Monday, April 7, 2014 - 14:00 , Location: Skiles 005 , Ming-Jun Lai , University of Georgia , Organizer: Martin Short
I mainly discuss the following problem: given a set of scattered locations and nonnegative values, how can one construct a smooth interpolatory or fitting surface of the given data? This problem arises from the visualization of scattered data and the design of surfaces with shape control. I shall start explaining scattered data interpolation/fitting based on bivariate spline functions over triangulation without nonnegativity constraint. Then I will explain the difficulty of the problem of finding nonnegativity perserving interpolation and fitting surfaces and recast the problem into a minimization problem with the constraint. I shall use the Uzawa algorithm to solve the constrained minimization problem. The convergence of the algorithm in the bivariate spline setting will be shown. Several numerical examples will be demonstrated and finally a real life example for fitting oxygen anomalies over the Gulf of Mexico will be explained.
Monday, March 31, 2014 - 14:00 , Location: Skiles 005 , Benjamin Seibold , Temple University , Organizer: Martin Short
Initially homogeneous vehicular traffic flow can become inhomogeneous even in the absence of obstacles. Such ``phantom traffic jams'' can be explained as instabilities of a wide class of ``second-order'' macroscopic traffic models. In this unstable regime, small perturbations amplify and grow into nonlinear traveling waves. These traffic waves, called ``jamitons'', are observed in reality and have been reproduced experimentally. We show that jamitons are analogs of detonation waves in reacting gas dynamics, thus creating an interesting link between traffic flow, combustion, water roll waves, and black holes. This analogy enables us to employ the Zel'dovich-von Neumann-Doering theory to predict the shape and travel velocity of the jamitons. We furthermore demonstrate that the existence of jamiton solutions can serve as an explanation for multi-valued parts that fundamental diagrams of traffic flow are observed to exhibit.
Monday, March 24, 2014 - 14:00 , Location: Skiles 005 , Seth Marvel , University of Michigan , Organizer: Martin Short
In this talk, I will present work on two very different problems, with the only common theme being a substantial departure from standard approaches. In the first part, I will discuss how the spread of many common contagions may be more accurately modeled with nonlocal approaches than with the current standard of local approaches, and I will provide a minimal mathematical foundation showing how this can be done. In the second part, I will present a new computational method for ranking items given only a set of pairwise preferences between them. (This is known as the minimum feedback arc set problem in computer science.) For a broad range of cases, this method appears to beat the current "world record" in both run time and quality of solution.
Monday, March 10, 2014 - 14:00 , Location: Skiles 005 , Ray Treinen , Texas State, San Marcos , Organizer: John McCuan
The symmetric configurations for the equilibrium shape of a fluid interfaceare given by the geometric differential equation mean curvature isproportional to height. The equations are explored numerically tohighlight the differences in classically treated capillary tubes andsessile drops, and what has recently emerged as annular capillary surfaces. Asymptotic results are presented.
Monday, March 3, 2014 - 14:00 , Location: Skiles 005 , Seong Jun Kim , GT Math , Organizer: Sung Ha Kang
In this talk, the two approaches for computing the long time behavior of highly oscillatory dynamical systems will be introduced. Firstly, a generalization of the backward-forward HMM (BF HMM) will be discussed. It is intended to deal with the multiple time scale (>2) behavior of certain nonlinear systems where the non-linearity is introduced as a perturbation to a primarily linear problem. Focusing on the Fermi-Pasta-Ulam problem, I propose a three-scale version of the BF HMM. Secondly, I will consider a multiscale method using a signal processingidea. The dynamics on the slow time scale can be approximated by an averaged system gained by fltering out the fast oscillations. An Adaptive Local Iterative Filtering (ALIF) algorithm is used to do such averaging with respect to fast oscillations.
