is God" (Heb 3:4) Renata Maria C. R. de Souza PhD student in Computer Science Universidade Federal de Pernambuco - UFPE Fone: 55 81 32718430 ___________________________________________ From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Dec 20 10:52:37 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBKGqbD18498 for reliable_computing-outgoing; Fri, 20 Dec 2002 10:52:37 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBKGqU618494 for ; Fri, 20 Dec 2002 10:52:31 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBKGqSe00617 for ; Fri, 20 Dec 2002 09:52:28 -0700 (MST) Message-Id: <200212201652.gBKGqSe00617 [at] cs [dot] utep.edu> Date: Fri, 20 Dec 2002 09:52:26 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Last Call for Papers - ISIPTA '03 To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=ISO-8859-1 Content-MD5: psH3Cja3IBcgvOWKNuRouQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by interval.louisiana.edu id gBKGqW618495 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk ------------- Begin Forwarded Message ------------- Content-Disposition: inline Content-Transfer-Encoding: binary MIME-Version: 1.0 Date: Fri, 20 Dec 2002 08:31:00 UT From: "ISIPTA '03" Subject: Last Call for Papers - ISIPTA '03 To: vladik [at] cs [dot] utep.edu Your help with circulating this announcement locally is much appreciated. Apologies for multiple postings. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ISIPTA '03 3rd International Symposium on Imprecise Probabilities and Their Applications Last Call for Papers July 14-17, 2003 Lugano, Switzerland http://www.sipta.org/~isipta03 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The ISIPTA meetings are one of the primary international forums to present and discuss new results on the theory and applications of imprecise probabilities. Imprecise probability has a wide scope, being a generic term for the many mathematical or statistical models which measure chance or uncertainty without sharp numerical probabilities. These models include belief functions, Choquet capacities, comparative probability orderings, convex sets of probability measures, fuzzy measures, interval-valued probabilities, possibility measures, plausibility measures, and upper and lower expectations or previsions. Imprecise probability models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete. Themes of the symposium ----------------------- Although the third symposium will be open to contributions on all aspects of imprecise probability, three main themes will be emphasised: inference, algorithms and computational complexity, real applications. http://www.sipta.org/~isipta03/themes.html Location -------- ISIPTA '03 will be held at the University of Lugano, Switzerland. http://www.sipta.org/~isipta03/venue.html Important dates --------------- Paper submission deadline: 1 February 2003 Notification of acceptance: 1 April 2003 Deadline for revised papers: 1 May 2003 Tutorial day: 14 July 2003 Symposium: 15-17 July 2003 Submissions ----------- There is a strict limit of 10 pages for papers submitted to the symposium. See http://www.sipta.org/~isipta03/submit.html for detailed instructions. *** Latest news --------------- - Financial support for travel and subsistence expenses of Eastern European scientists. People who are eligible for support must have a paper accepted at the conference and must work in one of the following countries: Albania, Armenia, Azerbaijan, Belarus, Bosnia-Herzegovina, Bulgaria, Georgia, Kazakhstan, Kyrgyzstan, Croatia, Macedonia, Moldova, Romania, Russia, Tajikistan, Turkmenistan, Ukraine, Uzbekistan. More information will be available from the web site soon. - Tutorial speakers and banquet speaker. The following speakers will give tutorials on imprecise probabilities on July the 14th: Jean-Marc Bernard (France), Gert de Cooman (Belgium), Fabio G. Cozman (Brazil), Charles Manski (USA), and Sujoy Mukerji (UK). Terrence Fine (USA) will be our banquet speaker. More information will be available from the web site soon. Program Board ------------- Jean-Marc Bernard (Université Paris 5, France) Teddy Seidenfeld (Carnegie Mellon University, USA) Marco Zaffalon (IDSIA, Switzerland) Steering Committee ------------------ Gert de Cooman (Universiteit Gent, Belgium) Serafin Moral (Universidad de Granada, Spain) Questions --------- If you have any questions about the symposium, please contact the Organising Committee, at the following address: Marco Zaffalon IDSIA Galleria 2 CH-6928 Manno Switzerland phone +41 91 610 8665 fax +41 91 610 8661 e-mail zaffalon [at] idsia [dot] ch (If you did not receive this e-mail through a mailing list and you do not want to receive further announcements concerning ISIPTA '03, please reply to this message writing "remove" in the body of the e-mail.) ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Dec 21 23:33:57 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBM5Xus23092 for reliable_computing-outgoing; Sat, 21 Dec 2002 23:33:56 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBM5Xpf23086 for reliable_computing [at] interval [dot] louisiana.edu; Sat, 21 Dec 2002 23:33:51 -0600 (CST) Received: from pheriche.sun.com (pheriche.sun.com [192.18.98.34]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gB8NLUi03653 for ; Sun, 8 Dec 2002 17:21:30 -0600 (CST) Received: from heliopolis.eng.sun.com ([152.70.24.37]) by pheriche.sun.com (8.9.3+Sun/8.9.3) with ESMTP id QAA03872 for ; Sun, 8 Dec 2002 16:21:29 -0700 (MST) Received: from sun.com (vpn-129-149-241-129.SFBay.Sun.COM [129.149.241.129]) by heliopolis.eng.sun.com (8.9.3+Sun/8.9.3/ENSMAIL,v2.1p1) with ESMTP id PAA07472; Sun, 8 Dec 2002 15:21:27 -0800 (PST) Message-ID: <3DF3D3A8.7FEC46E5 [at] sun [dot] com> Date: Sun, 08 Dec 2002 15:20:08 -0800 From: Bill Walster X-Mailer: Mozilla 4.76 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: "reliable_computing [at] interval [dot] louisiana.edu" Subject: intervals in Maple Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk I was surprised and pleased to find this web site: http://www.mapleapps.com/powertools/interval/Interval.shtml If any of you have experience with it, I would be most interested to receive your impressions. Also, I believe *rigorous* interval bounds are computed with this software. Best regards, Bill From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Dec 21 23:34:17 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBM5YG023114 for reliable_computing-outgoing; Sat, 21 Dec 2002 23:34:16 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBM5YB323108 for reliable_computing [at] interval [dot] louisiana.edu; Sat, 21 Dec 2002 23:34:11 -0600 (CST) Received: from lcyoung.math.wisc.edu (lcyoung.math.wisc.edu [144.92.166.90]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBAHBHi08618 for ; Tue, 10 Dec 2002 11:11:18 -0600 (CST) Received: from ultra7.math.wisc.edu (ultra7.math.wisc.edu [144.92.166.188]) by lcyoung.math.wisc.edu (8.11.6/8.11.6) with ESMTP id gBAHAlX15017; Tue, 10 Dec 2002 11:10:47 -0600 (CST) Date: Tue, 10 Dec 2002 11:10:47 -0600 (CST) From: Hans Schneider To: NETS -- at-net , E-LETTER , Pradeep Misra , Shaun Fallat , "na.digest" , ipnet-digest [at] math [dot] msu.edu, SIAGLA-DIGEST , wim@bell-labs.com, hjt [at] eos [dot] ncsu.edu, SMBnet [at] smb [dot] org, vkm [at] eedsp [dot] gatech.edu, reliable_computing [at] interval [dot] louisiana.edu cc: Billy Stewart Subject: CORRECTION to LAA announcement: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-MailScanner: Found to be clean Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Net organizer: I've had to change one of the web addresses in the LAA announcement I sent earlier today. Please circulate this version. Apologies hans ********************************************************************* Hans Schneider Office: Home: Mathematics Department 910 S. Midvale Blvd. Van Vleck Hall Madison, WI 53711 USA University of Wisconsin 608-271-7252 480 Lincoln Drive Madison, WI 53706-1313 USA Email: hans [at] math [dot] wisc.edu Office Phone: 608-262-1402 WWW: http://www.math.wisc.edu/~hans Math Dept Phone: 608-263-3054 Math Dept Fax: 608-263-8891 ********************************************************************* LAA special issue Proceedings of the 2003 conference on the Numerical Solution of Markov Chains LAA will publish the proceedings of this conference to be held at the University of Illinois at Urbana-Champaign, September 3 - 5, 2003. The special issue editors are: Winfried Grassmann, Carl Meyer, Billy Stewart and Daniel Szyld. Papers should be submitted to billy [at] csc [dot] ncsu.edu or anlangvi [at] unity [dot] ncsu.edu by March 17, 2003. For details see the conference announcement at http://www.csc.ncsu.edu/nsmc2003 or at http://www.math.wisc.edu/~hans/laa.html . From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Dec 21 23:34:36 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBM5YZZ23142 for reliable_computing-outgoing; Sat, 21 Dec 2002 23:34:35 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBM5YUK23137 for reliable_computing [at] interval [dot] louisiana.edu; Sat, 21 Dec 2002 23:34:30 -0600 (CST) Received: from mailhub-2.iastate.edu (mailhub-2.iastate.edu [129.186.140.4]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBHIED610050 for ; Tue, 17 Dec 2002 12:14:14 -0600 (CST) Received: from mailout-2.iastate.edu (mailout-2.iastate.edu [129.186.140.2]) by mailhub-2.iastate.edu (8.9.3/8.9.3) with SMTP id MAA05619; Tue, 17 Dec 2002 12:14:05 -0600 Received: from pixie-1.ee.iastate.edu(129.186.205.225) by mailout-2.iastate.edu via csmap id 30999; Tue, 17 Dec 2002 12:06:13 -0600 (CST) Message-ID: <004301c2a5f8$169cea50$e1cdba81 [at] ee [dot] iastate.edu> From: "Jianzhong Zhang" To: Cc: "Jianzhong Zhang" Subject: Cumulative distribution function envelopes from interval-valued parameters Date: Tue, 17 Dec 2002 12:14:06 -0600 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0040_01C2A5C5.CBF7CBF0" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------=_NextPart_000_0040_01C2A5C5.CBF7CBF0 Content-Type: text/plain; charset="gb2312" Content-Transfer-Encoding: quoted-printable Hello, Would anybody recommend me some references on the generation of p-boxes = or envelopes around cumulative distribution functions, given from = interval-valued parameters of distributions? For examples, consider the = normal distribution with interval-valued mean and/or variance. If we = only know the intervals, how I can get the safe envelopes to cover all = possible CDFs? Thank you for any references you can provide! Jianzhong Zhang ------=_NextPart_000_0040_01C2A5C5.CBF7CBF0 Content-Type: text/html; charset="gb2312" Content-Transfer-Encoding: quoted-printable
Hello,
 
Would anybody recommend = me some=20 references on the generation of p-boxes or envelopes around cumulative=20 distribution functions, given from interval-valued parameters of=20 distributions? For examples, consider the normal distribution with=20 interval-valued mean and/or variance. If we only know the intervals, how = I can=20 get the safe envelopes to cover all possible CDFs?

