- Today's Editor:
- Cleve Moler
- The MathWorks, Inc.
- moler@mathworks.com

- Help with Ordinary Differential Equation
- Diagonal Perturbation of an Indefinite Matrix
- Olin Johnson Publishes Historical Novel
- SIAM Student Paper Prizes
- Conference in Minneapolis on Foundations of Computational Mathematics
- Conference in Chambery on Shallow Water Equations
- Postdoctoral Position at INRIA Sophia Antipolis
- Postdoctoral Position at Washington University School of Medicine
- Financial Engineer Position
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-------------------------------------------------------

From: Luis Almeida <luis.almeida@inesc-id.pt>

Date: Mon, 04 Mar 2002 17:06:48 +0000

**Subject: Help with Ordinary Differential Equation**

Dear colleagues,

A brother of mine, who works on physics, needs to find solutions of the

following differential equation (in Mathematica notation):

x^4 y''[x] y[x] == -1

He needs solutions that are real at least for some values of x, and that

are as general as possible. Until now he knows a pair of solutions which

are imaginary:

y[x] = I Sqrt[2]/(2 x) and its symmetrical.

We've found solutions of equations which are somewhat similar to the

original one, and which might give an indication of the kind of form the

solutions of the original equation might have.

The equation y''[x] y[x] == -1 has solution

y[x] = Sqrt[2/Pi] 1/a Exp[-(InverseErf[a (x-b)])^2]

with a and b arbitrary constants.

The equation x^2 y''[x] y[x] == -1 has solution

y[x] = Sqrt[2/Pi] 1/a x Exp[-(InverseErf[a/x])^2]

with a an arbitrary constant. Since the equation is of second order,

this shouldn't be the most general form of the solution.

Any help is greatly appreciated.

Just to give you an idea of where this problem comes from, this is part

of the solution of a certain wave equation. The solution has a factor

dependent on the distance from the origin, and another factor dependent

on angles. Here, y is the inverse of the radial factor, and x is the

inverse of the radius. Using these inverses allowed a significant

simplification of the form of the equation.

Thanks in advance for your help,

Luis B. Almeida

Phone: +351-213100246

INESC-ID Fax: +351-213145843

R. Alves Redol, 9 E-mail: luis.almeida@inesc-id.pt

1000-029 Lisboa, Portugal http://neural.inesc-id.pt/~lba/

------------------------------

From: Kartikkrishnan Sivaramakrishnan <kartis@rpi.edu>

Date: Thu, 7 Mar 2002 23:35:26 -0500

**Subject: Diagonal Perturbation of an Indefinite Matrix**

Hello all,

I have the following problem. I am given an indefinite matrix G. I want

to find a diagonal perturbation E, s.t. G+E is positive semidefinite [psd].

i.e. find a diagonal perturbation E, that is "as small as possible" s.t.

G + E is positive semidefinite, where G by itself is indefinite. All

matrices are of size n.

A few points here :-

(i) I know this problem can be formulated as a semidefinite programming

problem [SDP] to find the optimal E, but I want something much cheaper.

Actually, I need this to update my upper bounds in a cutting plane approach,

and I am looking for something cheap and dirty.

(ii) Currently the best E , I could come up with is E = lambda I, where

lambda is the absolute value of the most negative eigenvalue of G, and I is

the identity matrix of the appropriate size. Note that this choice for E

ensures that G+E is positive semidefinite.

(iii) My question is whether one could come up with a better diagonal

matrix E such that trace(E) <= trace(lambda I) = n*lambda. This will give

me the desired 'lower' upper bound.

(iv) I had a look at a number of Modifed Cholesky factorization schemes

[Gill, Murray, Wright], [Schnabel, Esknow], but these are not directly

applicable to my problem, since they give a diagonal E, such that

G+E is positive definite [not positive semidefinite], besides

||E|| is usually much greater than the absolute value of the most negative

eigenvalue of G.

To summarize, my question is whether it is possible to come up with

a diagonal E, such that trace(E) <= n*lambda [with lambda defined as above],

without solving an SDP?

Comments, suggestions, and pointers to any existing software would be

welcome.

Thank you.

Sincerely,

Kartik

------------------------------

From: Austin Dubrulle <adubrulle@worldnet.att.net>

Date: Sun, 10 Mar 2002 19:02:50 -0800

**Subject: Olin Johnson Publishes Historical Novel**

Just to show that numerical analysts are people of many talents---as if

that were necessary.

