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Monday, February 22, 2010 - 13:00 ,
Location: Skiles 255 ,
Heasoon Park ,
CSE, Georgia Institute of Technology ,
Organizer: Sung Ha Kang

Nonnegative Matrix
Factorization (NMF) has attracted much attention during the past
decade as a dimension reduction method in machine learning and data
analysis. NMF provides a lower rank approximation of a nonnegative
high dimensional matrix by factors whose elements are also
nonnegative. Numerous success stories were reported in application
areas including text clustering, computer vision, and cancer class
discovery.
In
this talk, we present novel algorithms for NMF and NTF (nonnegative
tensor factorization) based on the alternating non-negativity
constrained least squares (ANLS) framework. Our new algorithm for NMF
is built upon the block principal pivoting method for the
non-negativity constrained least squares problem that overcomes some
limitations of the classical active set method. The proposed NMF
algorithm can naturally be extended to obtain highly efficient NTF
algorithm for PARAFAC (PARAllel FACtor) model. Our algorithms
inherit the convergence theory of the ANLS framework and can easily
be extended to other NMF formulations such as sparse NMF and NTF with
L1 norm constraints. Comparisons of algorithms using various data
sets show that the proposed new algorithms outperform existing ones
in computational speed as well as the solution quality.
This
is a joint work with Jingu Kim and Krishnakumar Balabusramanian.

Monday, February 15, 2010 - 13:00 ,
Location: Skiles 255 ,
Lek-Heng Lim ,
UC Berkeley ,
Organizer: Haomin Zhou

Numerical linear algebra is often regarded as a workhorse of scientific and
engineering computing. Computational problems arising from optimization,
partial differential equation, statistical estimation, etc, are usually reduced
to one or more standard problems involving matrices: linear systems, least
squares, eigenvectors/singular vectors, low-rank approximation, matrix
nearness, etc. The idea of developing numerical algorithms for multilinear
algebra is naturally appealing -- if similar problems for tensors of higher
order (represented as hypermatrices) may be solved effectively, then one would
have substantially enlarged the arsenal of fundamental tools in numerical
computations.
We will see that higher order tensors are indeed ubiquitous in applications;
for multivariate or non-Gaussian phenomena, they are usually inevitable.
However the path from linear to multilinear is not straightforward. We will
discuss the theoretical and computational difficulties as well as ways to avoid
these, drawing insights from a variety of subjects ranging from algebraic
geometry to compressed sensing. We will illustrate the utility of such
techniques with our work in cancer metabolomics, EEG and fMRI neuroimaging,
financial modeling, and multiarray signal processing.

Monday, February 1, 2010 - 13:00 ,
Location: Skiles 255 ,
Manu O. Platt ,
Biomedical Engineering (BME), Georgia Tech ,
Organizer:

Tissue remodeling
involves the activation of proteases, enzymes capable of degrading
the structural proteins of tissue and organs. The implications of
the activation of these enzymes span all organ systems and therefore,
many different disease pathologies, including cancer metastasis.
This occurs when local proteolysis of the structural extracellular
matrix allows for malignant cells to break free from the primary
tumor and spread to other tissues. Mathematical models add value to
this experimental system by explaining phenomena difficult to test at
the wet lab bench and to make sense of complex interactions among the
proteases or the intracellular signaling changes leading to their
expression. The papain family of cysteine proteases, the cathepsins,
is an understudied class of powerful collagenases and elastases
implicated in extracellular matrix degradation that are secreted by
macrophages and cancer cells and shown to be active in the slightly
acidic tumor microenvironment. Due to the tight regulatory
mechanisms of cathepsin activity and their instability outside of
those defined spaces, detection of the active enzyme is difficult to
precisely quantify, and therefore challenging to target
therapeutically. Using valid assumptions that consider these complex
interactions we are developing and validating a system of ordinary
differential equations to calculate the concentrations of mature,
active cathepsins in biological spaces. The system of reactions
considers four enzymes (cathepsins B, K, L, and S, the most studied
cathepsins with reaction rates available), three substrates (collagen
IV, collagen I, and elastin) and one inhibitor (cystatin C) and
comprise more than 30 differential equations with over 50 specified
rate constants. Along with the mathematical model development, we
have been developing new ways to quantify proteolytic activity to
provide further inputs. This predictive model will be a useful tool
in identifying the time scale and culprits of proteolytic breakdown
leading to cancer metastasis and angiogenesis in malignant tumors.