Thank you for = any=20 references you can provide!

Jianzhong=20 Zhang

------=_NextPart_000_0040_01C2A5C5.CBF7CBF0-- From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Dec 22 13:32:49 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBMJWmh25503 for reliable_computing-outgoing; Sun, 22 Dec 2002 13:32:49 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBMJWg625499 for ; Sun, 22 Dec 2002 13:32:43 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBMJWYi17963; Sun, 22 Dec 2002 12:32:35 -0700 (MST) Message-Id: <200212221932.gBMJWYi17963 [at] cs [dot] utep.edu> Date: Sun, 22 Dec 2002 12:32:35 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: intervals in Maple To: reliable_computing [at] interval [dot] louisiana.edu, bill.walster [at] sun [dot] com MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: 9GkUptwICWBtTxbf6F24SQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk I added the link to the Instreval Software part of the interval website. Thanks a lot to Bill for noticing it. Caution: at present, I am unable to onnect to the site, I get an error message, their server may be temporarily down or something. Vladik > Date: Sun, 08 Dec 2002 15:20:08 -0800 > From: Bill Walster > X-Accept-Language: en > MIME-Version: 1.0 > To: "reliable_computing [at] interval [dot] louisiana.edu" > Subject: intervals in Maple > Content-Transfer-Encoding: 7bit > > > I was surprised and pleased to find this web site: > > http://www.mapleapps.com/powertools/interval/Interval.shtml > > If any of you have experience with it, I would be most interested > to receive your impressions. Also, I believe *rigorous* interval > bounds are computed with this software. > > Best regards, > > Bill From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Dec 22 13:34:27 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBMJYQx25535 for reliable_computing-outgoing; Sun, 22 Dec 2002 13:34:26 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBMJYL625530 for ; Sun, 22 Dec 2002 13:34:22 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBMJYGU17977; Sun, 22 Dec 2002 12:34:16 -0700 (MST) Message-Id: <200212221934.gBMJYGU17977 [at] cs [dot] utep.edu> Date: Sun, 22 Dec 2002 12:34:16 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: Cumulative distribution function envelopes from interval-valued parameters To: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu Cc: zjz [at] indian [dot] eng.iastate.edu, scott [at] ramas [dot] com MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: HINexuK6vYPlqFhv8lxRqw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Scott Ferson may have it (or at least know who has it). I am sending a copy of this message to him. Vladik > From: "Jianzhong Zhang" > To: > Cc: "Jianzhong Zhang" > Subject: Cumulative distribution function envelopes from interval-valued parameters > Date: Tue, 17 Dec 2002 12:14:06 -0600 > MIME-Version: 1.0 > X-Priority: 3 > X-MSMail-Priority: Normal > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 > > Hello, > > Would anybody recommend me some references on the generation of p-boxes or envelopes around cumulative distribution functions, given from interval-valued parameters of distributions? For examples, consider the normal distribution with interval-valued mean and/or variance. If we only know the intervals, how I can get the safe envelopes to cover all possible CDFs? > > Thank you for any references you can provide! > > Jianzhong Zhang > From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Dec 22 14:36:57 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBMKav225822 for reliable_computing-outgoing; Sun, 22 Dec 2002 14:36:57 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBMKap625818 for ; Sun, 22 Dec 2002 14:36:52 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBMKakQ18342; Sun, 22 Dec 2002 13:36:46 -0700 (MST) Message-Id: <200212222036.gBMKakQ18342 [at] cs [dot] utep.edu> Date: Sun, 22 Dec 2002 13:36:46 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: Cumulative distribution function envelopes from interval-valued parameters To: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu Cc: zjz [at] indian [dot] eng.iastate.edu, scott [at] ramas [dot] com MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: dkYqqAY8o5SD5o6/F5AsnA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk For normal distribution with parameters a and sigma, the CDF F(x) has the form F(x)=F0(t), where t=(x-a)/sigma, and F0(x) is the CDF os the normalized Gaussian distribution, with 0 mean and standard deviation 1. Thus, if we know the intervals [a-,a+] and [sigma-,sigma+] for a and sigma, we can, for every x, compute the interval [t-,t+] of possible values of t (this can be done by straightforward interval computations), and then, since F0 is increasing function, we can take [F0(t-),F0(t+)] as the range for F(x). I believe that this is implemented in RiskCalc, but I am not 100% sure. Vladik > From: "Jianzhong Zhang" > To: > Cc: "Jianzhong Zhang" > Subject: Cumulative distribution function envelopes from interval-valued parameters > Date: Tue, 17 Dec 2002 12:14:06 -0600 > MIME-Version: 1.0 > X-Priority: 3 > X-MSMail-Priority: Normal > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 > > Hello, > > Would anybody recommend me some references on the generation of p-boxes or envelopes around cumulative distribution functions, given from interval-valued parameters of distributions? For examples, consider the normal distribution with interval-valued mean and/or variance. If we only know the intervals, how I can get the safe envelopes to cover all possible CDFs? > > Thank you for any references you can provide! > > Jianzhong Zhang > From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Dec 27 15:41:38 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBRLfcP10099 for reliable_computing-outgoing; Fri, 27 Dec 2002 15:41:38 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBRLfZI10094 for reliable_computing [at] interval [dot] louisiana.edu; Fri, 27 Dec 2002 15:41:35 -0600 (CST) Received: from company.mail (pool-151-202-118-213.ny5030.east.verizon.net [151.202.118.213]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBMMhn626127 for ; Sun, 22 Dec 2002 16:43:50 -0600 (CST) Received: from ramas.com [192.0.0.24] by company.mail [127.0.0.1] with SMTP (MDaemon.v3.1.0.R) for ; Sun, 22 Dec 2002 17:43:11 -0500 Message-ID: <3E063FFB.820E485C [at] ramas [dot] com> Date: Sun, 22 Dec 2002 17:43:07 -0500 From: Scott Ferson Organization: Applied Biomathematics X-Mailer: Mozilla 4.73 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 CC: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu Subject: Re: Cumulative distribution function envelopes from interval-valued parameters References: <200212222036.gBMKakQ18342 [at] cs [dot] utep.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-MDaemon-Deliver-To: reliable_computing [at] interval [dot] louisiana.edu X-Return-Path: scott [at] ramas [dot] com X-MDRcpt-To: zjz [at] indian [dot] eng.iastate.edu X-MDRemoteIP: 192.0.0.24 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk For all of the commonly used distributions, you can compute the p-box by enveloping a small number of CDFs with extremal parameters. For instance, the normal p-box with interval parameters mean = [m1, m2] and standard deviation s = [s1, s2] can be found by enveloping the four CDFs normal(m1, s1), normal(m1, s2), normal(m2, s1), and normal(m2, s2). Enveloping just means that, for every x-value, you take the largest and smallest p-values from the four above to form the p-box. (Or equivalently, for every p-value, you take the largest and smallest of the four x-values.) This is rigorous in that, if the parameters are really in the specified ranges and the distribution really is normal, then the bounds of the p-box are guaranteed. It's also best possible in that they couldn't be any tighter and still enclose all normal distributions with parameters in the given ranges. Most distributions have been parameterized in a way that makes this work out easily. The uniform, triangular, trapezoidal distributions and the log-transformed cousins are even easier, as they require one to envelope only two distributions. Scott Vladik Kreinovich wrote: > For normal distribution with parameters a and sigma, the CDF F(x) has the form > F(x)=F0(t), where t=(x-a)/sigma, and F0(x) is the CDF os the normalized > Gaussian distribution, with 0 mean and standard deviation 1. Thus, if we know > the intervals [a-,a+] and [sigma-,sigma+] for a and sigma, we can, for every x, > compute the interval [t-,t+] of possible values of t (this can be done by > straightforward interval computations), and then, since F0 is increasing > function, we can take [F0(t-),F0(t+)] as the range for F(x). > > I believe that this is implemented in RiskCalc, but I am not 100% sure. > > Vladik > > > From: "Jianzhong Zhang" > > To: > > Cc: "Jianzhong Zhang" > > Subject: Cumulative distribution function envelopes from interval-valued > parameters > > Date: Tue, 17 Dec 2002 12:14:06 -0600 > > MIME-Version: 1.0 > > X-Priority: 3 > > X-MSMail-Priority: Normal > > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 > > > > Hello, > > > > Would anybody recommend me some references on the generation of p-boxes or > envelopes around cumulative distribution functions, given from interval-valued > parameters of distributions? For examples, consider the normal distribution > with interval-valued mean and/or variance. If we only know the intervals, how I > can get the safe envelopes to cover all possible CDFs? > > > > Thank you for any references you can provide! > > > > Jianzhong Zhang > > -- Scott Ferson Applied Biomathematics 100 North Country Road Setauket, New York 11733 631-751-4350, fax -3435 From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Dec 27 15:41:53 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBRLfqN10121 for reliable_computing-outgoing; Fri, 27 Dec 2002 15:41:52 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBRLfn610114 for reliable_computing [at] interval [dot] louisiana.edu; Fri, 27 Dec 2002 15:41:49 -0600 (CST) Received: from fsc.cpsc.ucalgary.ca (fsc.cpsc.ucalgary.ca [136.159.2.