From Thu Dec 23 20:43:50 2004 Date: Thu, 23 Dec 2004 20:43:50 -0600 (CST) From: Postmaster Subject: Message from mail server Content-Length: 94 Mime-Version: 1.0 Status: RO X-IMAP: 1103856230 10 Delete. This is a system message. --END+PSEUDO-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Dec 1 06:40:23 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB1CeMKQ003700 for ; Wed, 1 Dec 2004 06:40:22 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB1CeLou003699 for reliable_computing-outgoing; Wed, 1 Dec 2004 06:40:21 -0600 (CST) Received: from ms-smtp-04-eri0.ohiordc.rr.com (ms-smtp-04-smtplb.ohiordc.rr.com [65.24.5.138]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB1CeClv003694 for ; Wed, 1 Dec 2004 06:40:17 -0600 (CST) Received: from Moore (wor226164.columbus.rr.com [204.210.226.164]) by ms-smtp-04-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id iB1CdiHI008583; Wed, 1 Dec 2004 07:39:46 -0500 (EST) Message-ID: <001f01c4d7a2$d9f89fc0$1702a8c0@Moore> From: "Ray Moore" To: "reliable computing" Cc: Subject: Fw: Interval methods for uncertain mechanical systems Date: Wed, 1 Dec 2004 07:39:50 -0500 MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_NextPart_000_001B_01C4D778.F0CA65A0" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Virus-Scanned: Symantec AntiVirus Scan Engine Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: RO X-Status: $$$$ X-UID: 0000000001 This is a multi-part message in MIME format. ------=_NextPart_000_001B_01C4D778.F0CA65A0 Content-Type: multipart/alternative; boundary="----=_NextPart_001_001C_01C4D778.F0CA65A0" ------=_NextPart_001_001C_01C4D778.F0CA65A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear All: I am forwarding this from M.V.Rama Rao. I am retired from the university, but perhaps some of you might be able = to point him to possible post-doc positions. Ray Moore ----- Original Message -----=20 From: M.V.Rama Rao=20 To: Ray Moore=20 Sent: Wednesday, December 01, 2004 12:25 AM Subject: Interval methods for uncertain mechanical systems Sir, I submitted my Ph.d thesis on " Analysis of Cable stayed bridges by = Fuzzy-finite element modelling" in May,2004 at Osmania = University,Hyderabad,India. The thesis is currently under review by = examiners. I am currently awaiting the result.=20 I made an attempt to extend the methodology of Prof. Rafi Muhanna to = include to effect of simulatneous presence of multiple uncertainties. I = considered uncertainties in Young's modulus, live load and mass density = in my analysis. I used object oriented programmming approach and = developed a class "Fuzzy" and used objects of that class (interval = variables) in my finite element program in place of floating point = variables. I used my program to analyse a cable-stayed bridge existing = in Belgium (Centre canal bridge). I tabulated the results for various = combinations of uncertainties. I was able to get good results. I herewith enclose the abstract of my Ph.d thesis for your kind = comments. I propose to pursue Post-doctoral research in this area as soon as I = obtain my Ph.d degree. Can you please help me in this regard? With warm regards M.V.Rama Rao Ray Moore wrote: This well-written paper by Neumaier and Pownuk offer a new method=20 representing an advance over pre-existing methods for a particular = class of=20 problems: uncertainty analysis in structural mechanics based on finite = element analysis when the only uncertainty is in the element stiffness = coefficients. The authors intelligently exploit the structure of such=20 problems with "proper pre-conditioning" and iterative methods. = Well-chosen=20 examples illustrate the advantages over other methods. Perhaps only two suggestions are in order. (1) Some brief summary of = the key=20 ideas of "the new approach" should be included in the abstract and in = the=20 introduction. (2) On page 22, lines 4 and 5 from the top, the u's = should=20 have double-primes. Congratulations Arnold and Andrzej, this is an excellent paper. Ramon Moore ----- Original Messa! ge -----=20 From: "Arnold Neumaier"=20 To: "interval"=20 Sent: Monday, November 29, 2004 10:24 AM Subject: Interval methods for uncertain mechanical systems > The following paper can be downloaded from > http://www.mat.univie.ac.at/~neum/papers.html#linunc > > > > A. Neumaier and A. Pownuk, > Linear systems with large uncertainties, with applications to truss > structures > > > Abstract > -------- > Linear systems whose coefficients have large uncertainties > arise routinely in finite element calculations for > structures with uncertain geometry, material properties, or loads. > However, a true worst case analysis of the influence of such > uncertainties was previously possible only for very small systems > and uncertainties, or in special cases where the coefficients do > not exhibit dependence. > > This paper presents a method for computing rigorous bounds on the > solution of such systems, with a computable overestimation factor = that > is frequently quite small. The merits of the new approach are > demonstrated by computing realistic bounds for some large, uncertain > truss structures, some leading to linear systems with over > 5000 variables and over 10000 interval parameters, with excellent > bounds for up to about 10% input uncertainty. > > Also discussed are some counterexamples for the performance of > traditional approximate methods for worst case uncertainty analysis. > >=20 M.V.Rama Rao M.Tech,MIE,MICI,MISTE Assistant Professor in Civil Engineering(Selection Grade),=20 Vasavi College of Engineering,Hyderabad-31 INDIA=20 Phone : 91-40-2353 2350 (R) 91-40-2351 7494(R)=20 FAX 91-040-2352 5323 College=20 e-mail ramu_mallela [at] yahoo [dot] com -------------------------------------------------------------------------= ------- Do you Yahoo!? The all-new My Yahoo! - What will yours do? ------=_NextPart_001_001C_01C4D778.F0CA65A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Dear All: I am forwarding this from M.V.Rama=20 Rao.
I am retired from the university, but = perhaps some=20 of you might be able to point him to possible post-doc = positions.
 
Ray Moore
 
----- Original Message -----=20
From: M.V.Rama=20 Rao
Sent: Wednesday, December 01, 2004 12:25 AM
Subject: Interval methods for uncertain mechanical=20 systems

Sir,
I submitted my Ph.d thesis on " Analysis of Cable stayed bridges by = Fuzzy-finite element modelling" in May,2004 at Osmania=20 University,Hyderabad,India. The thesis is currently under review by = examiners. I=20 am currently awaiting the result.
I made an attempt to extend the methodology of Prof. Rafi Muhanna = to=20 include to effect of simulatneous presence of multiple uncertainties. I=20 considered uncertainties in Young's modulus, live load and mass density = in my=20 analysis. I used object oriented programmming approach and developed a = class=20 "Fuzzy" and used objects of that class (interval variables)  in my = finite=20 element program in place of floating point variables. I used my program = to=20 analyse a cable-stayed bridge existing in Belgium (Centre canal bridge). = I=20 tabulated the results for various combinations of uncertainties. I was = able to=20 get good results.
I herewith enclose the abstract of my Ph.d thesis for your kind=20 comments.
I propose to pursue Post-doctoral research in this area as soon as = I obtain=20 my Ph.d degree.
Can you please help me in this regard?
With warm regards
M.V.Rama Rao
Ray Moore = <rmoore17 [at] columbus [dot] rr.com>=20 wrote:
This=20 well-written paper by Neumaier and Pownuk offer a new method =
representing=20 an advance over pre-existing methods for a particular class of =
problems:=20 uncertainty analysis in structural mechanics based on finite =
element=20 analysis when the only uncertainty is in the element stiffness=20
coefficients. The authors intelligently exploit the structure of = such=20
problems with "proper pre-conditioning" and iterative methods. = Well-chosen=20
examples illustrate the advantages over other = methods.

Perhaps only=20 two suggestions are in order. (1) Some brief summary of the key =
ideas of=20 "the new approach" should be included in the abstract and in the=20
introduction. (2) On page 22, lines 4 and 5 from the top, the u's = should=20
have double-primes.

Congratulations Arnold and Andrzej, = this is an=20 excellent paper.

Ramon Moore

----- Original Messa! ge = -----=20
From: "Arnold Neumaier"
To: = "interval"=20
Sent: Monday, November = 29, 2004=20 10:24 AM
Subject: Interval methods for uncertain mechanical=20 systems


> The following paper can be downloaded = from
>=20 = http://www.mat.univie.ac.at/~neum/papers.html#linunc
>
>
&= gt;
>=20 A. Neumaier and A. Pownuk,
> Linear systems with large = uncertainties,=20 with applications to truss
> structures
>
>
>=20 Abstract
> --------
> Linear systems whose coefficients = have large=20 uncertainties
> arise routinely in finite element calculations=20 for
> structures with uncertain geometry, material properties, = or=20 loads.
> However, a true worst case analysis of the influence of = such
> uncertainties was previously possible only for very small = systems
> and uncertainties, or in special cases where the = coefficients=20 do
> not exhibit dependence.
>
> This paper presents = a=20 method for computing rigorous bounds on the
> solution of such = systems,=20 with a computable overestimation factor that
> is frequently = quite=20 small. The merits of the new approach are
> demonstrated by = computing=20 realistic bounds for some large, uncertain
> truss structures, = some=20 leading to linear systems with over
> 5000 variables and over = 10000=20 interval parameters, with excellent
> bounds for up to about 10% = input=20 uncertainty.
>
> Also discussed are some counterexamples = for the=20 performance of
> traditional approximate methods for worst case=20 uncertainty analysis.
>
>=20




M.V.Rama Rao = M.Tech,MIE,MICI,MISTE
Assistant=20 Professor in Civil Engineering(Selection Grade),
Vasavi College of=20 Engineering,Hyderabad-31 INDIA
Phone : = 91-40-2353 2350=20 (R) 91-40-2351 7494(R)
FAX 91-040-2352 5323 College =
e-mail ramu_mallela [at] yahoo [dot] com<= /DIV>

Do you Yahoo!?
The all-new My = Yahoo! =96 What=20 will yours do? ------=_NextPart_001_001C_01C4D778.F0CA65A0-- ------=_NextPart_000_001B_01C4D778.F0CA65A0 Content-Type: application/pdf; name="abstract of phd thesis.pdf" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="abstract of phd thesis.pdf" JVBERi0xLjMKJcfsj6IKOCAwIG9iago8PC9MZW5ndGggOSAwIFIvRmlsdGVyIC9GbGF0ZURlY29k ZT4+CnN0cmVhbQp4nOVdSXMdNRC++1e8Y6giw+zLMWwFB6gi+JgLJISlCBDC/uvx+D07Uunr0dct zfNMnn1xyaOeVqvV6n1eH8qiqg/l/Hv3x/NXV6+vPnjaH75/c/X6MBbN/HP7H/fv568OH17fPHYz qWqLsj1cv7wqi2kay6m9faA61P1QjO1hKIfb/7+6evTkveufrqqyKKdpftf1i6tHH85DU9EMwzic hr6eh26mVu10GrkOH3oaggLQPwqHAKzDPHSzlO5ws5q36zgto6r7Qz+2xdTfruHj+eGx6Lu+a07z v5uHuqKeyuo08mYeaYt+HG9mHYd+nIeaoun79m7e98d541TV3Wnol3moL8qqakcXu64Yhqq8W8Ov 4VMvj+CnfugWJn4TYAoeAsj/ESL/e/jCP0O0ngcvBKDAPAA9xP3nEBS3nH+PT/VdOUyqRYc7/eqe naYFkoLlhKBeh2QAlAF8REEHCzyEZABr/iHEIdwKMM8MPcQdgPqNmQcIA84JOE1gItjokAzg+IYn gFqf6oivRON1Tk45yBQFSHxLI/+4bepirIfD47oshl4SseBMhRtJyR+w25TMCEdeCGK/KfqyHxd4 4i/jMQDQgWABq5HEiA8LSGYAHjB0iDzAAYACvBSCKo7zyrIbWhn301A79v3dCj8/Dg31UNUyWmAi wFQmoDuRkt9gKJzHMSlAlL9vfdRzXyE+9I0qJ/x96y8H7E6avIjsBBAhYCIvc/154BSCFwLkQ+iA 18CQlTIh94W8EI44rNDJrEBxNrVgcNmGF13fSgdYtiUiigZYFLVn0j0TVVAkroyqfNRJBLgDalHC IKO+xenxVoWIkrhAeQBYgc3hZCLAHWwFB4tjb6DtbWHHqMOzgsuga8ruDlZGjQxAt1pjHLsB+kmq nI/Wl/OQ76vJaOxxVxQQ4u9TyDunsxNxMNMUHDtJY0F2FdhwoxFFae7UDQpeJythYzs0nUweydb2 JwruNN9S2I3GCnDPr8u70DmhDrYCHDOwaMoWot0zUdRVxrILazcXuiS3/OVQcsBKZOoqNZu8gNXA UxqjY5kwAFErqIw0pk4Jd48618SCsM1nREnUS7SY2qKp59mLUt9/iNIgrJqoFThl9vB+n7aoy7Fs ZaQyGv/ghYpr25+Y5CL3Qe3mcpcUZn85t/HSsSi7rllw5YYcwjknV2U/TnaDE85d5RQ3UJxMHWfr pQaQoq4diupc8Efh8/YRNU9cJxa44OKjNoy6i07mFBBl0l3UF1VTDak3CAB1CTeWj+YZbqyoms2p gLyvNSohNOyxLCHAsQNDnOOJ2VSOPVRHyR1SqBOrERm498ASqaAvt2iwO4AO4V4AHpVkdQyUwgiK 7g5nXCzZ/PfZCdbl8IYYMkrCR8FmU/KOSnOwGlVyJN2NsoGhz+ahqEf27/ApijCUmJS9GBHyGb1H AAVA9nBvOO2VE4qa8HQOTR/saUgqKucgyez35wGu4nR/IM0BeKuKYw2UaPIzluep3FCRaFS4GsAL Vp8/R5iQ0wDqXDAZ4G41NrQHNXoRRW9tOYaxzA6ilUJdbVZlPHeAMqqcbNNPQ+kYnG5C3aJcEDMj Vhm1ZSr/DVCdC5PQkaHNadQUg6ZmVLhDCpsratzIWTfuRCogAc4g2B3pqotmWYA3csjz6XX+PFvW GnBpccptbuMA2Tu7cjj7rs+HcTj7OGzE4ewjtU2Hs5x0kyNVC2iFGbc5LdsgtjtgzZTTgWOQcB5l NZh3UBFF8CemSvgIl3KlXEnmbkKerZt4RqWacDbjojQqBxkHjoChMJdMdWTOXKqLZyiaplXicJpY V82QRZH3QW3UOuM1A385O0+O9BeT5C7yQVnrZgA9OYuDMhABolwlrvVG5MR+4hF3lwNAAR2dzxnx oT+c3/P+AuGOZRInI+NlZ+5PN+1v8+5Pgx7or3BdPwyHA1d5xEk8yixmlJWMxp+ZMFzmxbqYrpuh u0pweuFQqGqb3aHro6B0VUKgxinKRXzwVi1Rk88cqWLnEBVrOdyHHHaQJb61vF9hsCFz5myZ3Dp+ NuoCh3DTEtN2l7VAcF6pWBNfNhqNkMvJyzmowOvCUbP7IqzkqI9RLhZYiWkvIUEzuuL8JQXuC5MU gLbo+nFQpVloveC6WIfM2i6iCkmEjKCN+m40GU+u0qQ46P7EM/RR8F+o6u7hTtxKHwUfq43ykSbL yl3Oboo6c54BUYd2H6J4jcsGCt8HyE5FRAGe1oZvVEsfQATZggsj6U3Z3MhhV/sHLarkPdO3a6La /1gFS8Y+VgArTrCAwwLknaKZQ7QzEpedwqlcnL+I2sRL1fd9KlB8SxmIssjN0qor4/HllMqcnEzJ U8qlrvJPPaTMentw7qMX1OZkD14kGqZjOVULPjdrWRsVXrACV5XQuguk0mGsWfvZy9p83FWOJnfi pV4Emci33XIQH88tRAKlRoc+ps8ehcA+mYf86MWz98LHJCXNfwFndFB1Zxx0a0ASQNfeD50PSu1n 5BJwxWCFVV5zOgrHYpzBxcXHUvzt/vsuVezGPAmagKALiQp4mTnN6s/TxAiX6cLRE9xZgNH+O0Jv q7Jp5CFJWlucSNYL0FoVDRDNWGCdGKkP/Tz1VBVd5+ntnx5f21d1v4BJ2k72xdDUYy/zzhkKHfwl bqTQwUdqm4UOAFHKz8yBSsuS92FRPnJNZ4vIms3V3ta7VXLhxNgoZ2cV/qbxsTIvJ7HA0wWldt12 