Colloquium
Wednesday,
May 8th at 3:30 in Humanities 428
Speaker:
Jon Wellner, Department of Statistics, University of Washington
Title: Estimation and Testing with Interval-Censored
Data
Colloquium
Tuesday,
May 7th at 3:30 in Humanities 428
Speaker:
Professor Alexandru Dimca (Univ of Bordeaux, France)
Title: On the degree of gradient mappings
Statistics
Seminar :
Friday,
May 3rd, 12:00pm HUM 428
Cookies
and coffee at 11:40am
Speaker: Guy
Brock will present research he has been working on in collaboration with Drs.
Honghui Wan and Bill Beavis from the National Center for Genome Resources in
Sante Fe.
Title:
An N-State
Fuzzy Logic Model for Determining Gene Regulatory Networks
S.C.A.M.
Seminar
Friday, May 3rd at 3:30 in Humanities 428
Speaker:
Marcel Oliver,candidate for the Applied Analysis position
Title: Variational asymptotics for rotating
fluids near geostrophy
Colloquium
Friday,
May 3rd at 3:30 in Humanities 428
Speaker:
Marcel Oliver, candidate for the Applied Analysis position
Title: Variational asymptotics for rotating
fluids near geostrophy
Geometry
Seminar
Date: Wednesday, May 1, 2002
Time: 4:00-5:00
Place: HUM 428
Speaker:
Sarah Rich
Title: On Hyper-Sasakian Structures, II.
Colloquium
Tuesday,
April 30th at 3:30 in Humanities 428
Speaker:
Irina Vlaicu
Title: Derivation of the nonlinear Schroedinger
equation from the Vlasov-Poisson system in the plasma case
Colloquium
Thursday, April 25, 3:30, HUM 428
Title:
Molecular Modeling of Self-Assembly
Speaker: Dr. Frank van Swol, Sandia National
Laboratories and The Chemical and Nuclear Engineering Department, University
of New Mexico
S.C.A.M.
Seminar
Wednesday, April 24th, 2:30p.m. HUM 428
Speaker:
Vageli Coustsias
Title: Some mathematics of drug design
Statistics
Seminar :
Friday, April 19, 2002 12:00
HUM 428
Cookies and coffee at 11:40am
Speaker:
Dr. Bimal Sinha, University of Maryland Baltimore County
Title:
Meta-Analysis: Combination of independent F-tests.
Geometry
Seminar
Wednesday,
April 17, 2002 4:00-5:00pm HUM 428
Speaker: Sarah
Rich
Title: On Hyper-Sasakian Structures
Geometry
Seminar
Wednesday,
April 10, 2002 4:00-5:00pm HUM 428
Speaker: Ken Zimmerman
Title: Discrete Dynamical Systems on Elliptic
Curves, II.
Colloquium
Tues.,
April 9th, 3:30 HUM 428
Speaker: Doug
Hardin, Vanderbilt University
Title:
Squeezable
bases and orthogonal wavelets on irregular grids.
Click
here for Abstract
Statistics
Seminar :
Friday, April
5, 2002 12:00 HUM 428
Cookies and coffee at 11:40am
Speaker:
Mark Glickman, Boston University
Title:
MODELING THE EFFECTS OF GENETIC FACTORS ON LATE-ONSET DISEASES IN COHORT STUDIES
Statistics
Seminar :
Thurs., Apr. 4th, 3:30pm HUM 428
Speaker:
Joe
Cavanaugh, University
of Missouri, Columbia
Title:
Discrepancy-Based
Model Selection Criteria Using Cross Validation
Geometry
Seminar
Wed., April 3rd, 4:00-5:00
HUM 428
Speaker:
Ken
Zimmerman
Title:
Discrete
Dynamical Systems on Elliptic Curves
Teaching
Workshop
Tues., April 2nd, 4:00
HUM 428
Speaker:
TJ Middleton
Title:
Using Geometer's
Sketchpad to Interactively and Inductively Improve Student Understanding of
Polynomials
Abstract: Using "sliders," the software package Geometer's Sketchpad allows instructors to instantly and continuously "morph" the graph of a polynomial. By presenting a discovery-based lesson investigating the effects of the various coefficients on the graph, students inductively gain insight into the possibilities regarding relative extrema (local max/min values), zeros, and end behavior of polynomials. The speaker will actually model this lesson as it is presented to students and then answer questions from instructors about pedagogical concerns. NOTE: Both instructors and students are invited to this workshop!