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBO236629435 for ; Mon, 23 Dec 2002 20:03:07 -0600 (CST) Received: from imgw1.cpsc.ucalgary.ca (ons-imgw1 [192.168.1.66]) by fsc.cpsc.ucalgary.ca (8.12.2/8.12.6) with ESMTP id gBO22dq1007422; Mon, 23 Dec 2002 19:02:39 -0700 Received: from MARINA (ict709 [136.159.7.166]) by imgw1.cpsc.ucalgary.ca (8.12.3/8.12.3) with SMTP id gBO22UQr022338; Mon, 23 Dec 2002 19:02:37 -0700 From: "Marina Gavrilova" To: , , , , , Subject: CGA'03 CFP Date: Mon, 23 Dec 2002 19:02:36 -0700 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook IMO, Build 9.0.2416 (9.0.2911.0) Importance: Normal X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 In-Reply-To: <200211291236.45646.mueller@uni-trier.de> X-Virus-Scanned: by amavis-milter (http://amavis.org/) X-Spam-Status: No, hits=0.6 required=7.5 tests=DEAR_SOMEBODY,IN_REP_TO,SPAM_PHRASE_02_03,SUBJ_ALL_CAPS, USER_AGENT_OUTLOOK version=2.43 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Colleagues, Please find attached the CFP for CGA'03: CALL FOR PAPERS ============================================================ International Workshop on Computational Geometry and Applications CGA'03 in conjunction with The 2003 International Conference on Computational Science and its Applications (ICCSA 2003) http://www.ucalgary.ca/iccsa/events.htm May 18, 2003 -- May 21, 2003 Montreal, Canada ============================================================ Workshop Web Site: http://http://pages.cpsc.ucalgary.ca/~marina/Newweb/session.htm Conference web sites: http://www.ucalgary.ca/iccsa/ http://www.cs.qub.ac.uk/iccsa/ http://www.optimanumerics.com/iccsa/ http://www.sharcnet.ca/iccsa/ ============================================================ Workshop Chair: Marina Gavrilova, University of Calgary Workshop Co-Chair: Ovidiu Daescu (University of Texas at Dallas, USA) Important Dates --------------- February 1, 2003: Deadline for paper submission. February 21, 2003: Notification of acceptance. February 28, 2003: Camera Ready Papers and Pre-registration. May 18 -- 22, 2003: ICCSA 2003 Conference in Montreal, Canada. Workshop Description -------------------- The Workshop, held for the third year in a row in conjunction with the International Conference on Computational Science, is intended as an international forum for researchers in all areas of computational geometry. Submissions of papers presenting a high-quality original research are invited to one of the two Workshop tracks: - theoretical computational geometry - implementation issues and applied computational geometry. Topics of interest: ----------------------- - Algorithmic methods in geometry - Animation of geometric algorithms - Lower bounds and algorithm complexity - Solid modeling - Geographic information systems - Computational methodology - Computer graphics and image processing - Illumination problems - Visibility graphs - Space Partitioning - Data structures (including Voronoi Diagrams and Delaunay triangulations) - Geometric computations in parallel and distributed environments - Mesh generation - Interpolation and surface reconstruction - Spatial and terrain analysis - Computer graphics and image processing - Computational methods in manufacturing - Applications in molecular biology, granular mechanics, computational physics, oceanography - Exact computations - Robotics - Path planning - Algorithm Implementation - CAD/CAM Submissions in other related areas will also be considered. The design and implementation of geometric algorithms in parallel and distributed environments, exact computations, and applications in mechanics, physics and biology, are of special interest. Proceedings ------------- Proceedings of the Workshop will be published in the Springer-Verlag Lecture Notes in Computer Science (LNCS) series. The proceedings will also be available separately for purchase from Springer-Verlag (proceedings of the previous Workshops on Computational Geometry and Applications appeared in LNCS vol. 2073, vol. 2329-2331). Papers from the Workshop may be invited to special issues of International Journal of Computational Geometry and Applications, Journal of CAD/CAM, Journal of Computational Methods in Sciences and Engineering (JCMSE) and the Journal of Supercomputing (pending agreement). Best Student Paper Award and Travel Grant ------------------------------------------ This year, a best student paper will be selected for a Best Student Paper Award. This award will be available exclusively to CGA'03 participants. A paper is eligible if at least one of its authors is a full or part-time student at the time of submission. Author of the paper submitted to CGA'03 will be also eligible to apply for Travel Grant, provided by ICCSA'03 sponsors. The ICCSA'03 program committee may decline to make the award, or may split it among more than one participant. Available Financial Assistance ------------------------------ Author of the paper submitted to CGA'03 will be automatically eligible for assistance, if he belongs to Canadian University, educational institution, government agency or industry. Students enrolled at Canadian institutions are also eligible for a discount of registration fees. Paper Submission Conference fees ---------------- For all details with respect to the conference fees see http://www.ucalgary.ca/iccsa/. Special discounts for students and participants from some academia/research institutions are available. For more information, please visit the Workshop web site. Submission ----------- We invite you to submit a draft of the paper of up to 10 pages (Letter or A4) paper. Please include a cover page (in ascii format) which lists the following: - Title of the paper - List of authors - name, affiliation, address and e-mail address of each author - name of the contact author - preferred track (theoretical or applied track) - a maximum of 5 keywords - intent to be considered for the Best Student Paper Award (exclusively for CGA'03 participants) - intent to apply for Travel Grant (available for all ICCSA'03 participants) The submission must be camera-ready and formatted according to the rules of LNCS. Electronic submissions in PS, PDF, or LaTex (please also submit all .eps, .dvi, and .ps files). MS Word submissions will also be accepted. Please submit your paper directly to e-mall address: iccsa [at] sharcnet [dot] com or marina [at] cpsc [dot] ucalgary.ca Indicate in the header of the message "CGA'03 submission". Organizing Committee Conference ChairsVipin Kumar (Army High Performance Computing Center, USA and University of Minessota, USA) Honorary Chair Marina Gavrilova (University of Calgary, Canada) Conference Chair C. J. Kenneth Tan (Heuchera Technologies, Canada and SHARCNET, Canada) Conference Chair Pierre L'Ecuyer (University of Montreal, Canada) Local Organizing Committee Chair Program Committee Sergei Bespamyatnikh (Duke University, USA) Tamal Dey (Ohio State University, USA) Frank Dehne (Carleton University, Canada) Ovidiu Daescu (University of Texas at Dallas, USA) Christopher Gold (Hong Kong Polytechnic University) Deok-Soo Kim (Hanyang University, Korea) Andres Iglesias (University de Cantabria, Spain) Kokichi Sugihara (University of Tokyo, Japan) Vaclav Skala (University of West Bohemia, Czech Republic) Stephen Wismath (University of Lethbridge, Canada) J. A. Rod Blais (University of Calgary, Canada) Marian Bubak (AGH, Poland) Toni Cortes (Universidad de Catalunya, Barcelona, Spain) Brian J. d'Auriol (University of Texas at El Paso, USA) Ivan Dimov (Bulgarian Academy of Sciences, Bulgaria) Matthew F. Dixon (Heuchera Technologies, UK) Geoffrey Fox (Indiana University, USA) Marina L. Gavrilova (University of Calgary, Canada) Bob Hertzberger (Universiteit van Amsterdam, The Netherlands) Chris Johnson (University of Utah, USA) Benjoe A. Juliano (California State University at Chico, USA) Vipin Kumar (University of Minnesota, USA) Antonio Lagana (Universita Degli Studi di Perugia, Italy) Michael Mascagni (Florida State University, USA) Cathy McDonald (Department of Defense HPC Modernization Program, USA) Graham Megson (University of Reading, UK) Jiri Nedoma (Academy of Sciences of the Czech Republic, Czech Republic) Robert Panoff (Shodor Education Foundation, USA) Renee S. Renner (California State University at Chico, USA) David Taniar (Monash University, Australia) Koichi Wada (University of