8hJlWee+MTEYSikbQChZ/bf/HOe5bZzMZNxwiNZfjiI8Fd3c3CHaTGdo3UZRHD8kduqJ7JgiR3MX zKxpe+AuZ5s1EZKO2hftVMsjVltZ0xnBeR0lD5eVJhM7Oihw6pDoBuGucKuRRPkbrbJajntWdTfd xTZADwpOMeNL+/wXvltZsLJx765528FlF9PLdW7peRRMTAz2uqA2bLsaEOWcZw/zHZZomqDcp4n2 Y97hcAbT4h3NAa3bPrUlPucj5LIoFa14PNyZ3GtrjtzjkMJWSwLIDI1H3FkwWAwXLwXQrY0pZI+u g2g4okrZc+Yl3gIOJE79BGQB75OT8ZwXqqTfKkumjoP1Q6ucTqxoehWdyN2hVKIapx+atRLNR4JS dJ77tCpNwDALlRWdFDN/9tOP16i8Tu7EjI5oc2TpHY1luThsJpblImXtSQDOIleiBZ7iMmTAdcTt vflchIR4+Kbc3PqsgZeHqI81B2L8icvOkE7emzM4Q5DtdKkukUwdRJOY3ge1UStW05/SXc42IwsA UdWnqyNMk//T1RFmk1vqRewlqtCPop+gdxq4gWI1Tj+2loqfUB+GqqxFPM99/abl48+rKSdDQrlP hrQgKrJCdlOjKocjQeZDZOjJPORHpACncN+0kOz9PN/osvaLV6WJLe8reCi76RpRMmQVPXL35Czy 5FC19rF/GG07csGv++0rXleIyouL0JbF7YpFnzIyLbJeKLcBeIi6erjUJS6fAGi15jR5iuNyqhFc jr85tJjoXX+Hu3hs2IbyEd1zx1pFQQRbNjFUxdhMxv4YfgIbdzgUOpcFvDVNQdGg00dLUAX9h8zt ubgPOyUls0cx3b93O9rkeTeJb2kJEKu1pQ+JBWSqOfnOShneTeSvJt3KuA+t8maGj0JidcWW8xx9 k/8CzRTOF6LyTbgTc7YpAE9ReheQ89yqrf5KLm0p80dTfdQzfq/Z3A2dksNcQwKKDLK70X3KWuxA OYDOnREAcvuAiQ40ETBxcTXnWIzo8D5DP9lYaae5yAmwPFCIrCmMiRLDqYjh2Cac98U8Ut1sVVku tMKwfpuKSm4PkVr3U1hpaq+HKGcOctA1So+Dwo51HopBVaqLM2/LVrKHqCr4gg+JHJLO8L04izN6 M/ZBWzT1jO7uz0puL59PGBCdBU9RMUhQengCVZfj/R1jtiuYzQEcnvRdcB918ydmODJwVhKnS65K ZfO3gBWXrU8t1dcg3ImJTTf1jGuMvBqFEUBT1T/RnbibPM4L/5porHSOmrcve2d71bxnjyLJMTsX Lc5FYi642dXdnanIiOvIbZVuGZ0w1uOk6oQe4YbNqzD3ERVFO9WMQoSs5eaCmeB0ZE+lNdRpA5qd 5VM9WXgaPAX8axm1A6qskeuyo8m5iRSrrvrlTK5ol0pY45wcqeX+kdYvD/Uh1YxNO1xQXMYfU8vA ndVzs99GNUqtebl0k+W1Lz+5Pnx1Nf/+D3SXaX1lbmRzdHJlYW0KZW5kb2JqCjkgMCBvYmoKMzE1 MwplbmRvYmoKMTkgMCBvYmoKPDwvTGVuZ3RoIDIwIDAgUi9GaWx0ZXIgL0ZsYXRlRGVjb2RlPj4K c3RyZWFtCnic7V3Lltw0EN33V3iZnMMofj+WcA5LFgy9zAYSAgQGGN7wGXwx9rg7UaEr+5Zsd8uZ STY5iqu6qlSqt+X7JDVZnqTD3/M/Xt0d7g/3SWuK4c/Dkv3vV3fJJ8fDi9usSnqA45tDarquTbuH /8ySLk2atDNpmxzvDs9+en58e6hNmmVl2//38fXh2ZthqTBd3VTnpWRYavrfKNPstHQ3LHWmaJru vPS7i+uHEVdR12VxWvrNXfrOXfqZwvX1sFSZvHtHFqAUkPWju/TKQeUi/8WVDODmSwcO8Aco4ATj UvXrsFKaum27+rRkRrg0rZpSCibPiub8g7fDUmvSqio6DXawN0CNAIcAl3cHbUJVSmoDvnYBgUgB LrBEqYP7ELfRgHYgLAAIaAD67io3QAXgKA4BoYCdP0dlq6u6mtBuQNa3LlkAPTBH7jkElHLEu6jA tgJlmyS09WMHYqDUD0jURQ7s6AOdN2WRmzZvkps8NXX5WG1nMsLVad12/qeAYL5yl94yNFCH0wXz qZskHaAC1vQEWLZ1fWYQWEDA8z8jWWWWFoV/6e9xqa7SpvP/YvBOU8r2h4uKPxqSUPAUkKmLnfNG gOdvRlRtl+WVSn5+9bYBXfmFCgtoSKBxA7LyBTWSmeNocu0AEHgQT9ghUYE4BygW2HouQKKiIf8p tykF3s9FxflWQKhFQ+V/ijsVQJV91kH4o6bW6njZpzhN6xcHkBmXdACuAAuarZxRJ2ARACClTuBg U9ZTYypniAJbGLwV3mM8Q0MMgXSoSIOtEohPKJGC3fH7lWkOFVHzbKioseo2qtCcJri6ESosilCA KdR5g4MJNmc9fw5In04SVbqwthKh7MiVBSV7IGiwHS5c6AE+ucM8bdNStf2hsTalI6HlBl8YKBlc FAZKVKEG4wJlMkmookwmASP1kHy6PssORajPikjsVFkJwIHT6zLoIue870fUoQjeVK5wFrpfi+IE iQroO2WfqARqmhtduwGwQ5lWb2Z0mXqNrWBR12tsQles1/hjuRnJcIA7qcQAyhfG+jaqhbG+jWr3 jm1OyJocwcbEpYeUjefObqheqerXNiDlboFeUTE9JWPOEQBbce8+BXC5NAAzACy5FT/LBKdoM9OJ /ObjYV2mYz5FrU3Z5X49dZ9xjxMVWHkkL1Bzpx6IFKgkEKAv1tpEBKE53417KjmxuCQsKm7WfUyV Z42fG66LCdCDSrJXOWwaFM5ZAlIujnLOQKKLmgGSTi5+X9Z5kr+4q4qTJP0SYfP4ixMpCrcXoQUa b8pAeRCqHrxo7KUwTd48jLZd45SpYnWbUG7TACCIX4ARXJQgLpgBsAFjTEc4/jQJwzTHocNhVLoA KFAU8SRgzAOZktKnoSLPRvvtx0bqvkZ+XHn36wKtUdSVibNe72tbwAjFXlrUyZilfdNWDSBBYd5m D2OoGC4T89m4qJAJPEQVMcBWAI0EwuKsfLAAKZvO2djgcxipBkZal+Tt7rIS54S2rd0hRXkPV1+j EhFOfdcOJGqTV1mn68MAwIUKbaPihpIoDqlckgkOT2RmRfau0Kk6+zZgzMG1pPSxBtdSCqoi3wwg IJ5qCXBGHvwgKLptP0UtxbAw6Jw5OtrYx1/fvUTsg3KMnUVApSnygQO1FZSAixyGRLX7CCjSGbEX t1meZO27136H3x7e+s3rwlR5UuW9KpcPb/4mp8fxW8J53Zm8tZ/ffdQ0OynEFWYBLqoqyjW6AA1c PweQ5Z4LgJ3LOjm3SHmpDYzbKkOQ1wuc0onW5AUiJ5QiLZk0KU1ZtmeXHfxKDeBy7ZBHEAoiHso/ AAZdokDhCLAc2g71uyiLv92XoAQ3u4u/LNpXO1vcENeKORvfZBd0KgoUm8Wb0RYoVgrNpwsU5524 ToHi6WKB97KQ161wUuAmZ76nT4akgUu7qJsluAEirnBGWUnAzu79XGO6osp01zBE4+gk8dT8CBf1 LLxYx6ZK4Y4k4JpTdJrLrGwaNrGblV9+K9pNzXv+Lrl/jb9hVxap0JuzZav5dG6qHRgb7p2bz4al rBdTOpW3UmPtgEEqpf+XsoGA9otdUjGX94Glm6xoTd2fTitE+WLE2PRhlir048wEZ405e6k4bAEu /FrDljOi8QPmZX2etQw1EcHVQUrJ/UbCIl01tWnBRTy0Oc2dZojNwkSlcVSAGXwkGTIfa8IjhKAa brXgPqw5xVOME03PCGluWzbFWWK77/xIdjifCkq2/njCRs/d8sbtK2W2GJux4jsbitsHpGC4W4oo U7ZxKsvxExwjMBvGqfLCt65tVEBDuG7hinpEcRj6GhF4COTloQ6fe/UHPGUJecKCeO30NM9Uy++U 7oC7l6g4ihuQCL01Behg6B12FFXgIcpt+rRypeb0BTRV/uC0pk6YFsqUcXc4cUsr3vQU2uyJOuOX 92C+fObqW7wZlKR9xTGbbUMKQLvq5NuAseeNE7VjoJEvn1NMK6SFMqvdDxe2vaWvu86PKpZEURK6 +0RRsqOowEnA4JtffFGERE/dXBfanaU2WtFCk4D7MuGSdoVRak3T1M0G98UD7ItyQInq6dsU+6io Pqa75hRNPNzXS02Rd3Z0MD7b/8r79+AXfjTAfqX+0oNm3K0SILnnalVgqgigp/JArsLEhSNcOBeo hdz9Dfu9dWTFygElvOD7MPy9oet+qeY6VzjNfbTlSpc3zXyHJLS+yX2KRxGioxAiRh8IiuALTY2N avep8WxPKZbUWBKqui1so72PdgZekqlyBDMtrGhe0pedmkeYuvjjeFswCwPxGRlTimzpmm5ife3w CFU2g7+E6ul0zX4ulep0hX7ihJ+Mm/006v77NAFfHL3OZGZj0q6oAhybBLzANZjyBxWxogTc9osO odcyq75AOyMH3sZKVPF2DiWdkRmMibOjMhgzx4lqmZ0yoQ8gL7BDi6jzglXKt5RkACru6wncK2yg fQQAudcXOVxrV5FvsrY0RR8z/r8+/Okx+fww/P0Pux7E1WVuZHN0cmVhbQplbmRvYmoKMjAgMCBv YmoKMjI1MAplbmRvYmoKNyAwIG9iago8PC9UeXBlL1BhZ2UvTWVkaWFCb3ggWzAgMCA2MTIgNzky XQovUm90YXRlIDAvUGFyZW50IDMgMCBSCi9SZXNvdXJjZXM8PC9Qcm9jU2V0Wy9QREYgL1RleHRd Ci9FeHRHU3RhdGUgMTYgMCBSCi9Gb250IDE3IDAgUgo+PgovQ29udGVudHMgOCAwIFIKPj4KZW5k b2JqCjE4IDAgb2JqCjw8L1R5cGUvUGFnZS9NZWRpYUJveCBbMCAwIDYxMiA3OTJdCi9Sb3RhdGUg MC9QYXJlbnQgMyAwIFIKL1Jlc291cmNlczw8L1Byb2NTZXRbL1BERiAvVGV4dF0KL0ZvbnQgMjEg MCBSCj4+Ci9Db250ZW50cyAxOSAwIFIKPj4KZW5kb2JqCjMgMCBvYmoKPDwgL1R5cGUgL1BhZ2Vz IC9LaWRzIFsKNyAwIFIKMTggMCBSCl0gL0NvdW50IDIKL1JvdGF0ZSAwPj4KZW5kb2JqCjEgMCBv YmoKPDwvVHlwZSAvQ2F0YWxvZyAvUGFnZXMgMyAwIFIKPj4KZW5kb2JqCjYgMCBvYmoKPDwvVHlw ZS9FeHRHU3RhdGUvTmFtZS9SNi9UUi9JZGVudGl0eS9CRyA0IDAgUi9VQ1IgNSAwIFIvT1BNIDEv U00gMC4wMj4+CmVuZG9iagoxNiAwIG9iago8PC9SNgo2IDAgUj4+CmVuZG9iagoxNyAwIG9iago8 PC9SMTIKMTIgMCBSL1IxNQoxNSAwIFI+PgplbmRvYmoKNSAwIG9iago8PC9GaWx0ZXIvRmxhdGVE ZWNvZGUKL0Z1bmN0aW9uVHlwZSAwCi9Eb21haW5bMAoxXQovUmFuZ2VbLTEKMV0KL0JpdHNQZXJT YW1wbGUgOAovU2l6ZVsyNTZdL0xlbmd0aCAxMj4+c3RyZWFtCnica2gY2QAARMCAAQplbmRzdHJl YW0KZW5kb2JqCjQgMCBvYmoKPDwvRmlsdGVyL0ZsYXRlRGVjb2RlCi9GdW5jdGlvblR5cGUgMAov RG9tYWluWzAKMV0KL1JhbmdlWzAKMV0KL0JpdHNQZXJTYW1wbGUgOAovU2l6ZVsyNTZdL0xlbmd0 aCAxMj4+c3RyZWFtCnicY2AY2QAAAQAAAQplbmRzdHJlYW0KZW5kb2JqCjIxIDAgb2JqCjw8L1Ix MgoxMiAwIFIvUjE1CjE1IDAgUj4+CmVuZG9iagoxNCAwIG9iago8PC9UeXBlL0ZvbnREZXNjcmlw dG9yL0ZvbnROYW1lL0xEWUNOSStUaW1lcy1Sb21hbi9Gb250QkJveFstMTY4IC0yODEgMTAwMCA5 MjRdL0ZsYWdzIDM0Ci9Bc2NlbnQgOTI0Ci9DYXBIZWlnaHQgNjc2Ci9EZXNjZW50IC0yODEKL0l0 YWxpY0FuZ2xlIDAKL1N0ZW1WIDExMQovTWlzc2luZ1dpZHRoIDI1MAovWEhlaWdodCA0NjEKL0No YXJTZXQoL3NwYWNlL3F1b3RlcmlnaHQvcGFyZW5sZWZ0L3BhcmVucmlnaHQvY29tbWEvaHlwaGVu L3BlcmlvZC9BL0MvRC9FL0YvSC9JL00vTi9SL1MvVC9hL2IvYy9kL2UvZi9nL2gvaS9qL2svbC9t L24vby9wL3Evci9zL3QvdS92L3cveC95L3opCi9Gb250RmlsZTMgMTMgMCBSPj4KZW5kb2JqCjEz IDAgb2JqCjw8L1N1YnR5cGUvVHlwZTFDL0ZpbHRlci9GbGF0ZURlY29kZS9MZW5ndGggMjIgMCBS Pj5zdHJlYW0KeJydV3lYk1fWf2NM3lerWEkzkmKTTOtSq1K7Y1tXsGpFRARkkbIGCIQkJAGSkJUk bJcEsgBJgERAdmQREXEZ6lpordPa6qhd1OnY6fbV2uk892Venu/5bnCe6Twz/et7nvyR5N57zj2/ c8/v/A4Nmz8Po9ForKjIpIjo3WvjhIUC+fpYSWGGOPD3WjKURi6fRz5Fp96kjv5D848NjKewqFb6 YpK7CDu8nD0RPCNZOvPEEvL+448MWWndtAnazLPxsQfXrF27LkIiVcmEuXkK/gsbN27kZ6r4/1zh RwrkwlwxfxX6UiIQSaSFArEijH9AIOAr8gT8HKFIwI/YF5O0O3on/9md0fH8nQKxQJYh4scUZ4qE WfwoYZZALBes4edIZHzRox/8LIk4W6gQSsTyMP42OT+DL5cKsoTokECZJZAGFtbxpQJZoVAuR9/5 Qjk/V5YhVgiy+QoJXyjOEhVnB9yj/3MkYgVfKpOg9UK0gkzFSOQKeZZMKFXwkceYyLce3VGRl6EI +JUL0TJfkoN2ZkuyigPR/GtNkSEUy/kKgVIR8JMp4GcL5VJRhgr5RaakMuHcFYrlQnHur97X8WWC 3AxZtkggn7MbQOXX+Pj/FnWGVCpSzZ2VzO36l3+hQi4Q5YRFCwszi+X8uZzyoyUb+VH8WEFusShD 9t8rv+br/5dBDMPWb1OJs/aqJdnREVJBZFHODlnuW/K8WIXwwK7i/LjdJQWlogxlYeYa/rr1Yauf xbCnsWRsHxaJhWEpWAy2A3seW4Htx97CVmKx2E5sFXYA24WtxuKw3dhLWDz2NvYytgZLwPZgr2DP YQexKCwR24ttx5KwaCwCW4jRsMVYELYEI7AFWBh6kNh8TIDdpx2kDc0LnffOvD76GnrT/MXz6+b/ yMhj3GVuYk7hq/H/JUQL6AtUC+kLcxZefEzw2GeLohadWxy0eNfi3qCtQTeWsJaMPb7l8QdL9yyt X+pcem3p18G04I3BOmgLmskBfph4nPy9nzaT4GO/YzM25F2nrOSVkFImlT2r30Ot0pelVHOUMNmH p5S6u5tsnno3bwIuYEAv8/jaJqmjCGg5QKY2JdQQSujEZ3WwgQ1x2A0JqpsRRFZR4jvklJ9GSsgE NhWqYfY3l5dV1liqzLznqB4Kh3aLp9INGjmg1es4YSW8VKYW76xsMTjVkEnVhNhM3sLupOZcoOEA jSJKXagtKlZqgQWUW431Soe6Tg0IRWmpPL9fNnb19AW44hwPhpHr3P2NDR02DvIPvOST52kf3IGR d+jN5NNsu62hthEQ3S5NMo+qxUGsQZtYSWhgnhdPrNM0gSECHsVPn2xrGgDEmQ7Rbh4lwEGUTp0U 2JTtxZPr9U3gDAFV+LdpF7alitR7dnJv42ZrskpoiCtDHmOMn5CMHhq4SSefhhvYKTty5bGA2LDn M4j/fP7a50NuQ04Dz17slLSqDgNOZ5uv/cKOU68lJ5bmZvKS0iQ7wZsE9bvbYZB+crS5b4jb1eHr 6r1MBP1jMfDNzPfRfhgnWx/SZ14lP2bPJuEgXK97swIhP+DDt9drPeAaQcbg4Jrbfd1O+KgUnCqa tVJlpJVBJSuZX1S49WA7MfscDlZoleEWdE7vwzfXqdvBTwS5God1s6cYHiaKAfSST/bSyFdhKFtV Z0yylOnUHK1aWJ4ICIrLhG3kGoaXeoBXUQsZrUzXp17ve4CAXCblm13D0JCLcQS8sZt8sZsG7kPP fTq0kels6ncb1lJcKvSbVTAYBn//d8iFy57/jnqCp5Ow71xeSz1FMd7ZuTU7p2O0hCeZLPsYxfLd qelr3ICtSdBMLkTW7sHSO3T4g5ENV08ymnFVTTWoAkSuqXGCR36AV1hT1HnGPWpOGe6stQMnIIZd xkwetQEX9Esbs9Dd8TCKQT1NPXHjZTjvwoj/1FHeHhzS5gOzWW80qEplRjEgwuM+g0sg48z1P717 5lACDxWJwV8ewD4YYf/S+DLWSZI0sMl2HLzXMOxzexo8dSN1CGy9Eh+p8lR6y/1aVy7YS1D38Vk2 qWRQW5TME8BjGj1EzO7FWYm/hf1ynOUmoxH6QTPPa8fJn0dpABL0GQwVTTksYZQwLSVl+lJQDjQ2 jT25Ocl5CGwE4aK9cTv2CsIANQ+E9b7yh9j33v6r4EcAGeDHianPCVXrtsjdheGAEwUO+NNH4s6I 7gNIJ+Dub+ACuPLiZEnWKLe/wCvxvU0E6rSwRd2qgoXGfjLoveCP78Die8tYFS7yKbar1gFcgDjq MB7izebh4KDBEGMhWKvUsAJnvdOKb63VNYL3CfgCPpjfYRxDD2HhX+F8uBI+vuMvzx1Ik8Wn8W7i Fmt8SZ4uTs2Bz21l914Ymrh+ZgtFUPTkrRGHYod6uYG6+QiK+yE+RCPXwXB2ypZ08R4QC9J7xBdV I+aB6ikCTjFNV4w9sv7CodTDB0ESOKQSCA9lSiPBRvQqP3kF4t/duAyxMS51C65jN946OjwFpkCH xP0yEWA6n3KYvDus9AV/9ZBkQtoyVu3fII0NIvS6LRUES6SEwzgkwC8D0xeuXB7+C/gB3C+8FXd+ 50cUbYh6Cr2ddiZruRK/bXaVg21o/8MBdl+j8/i9K2XC09xb8cdfARQGqIWZr71+KFG8X/8yILL0 rn7eHLQebQuMnSKDu4PRCy67s4ylgbPkJnZqV6ErG1leupaaT62ggj988dtL5ztPj/MoVMMHVJpI dK8zamjw4HFNJicYI8jvDPh26ks2kFfqjKZiZb5eBERA2lDqL+gpuQI+RNC/e/3udF/+Lm4QvIeo b3U/zOimfYlqZjrAv0sgwbzk6xs57DGKW7nNRU3GFkC0+1rbh9I69+1NkKYW8YrSTLk1bxAbC76g rjLBdoM+IkB8bi++0WZoBDcIeBUGofKGATjhiePQNYIQ/fPDZSwF+S3cxJYwkygsXU49AwgpMxlk 1JsdFbbqRtBCQADD8C+AV+cOJ9qhRsE0Z1ZqDFqdWmI6hDAIgzJmt93exYWhTPSC2zQtLxBHmFXw GcZsN5NVq8SvW9xasIOYRdDs0Gq2I2gileQw/ijOTX7atTt0B/kk22Nz1TYB4oirLI1H2XCQZDbv 0aMIzF58p03tBRcJWIz3nzjbZXdVGBu5zdpGixsQHd6W7oESvxDJqchk3l8RkyQU5+pilJy5DnYR vuSHy47A/GP1iIM+hmU3u7rpZD4Zwj62GS9FNVnqKHaGSBuk9UWACNsWsSGqS/BhPk+pUqktFfli XSkoBSVN+uOlkQel+SCHSLiV9t2NW51jk9yRvpZ+MAKmD41ts1Fse0iCVeYCzcA/MNjldNU4amzA V+2usYNhMOrt6xro9g6Cs6Cnol3bT1Dm2SfZA+bPLGcA8fWALnf/lmyK8dL+nvF2h3vsLK8efsO+ 3D040depLmzmtuY1pYJs4oA4L3VfxpXvUbm9C3xw6t/Sl0fKYRkb5QXXv6HSvIEysjKQkfpARpb/ RkZu/pqRHagNGQJFNNeGNtehNvQJAcVwJf45aNE0vY7ohWNs0/vJML+uLRhMw40fL2Otg3+EV9mV cDnDwKyuLjfX1FQCjgUYrYZ6gtXiLC6uKwp9MzYx4kB/1t0U3qX8wdIWORBx0gokiUKRu03JLTlS 3q67SJRRG9xMR0OdFSWdFeUCnup2RE4tlu6uytbQmx9c+visfGDfEI/CPpA0a46ALs5oX/fExV7h i+3cR+og9FxAHUSjEnkBfs8em+htOQaIs0dyd/CoZBzsNOr2Wx7Jg/gGixN8RMAU/JeMc6/HZMj3 pXLhRbzCJtTLTAfKOFITowyvq7WBekCccJrSebMF6Klayveb0HmRF99vNzah84jhgY/8OUBEdx9C XYCIbs6s9rEFttIG8VEqE9pDrrp7mwa6+jt9Y+AUOKEbLuoRHA/vXI9y0sNknVTiN0wNBhD5CHij fmugl/Qi4Ot17gDwSfgFKyynphjwFSYrcTaFvMfubnSOwqWX0tcnlWTkKrmpRXmWtdVEEOwzTpKL +oMBrKD2Ila6C52IJVgfrUI00VBjs3DN5ZZys1EQl55SVkmw7hrMFnPFk6CqttpWTbA+epc6x3yt N/3ymZGOyQGurrFEpjYWA06Oput9HjyGs+7+xEQuEMSPeQf9cPHD4OmHryIvv8CIgBp4Po6hQW26 yequdQFOx1y9anAQYTS8FWAcoxffXW9qCAQEcRaZCEvYUoVCImlTdPe0t/V0K9rFiFvf1Q4V+0nq uNAf3HMPan9axlpOHpgJZ5cwKxUGgxoYAVKIToI14MnJcRaEpoM0db44T6TKAAfBG+MH4PyYTwST mUcELl19CZATu5JSt78YdR4GJXEVzF4qj9HGZEX5aps83lBEYZU+M7KkGRk1jYZC/C+3f/4i7goV co339KWMcXCOOD82Mn1yTJk7yO0r8BQ1x6BimWs78Mw4HPbRvnoILzykQwGk2DABB580Nt50INXQ p8RvmhsNIGIuna8Z9ZsCddTnw7faUTqvETATXqAO/tZKQOj9txUqYU58XYr1k6+3aD3B03fgW3cC sMjPsiuYqQaklOD31Is4a0CNT1c1GUESQelxIKnQag3SYpG+EBDZBUfHeKwWeJtapcVPV3k0IJWg 6vE3Tyd+OnysuauLe+IEIxxnRdVVn/UPNf7Bw0FZpsRHZ+bPJRm+Opflb2A8mcqusMUoBLoYFVJk 9bVeq7e2AXDaXWpUG0twsKVKZii1GLUmLdAAo0N9WNWudZUhPa9SFxeMKs7BeZf/BJ/msX5KnNny W8lHPYj8nzEaNCJYHTMYe7YKB68aDOEBmE768I11Wjf4lCCd53DIBG2qdmoe0cG0wM2M2SmmhdrM 6GB2QFq7D84HRKCLPJLXyBYekAVbdfrXqpChs8iQrcwTMITw/tTjvhPQemeV+N2KJgMSAghsrZ98 E004RYEOy0MTTpXXCJTAWG2sND5LNYWshC6Lp8oDXGjGaXQM2tCMk6jBR6odxokVcBE1GmK12Mw2 k11lN9mBHTjc3mH4BLwe0vNHu6PXRjxiqXAv7QZqcDN0NioXhCIx0KBL4c2WIDlWVRURaHA6L15a m2XVeMAgB0bhkE/ts1Vaq6xVtiqO02izgAqivNyi5yo1UOxlptlEvow/UOthQkhP17UPpyd6nBxv nceK9IDTS6VrmcdqGiuBFpjKtVo9kuZBIWQ4XmkV6MWm/WWcQhMSqjn/jPuPKG4NftTcYAZqoLHI DdIXKFnIa1ChngAAuDmgrdFxyoGiTtPgw5VNBn+8Q+lQ2lUbqJSQZ6GnsqG6ATRwwOEm59E6tGuX Bm+vdhrbEmEo9V1IU6FTa0eM6nQ3dSJRaQ75mjJ4cuosdsBxgHpX8yiaIn4MaR2z1fuRC3yOb2i3 79B9CCk7s7G2qRZNAf0NWiRdi3AQr9VFVSCsDF48qk7fAM4T5LcoqoNqgfEt9dzsdjH2EhnSEez7 Ej77eUDpR3/IVmv1FRr0Ks2ecR5ElThZ0aPpKB5K98UAYv225CiFv7S947C/ra6mvsbBq3bVOIGD 6OpvGz3TJY7nRuNU2F61KV1QXKoVgnyClRg1njY1fvzw5BSX5T5Y31pyPPQoCn5wBC1RzyNtJ6oo L9HLtZLyEkDkSY6e4NXh4PLxIbh4fO4t+MmXvDTY9zuY6mWKQGmzaJx6AiaGfAkXoUGxub+W46Ve 1OC91Q0WlD69vlgmqrDoVbpSrT9EMqY6CtzA43b01iKkszQuvBc06/oOfUutCKGY1MbCTKM5v4qj gSu9uERf77Y7vG4/7zZc8jXFr7NYLcDCASpzZT7qHTM+9CqfmqShSSEq8KH70HDttjkDw3WnqyyF R9kDeGsO1CC8ZV48wappBMcIOIgDq7PB4TjSfqJlEBDjbXmo0RYiuWswxAZ4X+HFY2s1LWCagPV4 74mB1glAXGyVhvOoXDSsm0z7zWiTxIsXWQutulZwjAMzcbgw+73N+xOL9sdzVReFXfEgDUi04VHE DTSXJyrRXK4J6Dg02Tz2Pu3DO7D0KzpcP7OJXWHN0EhNh3QccaBz22vrgAMQo67yDN5sMy66m/8Z DHkI58Fn4JIt366O3p+bXMpNmH/s1NDkrbObqCCKnrJn48F32o8EpPbMCj8Nbr5HH6F2sK+f7u0c nrj258EHAC4A8ImcH156mHm6qO1gv74s5LOorrzurR27GreA1eAZXbg0WhJVmBuxHzGQDX0s/rK/ BT84toyV/iX1e/bVgZNT4D3ibN6xd/LkCiGXdbigXTlkd9TW2rmsdKsDgNpQp91iKpDkxOfw0DVg wvtocKyhH4MN7ChY8z6qB5sB3WzpA3ahrEgkPiLr6es80tNX1FkY2E5+9Dfag2P0v5M7/tPVr34c VuQFkQJyky/JfeQmEC24R4enUafdllJYlJMa+XLeakAtABRreM1XK4+ndBZPFjQ1h7zxvmRQekN+ 1fAn8AD84v6ia7p7unfok0tEUKmfTPDDOD+zd+Hdx3qdixbdbV20GMP+D9UpM5wKZW5kc3RyZWFt CmVuZG9iagoyMiAwIG9iago0ODgzCmVuZG9iagoxMSAwIG9iago8PC9UeXBlL0ZvbnREZXNjcmlw dG9yL0ZvbnROYW1lL0RLWkROSStUaW1lcy1Cb2xkL0ZvbnRCQm94Wy0xNjggLTM0MSAxMDAwIDk2 