Our colleague and friend Olin Johnson (University of Houston) has

recently published a historical novel, "The Newlanders," based on his

family genealogy. It starts in the eighteenth century with David

Jansohn's journey from Germany to America---and ends in 1968 with

a Galerkin solution of the Sturm-Liouville problem at UC Berkeley

(just kidding; not part of the book).

Historical novel is a challenging genre that demands massive research

for historical accuracy (another sort of epsilon). Customers rate the

book at 4+ stars on the Amazon and Barnes & Noble web sites for style

and content.

Good show, Olin!

adubrulle@att.net

------------------------------

From: Allison Bogardo <bogardo@siam.org>

Date: Tue, 05 Mar 2002 07:36:17 -0500

**Subject: SIAM Student Paper Prizes**

Deadline Near for SIAM Student Paper Prize Competition

Principal Guidelines

The SIAM Student Paper Prizes are awarded every year to the

student author(s) of the most outstanding paper(s) submitted

to the SIAM Student Paper Competition. This award is based

solely on the merit and content of the student's

contribution to submitted paper(s).

The purpose of the Student Paper Prizes is to recognize

outstanding scholarship by students in applied mathematics

or computing.

Selection Procedures

Eligibility

Eligibility is restricted to students in good standing who

have not received their Ph.D. at the time of submitting

their entry or who have completed their degree within one

year of submission of their entry.

Submissions may be based on co-authored papers, provided

that the student's advisor will attest that the student's

work played a pivotal role in the results.

A letter from the student's advisor or department chair must

accompany each entry to verify these conditions.

To enter the competition, a student must submit: (1) an

extended abstract in English of a paper, and (2) a short

biography. The total length of the submitted abstract

(including bibliography) may not exceed five pages. The

student also must submit the complete paper that will be

used for clarification of any questions the selection

committee may have on the extended abstract. In addition,

the student's advisor or an interested faculty member must

submit a letter describing and evaluating the paper's

contribution to the literature, and the student's role in

the scholarship.

For the 2002 award, all papers and accompanying

documentation must be received at the SIAM office by

March 15, 2002.

Notification of Prize Winner

The SIAM president will notify the recipient(s) at least six

weeks before the award date.

Each recipient is required to present his or her paper at

the meeting where the prizes are awarded; if attending

the meeting poses a serious hardship, an exception may be

granted by the SIAM president.

Description of the Award

Each recipient of the SIAM Student Paper Prize shall receive

a framed certificate and a cash award of $1,000, plus $500 toward

travel expenses.

------------------------------

From: Arieh Iserles <A.Iserles@damtp.cam.ac.uk>

Date: Mon, 4 Mar 2002 10:41:46 GMT

**Subject: Conference in Minneapolis on Foundations of Computational Mathematics**

Second Announcement & Call for Registration

FOUNDATIONS of COMPUTATIONAL MATHEMATICS CONFERENCE

Minneapolis, 5-14 August 2002

The next Foundations of Computational Mathematics conference will be

held at University of Minnesota on 5-14 August 2002, as guests of the

Institute for Mathematics and its Applications.

The conference, organised by Society for Foundations of Computational

Mathematics, is next in a sequence that commenced with Park City, Rio

de Janeiro and Oxford FoCM meetings. The format will be similar:

plenary invited lectures in the mornings, theme-centred parallel

workshops in the afternoons. Each workshop will be go on for three

days and the conference will consist of three `periods', comprising of

different themes.

PLENARY SPEAKERS:

Ian ANDERSON (Utah State) Teresa KRICK (Buenos Aires)

Philippe CIARLET (Paris 6) Pierre Louis LIONS (Paris 9)

Albert COHEN (Paris 6) Dan LOZIER (NIST)

Tony DeROSE (Pixar) Volker MEHRMANN (TU Berlin)

Herbert EDELSBRUNNER (Duke) Andrew ODLYZKO (Minnesota)

Michael FREEDMAN (Microsoft) Edriss TITI (UC Irvine)

Wolfgang HACKBUSCH (Kiel) Mike TODD (Cornell)

Stefan HEINRICH (Kaiserslautern) Vladimir VAPNIK (AT&T Research)

Pascal KOIRAN (ENS Lyon) Grace WAHBA (Wisconsin)

The overall oversight of FoCM'02 is the responsibility of the FoCM

Executive Committee whose current Chair is Ron DeVORE (University

of South Carolina). The organisation is managed by the Local

Organising Committee: Carme CALDERER, Bernardo COCKBURN, Jianhong

(Jackie) SHEN, Willard MILLER, Peter OLVER and Victor REINER.