S.C.A.M.
Seminar
Wed., March 27th, 2:30
HUM 428
Speaker: Karl
Frinkle
Title:
Extending
Geometric Singular Perturbation Theory
Colloquium
Thursday,
Mar. 21st, 3:30-4:30pm HUM 428
Cookies
and Coffee at 3:00
Speaker: Gary
Dilts
Affiliation:
Los Alamos National Laboratory
Title:
Local Regression Analysis:
Back to the Statistical Roots of Meshfree Methods for Differential Equations
Abstract: Smooth Particle Hydrodynamics (SPH) has demonstrated remarkable utility in providing reasonable Lagrangian solution estimates for a wide variety of large-deformation flow problems ranging from galaxy collisions to water wave motion to high-velocity impact and fragmentation, with relatively little software investment. But "reasonable" is not always "accurate". A number of numerical difficulties plague the technique, resulting in numerous attempted fixes based on some variant of< moving-least-squares (MLS) derivative estimates: EFG, RKPM, CSPH, MLSPH,DPD, etc., which go under the general heading of "meshfree methods". The problem is that a good hydrodynamics method requires the presence of a number of properties which are in conflict in moving least squares enhancements of SPH: linear completeness, conservation, positive entropy generation across shocks, diffusiveness, and stability in tension. On top of this is, it must work uniformly well for reasonable arbitrary particle distributions.
SPH was originally based on the statistical "kernel density estimator". Since its invention though, there has been a class of data smoothers in use in the statistics community, known as "local regression estimators," which extend the idea of the kernel density estimator, and in fact extend the moving-least-squares estimate. These have remarkable theoretical properties, not the least of which is being optimal among the class of all linear smoothers at estimating derivatives. Unfortunately, they have remained largely unknown to the physics and engineering simulation community until now.
The talk will summarize the results of recent work on the exploitation of "tuned" local regression estimators for the numerical solution of< differential equations in an attempt to reconcile the conflicting demands facing MLS methods mentioned above. Tuning is a new concept which seeks to constrain local regression estimates to satisfy a general set of differential relations which can include an equation, its derivatives, boundary conditions, symmetries, etc. I will also address the application of local regression to the problems of integration and discontinuities. The ultimate hope is to construct a least-squares numerical analysis which is as robust and complete as that of finite elements, finite volumes, or finite differences, but which applies to arbitrary distributions of points without regard to connectivity.
Colloquium
Mon.,
Mar. 18th, 4:00pm HUM 428
Speaker: Keith
Promislow
Affiliation:
Simon Fraser University
Title:
Pattern
formation in Optical Parametric Processes
Abstract: The transparency and the weak nonlinear and dispersive properties of fiber optics are excellent for pulse propagation over great distance, but rather poor for manipulation of coherent radiation. It< is the strong nonlinear and dispersive properties of Chi-2 optical crystals which make them well suited for building the switches and routers of optical networks. The tunability, or optical parametric resonance, afforded by these devices corresponds to a rich class of mathematical models for three-wave interaction. I will give an overview of a rigorus quasi-stationary manifold treatment of pulse-pulse interactions and surprisingly robust transverse pattern formation in these important devices.
