The traveling salesman problem, or TSP for short, is easy to state: given a number of 'cities' along with the cost of travel between each pair of them, find the cheapest way of visiting all the cities and returning to your starting point. The simplicity of the statement is deceptive - the TSP is one of the most intensely studied problems in comp...

Creator:

Cook, William (Georgia Institute of Technology)

Created:

2002-10-16

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The first completely sequenced genome, the virus Lambda at 50,000 nucleotides, was sequenced via the shotgun method by Sanger and coworkers at Cambridge in 1981. The shotgun method consists of randomly sampling and determining 500-700 nucleotide 'reads' and then assembling them to reconstruct the sampled sequence. It was long believed that this ...

Creator:

Myers, Gene (University of California, Berkeley)

Created:

2003-05-06

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The Human Genome Project has catalyzed the emergence of a new approach to biology termed systems biology. Systems biology analyzes all the interrelationships of the elements in a biological system, rather than studying them one at a time, as has been the modus operandi in biology for the past 30 years. This systems approach has also emerged in t...

Creator:

Hood, Leroy E. (Institute for Systems Biology)

Created:

2003-09-15

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Throughout his life, either as participant, support individual, or involved spectator, the speaker has been involved in some aspect of drag racing. As such he has witnessed the birth and growth of many myths concerning dragster speed and acceleration. In this talk the speaker uses his mathematical training to identify rather elementary mathemati...

Creator:

Tapia, Richard (Rice University)

Created:

2003-11-20

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Secrets of the heart include the changes in the circulation occurring at birth, the muscular fiber architecture of the cardiac ventricles, the collagen fiber architecture of the heart valves, the electrical activity that coordinates and controls the heartbeat, and the vortex flow patterns of blood in the cardiac chambers. In this lecture, mathem...

Creator:

Peskin, Charles S. (New York University)

Created:

2003-06-05

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Frustrated by difficulties in explaining seemingly aberrant financial market behavior using contemporary methods of financial economics, a new school of behavioral finance has arisen that mixes psychology and economics. Despite the superficial appeal of this multi-disciplinary approach, this talk critiques behavioral finance by using the analyti...

Creator:

Ross, Stephen (Massachusetts Institute of Technology)

Created:

2004-03-30

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Is there something remarkable about the great precision and subtlety of the mathematical laws that appear to govern, in full detail, the behavior of the physical universe? Or do the perceived laws of physics merely reflect our own attempts to make some order out of the complication of observed physical action? Are all our own actions governed co...

Creator:

Penrose, Roger FRS (University of Oxford)

Created:

2004-10-05

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

What caused hundreds of Japanese children to fall into seizures while watching an episode of the cartoon show Pokemon? Why do women roommates sometimes find that their menstrual periods occur in sync?The tendency to synchronize is one of the most mysterious and pervasive drives in all of nature. Every night along the tidal rivers of Malaysia, th...

Creator:

Strogatz, Steven H. (Cornell University)

Created:

2004-01-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The rise in divorce rates in developed countries, including the US, is a widespread, important and poorly understood phenomenon. The benefits of happy marriages are clear. Laboratory methods have been developed to observe interactions of couples to identify patterns that are predictive of divorce or whether the couple will be unhappily married.M...

Creator:

Murray, James D. (University of Washington)

Created:

2004-11-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

3D optical elements modulate light through interaction with an entirevolume of variable refractive index (as opposed to a sequence of surfacesused in traditional optics.) One commonly used form of 3D optics isgradient-index (GRIN) where the modulation is base-band. Instead, we haveemphasized use of modulations on a spatial carrier (grating.) We ...

Creator:

Barbastathis, George (Massachusetts Institute of Technology)

Created:

2005-11-11

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Adaptive sampling, also called 'Active Learning', uses informationgleaned from previous measurements (e.g., feedback) to guide and focusthe sampling process. Theoretical and experimental results have shownthat adaptive sampling can dramatically outperform conventionalnon-adaptive sampling schemes. I will review some of the mostencouraging theore...