Tsukuba, Japan) Jerzy Wasniewski (Danish Computing Center for Research and Education, Denmark) Roy Williams (California Institute of Technology, USA) Osman Yasar (SUNY at Brockport, USA) Zahari Zlatev (Danish Environmental Research Institute, Denmark) CGA'01 and CGA'02 profiles To view electronic proceedings of the CGA'01, follow the link to LNCS web site: http://turing.zblmath.fiz-karlsruhe.de/cs/www_lncs.1.html Volume 2073, Springer Verlag. Invited speaker for CGA'01: Kokichi Sugihara, University of Tokyo, Japan Invited speakers for CGA'02: Mark Overmars, Utrecht University Contributed Presentation: Pieter Huybers, the Netherlands List of papers appeared at CGA'01 and CGA'02 can be found on Workshop web site. With regards, Marina L. Gavrilova ICCSA 2003 Chair Department of Computer Science, University of Calgary, 2500 University Drive, Calgary, Alberta, Canada, T2N1N4 Telephone: (403) 241-6315 Fax: (403) 284-4707 E-mail: marina [at] cpsc [dot] ucalgary.ca From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Dec 27 16:37:08 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBRMb8A10435 for reliable_computing-outgoing; Fri, 27 Dec 2002 16:37:08 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBRMb2610431 for ; Fri, 27 Dec 2002 16:37:02 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBRMarr23507; Fri, 27 Dec 2002 15:36:53 -0700 (MST) Message-Id: <200212272236.gBRMarr23507 [at] cs [dot] utep.edu> Date: Fri, 27 Dec 2002 15:36:52 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: Cumulative distribution function envelopes from interval-valued parameters To: scott [at] ramas [dot] com Cc: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: 0QbfPUCrr07hwsbuQ7MZng== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is true if the CDF monotonically depends on each of its parameters, which seems to be indeed the case for all the standard classes of distributions. If we know the direction of monotonicity we indeed know when the mimum and maximum are attained so we indeed need only two. > Date: Sun, 22 Dec 2002 17:43:07 -0500 > From: Scott Ferson > X-Accept-Language: en > MIME-Version: 1.0 > CC: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu > Subject: Re: Cumulative distribution function envelopes from interval-valued parameters > Content-Transfer-Encoding: 7bit > X-MDaemon-Deliver-To: reliable_computing [at] interval [dot] louisiana.edu > X-Return-Path: scott [at] ramas [dot] com > X-MDRcpt-To: zjz [at] indian [dot] eng.iastate.edu > X-MDRemoteIP: 192.0.0.24 > > > For all of the commonly used distributions, you can compute the > p-box by enveloping a small number of CDFs with extremal > parameters. For instance, the normal p-box with interval > parameters mean = [m1, m2] and standard deviation s = [s1, s2] > can be found by enveloping the four CDFs > normal(m1, s1), > normal(m1, s2), > normal(m2, s1), and > normal(m2, s2). > Enveloping just means that, for every x-value, you take the largest > and smallest p-values from the four above to form the p-box. (Or > equivalently, for every p-value, you take the largest and smallest > of the four x-values.) > > This is rigorous in that, if the parameters are really in the specified > ranges and the distribution really is normal, then the bounds of the > p-box are guaranteed. It's also best possible in that they couldn't > be any tighter and still enclose all normal distributions with parameters > in the given ranges. Most distributions have been parameterized > in a way that makes this work out easily. The uniform, triangular, > trapezoidal distributions and the log-transformed cousins are even > easier, as they require one to envelope only two distributions. > > Scott > > > > > Vladik Kreinovich wrote: > > > For normal distribution with parameters a and sigma, the CDF F(x) has the form > > F(x)=F0(t), where t=(x-a)/sigma, and F0(x) is the CDF os the normalized > > Gaussian distribution, with 0 mean and standard deviation 1. Thus, if we know > > the intervals [a-,a+] and [sigma-,sigma+] for a and sigma, we can, for every x, > > compute the interval [t-,t+] of possible values of t (this can be done by > > straightforward interval computations), and then, since F0 is increasing > > function, we can take [F0(t-),F0(t+)] as the range for F(x). > > > > I believe that this is implemented in RiskCalc, but I am not 100% sure. > > > > Vladik > > > > > From: "Jianzhong Zhang" > > > To: > > > Cc: "Jianzhong Zhang" > > > Subject: Cumulative distribution function envelopes from interval-valued > > parameters > > > Date: Tue, 17 Dec 2002 12:14:06 -0600 > > > MIME-Version: 1.0 > > > X-Priority: 3 > > > X-MSMail-Priority: Normal > > > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 > > > > > > Hello, > > > > > > Would anybody recommend me some references on the generation of p-boxes or > > envelopes around cumulative distribution functions, given from interval-valued > > parameters of distributions? For examples, consider the normal distribution > > with interval-valued mean and/or variance. If we only know the intervals, how I > > can get the safe envelopes to cover all possible CDFs? > > > > > > Thank you for any references you can provide! > > > > > > Jianzhong Zhang > > > > > -- > > Scott Ferson > Applied Biomathematics > 100 North Country Road > Setauket, New York 11733 > 631-751-4350, fax -3435 > From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Dec 27 19:07:34 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBS17XI10830 for reliable_computing-outgoing; Fri, 27 Dec 2002 19:07:33 -0600 (CST) Received: from pheriche.sun.com (pheriche.sun.com [192.18.98.34]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBS17S610826 for ; Fri, 27 Dec 2002 19:07:28 -0600 (CST) Received: from heliopolis.eng.sun.com ([152.70.8.30]) by pheriche.sun.com (8.9.3+Sun/8.9.3) with ESMTP id SAA02685; Fri, 27 Dec 2002 18:07:25 -0700 (MST) Received: from sun.com (sml-mtv29-dhcp-33-189 [152.70.33.189]) by heliopolis.eng.sun.com (8.9.3+Sun/8.9.3/ENSMAIL,v2.1p1) with ESMTP id RAA20709; Fri, 27 Dec 2002 17:07:25 -0800 (PST) Message-ID: <3E0CF8B2.C7AE72C1 [at] sun [dot] com> Date: Fri, 27 Dec 2002 17:04:50 -0800 From: Bill Walster X-Mailer: Mozilla 4.76 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: Vladik Kreinovich CC: scott [at] ramas [dot] com, reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu Subject: Re: Cumulative distribution function envelopes from interval-valued parameters References: <200212272236.gBRMarr23507 [at] cs [dot] utep.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk The property you require is referred to in the statistical literature as "monotone likelihood ratio". A pdf f(x|a) has a MLR with respect to a given parameter a iff f(x'|a)/f(x'|a') <= f(x|a)/f(x|a') for all x <= x' and a <= a'. A consequence of the MLR property is that the CDF of the random variable X evaluated at any point x is a monotonically decreasing function of the parameter a. The difficulty is that when there is more than one parameter, I'm not sure what, if anything can be said. The normal distribution has a MLR with respect to its mean *given* its variance, but I don't think the same can be said about the variance, or other parameters of other distributions in general. The noncentral gamma (or equivalently the noncentral chi square), non-central beta (or equivalently the noncentral F) distributions have MLRs with respect to their noncentrality parameters. I do not believe that with respect to their other parameters that they do have MLRs. The problem is even more complicated when one considers more than one parameter simultaneously. BTW, it was the problem of solving two simultaneous equations in the inverse of noncentral CDFs that forced me to begin using intervals. There was no way to solve these problems and know the accuracy of computed results otherwise. Cheers, Bill Vladik Kreinovich wrote: > > This is true if the CDF monotonically depends on each of its parameters, which > seems to be indeed the case for all the standard classes of distributions. If > we know the direction of monotonicity we indeed know when the mimum and maximum > are attained so we indeed need only two. > > > Date: Sun, 22 Dec 2002 17:43:07 -0500 > > From: Scott Ferson > > X-Accept-Language: en > > MIME-Version: 1.0 > > CC: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, > zjz [at] indian [dot] eng.iastate.edu > > Subject: Re: Cumulative distribution function envelopes from interval-valued > parameters > > Content-Transfer-Encoding: 7bit > > X-MDaemon-Deliver-To: reliable_computing [at] interval [dot] louisiana.edu > > X-Return-Path: scott [at] ramas [dot] com > > X-MDRcpt-To: zjz [at] indian [dot] eng.iastate.edu > > X-MDRemoteIP: 192.0.0.24 > > > > > > For all of the commonly used distributions, you can compute the > > p-box by enveloping a small number of CDFs with extremal > > parameters. For instance, the normal p-box with interval > > parameters mean = [m1, m2] and standard deviation s = [s1, s2] > > can be found by enveloping the four CDFs > > normal(m1, s1), > > normal(m1, s2), > > normal(m2, s1), and > > normal(m2, s2). > > Enveloping just means that, for every x-value, you take the largest > > and smallest p-values from the four above to form the p-box. (Or > > equivalently, for every