Colloquium
Thurs.,
Mar. 14th, 3:30pm HUM 428
Refreshments at 3:00 in lounge
Speaker: Mary
Salter
Affiliation: University
of Pittsburgh and Franciscan University of Steubenville
Title:
Degree theory for compact
perturbations of proper, once
continuously differentiable Fredholm maps of index 0 and its applications
Abstract: Degree theory seeks to define an integer valued function that can be used to study the number and nature of solutions of functional equations. There is currently an active interest in degree theory due to its applicability to partial differential equations. After a brief introduction to the classical degree theories of Brouwer and Leray-Schauder, a brief description will be given of the current theory for proper, C^1, index 0, Fredholm maps between general Banach spaces. We will then outline the construction of a degree theory for compact perturbations of such maps, will discuss the main properties of the degree function, and will illustrate the usefulness of degree theory by considering two examples. The first example will establish the existence of solutions of a semi-linear elliptic differential equation over an unbounded domain. The second establishes bifurcation from the trivial branch of solutions for a Schrodinger type operator equation.
Geometry
Seminar
Wed.,
Mar. 6th, 4-5:00 HUM 428
Speaker:
Alex
Buium
Title:
Quotients
of algebraic varieties by dense equivalence relations, II.
Lecture
Wednesday Feb. 27th, 12 noon Hum 428
Coffee
at 11:40
Speaker:
Manny Knill, Los Alamos National Laboratory
Title:
Algebraic Methods for Quantum Noise Control
Abstract: To be useful, a model of information processing (computation, communication) needs to be robustly realizable using physical devices. The fundamental theorem of quantum technology is that quantum information processing can in principle be realized with constant error rates. The unifying idea underneath most approaches for controlling quantum noise is that of a subsystem, defined as a tensor factor of a subspace of a Hilbert space. There is a close relationship between subsystems and properties of matrix algebras. I will describe a few of the ways in which elementary algebra and representation theory are contributing toward understanding and using noisy quantum systems.
WebCT
Lecture
Wed.,
Feb. 27th, 3:30 HUM 428
Speaker:
Nicolas
Robidoux
Title:
A
lecturer's quick and dirty introduction to WebCT
Abstract:Organizing
class material and information by date and making it accessible through a clickable
web accessible calendar is intuitive and works well with students. We
will demonstrate the use of WebCT as a tool for information and class management.
We will discuss: making class announcements through the web, creating hyperlinks
to useful documents, converting files to pdf format, hiding/releasing class
material, making the classroom
"paperless," centralized grade keeping, releasing grades "in
real time," making class grade statistics accessible to students, computing
final grades, and discussion groups.
Geometry
Seminar
Wed.,
Feb. 27th, 4-5 HUM 428
Speaker:
Alex
Buium
Title:
Quotients
of algebraic varieties by dense equivalence relations.
Colloquium
Lecture, Mathematics Education Candidate
Tuesday,
Feb. 26th, 3:30 HUM 428
Speaker:
Dr.
Kristin L. Umland
Title:
The
K-16 Math Experience and UNM's Role in the Education of Math Students and Math
Teachers
Colloquium
Lecture, Mathematics Education Candidate
Thursday,
February 21st, 3:30 HUM 428
Speaker:
Jennifer
Christian Smith; Department of Mathematics, University of Arizona
Title:
The
Development of Mathematical Practices in a Number Theory Course
Abstract: Most universities in the US require prospective high school mathematics teachers to take a course in abstract algebra and number theory. In my dissertation study, I followed six above-average performing students enrolled in such a course. My study focused on the students' understanding of congruence of integers developed during a unit on modular arithmetic. Though the topics studied in these types of courses are closely related to those of high school mathematics, research on teacher education indicates that students generally do not see these connections and regard these courses as completely unrelated to the mathematics they will be teaching in the future.
The emergent perspective, as proposed by Yackel and Cobb (1995) assumes that mathematical learning is viewed as "a process of both active individual construction and enculturation" into the mathematical community (p. 20). This perspective was used to examine the relationship between the classroom mathematical practices that developed and the students' individual conceptions of congruence. In this talk we will examine this relationship in the context of solving linear congruences. In general, the students did not appear to view congruences as being analogous to equations. When solving a congruence such as 5x = 3 (mod 7), they did not tend to think of "dividing" both sides of the congruence by 5, or of using a "guess and check" strategy. A solution method introduced in the course was viewed by the students almost exclusively as an algorithm to be memorized, and they generally did not recognize the connection between this method and the solving of equations in elementary algebra.