WORKSHOPS and their organisers:

* Foundations of numerical PDEs

Philippe Ciarlet (Paris 6), Mitch Luskin (Minnesota) & Eitan Tadmor (UCLA)

* Geometric integration and computational mechanics

Debra Lewis (UC Santa Cruz) & Hans Munthe-Kaas (Bergen)

* Information-based complexity

Erich Novak (Jena), Greg Wasilkowski (Lexington) & Henryk

Wozniakowski (Columbia & Warsaw)

* Learning theory

Tomaso Poggio (MIT) & Steve Smale (UC Berkeley)

* Optimization

Michael Overton (NYU), Bill Pulleyblank (IBM Yorktown Heights) & Jim

Renegar (Cornell)

* Special functions

Tom Koornwinder (Amsterdam) & Adri Olde Daalhuis (Edinburgh)

* Approximation theory

Allan Pinkus (Haifa) & Amos Ron (Madison)

* Computational algebraic geometry

Askold Khovanskii (Toronto) & Teresa Krick (Buenos Aires)

* Computational number theory

Richard Brent (Oxford), Dennis Hejhal (Minnesota & Uppsala) & Carl

Pomerance (Bell Labs)

* Multiresolution and adaptivity in numerical PDEs

Wolfgang Dahmen (Aachen), Raytcho Lazarov (Texas A&M) & Endre S

------------------------------

From: Stephane Gerbi <Stephane.Gerbi@univ-savoie.fr>

Date: Sat, 9 Mar 2002 12:29:32 +0100

**Subject: Conference in Chambery on Shallow Water Equations**

SECOND SAVOISIENNES DAYS OF APPLIED MATHEMATICS

SHALLOW WATER AND SAINT-VENANT EQUATIONS.

THEORY AND APPLICATIONS

to be held 16-17 May 2002 at:

University of Savoie, Campus Scientifique, Le Bourget du Lac, France

Organised by C. Bourdarias, S. Gerbi, M. Gisclon

from the Mathematics Department of the Universty of Savoie, Chambery, France,

with support from Ecole Normale Superieure, PARIS and INRIA Rocquencourt.

List of Speakers:

M.O. BRISTEAU, (INRIA Rocquencourt),

T. GALLOUET, (University of Marseille),

N. GOUTAL, (EDF Paris),

Shi JIN, (University of Wisconsin-Madison),

S. KARNI, (University of Michigan),

D. LAIGLE, (Cemagref Grenoble,

A.Y. LE ROUX, (University of Bordeaux),

D. LEVY, (Stanford University),

M. NAAIM, (Cemagref Grenoble),

G. RUSSO, (Universit=E0 di Catania, Italy)

E. VAZQUEZ, (Universidade de Santiago de Compostela, Spain).

The program of these Days will include 11 invited 1 hour lectures.

Posters presentation by young researchers is also organised.

There are NO registration fees but the inscription is highly recommended

on the on-line registration page of the web site:

http://www.lama.univ-savoie.fr/jsma2002.

For more information send e-mail to: JSMA02@univ-savoie.fr

or consult the Web site: http://www.lama.univ-savoie.fr/jsma2002

Kindly inform your colleagues interested in this field.

------------------------------

From: Stephane Lanteri <Stephane.Lanteri@sophia.inria.fr>

Date: Fri, 08 Mar 2002 14:18:47 +0100

**Subject: Postdoctoral Position at INRIA Sophia Antipolis**

Postdoctoral position in biomedical engineering at INRIA Sophia

Antipolis

Applications are invited for a 12 month postdoctoral position

(starting September 2002) at INRIA Sophia Antipolis. This position is

supported by the multidisciplinary project ICEMA (standing for Images

of the Cardiac Electro-Mechanical Activity) which is a collaborative

research action between different INRIA teams from several INRIA

sites. Informations concerning INRIA, INRIA Sophia Antipolis and the

ICEMA project can be found at the URLs:

- http://www.inria.fr/inria/index.en.html=20

- http://www.inria.fr/inria/organigramme/fiche_ur-sop.en.html=20

- http://www-rocq.inria.fr/who/Frederique.Clement/icema.html=20

An important goal of the ICEMA project is to design an interactive

deformable model that can be used in a clinical context. For this

purpose, this ``Beating Heart Model'' has to be optimized both on the

numerical level (efficiency of linear system solvers) and on the

computer science level (adaptation to parallel architectures). For

the current version of this model, the total computation time for a

full heart beat is around 10 minutes. Ultimately, this computation

time should be decreased to a few seconds. The existing version of

this model consists in a sequential software extensively based on

object oriented pogramming (the software is written in C++). In this

context, the candidate will conduct research and development

activities for:

- the design and implementation of an appropriate parallelization

strategy,

- the interfacing of the software with a (public domain) linear

algebra library that will provide access to efficient (parallel)

iterative solvers and the selection of appropriate methods based on

the mathematical properties of the algebraic systems under

consideration.

