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2013 News Archive

December 05, 2013
Temlyakov publishes article in IMI Preprint Series
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Vladimir Temlyakov published his article "Sparse approximation and recovery by greedy algorithms in Banach spaces" in the IMI Preprint Series (2013:09). Please see the link above to the full article and visit Preprints to see other articles in this series.

December 04, 2013
Temlyakov publishes article in IMI Preprint Series
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Vladimir Temlyakov published his article "Chebyshev Greedy Algorithm in convex optimization" in the IMI Preprint Series (2013:08). Please see the link above to the full article and visit Preprints to see other articles in this series.

November 12, 2013
Temlyakov honored at the International Conference on Nonlinear Approximations and Applications
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Vladimir Temlyakov was recently honored at the International Conference on Nonlinear Approximations and Applications, in Moscow, Russia. Hosted by the Steklov Mathematical Institute of the Russian Academy of Sciences and Lomonosov Moscow State University, this conference was dedicated to Temlykov's 60th birthday. Over 30 presentations were given between October 29 - November 1, 2013, covering topics such as approximation theory, harmonic analysis and geometry of normed spaces.

The organizing committee consisted of: B. Kashin ( Chairman ), O. Besov, R. DeVore (IMI), A. Izaak, V. Kozlov, S. Konyagin, Y. Malykhin, P. Petrushev (IMI), N. Pustovoitov, and S. Telyakovskii.

For more details on the conference and to view video presentations of the lectures, please visit: http://naa2013.mi.ras.ru/

October 04, 2013
Ivanov and Petrushev publish article in IMI Preprint Series
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Kamen Ivanov and Pencho Petrushev published their article: "Irregular Sampling of Band-Limited Functions on the Sphere and in More General Settings" in the IMI Preprint Series (2013:07). Please see the link above to the full article and visit Preprints to see other articles in this series.

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September 16, 2013
Dove, Griggs, Kang and Sereni publish article in IMI Preprint Series
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Andrew P. Dove, Jerrold R. Griggs, Ross J. Kang and Jean-Sebastien Sereni published their article: "Supersaturation in the Boolean Lattice" in the IMI Preprint Series (2013:06). Please see the link above to the full article and visit Preprints to see other articles in this series.

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September 06, 2013
Paula Vasquez joins IMI as its newest member

On September 6th, the IMI Executive Committee voted unanimously to accept Paula Vasquez as the newest member to IMI. Vasquez was recently hired as an Assistant Professor in the Department of Mathematics. Prior to her arrival at USC, she worked as a Postdoctoral Fellow under Greg Forest at UNC Chapel Hill. The IMI is excited about this promising addition to its roster and looks forward to future research collaborations with Vasquez.

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September 06, 2013
Xinfeng Liu is awarded a National Science Foundation grant

Xinfeng Liu (IMI) is awarded a three year National Science Foundation grant totaling $192,674 for his research on: Mathematical Modeling and Computational Studies for Proliferation Kinetics of Cancer Tumor Growth with Spatial-Temporal Dynamics.

"Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumori- genic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. But the relative frequencies of CSCs span wide ranges even within tumors arising from the same tissue type. Understanding the tumor growth kinetics and composition is critical for development of novel strategies for cancer treatment. With a close integration with experiments, the theme of this proposed work is on the mathematical modeling, computational investigation of the dynamic control of CSC population in tumor.

To better simulate the dynamic changes in cancer cell populations, we first propose that terminal differentiated cancer cells have negative feedback regulations on the self-renewal probability and division rate of CSCs and/or progenitor cells. This novel control mechanism capitalizes on emerging evidences in literature, and correlates nicely with recent findings from new observed experimental data. The model with negative feedback suggests that overexpression of HER2 leads to an increase of CSCs by regulating the division mode or the proliferation rate of CSCs. It is widely believed that a key mechanism for proper maintenance of a cell lineage to occur is the formation and substance of s stem cell niche, a microenvironment where stem cells reside in a tissue. To better explore the spatial patterns for CSCs during tumor growth, we plan next to consider the dynamics of tumor growth in the context of a stochastic, three dimensional model corresponding to solid tumor growth with spatial structure. With a comparison of the stochastic model with the one on negative feedbacks, one goal of this work is to further investigate whether the observed experimental dynamics of cell populations is mainly due to feedbacks, or space competition or the combination of these two. To efficiently capture the temporal-spatial dynamics of tumor growth with large cell populations, we later extend the stochastic model to develop a continuous PDE model coupled with di ffusive molecules. Therefore, the aims of this proposal are (1) to further develop and evaluate mathematical models to explore underlying biological factors to control the balance of tumor growth; (2) to develop both stochastic and continuous mathematical models with spatial-temporal dynamics to better understand the spatial distributions of CSC populations during tumor growth; (2) to design fast and efficient numerical methods to solve the proposed mathematical models with moving and complex domains."