Monday, February 24, 2014 - 14:00 , Location: Skiles 005 , Le Song , Georgia Tech CSE , Organizer: Martin Short
Dynamical processes, such as information diffusion in social networks, gene regulation in biological systems and functional collaborations between brain regions, generate a large volume of high dimensional “asynchronous” and “interdependent” time-stamped event data. This type of timing information is rather different from traditional iid. data and discrete-time temporal data, which calls for new models and scalable algorithms for learning, analyzing and utilizing them. In this talk, I will present methods based on multivariate point processes, high dimensional sparse recovery, and randomized algorithms for addressing a sequence of problems arising from this context. As a concrete example, I will also present experimental results on learning and optimizing information cascades in web logs, including estimating hidden diffusion networks and influence maximization with the learned networks. With both careful model and algorithm design, the framework is able to handle millions of events and millions of networked entities.
Monday, February 17, 2014 - 14:00 , Location: Skiles 005 , Junshan Lin , Auburn University , Organizer: Haomin Zhou
Resonances are important in the study of transient phenomenaassociated with the wave equation, especially in understanding the largetime behavior of the solution to the wave equation when radiation lossesare small. In this talk, I will present recent studies on the scatteringresonances for photonic structures and Schrodinger operators. I will beginwith a study on the finite symmetric photoinc structure to illustrate theconvergence behavior of resonances. Then a general perturbation approachwill be introduced for the analysis of near bound-state resonances for bothcases. In particular, it is shown that, for a finite one dimensionalphotonic crystal with a defect, the near bound-state resonances converge tothe point spectrum of the infinite structure with an exponential rate whenthe number of periods increases. An analogous exponential decay rate alsoholds for the Schrodinger operator with a potential function that is alow-energy well surrounded by a thick barrier. The analysis also leads to asimple and accurate numerical approach to approximate the near bound-stateresonances. This is a joint work with Prof. Fadil Santosa in University ofMinnesota.
Wednesday, December 4, 2013 - 14:00 , Location: Skiles 005 , Prof. Riccardo March , Istituto per le Applicazioni del Calcolo "Mauro Picone" of C.N.R and University of Rome , Organizer: Sung Ha Kang
We consider a variational model for image segmentation which takes into account the occlusions between different objects. The model consists in minimizing a functional which depends on: (i) a partition (segmentation) of the image domain constituted by partially overlapping regions; (ii) a piecewise constant function which gives information about the visible portions of objects; (iii) a piecewise constant function which constitutes an approximation of a given image. The geometric part of the energy functional depends on the curvature of the boundaries of the overlapping regions. Some variational properties of the model are discussed with the aim of investigating the reconstruction capabilities of occluded boundaries of shapes. Joint work with Giovanni Bellettini.
Tuesday, November 5, 2013 - 11:00 , Location: Skiles 006 , Ha Quang, Minh , Istituto Italiano di Technologia (IIT), Genova, Italy , email@example.com , Organizer: Sung Ha Kang
Reproducing kernel Hilbert spaces (RKHS) have recently emerged as a powerful mathematical framework for many problems in machine learning, statistics, and their applications. In this talk, we will present a formulation in vector-valued RKHS that provides a unified treatment of several important machine learning approaches. Among these, one is Manifold Regularization, which seeks to exploit the geometry of the input data via unlabeled examples, and one is Multi-view Learning, which attempts to integrate different features and modalities in the input data. Numerical results on several challenging multi-class classification problems demonstrate the competitive practical performance of our approach.
Monday, November 4, 2013 - 14:05 , Location: Skiles 005 , Chad Higdon-Topaz , Macalester College , Organizer: Martin Short
From bird flocks to ungulate herds to fish schools, nature abounds with examples of biological aggregations that arise from social interactions. These interactions take place over finite (rather than infinitesimal) distances, giving rise to nonlocal models. In this modeling-based talk, I will discuss two projects on insect swarms in which nonlocal social interactions play a key role. The first project examines desert locusts. The model is a system of nonlinear partial integrodifferential equations of advection-reaction type. I find conditions for the formation of an aggregation, demonstrate transiently traveling pulses of insects, and find hysteresis in the aggregation's existence. The second project examines the pea aphid. Based on experiments that motion track aphids walking in a circular arena, I extract a discrete, stochastic model for the group. Each aphid transitions randomly between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid’s nearest neighbor. For large nearest neighbor distances, when an aphid is isolated, its motion is ballistic and it is less likely to stop. In contrast, for short nearest neighbor distances, aphids move diffusively and are more likely to become stationary; this behavior constitutes an aggregation mechanism.