The candidate will conduct research and development activities in

collaboration with researchers from the Epidaure

(http://www.inria.fr/recherche/equipes/epidaure.en.html) and Caiman

(http://www.inria.fr/recherche/equipes/caiman.en.html) teams.

The background required from a young researcher wishing to apply for

this position is a PhD in Applied Mathematics or Scientific Computing,

with a strong personal interest in numerical methods and scientific

computing. The ideal candidate should have experience in the

following areas: mathematical and numerical analysis of systems of

partial differential equations using the finite element method,

solving of sparse linear systems of equations using iterative methods

(essentially, preconditioned Krylov methods), object oriented

programming, parallel computing. A working knowledge of C++ is

mandatory. A background in medical research or bioengineering would

be an asset.

This position is open to candidates of any nationality and selection

will be based upon the candidate's area of interest and research

potential.

Candidates should send a CV, including a statement of research

interests, a list of publications and addresses of three references by

June 30, 2002 to:

- Nicholas Ayache (head of Epidaure team)

E-Mail: Nicholas.Ayache@inria.fr

- Herve Delingette (researcher in the Epidaure team)

E-Mail: Herve.Delingette@inria.fr

- Stephane Lanteri (researcher in the Caiman team)

E-Mail: Stephane.Lanteri@inria.fr

More details at the URL:

http://www-rocq.inria.fr/sosso/icema2/icema2.html

------------------------------

From: Nathan Baker <nbaker@chemcca33.ucsd.edu>

Date: Wed, 6 Mar 2002 09:55:26 -0800

**Subject: Postdoctoral Position at Washington University School of Medicine**

Postdoctoral Researcher

Multiscale Simulation of Biomolecular Systems

Washington University School of Medicine

St. Louis, Missouri

A vacancy exists for a postdoctoral researcher in the Department of

Biochemistry and Molecular Biophysics at Washington University

School of Medicine, beginning as early as September 1, 2002. The

position involves the development and application of computational

methods for the multiscale modeling of large biomolecular systems.

Research will be conducted in the laboratory of Nathan A. Baker

(http://wasabi.ucsd.edu/), who will be joining the Washington

University School of Medicine as an Assitant Professor in the summer

of 2002.

Due to the interdisciplinary nature of the research, applications

from all areas of computational science are welcome. However,

candidates must have a Ph.D. (or equivalent), a strong research

background, and a good command of written and spoken English.

Interested applicants should reply via email to

nbaker@wasabi.ucsd.edu. Please attach a current CV with the names

of at least three references and a brief statement of research

background and interests.

Washington University is an equal opportunity employer.

Thank you for your help.

------------------------------

From: Lester Ingber <ingber@ingber.com>

Date: Thu, 7 Mar 2002 16:15:51 -0500

**Subject: Financial Engineer Position**

If you have very strong credentials for the position described below,

please email your resume to:

Lester Ingber <ingber@ingber.com> Director R&D

Financial Engineer

A disciplined, quantitative, analytic individual proficient in

prototyping and coding (such as C/C++, Maple/Mathematica, or

Visual Basic, etc.) is sought for financial

engineering/risk:reward optimization research position with

established Florida hedge fund (over two decades in the

business and $1 billion in assets under management). A PhD in a

mathematical science, such as physics, statistics, math, or

computer-science, is preferred. Hands-on experience in the

financial industry is required. Emphasis is on applying

state-of-the-art methods to financial time-series of various

frequencies. Ability to work with a team to transform

ideas/models into robust, intelligible code is key. Salary:

commensurate with experience, with bonuses tied to the

individual's and the firm's performance. Start date for this

position may range anywhere from immediately to six months

hence, depending on both the candidate's and the firm's needs.

See http://www.ingber.com/open_positions.html for more information.

Prof. Lester Ingber ingber@ingber.com ingber@alumni.caltech.edu

www.ingber.com www.alumni.caltech.edu/~ingber

------------------------------

End of NA Digest

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