Creator:

Nowak, Robert (University of Wisconsin, Madison)

Created:

2005-12-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We propose a new approach to classical detection problem of discriminationof a true signal from an interferent signal. We show that the detectionperformance, as quantified by the receiver operating curve (ROC), can besubstantially improved when the signal is represented by a multi-componentdata set that is actively manipulated by a shaped probin...

Creator:

Levis, Robert J. (Temple University)

Created:

2005-11-09

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We present a direct imaging algorithm for both the location and geometry of extended targets. Our algorithm is based on a physical factorization of the response matrix of an active array. A resolution and noise level based thresholding is used for regularization. Our algorithm is extremely simple and efficient since no forward solver or iteratio...

Creator:

Zhao, Hongkai (University of California, Irvine)

Created:

2005-10-20

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

in collaboration with Gunther Uhlmann and Hart SmithIn reflection seismology one places sources and receivers on theEarth's surface. The source generates waves in the subsurface that arereflected where the medium properties vary discontinuously; thesereflections are observed in all the receivers. The data thus obtainedare commonly modeled by a s...

Creator:

De Hoop, Maarten (Purdue University)

Created:

2005-10-21

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Joint work with Doug Oldenburg.Image appraisal in geophysical inverse problem can provide insight into theresolving capability and uncertainty of estimates. Although a rigorous approachto solve nonlinear appraisal analysis is still lacking but several methods havebeen proposed in the past such as linearized Backus-Gilbert analysis, funnelfunctio...

Creator:

Routh, Partha S. (Boise State University)

Created:

2005-10-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

I will present a qualitative, model free theory forimaging in clutter with coherent interferometry.Coherent interferometry is a smoothed form of Kirchhoffor travel time migration that is implemented adaptivelyin order to optimize the bias-variance tradeoff in theimage quality, as it is being formed. I will show theresults of numerical simulation...

Creator:

Papanicolaou, George C. (Stanford University)

Created:

2005-10-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Classical detection theory for sensing relies on fixed targetillumination and independent identically distributed noise for target andclutter characterization. Unfortunately in many cases such as sensing andcommunications in urban or atmospheric scenarios, we encounter much morecomplex clutter and target conditions due to scattering from multipl...

Creator:

Bonneau, Bob (US Air Force Research Laboratory)

Created:

2005-10-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

ATR Theory, especially the performance prediction aspects, are fundamentalto integrated sensing and processing. Offline and online prediction andfeedback are essential processing tools for assessing which sensing actionswill likely provide the most information. I'll discuss the overlap betweenActive Vision, ATR Theory, and ISP and highlight rele...

Creator:

Arnold, D. Gregory

Created:

2005-12-05

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Imaging sensors, hardware, and algorithms are under increasingpressure to accommodate ever larger and higher-dimensional data sets;ever faster capture, sampling, and processing rates; ever lower powerconsumption; communication over ever more difficult channels; andradically new sensing modalities. Fortunately, over the past fewdecades, there has...

Creator:

Baraniuk, Richard G. (Rice University)

Created:

2005-11-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Optical spectroscopy offers an ideal area for testing and development of compressive sensing systems. Measurement costs can be high, generalized sampling strategies are easily implemented and prior information and feature specific tasks are common. This talk describes experimental and conceptual studies of compressive spectroscopy in the DISP gr...

Creator:

Brady, David J. (Duke University)

Created:

2005-12-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Conventional wisdom and common practice in acquisition andreconstruction of images or signals from frequency data follows thebasicprinciple of the Nyquist density sampling theory. This principlestates that to reconstruct an image/signal, the number of Fouriersamples weneed to acquire must match the desired resolution of the image/signal, e.g.the...

Creator:

Candès, Emmanuel J. (California Institute of Technology)

Created:

2005-12-05

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Computers crash, hang, succumb to viruses, run buggy programs, and harbor spyware. By contrast, mathematics is free of all imperfection. Why are imperfect computational devices so vital for the future of mathematics?