S.C.A.M.
Wed.,
Feb. 20th, 2:30 HUM 428
Speaker:
Todd
Kapitula
Title:
A
"Practical" Guide to Inverse Scattering
Geometry
Seminar
Wed.,
Feb. 20th, 4-5:00 HUM 428
Speaker:
Charles
Boyer
Title:
Contact
Riemannian Geometry on 5-Manifolds, III
Seminar
Tuesday, February
19th, 3:30 HUM 428
Speaker:
Nicolas
Robidoux,
University
of New Mexico and Simon Fraser University
Title:
Natural
Discretizations of the diffusion operator
Abstract:
Mixed
Finite Volume Difference discretizations of the steady diffusion equation div
k grad d = g, with arbitrary combinations of Dirichlet, Neumann and Robin boundary
conditions, will be discussed. The differential operators div and grad are discretized
with respect to the ``natural'' projections dictated by the (generalized) Stokes
Theorem. The diffusion coefficient k is then discretized by looking at its inverse
as an
operator mapping fluxes to tangential integrals (as a ``discrete Hodge star
operator'').
In 1D, provided that the diffusion coefficient is positive, measurable and bounded
away from zero and infinity, the computed point values of the temperature and
flux converge in max norm to the exact values of the weak solution if the source
term is integrable; at first order if the source term is square integrable;
at second order if the primal grid is aligned with the discontinuities of the
source term in such a way that the restriction of the source term to every grid
cell has a square integrable derivative.
Seminar
Friday, February
15th, 3:30 HUM 428
Refreshments at
3:00
Speaker:Gabriel
Huerta CIMAT, Mexico
Title:
Time
Series Modeling via Hierarchical Mixtures
Abstract: The problem of model comparison and model mixing in time series is addressed using the approach known as Hierarchical Mixtures-of-Experts. This methodology allows for comparisons of arbitrary models, not restricted to a particular class or parametric form. Additionally, the approach is flexible enough to incorporate exogenous information that can be summarized in terms of covariables or simply time, through weighting functions that define the hierarchical mixture. This talk shows how to estimate the parameters of such models using the EM-algorithm and presents some theoretical properties of the method in the context of time series modeling. In addition, model estimation using a full Bayesian approach based on Markov Chain Monte Carlo simulation is considered. Finally, the methodology is illustrated with the analysis of an economic-financial series.
Applied
Analysis Seminar
Thursday, February
14th, 3:30 HUM 428
Speaker:
Milena
Stanislavova
Title:
Semigroups
of Linear Operators and Applications to Nonlinear Partial Differential Equations
Abstract:
I
will outline the use of the abstract methods of the theory of one-parameter
semigroups of linear operators in PDE's. A major issue for
the infinite-dimensional dynamical systems is that the position of the spectrum
of the linearization does not determine the stability of the system. A spectral
mapping theorem is needed to show that in each case the spectrum can be exponentiated
in a correct way to produce the spectrum of
the semigroup. To illustrate this, I will explain how to prove the spectral
mapping theorem for a linearization of the nonlinear Schr\"odinger equation,
which arises in optical waveguide problems. This implies the existence of locally
invariant stable, unstable and center manifolds in the neighborhood of a standing
wave solution, such as waveguide mode. As another example, I will also characterize
the spectrum of the linearized Euler operator, obtained by linearizing the equations
of incompressible two-dimensional fluid at a steady state with vorticity that
contains only two nonzero Fourier modes. In addition, the spectral mapping theorem
holds for the group generated by the two-dimensional Euler operator.
Geometry
Seminar
Wednesday, February
13th, 4:00-5:00 HUM 428
Speaker:
Charles
Boyer
Title:
Contact
Riemannian Geometry on 5-Manifolds, II
Statistics
Seminar
Tuesday, February
12th, 3:30 HUM 428
Refreshments at
3:00
Speaker:
Ursula
U. Mueller,
Arizona
State University and University of Bremen
Title:
Plug-in
estimators for regression models
Abstract: This
talk addresses estimation of smooth functionals of distributions by plugging
in function estimators of unknown features such as regression functions or densities.