p-value, you take the largest and smallest > > of the four x-values.) > > > > This is rigorous in that, if the parameters are really in the specified > > ranges and the distribution really is normal, then the bounds of the > > p-box are guaranteed. It's also best possible in that they couldn't > > be any tighter and still enclose all normal distributions with parameters > > in the given ranges. Most distributions have been parameterized > > in a way that makes this work out easily. The uniform, triangular, > > trapezoidal distributions and the log-transformed cousins are even > > easier, as they require one to envelope only two distributions. > > > > Scott > > > > > > > > > > Vladik Kreinovich wrote: > > > > > For normal distribution with parameters a and sigma, the CDF F(x) has the > form > > > F(x)=F0(t), where t=(x-a)/sigma, and F0(x) is the CDF os the normalized > > > Gaussian distribution, with 0 mean and standard deviation 1. Thus, if we > know > > > the intervals [a-,a+] and [sigma-,sigma+] for a and sigma, we can, for > every x, > > > compute the interval [t-,t+] of possible values of t (this can be done by > > > straightforward interval computations), and then, since F0 is increasing > > > function, we can take [F0(t-),F0(t+)] as the range for F(x). > > > > > > I believe that this is implemented in RiskCalc, but I am not 100% sure. > > > > > > Vladik > > > > > > > From: "Jianzhong Zhang" > > > > To: > > > > Cc: "Jianzhong Zhang" > > > > Subject: Cumulative distribution function envelopes from interval-valued > > > parameters > > > > Date: Tue, 17 Dec 2002 12:14:06 -0600 > > > > MIME-Version: 1.0 > > > > X-Priority: 3 > > > > X-MSMail-Priority: Normal > > > > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 > > > > > > > > Hello, > > > > > > > > Would anybody recommend me some references on the generation of p-boxes > or > > > envelopes around cumulative distribution functions, given from > interval-valued > > > parameters of distributions? For examples, consider the normal distribution > > > with interval-valued mean and/or variance. If we only know the intervals, > how I > > > can get the safe envelopes to cover all possible CDFs? > > > > > > > > Thank you for any references you can provide! > > > > > > > > Jianzhong Zhang > > > > > > > > -- > > > > Scott Ferson > > Applied Biomathematics > > 100 North Country Road > > Setauket, New York 11733 > > 631-751-4350, fax -3435 > > From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Dec 27 19:34:38 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBS1YcN11008 for reliable_computing-outgoing; Fri, 27 Dec 2002 19:34:38 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBS1YW611004 for ; Fri, 27 Dec 2002 19:34:33 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBS1YRG24419; Fri, 27 Dec 2002 18:34:27 -0700 (MST) Message-Id: <200212280134.gBS1YRG24419 [at] cs [dot] utep.edu> Date: Fri, 27 Dec 2002 18:34:25 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: Cumulative distribution function envelopes from interval-valued parameters To: vladik [at] cs [dot] utep.edu, bill.walster [at] sun [dot] com Cc: scott [at] ramas [dot] com, reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: T/GTP/k8vIBT0XnDcvmgIA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Bill, Thanks for your email. Let me clarify my answer. > The difficulty is that when there is more than one parameter, I'm > not sure what, if anything can be said. The original question, in my understanding, was: we know that the actual (unknown) distribution belongs to a certain known finite-parameteric class of distributions, characterized by one or several parameters p1,...,pn. For example, this class can be the class of all normal duistributions. For distributions from this given class, we know how the CDF depends on the the parameters p1,...,pn: prob(xi \le x)=F(x,p1,...,pn). For example, for normal distributions, the parameters are p1=a and p2=sigma, and the dependence has the form F(x,p1,p2)=F0((x-p1)/p2), where F0(x) is a CDF of the normalized Gaussian distrbution with 0 mean and standard deviation 1. Dan Berleant is interested in the case when we do not know the exact values of the corresponding parameters pi, only intervals. As a result, for every value x, we have not a single value F(x) but several possible values corresponding to different possible values pi from the corresponding interval [pi]. These possible values form an interval [F(x)] depending on x. The corresponding interval-values function is called a p-bound or p-box. The objective is, for every x, to find the exact interval [F(x)] of possible values of F(x,p1,...,pn) when p1 is from the interval [p1], p2 is from interval [p2], ... At this point, we can forget about the probabilistic meaning because we have a standard problem of interval computations: * we have a function F(x,p1,...,pn) * we know the intervals [p1],...[pn] of possible values of the variables p1,...,pn * we want to know the range of the function F(x,p1,...,pn) on this box [p1] x [p2] x ... x [pn] What I was saying originally and what (in my understanding) Scott Ferson was saying is that if the function F is monotonically depending on each of the paramaters pi (and for normal distribution it has the form F0((x-a)/sigma), i.e., indeed monotonically depends on a (for given sigma) and on sigma (for given a)), then the computation of this range is easy : all we have to do is take the corresponding endpoints of the intervals [pi]. This is just a routine application of the known fact that computing the range of a monotonic function over a box is easy: since it is monotonic in each variable, we know for which endpoint is attains minimum over p1, for which it attains minimum over p2, etc. As you can see, I do not need the MLR property for Guassian distributions and for other distributions mentioned by Scott, because we can explicitly check that CDF is indeed monotonic in each of the parameters. I agree that there are other classes where there is no monotonicity at all, and for them, we have to use some more sophisctiated interval computation techniques to estimate the range. I hope this clarifies what I wrote. If this is still not clear please send me your new office phone number so that we can talk off-line. Vladik > Date: Fri, 27 Dec 2002 17:04:50 -0800 > From: Bill Walster > X-Accept-Language: en > MIME-Version: 1.0 > To: Vladik Kreinovich > CC: scott [at] ramas [dot] com, reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu > Subject: Re: Cumulative distribution function envelopes from interval-valued parameters > Content-Transfer-Encoding: 7bit > > > The property you require is referred to in the statistical literature > as "monotone likelihood ratio". A pdf f(x|a) has a MLR with respect to > a given parameter a iff > > f(x'|a)/f(x'|a') <= f(x|a)/f(x|a') > > for all x <= x' and a <= a'. > > A consequence of the MLR property is that the CDF of the > random variable X evaluated at any point x is a monotonically > decreasing function of the parameter a. > > The difficulty is that when there is more than one parameter, I'm > not sure what, if anything can be said. The normal distribution > has a MLR with respect to its mean *given* its variance, but I > don't think the same can be said about the variance, or other > parameters of other distributions in general. The noncentral > gamma (or equivalently the noncentral chi square), non-central beta > (or equivalently the noncentral F) distributions have MLRs with > respect to their noncentrality parameters. I do not believe that > with respect to their other parameters that they do have MLRs. > > The problem is even more complicated when one considers more > than one parameter simultaneously. > > BTW, it was the problem of solving two simultaneous equations in > the inverse of noncentral CDFs that forced me to begin using > intervals. There was no way to solve these problems and know > the accuracy of computed results otherwise. > > Cheers, > > Bill > > > Vladik Kreinovich wrote: > > > > This is true if the CDF monotonically depends on each of its parameters, which > > seems to be indeed the case for all the standard classes of distributions. If > > we know the direction of monotonicity we indeed know when the mimum and maximum > > are attained so we indeed need only two. > > > > > Date: Sun, 22 Dec 2002 17:43:07 -0500 > > > From: Scott Ferson > > > X-Accept-Language: en > > > MIME-Version: 1.0 > > > CC: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, > > zjz [at] indian [dot] eng.iastate.edu > > > Subject: Re: Cumulative distribution function envelopes from interval-valued > > parameters > > > Content-Transfer-Encoding: 7bit > > > X-MDaemon-Deliver-To: reliable_computing [at] interval [dot] louisiana.edu > > > X-Return-Path: scott [at] ramas [dot] com > > > X-MDRcpt-To: zjz [at] indian [dot] eng.iastate.edu > > > X-MDRemoteIP: 192.0.0.24 > > > > > > > > > For all of the commonly used distributions, you can compute the > > > p-box by enveloping a small number of CDFs with extremal > > > parameters. For instance, the normal p-box with interval > > > parameters mean = [m1, m2] and standard deviation s = [s1, s2] > > > can be found by enveloping the four CDFs > > > normal(m1, s1), > > > normal(m1, s2), > > > normal(m2, s1), and > > > normal(m2, s2). > > > Enveloping just means that, for every x-value, you take the largest > > > and smallest p-values from the four above to form the p-box. (Or > > > equivalently, for every p-value, you take the largest and smallest > > > of the four x-values.) > > > > > > This is rigorous in that, if the parameters are really in the specified > > > ranges and the distribution really is normal, then the bounds of the > > > p-box are guaranteed. It's also best possible in that they couldn't > > > be any tighter and still enclose all normal distributions with parameters > > > in the given ranges. Most distributions have been parameterized > > > in a way that makes this work out easily. The uniform, triangular, > > > trapezoidal distributions and the log-transformed cousins are even > > > easier, as they require one to envelope only two distributions. > > > > > > Scott > > > > > > > > > > > > > > > Vladik Kreinovich wrote: > > > > > > > For normal distribution with parameters a and sigma, the CDF F(x) has the > > form > > > > F(x)=F0(t), where t=(x-a)/sigma, and F0(x) is the CDF os the normalized > > > > Gaussian distribution, with 0 mean and standard deviation 1. Thus, if we > > know > > > > the intervals [a-,a+] and [sigma-,sigma+] for a and sigma, we can, for > > every x, > > > > compute the interval [t-,t+] of possible values of t (this can be done by > > > > straightforward interval computations), and then, since F0 is increasing > > > > function, we can take [F0(t-),F0(t+)] as the range for F(x). > > > > > > > > I believe that this is implemented in RiskCalc, but I am not 100% sure. > > > > > > > > Vladik > > > > > > > > > From: "Jianzhong Zhang" > > > > > To: > > > > > Cc: "Jianzhong Zhang" > > > > > Subject: Cumulative distribution function envelopes from interval-valued > > > > parameters > > > > > Date: Tue, 17 Dec 2002 12:14:06 -0600 > > > > > MIME-Version: 1.0 > > > > > X-Priority: 3 > > > > > X-MSMail-Priority: Normal > > > > > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 > > > > > > > > > > Hello, > > > > > > > > > > Would anybody recommend me some references on the generation of p-boxes > > or > > > > envelopes around cumulative distribution functions, given from > > interval-valued > > > > parameters of distributions? For examples, consider the normal distribution > > > > with interval-valued mean and/or variance. If we only know the intervals, > > how I > > > > can get the safe envelopes to cover all possible CDFs? > > > > > > > > > > Thank you for any references you can provide! > > > > > > > > > > Jianzhong Zhang > > > > > > > > > > > -- > > > > > > Scott Ferson > > > Applied Biomathematics > > > 100 North Country Road > > > Setauket, New York 11733 > > > 631-751-4350, fax -3435 > > > From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Dec 28 09:11:49 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBSFBmj12865 for reliable_computing-outgoing; Sat, 28 Dec 2002 09:11:48 -0600 (CST) Received: from kathmandu.sun.com (kathmandu.sun.com [192.18.98.36]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBSFBf612861 for ; Sat, 28 Dec 2002 09:11:41 -0600 (CST) Received: from heliopolis.eng.sun.com ([152.70.8.30]) by kathmandu.sun.com (8.9.3+Sun/8.9.3) with ESMTP id IAA10747; Sat, 28 Dec 2002 08:11:37 -0700 (MST) Received: from sun.com (vpn-129-149-240-70.SFBay.Sun.COM [129.149.240.70]) by heliopolis.eng.sun.com (8.9.3+Sun/8.9.3/ENSMAIL,v2.1p1) with ESMTP id HAA03124; Sat, 28 Dec 2002 07:11:36 -0800 (PST) Message-ID: <3E0DBE8B.4CD0A1EB [at] sun [dot] com> Date: Sat, 28 Dec 2002 07:08:59 -0800 From: Bill Walster X-Mailer: Mozilla 4.76 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: Vladik Kreinovich CC: scott [at] ramas [dot] com, reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu Subject: Re: Cumulative distribution function envelopes from interval-valued parameters References: <200212280134.gBS1YRG24419 [at] cs [dot] utep.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk OK, but I think you might be missing the fact that even for the Gaussian distribution with mean u and standard deviation s, then the behavior of the cdf as a function of s depends on the sign of x-u. For sure, the situation is more complicated for distributions such as the gamma, beta, and their noncentral extensions. No doubt if you simply use naive interval evaluation of any CDF with interval bounds on parameters, you will get bounds on the CDF. The question is whether they suffer from dependence. Notice that the Normal pdf is not a SUE with respect to its standard deviation. Cheers, Bill Vladik Kreinovich wrote: > > Dear Bill, > > Thanks for your email. Let me clarify my answer. > > > The difficulty is that when there is more than one parameter, I'm > > not sure what, if anything can be said. > > The original question, in my understanding, was: we know that the actual > (unknown) distribution belongs to a certain known finite-parameteric class of > distributions, characterized by one or several parameters p1,...,pn. > For example, this class can be the class of all normal duistributions. > > For distributions from this given class, we know how the CDF depends on the > the parameters p1,...,pn: > prob(xi \le x)=F(x,p1,...,pn). For example, for normal distributions, the > parameters are p1=a and p2=sigma, and the dependence has the form > F(x,p1,p2)=F0((x-p1)/p2), where F0(x) is a CDF of the normalized Gaussian > distrbution with 0 mean and standard deviation 1. > > Dan Berleant is interested in the case when we do not know the exact values of > the corresponding parameters pi, only intervals. As a result, for every value > x, we have not a single value F(x) but several possible values corresponding to > different possible values pi from the corresponding interval [pi]. These > possible values form an interval [F(x)] depending on x. The corresponding > interval-values function is called a p-bound or p-box. > > The objective is, for every x, to find the exact interval [F(x)] of possible > values of F(x,p1,...,pn) when p1 is from the interval [p1], p2 is from interval > [p2], ... > > At this point, we can forget about the probabilistic meaning because we have a > standard problem of interval computations: > * we have a function F(x,p1,...,pn) > * we know the intervals [p1],...[pn] of possible values of the > variables p1,...,pn > * we want to know the range of the function F(x,p1,...,pn) > on this box [p1] x [p2] x ... x [pn] > > What I was saying originally and what (in my understanding) Scott Ferson was > saying is that if the function F is monotonically depending on each of the > paramaters pi (and for normal distribution it has the form F0((x-a)/sigma), > i.e., indeed monotonically depends on a (for given sigma) and on sigma (for > given a)), then the computation of this range is easy : all we have to do is > take the corresponding endpoints of the intervals [pi]. > > This is just a routine application of the known fact that computing the range > of a monotonic function over a box is easy: since it is monotonic in each > variable, we know for which endpoint is attains minimum over p1, for which it > attains minimum over p2, etc. > > As you can see, I do not need the MLR property for Guassian distributions and > for other distributions mentioned by Scott, because we can explicitly check > that CDF is indeed monotonic in each of the parameters. I agree that there are > other classes where there is no monotonicity at all, and for them, we have to > use some more sophisctiated interval computation techniques to estimate the > range. > > I hope this clarifies what I wrote. > > If this is still not clear please send me your new office phone number so that > we can talk off-line. > > Vladik > > > Date: Fri, 27 Dec 2002 17:04:50 -0800 > > From: Bill Walster > > X-Accept-Language: en > > MIME-Version: 1.0 > > To: Vladik Kreinovich > > CC: scott [at] ramas [dot] com, reliable_computing [at] interval [dot] louisiana.edu, > zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu > > Subject: Re: Cumulative distribution function envelopes from interval-valued > parameters > > Content-Transfer-Encoding: 7bit > > > > > > The property you require is referred to in the statistical literature > > as "monotone likelihood ratio". A pdf f(x|a) has a MLR with respect to > > a given parameter a iff > > > > f(x'|a)/f(x'|a') <= f(x|a)/f(x|a') > > > > for all x <= x' and a <= a'. > > > > A consequence of the MLR property is that the CDF of the > > random variable X evaluated at any point x is a monotonically > > decreasing function of the parameter a. > > > > The difficulty is that when there is more than one parameter, I'm > > not sure what, if anything can be said. The normal distribution > > has a MLR with respect to its mean *given* its variance, but I > > don't think the same can be said about the variance, or other > > parameters of other distributions in general. The noncentral > > gamma (or equivalently the noncentral chi square), non-central beta > > (or equivalently the noncentral F) distributions have MLRs with > > respect to their noncentrality parameters. I do not believe that > > with respect to their other parameters that they do have MLRs. > > > > The problem is even more complicated when one considers more > > than