Creator:

Hales, Thomas (University of Pittsburgh)

Created:

2005-03-30

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this talk I will first show how to use simpleand classical results from distance geometry toaddress the problem of sensor localization underphysical constraints.Then I will move into presenting some recent resultsin video processing that I wish could be done at the sensorlevel. For example, I will show techniques thatreduce the video data to ...

Creator:

Sapiro, Guillermo R. (University of Minnesota, Twin Cities)

Created:

2005-12-09

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

An approximation of the solution to a hyperbolic equation with a damping term is introduced. It is built as the composition of Fourier integral operators (FIO). We prove the convergence of this approximation in the sense of Sobolev norms as well as for the wavefront set of the solution. We apply the introduced method tonumerically image seismic ...

Creator:

Le Rousseau, Jerome (Aix-Marseille Université, Université de Provence))

Created:

2005-10-20

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Data fusion and multi-cue data matching are fundamental tasks arisingin a variety of systems that process large amounts of data. Thesetasks often rely on dimensionality reduction techniques thattraditionally follow a data acquisition/reprocessing phase.In this talk, I will describe a powerful framework based on diffusionsthat can be used in orde...

Creator:

Lafon, Stephane (Google Inc.)

Created:

2005-12-06

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Dimensionality reduction methods have played a central role in exploration of parsimonious structural models, complexity regularizationin inverse problems, and data compression. Examples are PCA, Laplacian eigenmaps, ISOMAP, and matching pursuits which attempt to fit asubspace to the data. For integrated sensing and processing (ISP) systems dime...

Creator:

Hero, Alfred O. III (University of Michigan)

Created:

2005-12-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The human brain contains about 100 billion neurons, each making about 1000 synaptic connections with other neurons. This huge dynamical system communicates with itself and its environment via electrical impulses called spikes. How is incoming information turned into spikes, and how do spikes create decisions and behaviors? I will show how mathem...

Creator:

Holmes, Philip J. (Princeton University)

Created:

2005-12-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

It has been noted that many realistic networks have a power law degree distributionand exhibit the small world phenomenon. We consider graph drawing methods that takeadvantage of recent developments in the modeling of such networks.Our main approach is to partition the edge set of a graph into 'local' edgesand 'global' edges, and to use a force-...

Creator:

Chung Graham, Fan

Created:

2005-11-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Complex systems are ubiquitous in mathematics, biology,engineering, and physics, and the past ten years have witnessed an exponentialincrease in the literature associated such systems. A shared conceptualframework is becoming apparent among challenges as seemingly different as thefollowing: the search by mathematicians for exact high-order trigo...

Creator:

Sidles, John A. (University of Washington)

Created:

2005-11-09

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Detecting pathology using the 'stiffness' of the tissue is more that 2000 years old. Even today it is common for surgeons to feel lesions during surgery that have been missed by advanced imaging methods. Palpation is subjective and limited to individual experience and to the accessibility of the tissue region to touch. It appears that a means of...

Creator:

Greenleaf, James F. (Mayo Clinic)

Created:

2005-10-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Traditional optical design typically exploits only limitedprior knowledge of the object space to be imaged (e.g., resolution, field of view, nominal range, etc.) It is possibleto include stronger object space constraints (e.g., specificobjects of interest, operational SNR, background characteristics, etc.) into the optical design and thus genera...

Creator:

Neifeld, Mark A. (University of Arizona)

Created:

2005-11-11

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The talk will be divided in two parts. The first part will be devoted to diffraction tomography based on the scalar wave equationto obtain images of the refractive-index distribution of an object embedded in a homogeneous medium, with emphasis on experimentalverifications of this technique in applications using light or ultrasound. The second pa...

Creator:

Stamnes, Jakob J. (University of Bergen)

Created:

2005-10-19

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

One can trade off complexity in imaging system hardware and strictsystem tolerances for complexity in post-detection data processing.We describe an extreme example in this trade-off space: a coherentimaging approach that eliminates the imaging system hardware entirely(except for the detector array), relying on a phase retrievalalgorithm to form ...