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August 30, 2013
Permutahedron

Given a graph, a designated source vertex x, a designated sink vertex y, and a nonnegative vector v of dimension equal to the number of vertices, when is it possible to find a set of vertex weights so that a random walk starting from x, taking random steps to neighbors of the current vertex with probabilities proportional to their weights, and ending at its first visit to y has expected vertex occupation times given by v? Allowing "infinite weights" -- vertices which are always preferable to others -- invites the definition of an unusual kind of space: one that is homeomorphic to the so-called "permutahedron". This image is the result of applying such a map to the two-dimensional version of this space, filled with the Hilbert curve to illustrate the resulting distortions. (Joshua Cooper with David Collins.)

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August 29, 2013
Yi Sun is awarded a National Science Foundation Grant

Yi Sun (IMI) is awarded a three year National Science Foundation grant totaling $158,038 for his research on: Multiscale Computational Methods with Applications in Materials Science and Tissue Engineering.

"The focus of the proposed project is to develop new multiscale methods to study problems arising in materials science and tissue engineering. In this project, two thrusts are targeted for potential applications: (a) simulating epitaxial growth in materials science; (b) modeling of cellular aggregate fusion in organ biofabrication. Even though these problems arise from distinct disciplines, they all involve complex phenomena on multiple spatio-temporal scales across several orders of magnitude. Numerically solving these problems directly at the finest scale with standard algorithms inevitably leads to an enormous computational cost. Therefore, it is necessary to develop multiscale methods that share the efficiency of the macroscopic models while achieving the accuracy of the microscopic models. For both problems (a) and (b), the microscale dynamics is described by a lattice model based on the kinetic Monte Carlo (KMC) algorithm, while partial differential equations (PDEs) are used for modeling the macroscale dynamics on continuum level. Multiscale modeling and computation can be used in the form of either concurrent coupling or sequential (precomputing) coupling, depending on the problem to be solved. If the information needed for macroscopic models involves only a small number of parameter values or functions of very few variables, sequential coupling will be applied with these parameters precomputed in the microscopic models. Otherwise, the missing macroscopic information will be obtained “on the fly” from the microscopic models as the computation proceeds in the concurrent fashion. For epitaxial growth, both coupling strategies will be tested and compared. For cellular aggregate fusion, the concurrent coupling will be proposed to handle more complicated mechanochemical situations. In addition, the proposed research will include the code development for parallel computing using hybrid CPU/GPU computing hardware."

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August 21, 2013
Ivanov and Petrushev publish article in IMI Preprint Series
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Kamen Ivanov and Pencho Petrushev published their article: "Fast Memory Efficient Evaluation of Spherical Polynomials at Scattered Points" in the IMI Preprint Series (2013:05). Please see the link above to the full article and visit Preprints to see other articles in this series.

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July 19, 2013
László Székely and Linyuan Lu are awarded a National Science Foundation grant

László Székely and Linyuan Lu (IMI) are awarded a three year National Science Foundation grant totaling $184,111 for their research on: Extremal and Probabilistic Combinatorics with Applications.

"As there is increasing demand from other disciplines and also from the internal development of mathematics for advancement of theory and algorithms for discrete structures, there is increasing demand to understand "optimal" extreme structures and "typical" random structures in discrete mathematics. This project will investigate basic combinatorial questions about structures and will look for various applications of discrete mathematics in computer science, biology, and engineering.

The particular problems on which work is planned include:

  • making progress on the 70 years old Turán's Conjecture, improve current bounds on Turán type extremal problem on hypergraphs, using the connections to flag algebras;
  • building a Turán hypergraph theory for non-uniform hypergraphs;
  • using Turán hypergraph theory for non-uniform hypergraphs to build an extremal theory of excluded subpostes for posets;
  • further extending the use of the lopsided Lovász Local Lemma and apply it to asymptotic enumeration;
  • searching for new insights extremal set theory, especially investigating M-part Sperner families and the notoriously hard diamond problem;
  • working on crossing numbers of graphs in di fferent models of drawing and develop algorithms for graph drawing under several criteria;
  • building spectral analysis of hypergraphs;
  • contributing to the mathematical foundations of phylogenetics;
  • investigating extremal and structural properties of tree indices;
  • discovering new probabilistic or spectral methods and applying them to complex networks."