We prove that such estimators are, in many cases, root n consistent, and sometimes
efficient, even though the estimator plugged in converges with a slower rate.
We illustrate the plug-in procedure by constructing estimators of linear functionals
of the error distribution in nonparametric regression models. We derive an i.i.d.
representation for the empirical estimator based on residuals, using undersmoothed
estimators for the regression curve. Asymptotic efficiency of this estimator
is proved. Estimation of the error variance is an important example.
Statistics
Seminar
Friday, February
8th, 12:00 HUM 428
Speaker:
Barbara
Gonzalez-Arevalo
Title:
Buffer
Content of a Leaky Bucket System with Long Range Dependent Input Traffic
S.C.A.M
Seminar
Thursday February 7th, 3:30 pm, HUM 428
Speaker: Dr.
Darryl D. Holm (Theoretical Division and Center for Nonlinear Studies,
Los Alamos National Laboratory)
Title: Peakons and the 1D alpha
model
Statistics
Seminar
Wednesday Jan.
30th, 3:00-4:00 Hum 428
Speaker: Olivier
Bousquet (Ecole Polytechnique, France)
Title: A Bennett
Concentration Inequality for Empirical Processes
Abstract: I
introduce new concentration inequalities for functions on product spaces. These
inequalities are derived using the so-called entropy
method introduce by Ledoux. They allow to obtain a Bennett type deviation bound
for suprema of empirical processes indexed by upper bounded functions. The result
is an improvement on Rio's version of Talagrand's inequality for equidistributed
variables.
Seminar
Thursday, January 17, at 3:30 pm in Humanities 428
Speaker: Sanjeeva
Balasuriya (Oberlin College)
Title: A
weak finite-time Melnikov approach to 3-D Navier-Stokes flows
Abstract:
Nearly inviscid 3-D Navier-Stokes flows are examined, with regard
to how a viscous perturbation deforms distinguished manifolds of boundaryless
3-D steady Euler flows. A special Melnikov method is necessary in this analysis,
given the lack of knowledge of the differentiability of the Navier-Stokes velocity
with respect to the viscous parameter, and the fact that its closeness to the
Euler velocity cannot be valid for infinite time. An explicit expression for
the splitting of the manifold is obtained, and the consequences for viscous
fluid transport in the `bubble vortex' geometry discussed.
S.C.A.M.
Seminar
Tuesday, January 15, at 3:30 pm in Humanities 428
Speaker: Atanas
Stefanov, University of Massachusetts
Title: Harmonic
analysis and applications to nonlinear PDE
Abstract:
In this talk, I will present the Strichartz estimates approach
for proving local and global well-posedness for nonlinear Schroedinger and
wave equations. In particular, I will relate the oscillatory and asymptotic
properties of the Schroedinger and wave semigroups and the
range of the admissible indices in the corresponding Strichartz estimates. As
an example, I will present a local well posedness result for 1 D
Schroedinger equation arising in statistical physics. The conservation laws
easily allow one to iterate such local solutions to global ones. The
Strichartz estimates has also played an important role in the study of the wave
map problem. We have recently established the critical regularity
(i.e. global existence for solutions with small Cauchy data) of the resulting
nonlinear wave equation. I will also address some interesting
(and typical) nonlinear effects which usually arise in that context: high-high
interactions and the stability of higher Sobolev norms, given that the critical
norm is small.
Geometry
Seminar
Wednesday, December 5, 4:30-5:30, Hum. 428
Title: Numerical Characterization of Base Loci
of Linear Series. II
Speaker: Micheal Nakamaye
Statistics
Seminar
Friday,
November 30, 4:30-5:30, Hum. 428
SPEAKER: Erik Andries, Department of Mathematics
& Statistics
TALK: MOTIVATING SIMPLE SUPPORT VECTOR MACHINES:
FROM ELEMENTARY
ANALYTIC GEOMETRY TO NONLINEAR OPTIMIZATION
ABSTRACT:
The Support Vector Machine (SVMs) is a machine learning technique
for pattern recognition. Some trendy examples include
text categorization in hypertext documents and classification of gene
expression data from DNA microarrays.