Creator:

Fienup, James R. (University of Rochester)

Created:

2005-12-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Sensor networking is an emerging technology that promises anunprecedented ability to monitor the physical world via a spatiallydistributed network of small and inexpensive wireless sensor nodes.The nodes can measure the physical environment with a wide variety ofsensors, including acoustic, seismic, thermal, and infrared. While thepractically un...

Creator:

Nowak, Robert

Created:

2005-11-10

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Solving the phase retrieval problem, i.e. reconstructing a compact, multidimensional function from the modulus of its Fourier transform, has applications in astronomy, x-ray diffraction, optical wave-front sensing, and other areas of physics and engineering. To solve such problems, one must have constraints on the function in order to have a cha...

Creator:

Fienup, James R. (University of Rochester)

Created:

2005-11-09

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

An important problem (perhaps the most important problem to theDepartment of Defense) in modern remote sensing is that of correctlyidentifying potential targets at great distances and in all kind ofweather. Because of their ability to see through clouds and in theabsence of ambient radiation, active radar systems are usuallyrequired for this tas...

Creator:

Borden, Brett (Naval Postgraduate School)

Created:

2005-10-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We present recent work on imaging and reconstruction of objectsfrom radar backscatter measurements taken over wide aspect angles.Radar backscattering is a function of several variables, includinglocation, (complex-valued) amplitude, polarization, and the aspect(azimuth and elevation) of the interrogating sensor. Thishigh-dimensional data is ofte...

Creator:

Moses, Randy (The Ohio State University)

Created:

2005-10-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We consider a very general inverse problem on directed graphs.Surprisingly, this problem can actually be solved, explicitly, in a largeclass of examples. I will describe the construction of these examples, aswell as the method used to produce the inversion formulas. This is jointwork with F. Alberto Grunbaum.

Creator:

Matusevich, Laura Felicia (Texas A & M University)

Created:

2005-11-10

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Interbed multiples form a class of multiples in seismic data characterized by the property that all reflection points lie in thesubsurface. This sets them apart from surface multiples, which have at least one reflection point at the surface of the earth.For surface multiples there is a well established procedure to predict them from the data, i....

Creator:

Ten Kroode, Fons (The Shell Group)

Created:

2005-10-20

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We consider imaging the earth's topography using synthetic apertureRADAR (SAR), as well as real aperture RADAR (RAR). We use a simplescalar wave model for the radio waves. Instead of the common approachof singly-scattered waves, we consider the situation where a reflecting'wall' is located in the vicinity of the region of interest (ROI). Wewill ...

Creator:

Nolan, Clifford (University of Limerick)

Created:

2005-10-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Processing information at the sensor level can not only help reduce theamount of data acquired but also enhance the overall performance of thesystem. In this talk I will first present methods for shaping thethree-dimensional response of an optical system. Then I will discuss howto integrate tailored optical responses with digital postprocessinga...

Creator:

Piestun, Rafael (University of Colorado)

Created:

2005-12-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We consider the problem of determining earth properties fromseismic data, i.e. measurements with broadband acoustic wavesusing sources and receivers at the surface. For current dataprocessing methods this is considered as a partially linearizedinverse problem, where data is modelled by linearization about asmooth background medium, with a medium...

Creator:

Stolk, Chris (Universiteit Twente)

Created:

2005-10-19

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We present some of our recent work on coherent image reconstruction.The primary application that has driven this work has been syntheticaperture radar, although we have extended our approach to othermodalities such as ultrasound imaging as well. One of the motivationsfor our work has been the increased interest in using reconstructedimages in au...

Creator:

Cetin, Mujdat (Massachusetts Institute of Technology)

Created:

2005-10-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Joint work with Abhijit Mahalanobis.The concept of Integrated Sensing and Processing (ISP) suggests that asensor should collect data in a manner that is consistent with the endobjective. Thus ISP seeks to minimize the collection of redundant data,reduce processing time and improve overall performance. We present acase study of ISP using a multi-...