MF0vRmxhZ3MgMzQKL0FzY2VudCA5NjAKL0NhcEhlaWdodCA2OTIKL0Rlc2NlbnQgLTM0MQovSXRh bGljQW5nbGUgMAovU3RlbVYgMTY5Ci9NaXNzaW5nV2lkdGggMjUwCi9YSGVpZ2h0IDQ3MwovQ2hh clNldCgvc3BhY2UvQS9CL0MvUi9TL1QpCi9Gb250RmlsZTMgMTAgMCBSPj4KZW5kb2JqCjEwIDAg b2JqCjw8L1N1YnR5cGUvVHlwZTFDL0ZpbHRlci9GbGF0ZURlY29kZS9MZW5ndGggMjMgMCBSPj5z dHJlYW0KeJydUmtMFFcUnlnZnVEQLJuN790b2yoK0jY+Irb4ANRQcLtFrSCluuzeZQdmZ9aZWbsg 4KIo6LXQDUIpUFdxalFA8UW3tQbbNCZt04e2RZL+aWPSxsTExrS5s16adHZttEn/9d+59zvn+853 zqGpJANF03R6QdGOAnth5lbOB+WleSLvjv9manNpbZ5Bmz+FvETuPqx/uNU4nyp+zzhds6ZQ/fOM r6Vr5CntXpp2Z8Yjnrfo03SU1jK2lWxfnJmZlS/6ayWuyquAF3JyckBlLfgHAQVQ5qoEsFAP9kBe 9PugoGSDLRACxQuBh+MhyH/FUVZo3wQyNtm3gU1QgJKTB45AJc+5QDHngoIMFwOPKAH+0QO4RMHN KZwoyNlgvQycQPZDF6cXwaAL+uNAFvBDycfJsh4DTgZVklNQoBsoIuAEFx9wx+X1f48oKMAviTru 0xGdyiHKiuySOL8CdEVHwcZHPSpepxLXlTkdBqJHz3SLrkDczWNMcXKCDBQYVOI6lRC4OdnPO2t1 XZ3KL3GJFgIyJ1Q9Uc8CEqxySm4eygne+FSe+AP/cu30+/naRK2YyHqszyky5D3Zds5XGZBBiehz CsAu5oBisBm6uYDvv8CTdf2/BVIUxazPyy/ZshVQ1ALqaeoZahm1nFpB0RSrXweVRPHUH7SX/tPQ Zpgw/ITbUmMepOJ1F7EcwVsidGyDamkxudHeE2V4GpG1/lmiiUiTUZi9r758/2wJ71QZR7vShd5H 3R3qiU97Ls7CAdNw7jtVKID2NDZ5Dx9CjUcaDrMSnmAmW3HIche3/E5ajKmx55AqDWoPz0hq+h28 HD+Pc4gVr5tpXtIbW2Ux90jMdy3H96JSdjLIoNL6fXkHWHO1hMcZnIuTxrExGrzsPWvznuF6NvSw Zh6zw6OXb895kP05edFqJ79YzpjM1Q+ubSOGJZVlq3fW9X1o044mne/pvmg18zcHdy1dUC2StFab 7jd4NTZ1iEZ4w5TYszjL4thcI+8ICvuqD4qoEBWfE8aE6w3fo/ssdn2FDTjl49FaOGoddfdXn1vL qrjRb2rwhkJBtB/Vtwc6HafKu8oRS8rJYpJNdpFKvIgsxK5bN/pGPrMNnjwZiV5jEzPW/hpOOF+J i/DameaJ2E7VUosaw03dpAJfmHXjuNr9gTpwuvcSirKYyfiSFFnJuMkclZgfD71bj/LZSTuD8pqa cvfrs/1VZXI7m7rQLRaXnmawi3xtxE6TuXSySLtnQeH2nrZwuLP3bRWxv43sWlBU767ZY9tdxzWv PcKmateDQ7E5Z4OR9GOYxgdx8kzzKi2oiRbs8zHNuw8cqNOthdoCHax5ovf1mjCcS+atWkPSl40V 4+QS2zc1d5yndqPtszfueGPNq2XqJ9DqH2kYqrvJCgQNmMJqx7Fe1IG6Wk82X6sbaR5FLM64/zNO H68YLxq0kUU/rL4UUNHV2V9cufBt9ErQc9467O0VIi+ziQuJJUdoLOGVU3AYT7Wg9aHQimbdb0xl lodDneg2q51icFrLWEUfSWYHTIdxhXHynqmVVBgHTH04eewjPKOdTdXP+s2I5ozg7RHT0DQMkoeG UlIw6E+ZTlF/A/IBS9wKZW5kc3RyZWFtCmVuZG9iagoyMyAwIG9iagoxMjA1CmVuZG9iagoxMiAw IG9iago8PC9TdWJ0eXBlL1R5cGUxL0Jhc2VGb250L0RLWkROSStUaW1lcy1Cb2xkL1R5cGUvRm9u dC9OYW1lL1IxMi9Gb250RGVzY3JpcHRvciAxMSAwIFIvRmlyc3RDaGFyIDEvTGFzdENoYXIgMjU1 L1dpZHRoc1sgMzMzIDMzMyAzMzMgMjc4IDU1NiA1NTYgMTY3IDMzMyA2NjcgMjc4IDU3MCAzMzMg MzMzIDY2NyA0NDQKMjUwIDI1MCAyNTAgMjUwIDI1MCAyNTAgMjUwIDI1MCAyNTAgMjUwIDI1MCAy NTAgMjUwIDI1MCAyNTAgMjUwCjI1MCAzMzMgNTU1IDUwMCA1MDAgMTAwMCA4MzMgMjc4IDMzMyAz MzMgNTAwIDU3MCAyNTAgMzMzIDI1MCAyNzgKNTAwIDUwMCA1MDAgNTAwIDUwMCA1MDAgNTAwIDUw MCA1MDAgNTAwIDMzMyAzMzMgNTcwIDU3MCA1NzAgNTAwCjkzMCA3MjIgNjY3IDcyMiA3MjIgNjY3 IDYxMSA3NzggNzc4IDM4OSA1MDAgNzc4IDY2NyA5NDQgNzIyIDc3OAo2MTEgNzc4IDcyMiA1NTYg NjY3IDcyMiA3MjIgMTAwMCA3MjIgNzIyIDY2NyAzMzMgMjc4IDMzMyA1ODEgNTAwCjMzMyA1MDAg NTU2IDQ0NCA1NTYgNDQ0IDMzMyA1MDAgNTU2IDI3OCAzMzMgNTU2IDI3OCA4MzMgNTU2IDUwMAo1 NTYgNTU2IDQ0NCAzODkgMzMzIDU1NiA1MDAgNzIyIDUwMCA1MDAgNDQ0IDM5NCAyMjAgMzk0IDUy MCAyNTAKNTAwIDI1MCAzMzMgNTAwIDUwMCAxMDAwIDUwMCA1MDAgMzMzIDEwMDAgNTU2IDMzMyAx MDAwIDI1MCAyNTAgMjUwCjI1MCAzMzMgMzMzIDUwMCA1MDAgMzUwIDUwMCAxMDAwIDMzMyAxMDAw IDM4OSAzMzMgNzIyIDI1MCAyNTAgNzIyCjI1MCAzMzMgNTAwIDUwMCA1MDAgNTAwIDIyMCA1MDAg MzMzIDc0NyAzMDAgNTAwIDU3MCAyNTAgNzQ3IDMzMwo0MDAgNTcwIDMwMCAzMDAgMzMzIDU1NiA1 NDAgMjUwIDMzMyAzMDAgMzMwIDUwMCA3NTAgNzUwIDc1MCA1MDAKNzIyIDcyMiA3MjIgNzIyIDcy MiA3MjIgMTAwMCA3MjIgNjY3IDY2NyA2NjcgNjY3IDM4OSAzODkgMzg5IDM4OQo3MjIgNzIyIDc3 OCA3NzggNzc4IDc3OCA3NzggNTcwIDc3OCA3MjIgNzIyIDcyMiA3MjIgNzIyIDYxMSA1NTYKNTAw IDUwMCA1MDAgNTAwIDUwMCA1MDAgNzIyIDQ0NCA0NDQgNDQ0IDQ0NCA0NDQgMjc4IDI3OCAyNzgg Mjc4CjUwMCA1NTYgNTAwIDUwMCA1MDAgNTAwIDUwMCA1NzAgNTAwIDU1NiA1NTYgNTU2IDU1NiA1 MDAgNTU2IDUwMF0KPj4KZW5kb2JqCjE1IDAgb2JqCjw8L1N1YnR5cGUvVHlwZTEvQmFzZUZvbnQv TERZQ05JK1RpbWVzLVJvbWFuL1R5cGUvRm9udC9OYW1lL1IxNS9Gb250RGVzY3JpcHRvciAxNCAw IFIvRmlyc3RDaGFyIDEvTGFzdENoYXIgMjU1L1dpZHRoc1sgMzMzIDMzMyAzMzMgMjc4IDU1NiA1 NTYgMTY3IDMzMyA2MTEgMjc4IDU2NCAzMzMgMzMzIDYxMSA0NDQKMjUwIDI1MCAyNTAgMjUwIDI1 MCAyNTAgMjUwIDI1MCAyNTAgMjUwIDI1MCAyNTAgMjUwIDI1MCAyNTAgMjUwCjI1MCAzMzMgNDA4 IDUwMCA1MDAgODMzIDc3OCAxODAgMzMzIDMzMyA1MDAgNTY0IDI1MCAzMzMgMjUwIDI3OAo1MDAg NTAwIDUwMCA1MDAgNTAwIDUwMCA1MDAgNTAwIDUwMCA1MDAgMjc4IDI3OCA1NjQgNTY0IDU2NCA0 NDQKOTIxIDcyMiA2NjcgNjY3IDcyMiA2MTEgNTU2IDcyMiA3MjIgMzMzIDM4OSA3MjIgNjExIDg4 OSA3MjIgNzIyCjU1NiA3MjIgNjY3IDU1NiA2MTEgNzIyIDcyMiA5NDQgNzIyIDcyMiA2MTEgMzMz IDI3OCAzMzMgNDY5IDUwMAozMzMgNDQ0IDUwMCA0NDQgNTAwIDQ0NCAzMzMgNTAwIDUwMCAyNzgg Mjc4IDUwMCAyNzggNzc4IDUwMCA1MDAKNTAwIDUwMCAzMzMgMzg5IDI3OCA1MDAgNTAwIDcyMiA1 MDAgNTAwIDQ0NCA0ODAgMjAwIDQ4MCA1NDEgMjUwCjUwMCAyNTAgMzMzIDUwMCA0NDQgMTAwMCA1 MDAgNTAwIDMzMyAxMDAwIDU1NiAzMzMgODg5IDI1MCAyNTAgMjUwCjI1MCAzMzMgMzMzIDQ0NCA0 NDQgMzUwIDUwMCAxMDAwIDMzMyA5ODAgMzg5IDMzMyA3MjIgMjUwIDI1MCA3MjIKMjUwIDMzMyA1 MDAgNTAwIDUwMCA1MDAgMjAwIDUwMCAzMzMgNzYwIDI3NiA1MDAgNTY0IDI1MCA3NjAgMzMzCjQw MCA1NjQgMzAwIDMwMCAzMzMgNTAwIDQ1MyAyNTAgMzMzIDMwMCAzMTAgNTAwIDc1MCA3NTAgNzUw IDQ0NAo3MjIgNzIyIDcyMiA3MjIgNzIyIDcyMiA4ODkgNjY3IDYxMSA2MTEgNjExIDYxMSAzMzMg MzMzIDMzMyAzMzMKNzIyIDcyMiA3MjIgNzIyIDcyMiA3MjIgNzIyIDU2NCA3MjIgNzIyIDcyMiA3 MjIgNzIyIDcyMiA1NTYgNTAwCjQ0NCA0NDQgNDQ0IDQ0NCA0NDQgNDQ0IDY2NyA0NDQgNDQ0IDQ0 NCA0NDQgNDQ0IDI3OCAyNzggMjc4IDI3OAo1MDAgNTAwIDUwMCA1MDAgNTAwIDUwMCA1MDAgNTY0 IDUwMCA1MDAgNTAwIDUwMCA1MDAgNTAwIDUwMCA1MDBdCi9FbmNvZGluZyAyNCAwIFI+PgplbmRv YmoKMjQgMCBvYmoKPDwvVHlwZS9FbmNvZGluZy9EaWZmZXJlbmNlc1sKMTQ2L3F1b3RlcmlnaHRd Pj4KZW5kb2JqCjIgMCBvYmoKPDwvUHJvZHVjZXIoR05VIEdob3N0c2NyaXB0IDcuMDUpCi9UaXRs ZShQREY5OTUsIEpvYiAyKQovQ3JlYXRvcihQU2NyaXB0NS5kbGwgVmVyc2lvbiA1LjIpCi9DcmVh dGlvbkRhdGUoNi8yLzIwMDQgMTE6OTo0MSkKL0F1dGhvcihSYW0pPj5lbmRvYmoKeHJlZgowIDI1 CjAwMDAwMDAwMDAgNjU1MzUgZiAKMDAwMDAwNTk4MCAwMDAwMCBuIAowMDAwMDE1ODU2IDAwMDAw IG4gCjAwMDAwMDU5MDUgMDAwMDAgbiAKMDAwMDAwNjMzNyAwMDAwMCBuIAowMDAwMDA2MTg5IDAw MDAwIG4gCjAwMDAwMDYwMjggMDAwMDAgbiAKMDAwMDAwNTYwMSAwMDAwMCBuIAowMDAwMDAwMDE1 IDAwMDAwIG4gCjAwMDAwMDMyMzggMDAwMDAgbiAKMDAwMDAxMjEzNiAwMDAwMCBuIAowMDAwMDEx ODg1IDAwMDAwIG4gCjAwMDAwMTM0NDggMDAwMDAgbiAKMDAwMDAwNjg5NSAwMDAwMCBuIAowMDAw MDA2NTI3IDAwMDAwIG4gCjAwMDAwMTQ2MTQgMDAwMDAgbiAKMDAwMDAwNjExNiAwMDAwMCBuIAow MDAwMDA2MTQ2IDAwMDAwIG4gCjAwMDAwMDU3NjEgMDAwMDAgbiAKMDAwMDAwMzI1OCAwMDAwMCBu IAowMDAwMDA1NTgwIDAwMDAwIG4gCjAwMDAwMDY0ODQgMDAwMDAgbiAKMDAwMDAxMTg2NCAwMDAw MCBuIAowMDAwMDEzNDI3IDAwMDAwIG4gCjAwMDAwMTU3OTIgMDAwMDAgbiAKdHJhaWxlcgo8PCAv U2l6ZSAyNSAvUm9vdCAxIDAgUiAvSW5mbyAyIDAgUgo+PgpzdGFydHhyZWYKMTYwMDgKJSVFT0YK ------=_NextPart_000_001B_01C4D778.F0CA65A0-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Dec 1 22:41:08 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB24ewj5004929 for ; Wed, 1 Dec 2004 22:41:02 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB24ewBP004928 for reliable_computing-outgoing; Wed, 1 Dec 2004 22:40:58 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB24ekMw004924 for ; Wed, 1 Dec 2004 22:40:52 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iB24eX029680; Wed, 1 Dec 2004 21:40:33 -0700 (MST) Message-Id: <200412020440.iB24eX029680 [at] cs [dot] utep.edu> Date: Wed, 1 Dec 2004 21:40:33 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: congratulations to Jean-Luc Lamotte To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: Jean-Luc.Lamotte [at] lip6 [dot] fr MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: VTKwHwY6udv2mxovYbcV0w== 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 Status: RO X-Status: $$$$ X-UID: 0000000002 Yesterday, on November 30, Jean-Luc Lamotte from Universite Pierre at Marie Curie, Paris, France, a specialist in probabilistic methods of interval estimations, was awarded Habilitation status - the next degree after Ph.D. that is roughly equivalent to the US full professor status. Congratulations to Jean-Luc! From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Dec 5 09:07:58 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB5F7vo4006164 for ; Sun, 5 Dec 2004 09:07:57 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB5F7v4G006163 for reliable_computing-outgoing; Sun, 5 Dec 2004 09:07:57 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB5F7qal006159 for ; Sun, 5 Dec 2004 09:07:52 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB5F7pVh006158 for reliable_computing [at] interval [dot] louisiana.edu; Sun, 5 Dec 2004 09:07:51 -0600 (CST) Received: from smtp1.uct.ac.za (smtp1.uct.ac.za [137.158.128.183]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB3F8wRG002160 for ; Fri, 3 Dec 2004 09:09:05 -0600 (CST) Received: from anubis.uct.ac.za ([137.158.128.125]) by smtp1.uct.ac.za with esmtp (Exim 4.30; FreeBSD) id 1CaF2j-000OSP-OQ; Fri, 03 Dec 2004 17:08:21 +0200 Received: from vasco-brattka-1.fsc.uct.ac.za ([137.158.37.4]) by anubis.uct.ac.za with esmtp (Exim 4.43 (FreeBSD)) id 1CaF2k-00024n-MG; Fri, 03 Dec 2004 17:08:22 +0200 Message-ID: <41B08162.4070208@FernUni-Hagen.de> Date: Fri, 03 Dec 2004 17:08:18 +0200 From: Vasco Brattka User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.3) Gecko/20040910 X-Accept-Language: de-de, de, en MIME-Version: 1.0 To: cca-list@FernUni-Hagen.de, comprox [at] doc [dot] ic.ac.uk, na.digest@na-net.ornl.gov, reliable_computing [at] interval [dot] louisiana.edu, THEORYNT [at] listserv [dot] nodak.edu, arp [at] cines [dot] fr, communaute [at] medicis [dot] polytechnique.fr, arinews.gdr.lip@ens-lyon.fr, calmet [at] ira [dot] uka.de Subject: Call for Papers: REAL NUMBERS special issue of Theoretical Informatics and Applications Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000003 ----------- CALL FOR PAPERS ---------- Please distribute and accept our apologies if you receive multiple copies. REAL NUMBERS Special issue of the journal Theoretical Informatics and Applications http://www.edpsciences.org/journal/index.cfm?edpsname=ita Guest editors: Vasco Brattka, Christiane Frougny, Norbert Mueller IMPORTANT DATES (tentative planning): - Deadline for submissions of manuscripts: June 1st 2005 (full papers only; extended abstracts will be rejected) - Notification of acceptance/rejection: October 1st 2005 - Deadline for reception of final papers: December 15th 2005 Efficient manipulation of real numbers in computers is still a challenge. Many interesting theoretical and algorithmic problems are linked with that topic and belong to quite distant fields such as computer science, number theory, numerical analysis, computer algebra and logics. Several special issues on real numbers and computers have been previously published in the journal Theoretical Computer Science, as follow-up to the RNC meetings on these topics. The last meeting was RNC6 which took place in Dagstuhl, Germany, in November 2004, see http://cca-net.de/rnc6/ However, this call for papers is open to authors who did not attend RNC6. TOPICS Scientists working on questions related to real computer arithmetic are encouraged to present the theoretical or algorithmic aspects of their results, even if they did not attend the RNC6 conference. Survey and tutorial articles may be suitable if clearly identified as such. Topics include (but are not restricted to) the following list: * 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 HOW TO SUBMIT The submission should contain a scholarly exposition of ideas, techniques, and results, including motivation and a clear comparison with related work. Submissions must not substantially duplicate work published or submitted for publication elsewhere. Prepare a PostScript or PDF version of your full 10-20 pages paper preferably using the latex style LaTeX2e class for RAIRO -Theoretical Informatics and Applications ftp://ftp.edpsciences.org/pub/ita/. The file should be sent by e-mail to Christiane.Frougny [at] liafa [dot] jussieu.fr before June 1st 2005. Make sure that your PostScript or PDF file can be printed on a standard laser printer. Language: English. From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 6 01:55:15 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB67tFK1000593 for ; Mon, 6 Dec 2004 01:55:15 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB67tE78000591 for reliable_computing-outgoing; Mon, 6 Dec 2004 01:55:14 -0600 (CST) Received: from mail02.infosat.net (mailout06.infosat.net [66.18.69.6]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB67t0eC000587 for ; Mon, 6 Dec 2004 01:55:07 -0600 (CST) Received: from [66.18.70.48] (HELO mail01.infosat.net) by mail02.infosat.net (CommuniGate Pro SMTP 4.1.8) with ESMTP id 162322360 for reliable_computing [at] interval [dot] louisiana.edu; Mon, 06 Dec 2004 09:54:52 +0200 Received: from [196.21.143.253] (account dbiyana [at] webmail [dot] co.za) by mail01.infosat.net (CommuniGate Pro WebUser 4.1.8) with HTTP id 546658267 for reliable_computing [at] interval [dot] louisiana.edu; Mon, 06 Dec 2004 09:54:52 +0200 From: "Mahlubandile Dugmore Biyana" Subject: linear regression using interval data To: reliable_computing [at] interval [dot] louisiana.edu X-Mailer: CommuniGate Pro WebUser Interface v.4.1.8 Date: Mon, 06 Dec 2004 09:54:52 +0200 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: 8bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: RO X-Status: $$$$ X-UID: 0000000004 I am trying to find parameter estimates in a linear regression model using interval data {[x_i],[y_i]}. Using the naive formula [b]=Cov([x],[y])/Cov([x],[x]) and [a]=E([y])-[b]E([x]) gives me very pessimistic intervals, especialy for [a]. Can anyone help, if possible can you email me any electronic version of articles addressing this type of problem. >From MD Biyana _____________________________________________________________________ For super low premiums, click here http://www.dialdirect.co.za/quote From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 6 08:38:08 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6Ec89T001546 for ; Mon, 6 Dec 2004 08:38:08 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6Ec8T3001545 for reliable_computing-outgoing; Mon, 6 Dec 2004 08:38:08 -0600 (CST) Received: from sunshine.math.utah.edu (IDENT:zqpixMNT4mZhwmazSB3FFhSK92W6FHeg [at] sunshine [dot] math.utah.edu [128.110.198.2]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6EbwWs001541 for ; Mon, 6 Dec 2004 08:38:04 -0600 (CST) Received: from sunbeam.math.utah.edu (IDENT:hlt4IMTt53PfdEFJRzhCLRljX+yZkBni [at] sunbeam [dot] math.utah.edu [155.101.96.161]) by sunshine.math.utah.edu (8.12.11/8.12.10) with ESMTP id iB6EbsZh025736; Mon, 6 Dec 2004 07:37:54 -0700 (MST) Received: from sunbeam.math.utah.edu (IDENT:YvkyTiGlTctJr7CJ/lt/e5+TuaP7xrJ8@localhost [127.0.0.1]) by sunbeam.math.utah.edu (8.12.11/8.12.10) with ESMTP id iB6Ebsv2029832; Mon, 6 Dec 2004 07:37:54 -0700 (MST) Received: (from beebe@localhost) by sunbeam.math.utah.edu (8.12.11/8.12.10/Submit) id iB6Eboh3029831; Mon, 6 Dec 2004 07:37:50 -0700 (MST) Date: Mon, 6 Dec 2004 07:37:50 -0700 (MST) From: "Nelson H. F. Beebe" To: "reliable computing" Cc: beebe [at] math [dot] utah.edu X-US-Mail: "Department of Mathematics, 110 LCB, University of Utah, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA" X-Telephone: +1 801 581 5254 X-FAX: +1 801 585 1640, +1 801 581 4148 X-URL: http://www.math.utah.edu/~beebe Subject: SCAN'2002 proceedings published Message-ID: Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: RO X-Status: $$$$ X-UID: 0000000005 The SCAN'2002 proceedings are now out in volume 37(1--4) of the Kluwer journal Numerical Algorithms: http://ipsapp009.kluweronline.com/IPS/frames/toc.aspx?J=5058&I=58 BibTeX entries for all articles in that journal are available in http://www.math.utah.edu/pub/tex/bib/index-table-n.html#numeralgorithms ------------------------------------------------------------------------------- - Nelson H. F. Beebe Tel: +1 801 581 5254 - - University of Utah FAX: +1 801 581 4148 - - Department of Mathematics, 110 LCB Internet e-mail: beebe [at] math [dot] utah.edu - - 155 S 1400 E RM 233 beebe [at] acm [dot] org beebe [at] computer [dot] org - - Salt Lake City, UT 84112-0090, USA URL: http://www.math.utah.edu/~beebe - ------------------------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 6 09:42:37 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6FgbjG001771 for ; Mon, 6 Dec 2004 09:42:37 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6FgKjR001770 for reliable_computing-outgoing; Mon, 6 Dec 2004 09:42:20 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6FgCko001766 for ; Mon, 6 Dec 2004 09:42:17 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iB6Fg5P07573; Mon, 6 Dec 2004 08:42:06 -0700 (MST) Message-Id: <200412061542.iB6Fg5P07573 [at] cs [dot] utep.edu> Date: Mon, 6 Dec 2004 08:42:06 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: PhD vacancy To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: MULTIPART/mixed; BOUNDARY=Cluster_of_Spiders_770_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 Status: O X-Status: $$$$ X-UID: 0000000006 --Cluster_of_Spiders_770_000 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: HI+Na1KYaaKO3pCcY+URoQ== ------------- Begin Forwarded Message ------------- Date: Mon, 06 Dec 2004 10:53:59 +0100 From: Gert de Cooman Dear Colleagues, In my research group, we have a vacancy for a 4-year PhD position in the field of Uncertainty Modelling (and Imprecise Probabilities), with applications in Computational Biology (cell cycle). You can find more information here (the first of the two projects mentioned): http://www.psb.ugent.be/cbd/vacancies.php. The announcement is alos scheduled to appear on my department web site http://www.systems.ugent.be. I would be most grateful if you could bring this vacancy to the attention of promising and talented students, or distribute it further among your colleagues. As the job market is a bit strained in Belgium right now, we are having difficulties finding good local people. I would welcome applications from abroad ... Best wishes, Gert de Cooman ------------- End Forwarded Message ------------- --Cluster_of_Spiders_770_000 Content-Type: TEXT/x-vCard; name="gert.decooman.vcf"; charset=us-ascii Content-Description: gert.decooman.vcf Content-MD5: xvN3XNqKcvEM8M7/e6sGww== begin:vcard fn:Gert de Cooman n:De Cooman;Gert org:Ghent University;SYSTeMS Research Group adr:;;Technologiepark - Zwijnaarde 9;Zwijnaarde;;9052;Belgium email;internet:gert.decooman [at] ugent [dot] be title:Professor in Uncertainty Modelling and Systems Science tel;work:+32-9-264.56.53 tel;fax:+32-9-264.58.40 x-mozilla-html:FALSE url:http://ippserv.ugent.be/~gert version:2.1 end:vcard --Cluster_of_Spiders_770_000-- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 6 10:36:05 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6Ga4MB000335 for ; Mon, 6 Dec 2004 10:36:04 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6GZxkX000334 for reliable_computing-outgoing; Mon, 6 Dec 2004 10:35:59 -0600 (CST) Received: from droog.sdf-eu.org (IDENT:root@sdf-eu.org [192.94.73.35]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6GZmou000330 for ; Mon, 6 Dec 2004 10:35:54 -0600 (CST) Received: from sdf-eu.org (IDENT:logistic@localhost [127.0.0.1]) by droog.sdf-eu.org (8.12.10/8.12.10) with ESMTP id iB6GT9Ym024176 for ; Mon, 6 Dec 2004 16:29:09 GMT Received: (from logistic@localhost) by sdf-eu.org (8.12.10/8.12.8/Submit) id iB6GT9mu024175 for reliable_computing [at] interval [dot] louisiana.edu; Mon, 6 Dec 2004 11:29:09 -0500 (EST) Date: Mon, 6 Dec 2004 11:29:09 -0500 From: "Janos G. Hajagos" To: reliable_computing [at] interval [dot] louisiana.edu Subject: Re: linear regression using interval data Message-ID: <20041206162909.GC9039@SDF-EU.ORG> References: Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.4.2.1i Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000007 Biyana, This is a difficult problem if your x_i are intervals also. If they are not then an interval hull solution can easily be computed by formulating the problem in terms of matrix algebra: (X' * X)^-1 * X' * Y = B The part (X' * X)^-1 * X' contains no thick intervals so it can be computed with thin intervals and little inflation will occur. This computation can easily be done in Intlab. The bounds on B, the slope and intercept, are interval hull bounds. If your intervals have a large width and a line can be drawn through all the data points then parameter bounding may be appropriate. See chapter 6 in Jaulin et al. (2002) Applied Interval Analysis. I wrote a short primer on this topic and have posted it to my website if your are interested. http://creativelimits.net/research/papers/fuzzyregression.pdf -Janos On Mon, Dec 06, 2004 at 09:54:52AM +0200, Mahlubandile Dugmore Biyana wrote: > I am trying to find parameter estimates in a linear > regression model using interval data {[x_i],[y_i]}. Using > the naive formula [b]=Cov([x],[y])/Cov([x],[x]) and > [a]=E([y])-[b]E([x]) gives me very pessimistic intervals, > especialy for [a]. Can anyone help, if possible can you > email me any electronic version of articles addressing this > type of problem. > From > MD Biyana > _____________________________________________________________________ > For super low premiums, click here http://www.dialdirect.co.za/quote -- Homepage: From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 6 12:52:51 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6Ga4MB000335 for ; Mon, 6 Dec 2004 10:36:04 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6GZxkX000334 for reliable_computing-outgoing; Mon, 6 Dec 2004 10:35:59 -0600 (CST) Received: from droog.sdf-eu.org (IDENT:root@sdf-eu.org [192.94.73.35]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6GZmou000330 for ; Mon, 6 Dec 2004 10:35:54 -0600 (CST) Received: from sdf-eu.org (IDENT:logistic@localhost [127.0.0.1]) by droog.sdf-eu.org (8.12.10/8.12.10) with ESMTP id iB6GT9Ym024176 for ; Mon, 6 Dec 2004 16:29:09 GMT Received: (from logistic@localhost) by sdf-eu.org (8.12.10/8.12.8/Submit) id iB6GT9mu024175 for reliable_computing [at] interval [dot] louisiana.edu; Mon, 6 Dec 2004 11:29:09 -0500 (EST) Date: Mon, 6 Dec 2004 11:29:09 -0500 From: "Janos G. Hajagos" To: reliable_computing [at] interval [dot] louisiana.edu Subject: Re: linear regression using interval data Message-ID: <20041206162909.GC9039@SDF-EU.ORG> References: Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.4.2.1i Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000008 Biyana, This is a difficult problem if your x_i are intervals also. If they are not then an interval hull solution can easily be computed by formulating the problem in terms of matrix algebra: (X' * X)^-1 * X' * Y = B The part (X' * X)^-1 * X' contains no thick intervals so it can be computed with thin intervals and little inflation will occur. This computation can easily be done in Intlab. The bounds on B, the slope and intercept, are interval hull bounds. If your intervals have a large width and a line can be drawn through all the data points then parameter bounding may be appropriate. See chapter 6 in Jaulin et al. (2002) Applied Interval Analysis. I wrote a short primer on this topic and have posted it to my website if your are interested. http://creativelimits.net/research/papers/fuzzyregression.pdf -Janos On Mon, Dec 06, 2004 at 09:54:52AM +0200, Mahlubandile Dugmore Biyana wrote: > I am trying to find parameter estimates in a linear > regression model using interval data {[x_i],[y_i]}. Using > the naive formula [b]=Cov([x],[y])/Cov([x],[x]) and > [a]=E([y])-[b]E([x]) gives me very pessimistic intervals, > especialy for [a]. Can anyone help, if possible can you > email me any electronic version of articles addressing this > type of problem. > From > MD Biyana > _____________________________________________________________________ > For super low premiums, click here http://www.dialdirect.co.za/quote -- Homepage: From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 6 16:43:15 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6MgtRa000398 for ; Mon, 6 Dec 2004 16:42:55 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6MgsaZ000397 for reliable_computing-outgoing; Mon, 6 Dec 2004 16:42:54 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6MgodH000393 for ; Mon, 6 Dec 2004 16:42:50 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6Mgnra000392 for reliable_computing [at] interval [dot] louisiana.edu; Mon, 6 Dec 2004 16:42:49 -0600 (CST) Received: from smtp1.uct.ac.za (smtp1.uct.ac.za [137.158.128.183]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB3F8wRG002160 for ; Fri, 3 Dec 2004 09:09:05 -0600 (CST) Received: from anubis.uct.ac.za ([137.158.128.125]) by smtp1.uct.ac.za with esmtp (Exim 4.30; FreeBSD) id 1CaF2j-000OSP-OQ; Fri, 03 Dec 2004 17:08:21 +0200 Received: from vasco-brattka-1.fsc.uct.ac.za ([137.158.37.4]) by anubis.uct.ac.za with esmtp (Exim 4.43 (FreeBSD)) id 1CaF2k-00024n-MG; Fri, 03 Dec 2004 17:08:22 +0200 Message-ID: <41B08162.4070208@FernUni-Hagen.de> Date: Fri, 03 Dec 2004 17:08:18 +0200 From: Vasco Brattka User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.3) Gecko/20040910 X-Accept-Language: de-de, de, en MIME-Version: 1.0 To: cca-list@FernUni-Hagen.de, comprox [at] doc [dot] ic.ac.uk, na.digest@na-net.ornl.gov, reliable_computing [at] interval [dot] louisiana.edu, THEORYNT [at] listserv [dot] nodak.edu, arp [at] cines [dot] fr, communaute [at] medicis [dot] polytechnique.fr, arinews.gdr.lip@ens-lyon.fr, calmet [at] ira [dot] uka.de Subject: Call for Papers: REAL NUMBERS special issue of Theoretical Informatics and Applications Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: RO X-Status: $$$$ X-UID: 0000000009 ----------- CALL FOR PAPERS ---------- Please distribute and accept our apologies if you receive multiple copies. REAL NUMBERS Special issue of the journal Theoretical Informatics and Applications http://www.edpsciences.org/journal/index.cfm?edpsname=ita Guest editors: Vasco Brattka, Christiane Frougny, Norbert Mueller IMPORTANT DATES (tentative planning): - Deadline for submissions of manuscripts: June 1st 2005 (full papers only; extended abstracts will be rejected) - Notification of acceptance/rejection: October 1st 2005 - Deadline for reception of final papers: December 15th 2005 Efficient manipulation of real numbers in computers is still a challenge. Many interesting theoretical and algorithmic problems are linked with that topic and belong to quite distant fields such as computer science, number theory, numerical analysis, computer algebra and logics. Several special issues on real numbers and computers have been previously published in the journal Theoretical Computer Science, as follow-up to the RNC meetings on these topics. The last meeting was RNC6 which took place in Dagstuhl, Germany, in November 2004, see http://cca-net.de/rnc6/ However, this call for papers is open to authors who did not attend RNC6. TOPICS Scientists working on questions related to real computer arithmetic are encouraged to present the theoretical or algorithmic aspects of