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July 05, 2013
Qi Wang and Yi Sun are awarded a SC EPSCoR/IDeA GEAR grant

Qi Wang and Yi Sun (IMI) are awarded a 15-month SC EPSCoR/IDeA GEAR Grant totaling $100,000 for their research on: Experimentally Guided In-Silico Analysis of Cellular Aggregate Fusion in Bioprinting (GEAR-CRP). This grant includes subawards to Christopher Drake of MUSC and Feng Gu of Voorhees College.

"This project aims to develop an experimentally guided, hybrid model coupling agent-based mechanical models with continuum models for the regulatory and functioning proteins important for cell adhesion and motility to study cellular aggregate fusion (CAF). Mounting experimental evidence in CAF suggests that adhesion molecules like cadherins may also function as signaling molecules, triggering intracellular actomyosin activities and thereby inducing mechanical polarization among interfacial cells. Motivated by this, the PIs propose to extend the classical Differential Adhesion Hypothesis (DAH) to address the new findings in CAF by integrating models for molecular signaling pathways with that for the mechanical motion. In the hybrid model, signaling pathways, actomyosin dynamics and the cellular level mechanical polarization are modeled by continuum variables, whose evolution and transport are governed by systems of reaction and reaction-diffusion (RD) equations. The mechanical motion of the cellular system is described by a lattice model based on the kinetic Monte Carlo (KMC) algorithm. The free energy in the hybrid model depends not only on the mechanical component but also on the concentrations of various regulatory and functioning proteins. Communication between the mesoscopic scale lattice model and the continuum one is carried out via a suite of multiscale protocols. Equipped with efficient numerical algorithms and powerful CPU-GPU hybrid computing hardware, the model can handle up to a few million individual cells in in-vitro cell aggregate systems or in-vivo tissue structures."

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June 28, 2013
Linyuan Lu is awarded an Office of Naval Research (ONR) grant

Linyuan Lu (IMI) is awarded a 28-month Office of Naval Research (ONR) grant totaling $196,226 for his research on: Spectral, Probabilistic, and Information-theoretic Analysis for Graphs and Hypergraphs.

"In the modern information age that we live in, there is a growing need to respond to the challenges of quickly processing big data, often modeled by large-scale graphs (or hypergraphs) that represent various communication networks, sensor networks, social networks, etc. These information graphs are huge in volume, contain uncertainty and misalignment, and change dynamically. In response to such challenges, we herein propose a framework using spectral, probabilistic, and information-theoretic analysis for graphs and hypergraphs. Part of these methods, such as random graph theory, spectral graph theory, Szemerédi regularity Lemma, has already been in the cornerstone of the graph theory. Other part, especially for hypergraphs, is largely unknown. Even the known methods are often in separated domains. Our proposed framework will unite these methods so that they all respond to the challenges of dealing with large information networks."

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June 27, 2013
Binev, Dahmen, DeVore and Vogt are on the organizing committee for the BIRS 2014 workshop

Peter Binev (IMI, University of South Carolina), Nigel Browning (Pacific Northwest National Lab), Wolfgang Dahmen (IMI, RWTH Aachen), Ronald DeVore (IMI, Texas A & M University), Thomas Vogt (IMI, University of South Carolina), and Paul Voyles (University of Wisconsin, Madison) have been selected to organize a 5-day workshop "Imaging and Modeling in Electron Microscopy - Recent Advances" (14w5048) at the Banff International Research Station for Mathematical Innovation and Discovery in Banff, Canada, on May 18-23, 2014.

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June 26, 2013
Jerrold Griggs is awarded a Simons Foundation grant

Jerrold Griggs (IMI) is awarded a 5-year Simons Foundation grant totaling $35,000 for his research on: Poset-free Families.

"Building on earlier collaborations with G. O. H. Katona and L. Lu, Griggs has concentrated most of his efforts in recent years on developing and promoting the project of determining the maximum size La(n, P) of a family of subsets of an n-set that contains no (weak) subposet P. An ordered set analogue of Turán theory for graphs, this project can provide insight into the structure of such P-free families.

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June 06, 2013
Dekel, Kerkyacharian, Kyriazis and Petrushev publish article in IMI Preprint Series
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Shai Dekel, Gerard Kerkyacharian, George Kyriazis and Pencho Petrushev published their article: "Compactly Supported Frames for Spaces of Distributions in the Framework of Dirichlet Spaces" in the IMI Preprint Series (2013:04). Please see the link above to the full article and visit Preprints to see other articles in this series.

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June 01, 2013
Peter Binev is invited to give a plenary talk in Pasasena, CA

Peter Binev has been invited to give a plenary talk on "Recent developments of approximation theory and greedy algorithms" at the first workshop on Reduced Order Modeling in General Relativity held at the California Institute of Technology, Pasadena, California on June 6 and 7, 2013.