Creator:

Muise, Robert (Lockheed Martin)

Created:

2005-12-05

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

COMP-I is a program under the DARPA MONTAGE program focusing on theconstruction of thin digital imaging systems. COMP-I uses opticalprefilters to encode the impulse response of multiple aperture imagingsystems. The COMP-I program is near the completion of phase Idevelopment and has produced both visible and IR imaging systems basedon focal plane...

Creator:

Brady, David J. (Duke University)

Created:

2005-11-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The representation of color for perception differs from therepresentation for displays. We consider the map from (r,g,b)-space to (Intensity, hue, saturation)-space, and show how this non-linear space is useful for sensingdevices.

Creator:

Zucker, Steven W. (Yale University)

Created:

2005-12-09

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Joint work with Florence Delprat-Jannaud. Geophysicists are quite aware of the important troubles that can be met whenthe seismic data are contaminated by multiple reflections. The situationthey have in mind is the one where multiple reflections are generated byisolated interfaces associated with high impedance contrasts. We here studya more ins...

Creator:

Lailly, Patrick (Institut Français du Pétrole)

Created:

2005-10-21

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

jointly with George Papanicolaou (Stanford) and Chrysoula Tsogka (U.Chicago)I will discuss a robust, coherent interferometric approach for arrayimaging in cluttered media, in regimes with significant multipathing ofthe waves by the inhomogeneities in clutter. In such scattering regimes,the recorded traces at the array have long and noisy codas a...

Creator:

Borcea, Liliana (Rice University)

Created:

2005-10-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this talk we examine a class of inverse problems that arise ongraphs. We provide a review ofrecent developments, including design aspects for identifiabilitypurposes, inference issues andapplications to computer networks.

Creator:

Michailidis, George (University of Michigan)

Created:

2005-11-10

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Many anomalous network events do not manifest themselves as abrupt,easily-detectable changes in the volume of traffic at a single switch.Rather, the footprint they leave is a modification of the pattern of trafficat a number of routers in this network. Anomaly detection is then a questionof whether the current traffic pattern is sufficiently div...

Creator:

Coates, Mark (McGill University)

Created:

2005-11-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In inverse boundary problems one attempts to determine the properties of amedium by making measurements at the boundary of the medium. In thelecture we will concentrate on two inverse boundary problems, ElectricalImpedance Tomography and Travel Tomography in anisotropic media. Theseproblems arise in medical imaging, geophysics and other fields. ...

Creator:

Uhlmann, Gunther A. (University of Washington)

Created:

2005-10-19

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Joint with R.-E. Plessix.The goal of seismic surveying is the determination of the structure and properties of the subsurface. Oil and gas exploration isrestricted to the upper 5 to 10 kilometers. Seismic data are usually recorded at the earth's surface as a function of time. Creating asubsurface image from these data is called migration.Seismic...

Creator:

Mulder, Wim (The Shell Group)

Created:

2005-10-21

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

When a moving object is imaged with conventional synthetic aperture radar (SAR) the result is a displaced smear. This is due tothe extra information the objectmotion is imparting to the radar return. When a sensor collects data from a moving extended object,estimation of the direction vectors from the object to the sensor is often essential to t...

Creator:

Stuff, Mark A. (General Dynamics Advanced Information Systems)

Created:

2005-10-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

A new form of coherent optical microscopy is described thatgenerates images (reconstructions) of two and three-dimensional,penetrable scatteringobjects computationally from sets of measured digital hologramsof scattered field data collected in a suite of scatteringexperiments. Themicroscope uses the technique of 'phase shifting holography'(expla...

Creator:

Devaney, Anthony J. (Northeastern University)

Created:

2005-10-21

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Measured bioresponses are often characterized byan intrinsic high frequency and strong persistent correlationsinhibiting statistical modeling by the traditional techniques.The talk overviews two novel wavelet-based techniquesfor modeling such challenging data.Wavelet domains provide natural modelingenvironments for data that scale, as well as fo...

Creator:

Vidakovic, Brani (Georgia Institute of Technology)

Created:

2005-12-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Given a near-perfect X-ray source, such as a synchrotron, then what are the reasonable options for image reconstruction? Back-projection reconstruction has dominated, with lambda tomography not receiving the attention it deserves. Give the computation power a the beamline, is it reasonable to perform both reconstructions so as to discern object ...