their results, even if they did not attend the RNC6 conference. Survey and tutorial articles may be suitable if clearly identified as such. Topics include (but are not restricted to) the following list: * 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 HOW TO SUBMIT The submission should contain a scholarly exposition of ideas, techniques, and results, including motivation and a clear comparison with related work. Submissions must not substantially duplicate work published or submitted for publication elsewhere. Prepare a PostScript or PDF version of your full 10-20 pages paper preferably using the latex style LaTeX2e class for RAIRO -Theoretical Informatics and Applications ftp://ftp.edpsciences.org/pub/ita/. The file should be sent by e-mail to Christiane.Frougny [at] liafa [dot] jussieu.fr before June 1st 2005. Make sure that your PostScript or PDF file can be printed on a standard laser printer. Language: English. From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 6 16:43:19 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6MhJ94000413 for ; Mon, 6 Dec 2004 16:43:19 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6MhIBD000412 for reliable_computing-outgoing; Mon, 6 Dec 2004 16:43:18 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB6Mgwll000401 for ; Mon, 6 Dec 2004 16:42:58 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iB6MgvDO000400 for reliable_computing [at] interval [dot] louisiana.edu; Mon, 6 Dec 2004 16:42:57 -0600 (CST) Received: from ns.ict.nsk.su (ns.ict.nsk.su [193.124.243.33]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iB66Sfgq000480 for ; Mon, 6 Dec 2004 00:28:53 -0600 (CST) Received: from COMP0 (COMP0.ict.local.net [192.168.0.124]) by ns.ict.nsk.su (8.13.1/8.13.1) with SMTP id iB66STFJ072871; Mon, 6 Dec 2004 12:28:29 +0600 (NOVT) (envelope-from shary [at] ict [dot] nsc.ru) X-Authentication-Warning: ns.ict.nsk.su: Host COMP0.ict.local.net [192.168.0.124] claimed to be COMP0 Message-ID: <002d01c4db5c$ee692980$7c00a8c0@COMP0> From: "Sergey P. Shary" To: Cc: Subject: Re: Interval methods for uncertain mechanical systems Date: Mon, 6 Dec 2004 12:29:24 +0600 Organization: ICT SB RAS MIME-Version: 1.0 Content-Type: text/plain; charset="windows-1251" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: RO X-Status: $$$$ X-UID: 0000000010 Interval regards to everyone, Two terminology comments on section 5 of the recently advertised paper A. Neumaier and A. Pownuk, Linear systems with large uncertainties, with applications to truss structures that may prove generally helpful: 1) The term "inner enclosure" used by the authors is something like "hot ice", which is possible, in principle, but is not quite adequate to the situation. I think that we should adopt a better term for this kind of estimation of the solution set, when one needs an inner estimate of its interval hull. E.g. "weak inner estimate" would be OK. 2) On the next line, one can read: "These [inner enclosures] are not tolerance solutions, where one would require that \Sigma itself contains u_tol". It is not correct since tolerance solutions are inner estimates of another solution set, not of the united solution set considered in the paper (see Neumaier's book of 1990). Sergey P. Shary From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Dec 27 23:44:11 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBS5iAVP015394 for ; Mon, 27 Dec 2004 23:44:10 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBS5iAoZ015393 for reliable_computing-outgoing; Mon, 27 Dec 2004 23:44:10 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBS5i1Zc015389 for ; Mon, 27 Dec 2004 23:44:07 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iBS5ggR10906; Mon, 27 Dec 2004 22:42:42 -0700 (MST) Message-Id: <200412280542.iBS5ggR10906 [at] cs [dot] utep.edu> Date: Mon, 27 Dec 2004 22:42:42 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: interval session at FUZZ-IEEE'05 To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: 31X8CkbWe4ltyJb3s+fsHA== 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, If you have submitted your paper to the interval session at FUZZ-IEEE'05 please let me know. If you have a paper ready it may still be possible to submit, let me know ASAP. Vladik From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 28 07:12:36 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBSDCaOd016423 for ; Tue, 28 Dec 2004 07:12:36 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBSDCa6Z016422 for reliable_computing-outgoing; Tue, 28 Dec 2004 07:12:36 -0600 (CST) Received: from sigma.ifpan.edu.pl (sigma.ifpan.edu.pl [148.81.44.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBSDCRsM016418 for ; Tue, 28 Dec 2004 07:12:33 -0600 (CST) Received: from ifpan.edu.pl (gutow [at] gutow [dot] ifpan.edu.pl [148.81.45.16]) by sigma.ifpan.edu.pl (8.12.6/8.12.6) with ESMTP id iBSDCgcb002468 for ; Tue, 28 Dec 2004 14:12:42 +0100 Message-ID: <41D15B7E.1070703 [at] ifpan [dot] edu.pl> Date: Tue, 28 Dec 2004 14:11:26 +0100 From: "Marek W. Gutowski" Organization: Institute of Physics, Polish Academy of Sciences User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.6) Gecko/20040413 Debian/1.6-5 X-Accept-Language: en-US, en, pl MIME-Version: 1.0 To: reliable_computing [at] interval [dot] louisiana.edu Subject: Linear independence Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-Virus-Scanned: by AMaViS[ Milter ]( http://amavis.org/ ) Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear intervallers, Is there a widely accepted deifinion of the linear independence of a set of interval vectors? I can think of at least two variants: Let X1, X2, ..., XN are interval vectors and x1, x2, ..., xN - ordinary, real vectors. 1. X1, X2, ..., XN are said to be linearly independent, if for any x1 \in X1, x2 \in X2, *** ..., xN \in XN the set {x1, x2, ..., xN} is linearly independent (in IR^m, m>=N) 2. the same, with 'any' replaced by 'some' Or, maybe, we have to deal with 'weak' and 'strong' linear inependence? It is easy to see, that the first definition quickly fails (i.e. says, that there cannot be the linear independence), when the intersection of Xi and Xj is non-empty for some pair (i,j). Or, maybe, there is no sense at all to speak about the linear independence of 'vectors', which do not belong to the linear space, like IR^M? Marek W. Gutowski -- Marek Gutowski, gutow [at] ifpan [dot] edu.pl Institute of Physics, ON-3.2, Al. Lotnikow 32/46, (PL) 02-668 Warszawa, POLAND, tel. +48-22-8436601 ext. 3122 >> To talk or not to talk? Yes, talk, plain ASCII please << ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 28 10:10:17 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBSGAGUP016784 for ; Tue, 28 Dec 2004 10:10:16 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBSGAG0E016783 for reliable_computing-outgoing; Tue, 28 Dec 2004 10:10:16 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBSGA7Fl016778 for ; Tue, 28 Dec 2004 10:10:13 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iBSG9AW13331; Tue, 28 Dec 2004 09:09:10 -0700 (MST) Message-Id: <200412281609.iBSG9AW13331 [at] cs [dot] utep.edu> Date: Tue, 28 Dec 2004 09:09:09 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: Linear independence To: reliable_computing [at] interval [dot] louisiana.edu, gutow [at] ifpan [dot] edu.pl MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: npzGYNbu5kpZ8Uo9PJMacA== 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 Marek, Thanks for a good question. You are right, in general, when we have a property defined on numbers, it can be extended to intervals in two possible ways: necessarily true (meaning true for all values from the corresponding intervals) and possibly true (meaning true for some values). Usually, just like with vector independence, properties involving equality are never necessarily true. This terminology is not only used in intervals, it is a general contents of modal logic which deals with properties under uncertainty. This a terminology is the reason for the name of modal interval computations promoted by the well-known Catalonia group. We mention it also in our complexity interval book where we analyze, in particular, the complexity of such problems. For the problem you mentioned, possible linear independent is also not a very efficient notion, because checking this possible linear dependence is NP-hard. Please do not feel disouraged by this. I am 100% with George Corliss who recently mentioned, in his email to this mailing list, that in questions like this, it is often beneficial to start with a practical problem that caused this question; usually, we can find a reasonable subclass of problems (that contains the practical one) for which an efficient algorithm is possible. Vladik > Date: Tue, 28 Dec 2004 14:11:26 +0100 > From: "Marek W. Gutowski" > User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.6) Gecko/20040413 Debian/1.6-5 > X-Accept-Language: en-US, en, pl > MIME-Version: 1.0 > To: reliable_computing [at] interval [dot] louisiana.edu > Subject: Linear independence > Content-Transfer-Encoding: 7bit > X-Virus-Scanned: by AMaViS[ Milter ]( http://amavis.org/ ) > > Dear intervallers, > > Is there a widely accepted deifinion of the linear > independence of a set of interval vectors? > > I can think of at least two variants: > Let X1, X2, ..., XN are interval vectors and > x1, x2, ..., xN - ordinary, real vectors. > > 1. X1, X2, ..., XN are said to be linearly > independent, if for any x1 \in X1, x2 \in X2, > *** > ..., xN \in XN the set {x1, x2, ..., xN} > is linearly independent (in IR^m, m>=N) > 2. the same, with 'any' replaced by 'some' > > Or, maybe, we have to deal with 'weak' and 'strong' > linear inependence? > It is easy to see, that the first definition quickly > fails (i.e. says, that there cannot be the linear > independence), when the intersection of Xi and Xj > is non-empty for some pair (i,j). > > Or, maybe, there is no sense at all to speak about > the linear independence of 'vectors', which do not > belong to the linear space, like IR^M? > > Marek W. Gutowski > -- > Marek Gutowski, gutow [at] ifpan [dot] edu.pl > Institute of Physics, ON-3.2, Al. Lotnikow 32/46, > (PL) 02-668 Warszawa, POLAND, tel. +48-22-8436601 ext. 3122 > >> To talk or not to talk? Yes, talk, plain ASCII please << > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 28 11:36:30 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBSHaU4C017038 for ; Tue, 28 Dec 2004 11:36:30 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBSHaUOi017037 for reliable_computing-outgoing; Tue, 28 Dec 2004 11:36:30 -0600 (CST) Received: from lakermmtao02.cox.net (lakermmtao02.cox.net [68.230.240.37]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBSHaLto017033 for ; Tue, 28 Dec 2004 11:36:26 -0600 (CST) Received: from Inspiron-8200 ([68.226.133.93]) by lakermmtao02.cox.net (InterMail vM.6.01.04.00 201-2131-117-20041022) with SMTP id <20041228173522.JKRR2202.lakermmtao02.cox.net@Inspiron-8200>; Tue, 28 Dec 2004 12:35:22 -0500 Message-Id: <2.2.32.20041228173509.009cf938 [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Tue, 28 Dec 2004 11:35:09 -0600 To: "Marek W. Gutowski" , reliable_computing [at] interval [dot] louisiana.edu From: "R. Baker Kearfott" Subject: Re: Linear independence Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Marek, Your first definition is, of course, equivalent to the associated interval matrix being regular, provided x_i\in\Rz^N, 1\le i \le N. (If the number of vectors is not equal to the dimension of the space, the condition can be formulated in terms of regularity of submatrices.) In terminology widely used by another well-known member of our community, your first definition corresponds to "certainly linearly independent," while your second definition corresponds to "possibly linearly independent." Other issues aside, I like this intuitive terminology. Best regards, Baker At 02:11 PM 12/28/2004 +0100, Marek W. Gutowski wrote: >Dear intervallers, > >Is there a widely accepted deifinion of the linear >independence of a set of interval vectors? > >I can think of at least two variants: >Let X1, X2, ..., XN are interval vectors and >x1, x2, ..., xN - ordinary, real vectors. > >1. X1, X2, ..., XN are said to be linearly > independent, if for any x1 \in X1, x2 \in X2, > *** > ..., xN \in XN the set {x1, x2, ..., xN} > is linearly independent (in IR^m, m>=N) >2. the same, with 'any' replaced by 'some' > >Or, maybe, we have to deal with 'weak' and 'strong' >linear inependence? >It is easy to see, that the first definition quickly >fails (i.e. says, that there cannot be the linear >independence), when the intersection of Xi and Xj >is non-empty for some pair (i,j). > >Or, maybe, there is no sense at all to speak about >the linear independence of 'vectors', which do not >belong to the linear space, like IR^M? > >Marek W. Gutowski >-- >Marek Gutowski, gutow [at] ifpan [dot] edu.pl >Institute of Physics, ON-3.2, Al. Lotnikow 32/46, >(PL) 02-668 Warszawa, POLAND, tel. +48-22-8436601 ext. 3122 > >> To talk or not to talk? Yes, talk, plain ASCII please << >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > > --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 28 21:58:29 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT3wTej017769 for ; Tue, 28 