one parameter simultaneously. > > > > BTW, it was the problem of solving two simultaneous equations in > > the inverse of noncentral CDFs that forced me to begin using > > intervals. There was no way to solve these problems and know > > the accuracy of computed results otherwise. > > > > Cheers, > > > > Bill > > > > > > Vladik Kreinovich wrote: > > > > > > This is true if the CDF monotonically depends on each of its parameters, > which > > > seems to be indeed the case for all the standard classes of distributions. > If > > > we know the direction of monotonicity we indeed know when the mimum and > maximum > > > are attained so we indeed need only two. > > > > > > > Date: Sun, 22 Dec 2002 17:43:07 -0500 > > > > From: Scott Ferson > > > > X-Accept-Language: en > > > > MIME-Version: 1.0 > > > > CC: reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, > > > zjz [at] indian [dot] eng.iastate.edu > > > > Subject: Re: Cumulative distribution function envelopes from > interval-valued > > > parameters > > > > Content-Transfer-Encoding: 7bit > > > > X-MDaemon-Deliver-To: reliable_computing [at] interval [dot] louisiana.edu > > > > X-Return-Path: scott [at] ramas [dot] com > > > > X-MDRcpt-To: zjz [at] indian [dot] eng.iastate.edu > > > > X-MDRemoteIP: 192.0.0.24 > > > > > > > > > > > > For all of the commonly used distributions, you can compute the > > > > p-box by enveloping a small number of CDFs with extremal > > > > parameters. For instance, the normal p-box with interval > > > > parameters mean = [m1, m2] and standard deviation s = [s1, s2] > > > > can be found by enveloping the four CDFs > > > > normal(m1, s1), > > > > normal(m1, s2), > > > > normal(m2, s1), and > > > > normal(m2, s2). > > > > Enveloping just means that, for every x-value, you take the largest > > > > and smallest p-values from the four above to form the p-box. (Or > > > > equivalently, for every p-value, you take the largest and smallest > > > > of the four x-values.) > > > > > > > > This is rigorous in that, if the parameters are really in the specified > > > > ranges and the distribution really is normal, then the bounds of the > > > > p-box are guaranteed. It's also best possible in that they couldn't > > > > be any tighter and still enclose all normal distributions with parameters > > > > in the given ranges. Most distributions have been parameterized > > > > in a way that makes this work out easily. The uniform, triangular, > > > > trapezoidal distributions and the log-transformed cousins are even > > > > easier, as they require one to envelope only two distributions. > > > > > > > > Scott > > > > > > > > > > > > > > > > > > > > Vladik Kreinovich wrote: > > > > > > > > > For normal distribution with parameters a and sigma, the CDF F(x) has > the > > > form > > > > > F(x)=F0(t), where t=(x-a)/sigma, and F0(x) is the CDF os the normalized > > > > > Gaussian distribution, with 0 mean and standard deviation 1. Thus, if > we > > > know > > > > > the intervals [a-,a+] and [sigma-,sigma+] for a and sigma, we can, for > > > every x, > > > > > compute the interval [t-,t+] of possible values of t (this can be done > by > > > > > straightforward interval computations), and then, since F0 is > increasing > > > > > function, we can take [F0(t-),F0(t+)] as the range for F(x). > > > > > > > > > > I believe that this is implemented in RiskCalc, but I am not 100% sure. > > > > > > > > > > Vladik > > > > > > > > > > > From: "Jianzhong Zhang" > > > > > > To: > > > > > > Cc: "Jianzhong Zhang" > > > > > > Subject: Cumulative distribution function envelopes from > interval-valued > > > > > parameters > > > > > > Date: Tue, 17 Dec 2002 12:14:06 -0600 > > > > > > MIME-Version: 1.0 > > > > > > X-Priority: 3 > > > > > > X-MSMail-Priority: Normal > > > > > > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 > > > > > > > > > > > > Hello, > > > > > > > > > > > > Would anybody recommend me some references on the generation of > p-boxes > > > or > > > > > envelopes around cumulative distribution functions, given from > > > interval-valued > > > > > parameters of distributions? For examples, consider the normal > distribution > > > > > with interval-valued mean and/or variance. If we only know the > intervals, > > > how I > > > > > can get the safe envelopes to cover all possible CDFs? > > > > > > > > > > > > Thank you for any references you can provide! > > > > > > > > > > > > Jianzhong Zhang > > > > > > > > > > > > > > -- > > > > > > > > Scott Ferson > > > > Applied Biomathematics > > > > 100 North Country Road > > > > Setauket, New York 11733 > > > > 631-751-4350, fax -3435 > > > > From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Dec 28 13:10:49 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBSJAmQ13404 for reliable_computing-outgoing; Sat, 28 Dec 2002 13:10:48 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBSJAh613400 for ; Sat, 28 Dec 2002 13:10:44 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBSJAZx28700; Sat, 28 Dec 2002 12:10:35 -0700 (MST) Message-Id: <200212281910.gBSJAZx28700 [at] cs [dot] utep.edu> Date: Sat, 28 Dec 2002 12:10:35 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: Cumulative distribution function envelopes from interval-valued parameters To: vladik [at] cs [dot] utep.edu, bill.walster [at] sun [dot] com Cc: scott [at] ramas [dot] com, reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: s8/StwR8jM6YlwN5R6Qs5Q== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Bill, Thanks a lot for a prompt reply. I am glad that we are converging. > OK, but I think you might be missing the fact that even > for the Gaussian distribution with mean u and standard > deviation s, then the behavior of the cdf as a function > of s depends on the sign of x-u. You got me here. I take back the statement about only two CDF's necessary for normal distribution. I should have checked before typing it in. The correct statement is this: since for every x and u, the dependence on s is monotonic, the maximum and mimimum are always attained at the endpoints on the s-interval and therefore, the global mininum and maximum over all u and s are also attained at the endpoints of the s-interval. In general, it is sufficient to require that for the function f(p1,...,pn), for each i, and for each selection of values p1,...,p(i-1),p(i+1),...,pn, the dependence on pi is monotonic, then we are guaranteed that the minimum and the maximum of the function f on a box is attained in one of its corners. > For sure, the situation > is more complicated for distributions such as the gamma, > beta, and their noncentral extensions. You are absolutely right here. Scott's point was that for many distributions, such as uniform, triangular (if I remember correctly), etc., the minimum and minimum are attained at the corners of the box. The question you are raising about gamma, beta, etc., distributions are worth exploiting. > No doubt if you simply use naive interval evaluation of > any CDF with interval bounds on parameters, you will get > bounds on the CDF. The question is whether they suffer > from dependence. You are making an important point here, and I am very glad you made it. It may clarify the issue for those who follow our discussion. The only reason I invoked naive interval computations in one of my original emails is that for normal distribution (which was part of the original question) the formula is SUE and thus, naive interval computations lead to an exact range. You are absolutely right in emphasizing that in general, we will not have SUE and therefore, we will have to use more sophisticated methods of interval computations. > Notice that the Normal pdf is not a > SUE with respect to its standard deviation. This is one of the reasons pdf is not as well suited for interval estimates, one of the reasons why Scott Freson and others chose bounds on CDF instead: for CDF, the dependence is SUE. Vladik From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 30 15:28:25 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBULSPF19557 for reliable_computing-outgoing; Mon, 30 Dec 2002 15:28:25 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBULSL619553 for ; Mon, 30 Dec 2002 15:28:21 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBULRnq12747 for ; Mon, 30 Dec 2002 14:27:50 -0700 (MST) Message-Id: <200212302127.gBULRnq12747 [at] cs [dot] utep.edu> Date: Mon, 30 Dec 2002 14:27:50 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: decision making session in May 2004 To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: HsS0GfHOJCLRnsp0rT0/0g== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, Irinel Dragan, a specialist in game theory and decision making from the University of Texas at Arlington, is planning to organize a session on game theory and decision making at the INFORMS/CORS meeting in Banff, Alberta, Canada, in May 16-19, 2004. In organizing such a session, he is encouraged by the organizers of the meeting. This is a major meeting of Operations Research folks: * INFORMS stands for Institute for Operations Research and the Management Sciences * CORS stands for Canadian Operational Research Society At present, he needs to present an official proposal for the session. Interval-related papers are very welcome. They are especially welcome since