Monday, January 11, 2010 - 13:00 ,
Location: Skiles 255 ,
Peter Blomgren ,
San Diego State University ,
Organizer: Sung Ha Kang

We describe two computational frameworks for the assessment of contractileresponses of enzymatically dissociated adult and neonatal cardiac myocytes.The proposed methodologies are variants of mathematically sound andcomputationally robust algorithms very well established in the imageprocessing community. The physiologic applications of the methodologies areevaluated by assessing the contraction in enzymatically dissociated adultand neonatal rat cardiocytes. Our results demonstrate the effectiveness ofthe proposed approaches in characterizing the true 'shortening' in thecontraction process of the cardiocytes. The proposed method not onlyprovides a more comprehensive assessment of the myocyte contraction process,but can potentially eliminate historical concerns and sources of errorscaused by myocyte rotation or translation during contraction. Furthermore,the versatility of the image processing techniques makes the methodssuitable for determining myocyte shortening in cells that usually bend ormove during contraction. The proposed method can be utilized to evaluatechanges in contractile behavior resulting from drug intervention, diseasemodeling, transgeneity, or other common applications to mammaliancardiocytes.This is research is in collaboration with Carlos Bazan, David Torres, andPaul Paolini.

Monday, November 30, 2009 - 12:00 ,
Location: Skiles 269 ,
David Hu ,
Georgia Tech ME ,
Organizer:

How do animals move without legs? In this experimental and theoretical
study, we investigate the slithering of snakes on flat surfaces.
Previous studies of slithering have rested on the assumption that
snakes slither by pushing laterally against rocks and branches. In this
combined experimental and theoretical study, we develop a model for
slithering locomotion by observing snake motion kinematics and
experimentally measuring the friction coefficients of snake skin. Our
predictions of body speed show good agreement with observations,
demonstrating that snake propulsion on flat ground, and possibly in
general, relies critically on the frictional anisotropy of their
scales. We also highlight the importance of the snake's dynamically
redistributing its weight during locomotion in order to improve speed
and efficiency. We conclude with an overview of our experimental
observations of other methods of propulsion by snakes, including
sidewinding and a unidirectional accordion-like mode.

Monday, November 23, 2009 - 13:00 ,
Location: Skiles 255 ,
Xiaoming Huo ,
Georgia Tech (School of ISyE) ,
xiaoming@isye.gatech.edu ,
Organizer: Sung Ha Kang

Many algorithms were proposed in the past ten years on utilizing manifold structure for dimension reduction. Interestingly, many algorithms ended up with computing for eigen-subspaces. Applying theorems from matrix perturbation, we study the consistency and rate of convergence of some manifold-based learning algorithm. In particular, we studied local tangent space alignment (Zhang & Zha 2004) and give a worst-case upper bound on its performance. Some conjectures on the rate of convergence are made. It's a joint work with a former student, Andrew Smith.