Dec 2004 21:58:29 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBT3wTAF017768 for reliable_computing-outgoing; Tue, 28 Dec 2004 21:58:29 -0600 (CST) Received: from its-exsmtp1.marqnet.mu.edu (email.marquette.edu [134.48.20.169]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT3wKnI017763 for ; Tue, 28 Dec 2004 21:58:26 -0600 (CST) Received: from its-exfe2.marqnet.mu.edu ([134.48.20.167]) by its-exsmtp1.marqnet.mu.edu with Microsoft SMTPSVC(6.0.3790.211); Tue, 28 Dec 2004 22:00:03 -0600 Received: from [192.168.1.103] ([67.53.8.244] RDNS failed) by its-exfe2.marqnet.mu.edu with Microsoft SMTPSVC(6.0.3790.211); Tue, 28 Dec 2004 22:00:03 -0600 User-Agent: Microsoft-Entourage/10.1.4.030702.0 Date: Tue, 28 Dec 2004 21:58:26 -0600 Subject: Re: Linear independence From: George Corliss To: "R. Baker Kearfott" , "Marek W. Gutowski" , Message-ID: In-Reply-To: <2.2.32.20041228173509.009cf938 [at] pop [dot] louisiana.edu> Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit X-OriginalArrivalTime: 29 Dec 2004 04:00:03.0372 (UTC) FILETIME=[DFF966C0:01C4ED5A] Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Friends, Let's see. We could define Certainly linearly independent Possibly linearly independent Possibly linearly dependent Certainly linearly dependent We might also define Structurally linearly independent Structurally linearly dependent to mean that vectors of that structure are dependent or independent, regardless of the values. For example X1 = ([a], 0) X2 = (0, [b]) Might be called "structurally linearly independent" (even "structurally orthogonal") as long as 0 is not in either [a] or [b]. Conjecture: Certainly linearly dependent ==> Structurally linearly dependent A set can be BOTH Possibly linearly independent Possibly linearly dependent In fact, that is quite common. That again suggests to me that the usefulness of the concept of "linear independence of interval vectors" might be primarily for publishing papers. If we want to solve practical problems, I reiterate, "Go back to the beginning. What are you REALLY trying to do? Do that." My recollection of real analysis is that the concept of linear independence most commonly arises when we want to 1. Solve some linear system, or 2. Define a basis for some linear space. So, if we really want to solve some linear system, we should ask whether we can solve that system, in either a "certainly" or a "possibly" sense. Basis? THAT is an interesting question. I don't know what a basis of interval vectors means. I'd think it better to work with a basis of point vectors with interval coefficients or with point coefficients plus an interval remainder term, as in Martin Berz's Taylor models. Consider an example [x_1] = ([1-d, 1+d], [1-d, 1+d]), [x_2] = ([1-d, 1+d], [-1-d, -1+d]), for d small. For d = 0, x_1 = (1, 1), x_2 = (1, -1), clearly independent. Let v = (2, 0) Then v = 1 * (1, 1) + 1 * (1, -1), with (1, 1) in [x_1] and (1, -1) in [x_2] But this is NOT a unique representation of v 1 * [x_1] + 1 * [x_2] = ([2-2d, 2+2d], [-2d, 2d]) Hence c_1 * [x_1] + c_2 * [x_2] for c_1 and c_2 near 1 "covers" the point (2, 0) That is, there is a continuous set of c_1 and c_2 not zero and vectors x_1 in [x_1] and x_2 in [x_2] such that v = c_1 x_1 + c_2 x_2 In this sense, a point vector CANNOT have a unique representation as a linear combination with point coefficients and point vectors from an interval basis. This even holds for an intervalized Euclidian basis: [x_1] = ([1-d, 1+d], 0, 0, ..., 0) . . . [x_i] = (0, ..., [1-d, 1+d], 0, ...) Let v = ( v_i ) then v = v_1 x_1 + v_2 x_2 + ... + v_n x_n, Where v_i = (0, ..., 1, 0, ...) But also v = v_1 y_1/(1-d) + ..., where y_i = (0, ..., 1-d, 0, ...) I must read the papers Markov mentioned. Dr. George F. Corliss Electrical and Computer Engineering Marquette University PO Box 1881 1515 W. Wisconsin Ave. Milwaukee WI 53201-1881 USA 414-288-6599; Fax: 288-5579; Dept. 288-6280 George.Corliss [at] Marquette [dot] edu > Your first definition is, of course, equivalent to > the associated interval matrix being regular, provided > x_i\in\Rz^N, 1\le i \le N. (If the number of vectors is > not equal to the dimension of the space, the condition > can be formulated in terms of regularity of submatrices.) > > In terminology widely used by another well-known member > of our community, your first definition corresponds to > "certainly linearly independent," while your second > definition corresponds to "possibly linearly independent." > Other issues aside, I like this intuitive terminology. > > Best regards, > > Baker > > At 02:11 PM 12/28/2004 +0100, Marek W. Gutowski wrote: >> Dear intervallers, >> >> Is there a widely accepted deifinion of the linear >> independence of a set of interval vectors? >> >> I can think of at least two variants: >> Let X1, X2, ..., XN are interval vectors and >> x1, x2, ..., xN - ordinary, real vectors. >> >> 1. X1, X2, ..., XN are said to be linearly >> independent, if for any x1 \in X1, x2 \in X2, >> *** >> ..., xN \in XN the set {x1, x2, ..., xN} >> is linearly independent (in IR^m, m>=N) >> 2. the same, with 'any' replaced by 'some' >> >> Or, maybe, we have to deal with 'weak' and 'strong' >> linear inependence? >> It is easy to see, that the first definition quickly >> fails (i.e. says, that there cannot be the linear >> independence), when the intersection of Xi and Xj >> is non-empty for some pair (i,j). >> >> Or, maybe, there is no sense at all to speak about >> the linear independence of 'vectors', which do not >> belong to the linear space, like IR^M? >> >> Marek W. Gutowski >> -- >> Marek Gutowski, gutow [at] ifpan [dot] edu.pl >> Institute of Physics, ON-3.2, Al. Lotnikow 32/46, >> (PL) 02-668 Warszawa, POLAND, tel. +48-22-8436601 ext. 3122 >>>> To talk or not to talk? Yes, talk, plain ASCII please << >> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ >> >> >> > > --------------------------------------------------------------- > R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) > (337) 482-5270 (work) (337) 993-1827 (home) > URL: http://interval.louisiana.edu/kearfott.html > Department of Mathematics, University of Louisiana at Lafayette > (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) > Box 4-1010, Lafayette, LA 70504-1010, USA > --------------------------------------------------------------- > > > From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 28 22:28:44 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT4SiBr017971 for ; Tue, 28 Dec 2004 22:28:44 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBT4Si5A017970 for reliable_computing-outgoing; Tue, 28 Dec 2004 22:28:44 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT4SYM5017966 for ; Tue, 28 Dec 2004 22:28:39 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iBT4RWk16567; Tue, 28 Dec 2004 21:27:32 -0700 (MST) Message-Id: <200412290427.iBT4RWk16567 [at] cs [dot] utep.edu> Date: Tue, 28 Dec 2004 21:27:32 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: CFP: To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: xgao [at] mmrc [dot] iss.ac.cn MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: Gizlb5I1Ge+oxCft4Z8Q2g== 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 FYI; interval methods are explicitly mentioned as one of the possible topics. ------------- Begin Forwarded Message ------------- Date: Wed, 22 Dec 2004 18:52:24 +0800 From: Xiaoshan GAO Apologize if you receive multiple copies _____________________________________________________________ CFP: Geometric Constraints A special issue of International Journal of Computational Geometry and Applications _____________________________________________________________ Geometric Constraints Solvers are today a key component of all geometric modelers. Geometric constraints occur for dimensioning and tolerancing mechanical parts in CAD-CAM, for modeling curves, surfaces and blends, for conception of mechanisms, for finding the configurations of robots in robotics or of molecules in chemistry. New applications of constraints modeling will likely arise. In recent years, research on geometry constraint solving is quite active. Besides many reports in large scale conferences, geometry constraint solving is one of the main themes of several specialized workshops including the ISICAD workshop held in Russia in June 2004, the ADG workshop held in USA in September 2004, and the Workshop on Geometric Constraint Solving held in China in October 2003. We feel that it is time to publish a special issue devoted to this important topic. Thus IJCGA is devoting a special issue to the subject of geometric constraints. Authors should note the benefits of publication in a special issue - a collection of high-quality related papers in one volume, with expedited handling of the review and revision of accepted papers. The journal has committed to giving priority in the publication queue for the special issue. Manuscripts are solicited on topics to include: -resolution of geometric constraints, with computer algebra, numerical analysis, interval analysis, logical approaches (e.g. provers), or other methods, -decomposition of systems of geometric constraints, -mixing geometric and non geometric constraints, white boxes, black boxes, geometric constraints and constraints programming, -detection of dependence between constraints, debugging geometric constraints, -constrained curves, surfaces, blends, -exotic (eg non cartesian) formulations of constraints, -comparison of resolution methods or constraints formulations for the same problems, -mathematical background: combinatorial rigidity, graph theory, matroid theory, computer algebra (polynomial systems, dimension of ideals), -detailed applications, in Computer Graphics, CAD-CAM, robotics, mechanism design, chemistry (eg molecule configurations), photogrammetry, virtual reality, -sensitivity to value parameters, and other robustness issues, -choice of the "good" solution, -dynamic geometry, -computer-human interfaces for geometric constraints, -geometric constraints and data exchange, -topological constraints, eg optimal curves or surfaces with prescribed, topology (homology, homotopy, isotopy), -shape optimization, -geometric constraints and geometric representations (boundary representation, constructive solid geometry, features), -integration of geometric solvers into modelers, -solvers architecture, -geometric solver industrial/market solutions. Authors should send their submission as a file attachment in pdf or postscript format to both guests editors by June 12, 2005. Xiao-Shan Gao Institute of Systems Science, Academia Sinica, Beijing 100080 China Email: xgao [at] mmrc [dot] iss.ac.cn http://www.mmrc.iss.ac.cn/~xgao Tel: 86-10-6254-1831 Fax: 86-10-6263-0706 Dominique Michelucci Laboratory Electroninics, Computer Science, Image Faculty sciences & techniques University of Burgundy BP 47870 21078 Dijon Cedex France Email: Dominique.Michelucci@u-bourgogne.fr Tel: 333.80.39.38.85 from abroad, 03.80.39.38.85 from France Fax: 333.80.39.59.10 from abroad, 03.80.39.38.85 from France While submissions may be in any standard format, accepted papers will need to be prepared using latex, following the journal guidelines available at http://www.worldscinet.com/journals/ijcga/mkt/guidelines.shtml and http://www.worldscinet.com/authors/stylefiles.shtml Authors are encouraged to submit as early as possible. All manuscripts will be promptly and carefully refereed. ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 28 22:49:53 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT4nqwQ018104 for ; Tue, 28 Dec 2004 22:49:52 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBT4nqGs018103 for reliable_computing-outgoing; Tue, 28 Dec 2004 22:49:52 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT4nhYT018099 for ; Tue, 28 Dec 2004 22:49:49 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iBT4mj516641; Tue, 28 Dec 2004 21:48:45 -0700 (MST) Message-Id: <200412290448.iBT4mj516641 [at] cs [dot] utep.edu> Date: Tue, 28 Dec 2004 21:48:46 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: announcement of interval meeting To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=ISO-8859-1 Content-MD5: jMOsy4Eye6kzPTDiufxLvw== 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 iBT4nnYT018100 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk From: Kaj Madsen A workshop focusing on applications of interval analysis is arranged by the Technical University of Denmark in colaboration with SUN Microsystems. It is entitled Second Scandinavian Workshop on INTERVAL METHODS AND THEIR APPLICATIONS and takes place in Copenhagen on August 25-27, 2005. The workshop is preceded by a one day tutorial on "Validated Scientific Computing Using Interval Analysis" given by Professor George Corliss, Electrical and Computer Engineering, Marquette University, Milwaukee, USA. The intension is to bring together engineers and researchers from different fields, who have the need and interest for application of interval methods in common. We accept contributed talks from people who have made applications (or who can report on other people's applications). However, we also accept a few talks from researchers in interesting application fields who have the need of using interval methods - without having done it yet. The following keynote speakers have accepted to participate: George Corliss, Marquette University, Milwaukee, USA William W. Edmonson, Hampton University, USA Scott Ferson, RAMAS Ecological Software by Applied Biomathematics, USA Vladik Kreinowich, University of Texas at El Paso Rafi Muhanna, Georgia Tech, USA Arnold Neumaier, Universität Wien, Austria Mark Stadtherr, University of Notre Dame, USA Further information can be found at http://www.imm.dtu.dk/~km/int-05/ Kaj Madsen From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Dec 28 23:26:27 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT5QRtY018299 for ; Tue, 28 Dec 2004 23:26:27 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBT5QRIO018298 for reliable_computing-outgoing; Tue, 28 Dec 2004 23:26:27 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBT5QICr018294 for ; Tue, 28 Dec 2004 23:26:24 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iBT5PLw16841 for ; Tue, 28 Dec 2004 22:25:21 -0700 (MST) Message-Id: <200412290525.iBT5PLw16841 [at] cs [dot] utep.edu> Date: Tue, 28 Dec 2004 22:25:21 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Second Announcement and CFP for ECCAD'05 To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: BIXaeGUNvTfdUs1JhWtmNg== 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 forwarding; it may be of interest to interval researchers ------------- Begin Forwarded Message ------------- From: "Iyad Ajwa" ECCAD 2005 The 12th Annual East Coast Computer Algebra Day CALL FOR PARTICIPATION Second Announcement ============================================ HOSTED BY: The Department of Mathematics and Computer Science Ashland University Ashland, Ohio, USA DATE: March 12, 2005 CONFERENCE WEBSITE: http://www.ashland.edu/~eccad CONFERNCE EMAIL: eccad [at] ashland [dot] edu ========================================= ECCAD, East Coast Computer Algebra Day, is an annual conference that provides opportunities to learn and share new developments and to present research results in the areas of symbolic and mathematical computation. The 12th Annual East Coast Computer Algebra Day (ECCAD 2005) will be held on Saturday, March 12, 2005. It will be hosted by the Department of Mathematics and Computer Science at Ashland University in Ashland, Ohio, USA. ECCAD 2005 will be in honor of Professor Bob Caviness's 65th birthday. Bob Caviness is a Professor Emeritus (with a joint appointment in Mathematical Sciences) and former Chair of the Department of Computer & Information Sciences at the University of Delaware. His research interests include the design and analysis of algebraic algorithms, in particular, algorithmic decision procedures for integration in finite terms and for computing closed form solutions of differential equations.More recently he has turned to web-based technologies. He has five Ph.D. and two M.S students. Professor Caviness has served in various editorial capacities for the following jourmals: ACM Transactions on Mathematical Software, ACM Computing Reviews, CONSTRAINTS, the online e-commerce journal ACM SIGecom Exchanges, and the Journal of Symbolic Computation. He served as Editor-in-Chief of the latter journal for the period 1995-2000. He has also lectured widely and served the profession in many other capacities. Happy Birthday, Bob! THEMES: - Algebraic Algorithms - Symbolic-Numeric Computation - Computer Algebra Systems - Mathematical Communication - Complexity of Algebraic Problems - Symbolic and Numerical Linear Algebra - Applications of Symbolic Computation INVITED SPEAKERS: The following speakers have been confirmed. Titles and abstracts will be announced on the Conference Website at http://www.ashland.edu/~eccad once they become available. 1. Professor Bruno Buchberger - Johannes Kepler University, Linz, Austria. 2. Professor Erich Kaltofen - North Carolina State University, Raleigh, NC. 3. Professor David Saunders - University of Delaware, Newark, DE. 4. Professor Paul Wang - Kent State University, kent, OH. REGISTRATION: Online Registration is available on the Conference Website at http://www.ashland.edu/~eccad. POSTER SESSIONS: Two poster sessions will be held at the conference. Participants are invited to submit their posters by the submission deadline of February 25, 2005. Poster abstracts received before the submission deadline will be included in The ECCAD'2005 Book of Abstracts which will be available at the conference. POSTER SUBMISSION: Poster abstracts may be up to 2 pages long. The submission deadline is February 25, 2005. To submit a poster, either use the Online Registration Form (available on the Conference Website at http://www.ashland.edu/~eccad) to provide the title and abstract of your poster, or send the title and abstract of your poster by email to eccad [at] ashland [dot] edu TRAVEL SUPPORT: Pending NSF support, the conference hopes to be able to provide limited travel support for some participants to attend ECCAD'2005. Graduate students and junior faculty are particularly encouraged to apply. Support may cover only partially travel expenses and lodging for up to two nights. There will be no stipends. Make sure the flight has a flight number of a US carrier. If you plan to attend and apply for support, please send your inquiry with an itemized estimate of your expenses to eccad [at] ashland [dot] edu. Please note that if your application is approved and if funding is available, you will receive your reimbursement after the conference. All applications for support are due by March 1, 2005. Support is subject to successful funding. ACCOMMODATIONS: Blocks of rooms have been reserved at two local hotels for participants of ECCAD'2005. Deatiled Information are posted on the Conference Website at http://www.ashland.edu/~eccad. ADVISORY COUNCIL: - Bruce Char - Drexel University, USA - Erich Kaltofen - North Carolina State University, USA - Ilias Kotsireas - Wilfrid Laurier University, CANADA - David Saunders - University of Delaware, USA - William Sit - The City College of the City University of New York, USA - Paul S. Wang - Kent State University, USA - Stephen Watt - University of Western Ontario, CANADA ORGANIZER: Iyad A. Ajwa Department of Mathematics and Computer Science Ashland University Ashland, Ohio 44805, USA +1 419.289.5798 iajwa [at] ashland [dot] edu SPONSORS: - Ashland University - College of Arts and Sciences - Department of Mathematics and Computer Science - National Science Foundation CONFERENCE CONTACT: Iyad A. Ajwa Department of Mathematics and Computer Science Ashland University Ashland, Ohio 44805 USA Tel: +1 419.289.5798 FAX: +1 419.289.5791 iajwa [at] ashland [dot] edu eccad [at] ashland [dot] edu OTHER INFORMATION: Previous ECCAD conference homepages can be consulted at: http://www.cis.udel.edu/~saunders/eccad/. Iyad... *********************************************************** Iyad A. Ajwa, Ph.D. Associate Professor Department of Mathematics and Computer Science Ashland University Ashland, OH 44805, USA Phone: +1 419.289.5798 FAX: +1 419.289.5791 www.ashland.edu/~iajwa/ *********************************************************** ------------- End Forwarded Message ------------- ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Dec 29 07:20:20 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTDKJtE019384 for ; Wed, 29 Dec 2004 07:20:19 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBTDKJXU019383 for reliable_computing-outgoing; Wed, 29 Dec 2004 07:20:19 -0600 (CST) Received: from shiva.bio.bas.bg (bas-bio.lines.bas.bg [195.96.252.58]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTDK5h7019379 for ; Wed, 29 Dec 2004 07:20:16 -0600 (CST) Received: from biomath8 (ihost_0_172.bio.bas.bg [10.0.0.172]) by shiva.bio.bas.bg (8.12.10/8.12.10) with ESMTP id iBTDIm8R016828 (version=TLSv1/SSLv3 cipher=DES-CBC3-SHA bits=168 verify=NO); Wed, 29 Dec 2004 15:18:49 +0200 From: "Svetoslav Markov" To: George Corliss Date: Wed, 29 Dec 2004 15:18:48 +0200 MIME-Version: 1.0 Subject: Re: Linear independence CC: Message-ID: <41D2CAD8.16264.E8AF5D@localhost> X-mailer: Pegasus Mail for Windows (4.21c) Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7BIT Content-description: Mail message body Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear George, Let me explain the idea of interval basis on your example: [x_1] = ([1-d, 1+d], 0, 0, ..., 0) . . . [x_i] = (0, ..., [1-d, 1+d], 0, ...) According to the theory of quasilinear spaces a general quasivector space (of group structure) decomposes in a vector space (for the midpoints) and a symmetric quasivector space (for the radii) -- the latter is in fact a vector space but with a different definition of multiplication with scalars (concerning negative scalars). So we use the natural midpoint-radius presentation. Denoting D = [-d, d] we can rewrite the above as: [x_1] = ([1-d, 1+d], 0, 0, ..., 0) = (1, 0, 0, ..., 0) + (D, 0, 0, ..., 0) . . . [x_i] = (0, ..., [1-d, 1+d], 0, ...) = (0, ..., 1, 0, ...) + (0, ..., D, 0...) Now we need to represent an interval vector (a_1, a_2, ..., a_n) + (D_1, D_2, ..., D_n) wherein a_i are real numbers (midpoints) and D_i are centred intervals D_i = [-d_i, d_i] as linear combination of the intervals [x_i]. Clearly the presentation decomposes in two parts: for the midpoints and for the radii. The first part is clear, for the second we have: (D_1, D_2, ..., D_n) = sum c_i * D with unique c_i = 1/d_i (whenever necessary, the radii d_i may take negative values, so-called generalized intervals, however in this case this is not needed). In my opinion the concept of linear (in)dependence is an auxiliary tool for the important concept of basis, resp. unique representation of elements by linear combinations. As you mention my name in your last letter I am posting this to the RC mailing list. The paper that I sent to you has been recently submitted, I shall gladly send it to anybody interested. Svetoslav references: S. MARKOV, QUASIVECTOR SPACES AND THEIR RELATION TO VECTOR SPACES submitted to EJMC Markov, S., On the Algebraic Properties of Intervals and Some Applications, Reliable Computing 7 (2), 2001, 113--127. From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Dec 29 07:31:40 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTDVeHX019540 for ; Wed, 29 Dec 2004 07:31:40 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBTDVeWm019539 for reliable_computing-outgoing; Wed, 29 Dec 2004 07:31:40 -0600 (CST) Received: from shiva.bio.bas.bg (bas-bio.lines.bas.bg [195.96.252.58]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTDVQOu019534 for ; Wed, 29 Dec 2004 07:31:37 -0600 (CST) Received: from biomath8 (ihost_0_172.bio.bas.bg [10.0.0.172]) by shiva.bio.bas.bg (8.12.10/8.12.10) with ESMTP id iBTDUU8R017618 (version=TLSv1/SSLv3 cipher=DES-CBC3-SHA bits=168 verify=NO); Wed, 29 Dec 2004 15:30:30 +0200 From: "Svetoslav Markov" To: George Corliss Date: Wed, 29 Dec 2004 15:30:30 +0200 MIME-Version: 1.0 Subject: correction CC: reliable_computing [at] interval [dot] louisiana.edu Message-ID: <41D2CD96.13628.F365B5@localhost> X-mailer: Pegasus Mail for Windows (4.21c) Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7BIT Content-description: Mail message body Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk sorry, correction: (D_1, D_2, ..., D_n) = c_1 *( D, 0, ...0) + c_2*(0,D,0....) + ... with unique c_i = d_i/d From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Dec 29 10:55:51 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTGtogY019905 for ; Wed, 29 Dec 2004 10:55:51 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBTGtoYl019904 for reliable_computing-outgoing; Wed, 29 Dec 2004 10:55:50 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTGtgXT019900 for ; Wed, 29 Dec 2004 10:55:48 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iBTGsfg19678; Wed, 29 Dec 2004 09:54:41 -0700 (MST) Message-Id: <200412291654.iBTGsfg19678 [at] cs [dot] utep.edu> Date: Wed, 29 Dec 2004 09:54:40 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: LSSC'05 To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: EtBBSgR1LEowSVlqCy+4Mg== 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, During the previous 2003 conference in this ancient city of Sozopol, Svetoslav Markov organized a very interesting interval session. If there is enough interest, we can have it this time as well. Vladik I myself am not sure I can attend this time, but this is a gorgeous place and I encourage everyone who has not been there to attend. ------------- Begin Forwarded Message ------------- Date: Wed, 15 Dec 2004 14:29:41 +0200 From: scicom05 [at] parallel [dot] bas.bg Dear colleagues and friends, The preparation of the Fifth International Conference on "Large Scale Scientific Computations", June 5-10, 2005 (LSSC'05), Sozopol, Bulgaria, follows the established schedule. Herewith, we would like kindly to remind you some of the important LSSC'05 deadlines: Deadline for submission of abstracts January 15, 2005 Deadline for submission of full papers March 15, 2005 Notification of acceptance of full papers May 1, 2005 Yours prompt contributions will be highly appreciated. If some of you have not registered yet, please do so using the on-line registration form provided by the conference www-cite. The cite is regularly up-dated and you will find there all currently available information. Please, do