Creator:

Butler, Les G. (Louisiana State University)

Created:

2006-01-12

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

I shall talk about building 3D models from image sequences, and inparticular about rendering new views of existing sequences in orderto create stereoscopic 3D from monocular footage. I shall show howexisting strategies for image-based rendering can be augmented usingimage-based priors to create realistic 3D views. In addition I willtalk about th...

Creator:

Fitzgibbon, Andrew (Microsoft Research)

Created:

2006-02-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this talk I will describe recent results in the segmentationof relevant structures in electron tomography.We have developed novel techniques based onPDEs to work with this extremely hard data.I will describe the problem and the proposed solution,both at a tutorial level for a general audience.This is joint work with A. Bartesaghi and S. Subra...

Creator:

Sapiro, Guillermo R. (University of Minnesota, Twin Cities)

Created:

2006-01-11

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Hilbert bases, Graver bases and toric Gröbner bases are at the heart of many problems arising in mathematics or in practice. In this talk we present the main functionality and the algorithmic theory behind the software package 4ti2. Furthermore, we present applications (theoretical and computational) from various mathematical fields such as tori...

Creator:

Hemmecke, Raymond (Otto-von-Guericke-Universität Magdeburg)

Created:

2006-10-25

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Joint work with I Vitebskiy.Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively differentfrom any uniform substance. The differences are particularly pronounced when the electromagnetic wavelengthis comparable to the minimal translation of the periodic structure. In such a case, the periodic medium canno...

Creator:

Figotin, Alexander (University of California, Irvine)

Created:

2006-10-04

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Differential algebra provides an algebraic viewpoint on nonlinear differential systems.The motivating questions for this talk are:How do we define the general solution of a nonlinear equations What are the conditions for a differential system to have a solutionHow do we measure the 'degrees of freedom' for the solution set of adifferential syste...

Creator:

Hubert, Evelyne (Institut National de Recherche en Informatique Automatique (INRIA))

Created:

2006-10-24

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Joint work with Gregor Kemper.I will discuss algorithms for finding generators ofrings of invariants, with emphasis on reductive groupsin positive characteristic and non-reductive groups.

Creator:

Derksen, Harm (University of Michigan)

Created:

2006-09-22

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Work in collaboration with the PSC-VB team and the Duke Center for InVivo Microscopy (CIVM) with support from the National Library of Medicine.Volumetric datasets (CT, MRI, EM, etc.) on the gigabyte scale are relativelycommon in the basic and clinic al Life Sciences, and datasets on the terabytescale will become increasingly common in the near f...

Creator:

Wetzel, Art W. (Pittsburgh Supercomputing Center)

Created:

2006-01-12

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

This talk presents a Maple/Matlab toolbox for basic polynomial computations with exact or approximate data. The toolbox includes software for computing the approximate GCD, approximate factorization, dual basis and multiplicity identification, as well as numerical elimination in solving polynomial systems. We shall present the underlying theory ...

In Numerical Algebraic Geometry, solution components of polynomial systems are characterized by witness points. Such nice points are computed efficiently by continuation methods.In this talk, which is joint work with Wenyuan Wu and Jan Verschelde, I will outline progress on extending these methods to Partial Differential Equations.I will describ...

Creator:

Reid, Gregory J. (University of Western Ontario)

Created:

2006-10-27

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

he reverse engineering of biological networks is an important andinteresting problem. Two examples of such networks are generegulatory networks, and the relationship of voxels in the brain. Wedescribe a method for determining possible 'wiring diagrams' for suchnetworks. The method is based on computational algebra, and a keypart of the method us...

Creator:

Stillman, Michael E. (Cornell University)

Created:

2006-09-19

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

A Shameful Act: Armenian Genocide and Turkish Responsibility. Taner Akcam discusses his new book, A Shameful Act: The Armenian Genocide and the Question of Turkish Responsibility (2006), with Eric Weitz. Taner Akcam was a Visiting Associate Professor in the Department of History during 2006-07 and is currently associate professor in the Departme...