non-interval folks have a perception (it may be a wrong perception but they do have it) that many folks who do non-probabilistic decision making do not present enough at their meetings -- and this is "the" meeting at which we will have a good chance of comparing what we are doing with what other researchers are doing and what problems the general decision making community is facing. If you are interested in participating, please send, ASAP, your name, preliminary title (maybe even abstract) to him at dragan [at] uta [dot] edu (copy to me at vladik [at] cs [dot] utep.edu). If you are not sure whether you will be able to attend please mark so, we just want to have a rough list of participants now. There is no strict deadline (and definitely deadline for actual abstracts is not coming for several months) so it will be possible to participate even if you did not express your preliminary interest now. However, these folks are indeed planning their sessions a year and a half ahead, so we must reserve space for our session ASAP. For most US folks, second part of May is a good time for a meeting, because it falls between the Spring and the Summer Semesters. Places around Banff are beautiful. One was to access Banff is to take the famous train that runs along the southern border of Canada, and thus supplement the meeting with a few extra days of vacation. Thanks Vladik From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 30 16:36:01 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBUMa0u19811 for reliable_computing-outgoing; Mon, 30 Dec 2002 16:36:00 -0600 (CST) Received: from company.mail (pool-151-202-118-213.ny5030.east.verizon.net [151.202.118.213]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBUMZs619807 for ; Mon, 30 Dec 2002 16:35:54 -0600 (CST) Received: from ramas.com [192.0.0.24] by company.mail [127.0.0.1] with SMTP (MDaemon.v3.1.0.R) for ; Mon, 30 Dec 2002 17:35:32 -0500 Message-ID: <3E10CA2E.AA0FDC87 [at] ramas [dot] com> Date: Mon, 30 Dec 2002 17:35:26 -0500 From: Scott Ferson Organization: Applied Biomathematics X-Mailer: Mozilla 4.73 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: Vladik Kreinovich CC: bill.walster [at] sun [dot] com, reliable_computing [at] interval [dot] louisiana.edu, zjz [at] eng [dot] iastate.edu, zjz [at] indian [dot] eng.iastate.edu Subject: Re: Cumulative distribution function envelopes from interval-valued parameters References: <200212281910.gBSJAZx28700 [at] cs [dot] utep.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-MDaemon-Deliver-To: reliable_computing [at] interval [dot] louisiana.edu X-Return-Path: scott [at] ramas [dot] com X-MDRcpt-To: zjz [at] indian [dot] eng.iastate.edu X-MDRemoteIP: 192.0.0.24 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk > Bill Walster wrote: > > > No doubt if you simply use naive interval evaluation of > > any CDF with interval bounds on parameters, you will get > > bounds on the CDF. The question is whether they suffer > > from dependence. > > Vladik Kreinovich wrote: > > You are absolutely right in emphasizing that in general, we will not have SUE > and therefore, we will have to use more sophisticated methods of interval > computations. > I think Bill and Vladik are making the problem of computing the p-boxes seem much harder than it really is in practice. One would never try to calculate upper and lower bounds on a CDF directly from specified interval parameters with naive interval methods applied to each value of x. There is a vastly easier, more macroscopic way to obtain these bounds. As I said in my earlier response to Zhang's query, all you need to do is compute (at most) four CDFs of the distribution. These CDFs are based on real (i.e., precise) parameters. Zhang asks how to get the p-box for a normal distribution when the mean and standard deviation are known to lie within intervals [m1, m2] and [s1, s2], respectively. The answer is envelope(N(m1, s1), N(m1, s2), N(m2, s1), N(m2, s2)) where N(m,s) is the (entire) CDF for a normal distribution with mean m and standard deviation s, and the envelope operation is pointwise. These four extremal CDFs form bounds which are both rigorous and best possible. Their envelope is the desired p-box because it encloses every normal distribution whose parameters fall with the specified intervals. This macroscopic approach has to be justified for each family of distributions, but this justification has already been done for all the distributions anybody's likely to want, including normal, beta, gamma, Cauchy, lognormal, Weibull, exponential, Pareto, logistic, F, Student's t, etc., etc. This is an entirely reasonable way to obtain bounds on distribution functions because, after all, there are only a limited number of named distribution families that get used in practice. It works because the folks who designed these distributions chose to use parameters that were well behaved. Of course, there could be other distributions with odd parameterizations that do not permit such a tidy solution. In that case, the problem could be as complicated as Bill and Vladik suggest. Best regards, Scott Scott Ferson Applied Biomathematics 100 North Country Road Setauket, New York 11733 631-751-4350, fax -3435 From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 30 22:05:49 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBV45m420522 for reliable_computing-outgoing; Mon, 30 Dec 2002 22:05:48 -0600 (CST) Received: from kathmandu.sun.com (kathmandu.sun.com [192.18.98.36]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBV45f620518 for ; Mon, 30 Dec 2002 22:05:42 -0600 (CST) Received: from heliopolis.eng.sun.com ([152.70.1.39]) by kathmandu.sun.com (8.9.3+Sun/8.9.3) with ESMTP id VAA06073; Mon, 30 Dec 2002 21:05:25 -0700 (MST) Received: from sun.com (vpn-129-149-241-37.SFBay.Sun.COM [129.149.241.37]) by heliopolis.eng.sun.com (8.9.3+Sun/8.9.3/ENSMAIL,v2.1p1) with ESMTP id UAA14952; Mon, 30 Dec 2002 20:05:24 -0800 (PST) Message-ID: <3E1116E1.FFDA4C43 [at] sun [dot] com> Date: Mon, 30 Dec 2002 20:02:41 -0800 From: Bill Walster X-Mailer: Mozilla 4.76 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: Vladik Kreinovich CC: reliable_computing [at] interval [dot] louisiana.edu Subject: Re: decision making session in May 2004 References: <200212302127.gBULRnq12747 [at] cs [dot] utep.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, Best wishes for a Happy New Year. If any of you who attended SC2002 and remember the talk in which some examples of floating-point failures were mentioned, I would be most grateful if you could send me a pointer to the paper, the author, or to the examples, themselves. Thanks in advance and again best wishes for a prosperous New Year. Cheers, Bill From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 31 07:37:17 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBVDbGn21899 for reliable_computing-outgoing; Tue, 31 Dec 2002 07:37:16 -0600 (CST) Received: from zmit1.ippt.gov.pl (zmit1.ippt.gov.pl [148.81.53.8]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBVDb6621894 for ; Tue, 31 Dec 2002 07:37:07 -0600 (CST) Received: (from zkulpa@localhost) by zmit1.ippt.gov.pl (8.8.5/8.7.3-zmit) id OAA29380; Tue, 31 Dec 2002 14:33:16 +0100 (MET) Date: Tue, 31 Dec 2002 14:33:16 +0100 (MET) From: Zenon Kulpa Message-Id: <200212311333.OAA29380 [at] zmit1 [dot] ippt.gov.pl> To: reliable_computing [at] interval [dot] louisiana.edu, vladik [at] cs [dot] utep.edu, bill.walster [at] sun [dot] com Subject: Re: decision making session in May 2004 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk > From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 31 05:44:44 2002 > From: Bill Walster > > Dear Friends, > > Best wishes for a Happy New Year. > > If any of you who attended SC2002 and remember > the talk in which some examples of floating-point > failures were mentioned, I would be most grateful > if you could send me a pointer to the paper, the > author, or to the examples, themselves. > Please, send them to me also. Or to the list, simply. > Thanks in advance and again best wishes for a > prosperous New Year. > The same to all of you Intervalers, -- Zenon Kulpa http://www.ippt.gov.pl/~zkulpa/quaphys/interval.html From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 31 13:50:47 2002 Received: (from daemon@localhost) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) id gBVJokp22660 for reliable_computing-outgoing; Tue, 31 Dec 2002 13:50:46 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.11.3/8.11.3/ull-interval-math-majordomo-1.3) with ESMTP id gBVJod622656 for ; Tue, 31 Dec 2002 13:50:40 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.3/8.11.3) with SMTP id gBVJoYv20405; Tue, 31 Dec 2002 12:50:34 -0700 (MST) Message-Id: <200212311950.gBVJoYv20405 [at] cs [dot] utep.edu> Date: Tue, 31 Dec 2002 12:50:34 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: congratulations to Anatoly Lakeyev To: reliable_computing [at] interval [dot] louisiana.edu Cc: lakeyev [at] icc [dot] ru MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: b/hAu5Az9MmCuCXC3Hgzxg== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, I have just learned that this week, our own Anatoly Lakeyev successfully defended his Habilitation (Doktor Nauk in Russian). Congratulations! Vladik