not hesitate to ask us any questions related to LSSC'05. With our best wishes for the New Year 2005! LSSC'05 organizers P.S. LSSC www-cite: http://parallel.bas.bg/Conferences/SciCom05.html ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Dec 29 11:03:36 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTH3aJe020027 for ; Wed, 29 Dec 2004 11:03:36 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBTH3axr020026 for reliable_computing-outgoing; Wed, 29 Dec 2004 11:03:36 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTH3S8u020022 for ; Wed, 29 Dec 2004 11:03:33 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id iBTH2R419716; Wed, 29 Dec 2004 10:02:27 -0700 (MST) Message-Id: <200412291702.iBTH2R419716 [at] cs [dot] utep.edu> Date: Wed, 29 Dec 2004 10:02:26 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: P.S. Sozopol conference To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: +xUsuAYWz341WW+orXDXJQ== 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 A special interval-related session CONTROL/UNCERTAIN SYSTEMS AND VALIDATED NUMERICS is organized by N. Dimitrova, M. Krastanov, and V. Veliov, From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Dec 29 17:21:34 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTNLXC9020542 for ; Wed, 29 Dec 2004 17:21:33 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBTNLXrl020541 for reliable_computing-outgoing; Wed, 29 Dec 2004 17:21:33 -0600 (CST) Received: from its-exsmtp1.marqnet.mu.edu (email.marquette.edu [134.48.20.169]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBTNLOOJ020537 for ; Wed, 29 Dec 2004 17:21:30 -0600 (CST) Received: from its-exfe2.marqnet.mu.edu ([134.48.20.167]) by its-exsmtp1.marqnet.mu.edu with Microsoft SMTPSVC(6.0.3790.211); Wed, 29 Dec 2004 17:23:18 -0600 Received: from [192.168.1.103] ([67.53.8.244] RDNS failed) by its-exfe2.marqnet.mu.edu with Microsoft SMTPSVC(6.0.3790.211); Wed, 29 Dec 2004 17:23:17 -0600 User-Agent: Microsoft-Entourage/10.1.4.030702.0 Date: Wed, 29 Dec 2004 17:21:40 -0600 Subject: Re: Linear independence From: George Corliss To: Svetoslav Markov CC: Message-ID: In-Reply-To: <41D2CAD8.16264.E8AF5D@localhost> Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit X-OriginalArrivalTime: 29 Dec 2004 23:23:17.0924 (UTC) FILETIME=[60C4DE40:01C4EDFD] Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Svetoslav, VERY interesting. Thank you for the explanation. Now if I try to apply that to solving a linear system, the real analysis connection is that A x = b has a solution if b is in the span of the columns of A, and the solution is unique if the columns of A are linearly independent. We would like those characterizations to carry over to interval analysis. If I understand your explanation correctly, for A x = b with thick interval elements in A and in b, assuming the columns of mid(A) are linearly independent (as point vectors), and assuming exact arithmetic. Then mid(b) is in the span of the columns of mid(A), the solution to mid(A) x = mid(b) is the vector of the coefficients in the linear combination, and it is unique. So far, all is ordinary. But now your procedure for working with the basis of think interval vectors (columns of A) in their midpoint-radius form yields unique radii (c_i in your work), leading to a unique interval vector, in midpoint-radius form) satisfying A x = b in the sense of expressing b as a unique linear combination of the columns of A. If I understand you correctly, that is a VERY COOL connection between the theory of linear independence and of a basis and the very practical challenge of solving a linear system. I do not recall ever seeing that technique for solving linear systems, although it might be equivalent to well known (by others) work. Do we then say that a set of interval vectors is linearly independent if the set of vectors of their midpoints is linearly independent in the usual sense? Their width does not matter? That would be an elegant AND useful definition. Dr. George F. Corliss Electrical and Computer Engineering Marquette University PO Box 1881 1515 W. Wisconsin Ave. Milwaukee WI 53201-1881 USA 414-288-6599; Fax: 288-5579; Dept. 288-6280 George.Corliss [at] Marquette [dot] edu > Let me explain the idea of interval basis on your example: > > [x_1] = ([1-d, 1+d], 0, 0, ..., 0) > . . . > [x_i] = (0, ..., [1-d, 1+d], 0, ...) > > According to the theory of quasilinear spaces > a general quasivector space (of group structure) > decomposes in a vector space (for the midpoints) and a > symmetric quasivector space (for the radii) -- the latter is > in fact a vector space but with a different definition of > multiplication with scalars (concerning negative scalars). > So we use the natural midpoint-radius presentation. > > Denoting D = [-d, d] we can rewrite the above as: > > [x_1] = ([1-d, 1+d], 0, 0, ..., 0) = (1, 0, 0, ..., 0) + (D, 0, 0, ..., 0) > . . . > [x_i] = (0, ..., [1-d, 1+d], 0, ...) = (0, ..., 1, 0, ...) + (0, ..., D, 0...) > > Now we need to represent an interval vector > > (a_1, a_2, ..., a_n) + (D_1, D_2, ..., D_n) > > wherein a_i are real numbers (midpoints) and D_i are centred intervals > > D_i = [-d_i, d_i] > > as linear combination of the intervals [x_i]. Clearly the presentation > decomposes in two parts: for the midpoints and for the radii. The first > part is clear, for the second we have: > > (D_1, D_2, ..., D_n) = c_1 *( D, 0, ...0) + c_2*(0,D,0....) + ... > > with unique c_i = d_i/d > > (whenever necessary, the radii d_i may take negative values, > so-called generalized intervals, however in this case this > is not needed). > > In my opinion the concept of linear (in)dependence is > an auxiliary tool for the important concept of basis, resp. > unique representation of elements by linear combinations. > > As you mention my name in your last letter I am > posting this to the RC mailing list. The paper that > I sent to you has been recently submitted, I shall > gladly send it to anybody interested. > > Svetoslav > > references: > > S. MARKOV, QUASIVECTOR SPACES AND THEIR > RELATION TO VECTOR SPACES > submitted to EJMC > > Markov, S., On the Algebraic Properties > of Intervals and Some Applications, Reliable Computing 7 (2), > 2001, 113--127. > From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Dec 30 07:04:55 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBUD4tjK022049 for ; Thu, 30 Dec 2004 07:04:55 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBUD4saF022048 for reliable_computing-outgoing; Thu, 30 Dec 2004 07:04:54 -0600 (CST) Received: from imap.univie.ac.at (mailbox-lmtp.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBUD4jrU022043 for ; Thu, 30 Dec 2004 07:04:51 -0600 (CST) Received: from univie.ac.at (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id iBUD3EFb155732; Thu, 30 Dec 2004 14:03:21 +0100 Message-ID: <41D3FC92.2040202 [at] univie [dot] ac.at> Date: Thu, 30 Dec 2004 14:03:14 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20041005 X-Accept-Language: en, de MIME-Version: 1.0 To: interval Subject: directed rounding in MATLAB? Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx7.univie.ac.at 4247; Body=2 Fuz1=2 Fuz2=2 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Is there a cheaper way in Matlab of a) obtaining the current rounding mode? b) switching rounding modes to up (towards +inf) or down (towards -inf)? c) getting the successor or predecessor of a floating point number? These are implemented in Rump's Intlab package, but on my LINUX machine their cost is about 1600 flops for a), 2300 flops for b), and 8900 flops for c), which seems exceedingly slow. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Dec 30 08:14:04 2004 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBUEE4up022240 for ; Thu, 30 Dec 2004 08:14:04 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id iBUEE4SQ022239 for reliable_computing-outgoing; Thu, 30 Dec 2004 08:14:04 -0600 (CST) Received: from sunshine.math.utah.edu (IDENT:F/al3NxOkdoCDMIia56KHvhUa8fWv+uv [at] sunshine [dot] math.utah.edu [128.110.198.2]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id iBUEDtb4022234 for ; Thu, 30 Dec 2004 08:14:01 -0600 (CST) Received: from psi.math.utah.edu (IDENT:nyMNs4lvDOiA/mhuX9jHDR+RIFLksloD [at] psi [dot] math.utah.edu [155.101.96.19]) by sunshine.math.utah.edu (8.12.11/8.12.10) with ESMTP id iBUECriN010996; Thu, 30 Dec 2004 07:12:53 -0700 (MST) Received: from psi.math.utah.edu (IDENT:0Sgxoww/u6dy08vJ7AtYdEscTTZGPTcW@localhost [127.0.0.1]) by psi.math.utah.edu (8.12.11/8.12.10) with ESMTP id iBUECrRx024265; Thu, 30 Dec 2004 07:12:53 -0700 (MST) Received: (from beebe@localhost) by psi.math.utah.edu (8.12.11/8.12.10/Submit) id iBUECrZ6024264; Thu, 30 Dec 2004 07:12:53 -0700 (MST) Date: Thu, 30 Dec 2004 07:12:53 -0700 (MST) From: "Nelson H. F. Beebe" To: interval Cc: beebe [at] math [dot] utah.edu, Arnold Neumaier X-US-Mail: "Department of Mathematics, 110 LCB, University of Utah, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA" X-Telephone: +1 801 581 5254 X-FAX: +1 801 585 1640, +1 801 581 4148 X-URL: http://www.math.utah.edu/~beebe Subject: Costs of floating-point rounding control and predecessor/successor computation In-Reply-To: Your message of Thu, 30 Dec 2004 14:03:14 +0100 Message-ID: Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Arnold Neumaier asks today about setting and getting the rounding mode in the Matlab Intlab package on GNU/Linux (presumably on Intel IA-32), reporting measured costs of 1600 flops for getting the mode, 2300 flops for setting the mode, and 8900 flops for getting the successor of a floating-point value, and observing that those costs seem rather high. While I cannot comment on the efficiency of Matlab's rounding mode access in the Intlab package, I can supply fresh evidence that it should have minimal cost. On IA-32, rounding mode access is available via the floating-point control word, which takes only one instruction to fetch or set. My C wrapper for GNU gcc looks like this: #define FE_FLTPREC 0 #define FE_DBLPREC 2 #define FE_LDBLPREC 3 #define _FPU_GETCW(cw) __asm__ ("fnstcw %0" : "=m" (*&cw)) #define _FPU_SETCW(cw) __asm__ ("fldcw %0" : : "m" (*&cw)) static fpu_control_t cw; int (fegetprec)(void) { _FPU_GETCW(cw); return ((int)((cw >> 8) & 0x3)); } int (fesetprec)(int prec) { /* return nonzero on success, zero on failure */ _FPU_GETCW(cw); if ((prec == FE_FLTPREC) || (prec == FE_DBLPREC) || (prec == FE_LDBLPREC)) { cw &= ~0x300; /* clear just the PC bits */ cw |= (prec << 8); /* set PC bits */ _FPU_SETCW(cw); /* store the control word */ return (1); } else return (0); } Here is a little experiment in a C-like interpreted language that I'm working on, run just now on a 600MHz Intel Pentium III in a 64-bit (C double) implementation. First, demonstrate the cost of floating-point addition (without overflow): sum = 0 t = second() for (k = 1; k <= 1000000; ++k) sum += BASE println "Time = ", second() - t Time = 2.350 Now, do the same, but also set the rounding mode each iteration; the loop and its timing are: for (k = 1; k <= 1000000; ++k) { fesetround(FE_DOWNWARD); sum += BASE } Time = 3.400 Once again, getting the rounding mode instead of setting it: for (k = 1; k <= 1000000; ++k) { r = fegetround(); sum += BASE } Time = 2.970 Finally, two bare loops that just get and set the rounding mode: for (k = 1; k <= 1000000; ++k) fegetround() Time = 1.610 for (k = 1; k <= 1000000; ++k) fesetround(FE_DOWNWARD) Time = 2.330 Thus, setting the rounding mode on this platform in this interpreted language costs somewhat less than a floating-point addition, and getting the rounding mode costs half as much as setting it. The successor function timing test looks like this for normal numbers: x = 1 for (k = 1; k <= 1000000; ++k) x = nextafter(x,Infinity) Time = 3.670 For subnormals, it looks like this: x = 0 for (k = 1; k <= 1000000; ++k) x = nextafter(x,Infinity) Time = 11.210 Thus, for normal numbers, nextafter() is about as expensive as a floating-point addition (i.e., the interpreter overhead swamps the actual numerical computation). Subnormals cost about three times as much. A similar experiment carried out on a brand-new AMD64 Opteron system showed subnormals in nextafter() costing twice as much. Other experiments on Sun SPARC, MIPS R10000, and PowerPC showed identical costs for normals and subnormals. On a MIPS R4400, the subnormal penalty is 1.5. On PA-RISC 8700, it is only 1.3. On a DEC Alpha 21164, the penalty is 5.8, and on an Alpha 21264, it is 6.5. My interpreter's implementation of nextafter() includes its own checks and code for NaN, Infinity, +MAXNORMAL, and -MAXNORMAL, and otherwise, calls the native C library nextafter() function. The initial special cases could be eliminated if native nextafter() were reliable and correct everywhere, but it isn't. ------------------------------------------------------------------------------- - Nelson H. F. Beebe Tel: +1 801 581 5254 - - University of Utah FAX: +1 801 581 4148 - - Department of Mathematics, 110 LCB Internet e-mail: beebe [at] math [dot] utah.edu - - 155 S 1400 E RM 233 beebe [at] acm [dot] org beebe [at] computer [dot] org - - Salt Lake City, UT 84112-0090, USA URL: http://www.math.utah.edu/~beebe - -------------------------------------------------------------------------------