Creator:

Institute for Advanced Study

Contributor:

Akcam, Taner

Created:

2006-11-29

Contributed By:

University of Minnesota, Institute for Advanced Study.

All too often we see mathematics and the arts as two sides of the science/humanities coin. In this talk we'll see a place in which the two come naturally together in exciting new research. In today's world in which almost all aspects of life are brought to the common medium of the computer, it is now possible to quantify and extract the style of...

Creator:

Rockmore, Daniel (Dartmouth College)

Created:

2006-02-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We show how a slightly lossy superlens of thickness d cloakscollections of polarizable line dipoles or point dipoles or finite energy dipole sources that liewithin a distance of d/2 of the lens. In the limit as the lossin the lens tends to zero, these become essentially invisiblefrom the outside through the cancelling effects of localized resona...

Creator:

Milton, Graeme Walter (The University of Utah)

Created:

2006-10-02

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

For almost 20 years the CoCoA project has been conducting research into computational commutative algebra, developing new algorithms and offering implementations in the interactive program 'CoCoA.' Recently we took the decision to rebuild the software from scratch with the specific aim of making excellent implementations available to all researc...

Creator:

Bigatti, Anna M. (Università di Genova)

Created:

2006-10-25

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

A geometric framework for comparing manifolds given by point cloudsis first presented in this talk. The underlying theory is based onGromov-Hausdorff distances, leading to isometry invariant andcompletely geometric comparisons. This theory is embedded in aprobabilistic setting as derived from random sampling of manifolds,and then combined with r...

Creator:

Sapiro, Guillermo R. (University of Minnesota, Twin Cities)

Created:

2006-04-03

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

I shall talk about some practical problems of special effects /animation production that could be broadly defined as Inverse Problems:data is recovered from observed images rather than generated on userspecification. Most of Computer Vision tasks in movie production,opposite to most Computer Graphics tasks, fall in Inverse Problemscategory. The ...

Creator:

Vendrovsky, Eugene (Rhythm & Hues Studios, Inc.)

Created:

2006-02-09

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The tropical variety of a polynomial ideal I in n variables over Q is a polyhedral complex in n-dimensional space. We may consider it as a subfan of the Groebner fan of I. The polyhedral cones in the Groebner fan can be computed using Groebner bases and by applying 'Groebner walk' techniques. This gives one method for computing the tropical vari...

Creator:

Jensen, Anders Nedergaard (Aarhus University)

Created:

2006-10-26

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this lecture, we discuss various results onboth complexity and algorithms for counting the numberof rational points on a hypersurface over a finite field, witham emphasis on p-adic methods.

Creator:

Wan, Daqing (University of California, Irvine)

Created:

2006-09-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Bayesian denoising of archival film requires a likelihood model that captures the image noise and a spatial prior that captures the statistics of natural scenes. For the former we learn a statistical model of film noise that varies as a function of image brightness. For the latter we use the recently proposed Field-of-Experts framework to learn ...

Creator:

Black, Michael (Brown University)

Created:

2006-02-10

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this talk, we give an overview of a discrete exterior calculus andsome of its multiple applications to computational modeling, rangingfrom geometry processing to physical simulation. We will focus ondiscrete differential forms (the building blocks of this calculus) andshow how they provide differential, yet readily discretizablecomputational ...

Creator:

Desbrun, Mathieu (California Institute of Technology)

Created:

2006-04-06

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The package D-modules for Macaulay 2 implements the majority ofthe now classical algorithms in the computational D-module theory. Basedon the ability of Macaulay 2 engine to compute Gröbner bases inthe Weyl algebra, the package provides, in particular, tools to work withholonomic D-modules such as the algorithms for b-functions, localizedmodules...

Creator:

Leykin, Anton

Created:

2006-10-26

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Already in 1968 one recognized that the transmission electron microscope could be used in a tomographic setting as a tool for structure determination of macromolecules. However, its usage in mainstream structural biology has been limited and the reason is mostly due to the incomplete data problems that leads to severe ill-posedness of the invers...