For introductory purposes, the discussion will be limited to the
two-class classification problem. A geometric interpretation
of the simplest SVM (as a linear classifer) will be stressed.
Then, it will be shown that this peculiar linear classifiers can
be represented in particularly useful form, which will be called
the Lagrangian dual problem.
Nonlinear
Series
Speaker:Prof.
Heinz-Otto Kreiss, Math Department, UCLA
November
29th, 30th 3:30-4:30 Humanities 428 (both
days)
Thursday,Nov.29th
Talk 
Problems with Different Time Scales
Friday,
Nov.30th Talk
Maximum Norm Estimates for the Solutions of the Incompressible
Navier-Stokes Equations
Statistics
Seminar
Friday, November 9th 4:00-5:00pm
HUM 428
Speaker:
Lyudmila A. Sakhanenko, Math and Stat Department, UNM
Title: The limit theorem for maximal deviation distribution of a weighted
Gaussian sequence.
Abstract: New limit theorem for maximal deviation distribution of a weighted
Gaussian sequence on the real line will be presented. This result generalizes
a well-known theorem for a Gaussian sequence on a finite interval. It also allows
one to study so-called continuous "versions". Applications to kernel
density estimation will be discussed as well.
Monday,
November 12th, 20th, 21st 2:00pm
Physics Department
A
SERIES OF INFORMAL TALKS ARRANGED BY THE CONSORTIUM OF THE AMERICAS FOR INTERDISCIPLINARY
SCIENCE OF UNM
Starting Nov 12, 2001, an informal series of talks on MATHEMATICAL MODELING
OF THE SPREAD OF INFECTIOUS DISEASES will be given by Guillermo Abramson,
a visitor to the Consortium of the Americas (see http://panda.unm.edu/consort/consortium.html).
Guillermo is one the co-authors of a recent article entitled "Small world
effect in an epidemiological model" (Physical Review Letters vol. 86, p.
2909 (2001) which has received acclaim among interdisciplinary scientists and
publicity in USA Today. At UNM, Guillermo has been studying reaction diffusion
systems with Alan Bishop of Los Alamos and Nitant Kenkre of UNM. The informal
series of talks he will give will provide an introduction to this timely and
intellectually exciting interdisciplinary topic.
The initial talk will be held in the Physics Department at 2 pm in room 4 on
Nov 12. The next ones will be on Nov 13, 20, 21 at 2 pm in room 5.
Contact abramson@unm.edu if you have any
questions.
S.C.A.M.
Seminar
Tuesday, November 13th 2:30pm
HUM 428
Speaker:
Pavel Lushnikov from LANL
Title: Nonlinear theory of the excitation of surface waves by wind due
to the Kelvin-Helmholtz instability
Abstract: A nonlinear theory of the Kelving-Helmholtz instability is
developed on a basis of the Hamiltonian description of a boundary surface of
two ideal fluids. Perturbation theory is constructed using a small-angle approximation
of surface elevation. The basic nonlinear process is the wave-wind interaction
which differs significantly from the nonlinear interaction in the absence of
wind. It is shown that nonlinearity does not saturate the linear instability
but, on the contrary, leads to an explosive growth of the amplitude. Near the
instability threshold, an envelope of surface elevation is described by a nonlinear
(2+1)-dimensional Klein-Gordon equation. An exact analytical proof of singularity
formation in a finite time is given and depends on the initial condition for
the nonlinear Klein-Gordon equation. Singularity formation allows one to explain
satellite and airplane observations of the very sharp dependence of the fraction
of sea surface covered by foam on the wind velocity.
Nonlinear
Series
November
29th and 30th
Nov.29th
Talk
Nov 30th Talk
Prof.
Heinz-Otto Kreiss,
UCLA, will speak in our Nonlinear Series.