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May 07, 2013
Qi Wang, Xiaofeng Yang and Qian Wang are awarded a SC EPSCoR/IDeA GEAR grant

Qi Wang (PI) and Xiaofeng Yang (Co-PI) from IMI, and Qian Wang (Co-PI) from Chemistry are awarded a 14-month SC EPSCoR/IDeA GEAR Grant totaling $57,778 for their research on: Computational Investigation of Cell-Substrate Interaction Guided by Experiments (GEAR-CI).

"This proposal focuses on a systematical study of cell migration on patterned substrates and cell motility by integrating experiments, mathematical modeling and high performance numerical computations. The cell, as a fundamental functioning unit in all living organisms, is a "cosmos" made up of many active composite materials including a bilayer membrane, a nucleus and the complex cytoskeleton/cytoplasm combo which contains various protein laments, large aqueous cytosol and other organelles. These active components are coordinated through a cascade of signaling molecules and functional proteins in order for the cell to move. Developing a whole cell model to simulate cell movements on a substrate and its interaction with the surrounding environment will enable one to investigate cell motility as the result of the dynamics of signaling molecules and cytoskeleton-substrate coupling. It could have signi ficant impacts on manipulating cell movement so as to e ffect nano-medicine and medical treatments of certain diseases."

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April 25, 2013
Xinfeng Liu is awarded an ASPIRE-I grant from the Office of VPR

Xinfeng Liu (IMI) is awarded a 16-month ASPIRE-I grant funded by the Office of the Vice President for Research, USC, totaling $15,000 for his research on: Mathematical modeling and computational studies for proliferation kinetics of tumor growth.

"The objective of this proposal is to investigate the phenotypic transition in populations of cancer cells using mathematical modeling and computation integrated with experiments. Cancer stem cells (CSCs) are one focus of this research, which are defined as a small subset of cancer cells within a cancer that can self-renew and replenish the heterogeneous lineage of cancer cells that comprise the tumor. According to the original CSC hypothesis, CSCs can either self-renew through symmetric division or generate more differentiated progenitor cancer cells through asymmetric division. Progenitor cancer cells (PCs) lack self-renewal capacity but retain limited proliferation ability to produce fully differentiated cancer cells. The broad objectives of this proposal are:

  • to explore mathematical models with negative feedbacks for better understanding the dynamics of tumor growth and CSC populations;
  • to develop spatial models to investigate the 3D tumor sphere formation."
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April 08, 2013
Bondarenko Awarded Popov Prize

Andriy Bondarenko of the Kyiv National Taras Shevchenko University has been awarded the seventh Vasil A. Popov Prize for his outstanding contributions to Approximation Theory. He along with Radchenko and Viazovska solved the spherical t-design conjecture by Korevaar and Meyers. Bondarenko has also advanced powerful new ideas in other areas of Approximation Theory, in particular, in monotone rational approximation. The Prize was awarded to Bondarenko at the 14th International Conference on Approximation Theory in San Antonio, Texas, where he gave a plenary lecture entitled "Fixed Point Theorems in Approximation Theory”.

The Popov Prize honors the memory of Vasil A. Popov (1942-1990), the Bulgarian analyst best known for his work in Nonlinear Approximation. The Prize is awarded every three years to a young mathematician who has made outstanding research contributions to Approximation Theory and/or related areas. For more information please visit Popov Prize.

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April 01, 2013
Peter Binev is invited to give a plenary talk in San Antonio, TX

Peter Binev has been invited to give a plenary talk on "Nonlinear Approximation in High Dimensions" at the 14th International Conference on Approximation Theory in San Antonio, Texas, on April 7-10, 2013. This conference is a continuation of the earlier conferences on approximation theory that have traditionally been the main general international conference on this topic for the past 40 years, and have been well attended by mathematicians from academia, industry, and government.

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March 14, 2013
Livshitz and Temlyakov publish article in IMI Preprint Series
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E. Livshitz and Vladimir Temlyakov published their article "Sparse approximation and recovery by greedy algorithms" in the IMI Preprint Series (2013:03). Please see the link above to the full article and visit Preprints to see other articles in this series.

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January 31, 2013
Temlyakov publishes article in IMI Preprint Series
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Vladimir Temlyakov published his article "An inequality for the entropy numbers and its application" in the IMI Preprint Series (2013:02). Please see the link above to the full article and visit Preprints to see other articles in this series.

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January 10, 2013
Temlyakov publishes article in IMI Preprint Series
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Vladimir Temlyakov published his article "A Remark on Covering" in the IMI Preprint Series (2013:01). Please see the link above to the full article and visit Preprints to see other articles in this series.

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