Creator:

Oktem, Ozan (Sidec Technologies)

Created:

2006-01-12

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Metamaterials, i.e. artificial engineered structures with properties not available in nature are expected to open a gateway to unprecedented electromagnetic properties and functionality unattainable from naturally occurring materials. Negative-refractive index metamaterials create entirely new prospects for guiding light on the nanoscale, some o...

Creator:

Shalaev, Vladimir (Purdue University)

Created:

2006-10-03

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this talk I will discuss algorithms for factoring polynomials over number fieldsto reach recent results on sparse polynomials, where the complexity of the algorithm takes into account the fact that the polynomial may have many zero coefficients. For simplicity I'll focus on rational polynomials in one or two variables. The talk will review re...

Creator:

Krick, Teresa (University of Buenos Aires)

Created:

2006-09-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Using the methods of numerical algebraic geometry, one can compute anumerical irreducible decomposition of the solution set of polynomialsystems. This decomposition describes the enitre solution set andits breakup into irreducible pieces over complex Euclidean space.However, in engineering or science, it is common that only the realsolutions are...

Creator:

Wampler, Charles W. (General Motors Company)

Created:

2006-09-20

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The Gauss-Manin system of a function is a direct image in the category of D-modules. For the case of isolated singularities there are two Singular libraries to compute it: gmssing.lib for (local) isolated hypersurface singularities, gmspoly.lib for (global) tame polynomial functions. In both cases the Gauss-Manin system carries a rich structure:...

Creator:

Schulze, Mathias (Oklahoma State University)

Created:

2006-10-27

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The L2 or H0 metric on the space of smooth plane regularclosed curves induces vanishing geodesic distance on the quotientImm(S1,R2)/Diff(S1).This is a general phenomenon and holds on all fulldiffeomorphism groups andspaces Imm(M,N)/Diff(M) for a compact manifold M and aRiemanninan manifoldN. Thus we have to consider more complicated Riemannian m...

Creator:

Michor, Peter W. (Universität Wien)

Created:

2006-04-04

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Crystalline materials such as most metals, ceramics, rocks, drugs, and bones are composed of a 3D space-filling network of smallcrystallites r the grains. The geometry of this network governs a range of physical properties such as hardness and lifetime beforefailure. Our group has pursued an experimental method r 3DXRD r which for the first time...

Creator:

Poulsen, Henning Friis (Technical University of Denmark)

Created:

2006-01-10

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Shadow patterns are all around us. We drive through them on the way to work and swim among them in pools. Similar patterns are also cast throughout the universe by the gravitational fields of stars and galaxies. We unveil some of the cosmic and mathematical secrets of these mysterious and beautiful patterns.

Creator:

Petters, Arlie O. (Duke University)

Created:

2006-03-22

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

A Gröbner basis for an ideal under an elimination order reflects much of thegeometric structure of the variety defined by the ideal. We discuss how thisrelationship can be used in decomposing polynomial systems (with or withoutparameters) and in primary decomposition of ideals. As an application, we showhow this technique can be used in designin...

Creator:

Gao, Shuhong (Clemson University)

Created:

2006-09-21

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Some problems in life are very hard (achieving world peace) while others are, at least for many of us, pretty easy (eating a good breakfast). How can we figure out which are which? Math can often tell us precisely how hard real-world problems are'but not always. We'll look at easy problems, hard problems, the sources of hardness, and puzzling in...

Creator:

Wright, Margaret H. (New York University)

Created:

2006-11-02

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

How many categories can you recognize? Currently the bestestimate is due to Irv Biederman: 3000 entry-level categories andperhaps 3*104 categories overall. This estimate was obtainedindirectly, by counting words in a dictionary. I will present a methodto obtain a direct estimate. Alongside the estimate one getsfrequencies of objects and categori...

Creator:

Perona, Pietro (California Institute of Technology)

Created:

2006-03-07

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.