Monday, November 16, 2009 - 13:00 ,
Location: Skiles 255 ,
Chris Rycroft ,
UC-Berkeley ,
Organizer:

Due to an incomplete picture of the underlying physics, the simulation
of dense granular flow remains a difficult computational challenge.
Currently, modeling in practical and industrial situations would
typically be carried out by using the Discrete-Element Method (DEM),
individually simulating particles according to Newton's Laws. The
contact models in these simulations are stiff and require very small
timesteps to integrate accurately, meaning that even relatively small
problems require days or weeks to run on a parallel computer. These
brute-force approaches often provide little insight into the relevant
collective physics, and they are infeasible for applications in
real-time process control, or in optimization, where there is a need to
run many different configurations much more rapidly.
Based upon a number of recent theoretical advances, a general
multiscale simulation technique for dense granular flow will be
presented, that couples a macroscopic continuum theory to a discrete
microscopic mechanism for particle motion. The technique can be applied
to arbitrary slow, dense granular flows, and can reproduce similar flow
fields and microscopic packing structure estimates as in DEM. Since
forces and stress are coarse-grained, the simulation technique runs two
to three orders of magnitude faster than conventional DEM. A particular
strength is the ability to capture particle diffusion, allowing for the
optimization of granular mixing, by running an ensemble of different
possible configurations.

Monday, November 9, 2009 - 13:00 ,
Location: Skiles 255 ,
Nicola Guglielmi ,
Università di L'Aquila ,
guglielm@univaq.it ,
Organizer: Sung Ha Kang

This is a joint work with Michael Overton (Courant Institute, NYU). The epsilon-pseudospectral abscissa and radius of an n x n matrix are respectively the maximum real part and the maximal modulus of points in its epsilon-pseudospectrum. Existing techniques compute these quantities accurately but the cost is multiple SVDs of order n, which makesthe method suitable to middle size problems. We present a novel approach based on computing only the spectral abscissa or radius or a sequence of matrices, generating a monotonic sequence of lower bounds which, in many but not all cases, converges to the pseudospectral abscissa or radius.

Monday, November 2, 2009 - 13:00 ,
Location: Skiles 255 ,
Rustum Choksi ,
Simon Fraser University ,
Organizer:

A density functional theory of Ohta and Kawasaki gives rise to nonlocal perturbations of the well-studied Cahn-Hilliard and isoperimetric variational problems. In this talk, I will discuss these simple but rich variational problems in the context of diblock copolymers. Via a combination of rigorous analysis and numerical simulations, I will attempt to characterize minimizers without any preassigned bias for their geometry.

Energy-driven pattern formation induced by competing short and long-range interactions is ubiquitous in science, and provides a source of many challenging problems in nonlinear analysis. One example is self-assembly of diblock copolymers. Phase separation of the distinct but bonded chains in dibock copolymers gives rise to an amazingly rich class of nanostructures which allow for the synthesis of materials with tailor made mechanical, chemical and electrical properties. Thus one of the main challenges is to describe and predict the self-assembled nanostructure given a set of material parameters.

Monday, October 26, 2009 - 13:00 ,
Location: Skiles 255 ,
Chiu-Yen Kao ,
Ohio State University (Department of Mathematics) ,
kao@math.ohio-state.edu ,
Organizer: Sung Ha Kang

The Kadomtsev-Petviashvili (KP) equation is a two-dimensional dispersivewave equation which was proposed to study the stability of one solitonsolution of the KdV equation under the influence of weak transversalperturbations. It is well know that some closed-form solutions can beobtained by function which have a Wronskian determinant form. It is ofinterest to study KP with an arbitrary initial condition and see whetherthe solution converges to any closed-form solution asymptotically. Toreveal the answer to this question both numerically and theoretically, weconsider different types of initial conditions, including one-linesoliton, V-shape wave and cross-shape wave, and investigate the behaviorof solutions asymptotically. We provides a detail description ofclassification on the results. The challenge of numerical approach comes from the unbounded domain andunvanished solutions in the infinity. In order to do numerical computationon the finite domain, boundary conditions need to be imposed carefully.Due to the non-periodic boundary conditions, the standard spectral methodwith Fourier methods involving trigonometric polynomials cannot be used.We proposed a new spectral method with a window technique which will makethe boundary condition periodic and allow the usage of the classicalapproach. We demonstrate the robustness and efficiency of our methodsthrough numerous simulations.