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2016 News Archive

September 30, 2016
Czabarka and Székely give talks in New Delhi, India

Éva Czabarka and László Székely gave invited talks at the International Conference on Current Trends in Graph Theory and Computing, September 17-19, 2016, New Delhi, India. For more information, please visit: http://sau.int/~ctgtc2016/

September 23, 2016
Hong Wang and Guiren Wang are awarded a National Science Foundation grant

Hong Wang (IMI) and Guiren Wang (Mechanical Engineering) are awarded a 3-year NSF grant totaling $249,999 for their project: Fractional PDEs and related nonlocal models: fast numerical methods, analysis, and application.

"Nonlocal models such as fractional partial differential equations (FPDEs), fractional Laplacian, and peridynamics are emerging as powerful tools for modeling challenging phenomena including anomalous transport and long-range time memory or spatial interactions in a wide range of fields such as biology, physics, chemistry, finance, engineering, and solute transport in groundwater. They open up opportunities for modeling multiphysics phenomena, e.g. seamless transition from wave propagation to diffusion, or from local to non-local dynamics. In other words, these models provide more appropriate description of many important problems in applications than integer-order PDE models do.
Two of the main reasons that nonlocal models have not been used extensively so far are as follows: (i) They generate numerical schemes with dense matrices and solutions with strongly local behavior, which are significantly more expensive to solve numerically than traditional integer-order PDE models. A naive simulation of a three-dimensional linear problem with a moderate number of grid points may take state of the art supercomputers hundreds of years to finish and so deemed unrealistic. (ii) Nonlocal models introduce mathematical difficulties, which were not encountered in the context of integer-order PDEs.
It is proposed to effectively address both points at this juncture. The fast numerical methods proposed herein will provide significant computational benefits for nonlocal models, and will facilitate their applications. Preliminary numerical experiments of a simple three-dimensional fractional PDE showed that the proposed method reduced the CPU time from 2 months and 25 days by a traditional method to 5.74 seconds and reduced storage significantly. The proposed mathematical and numerical analysis will provide a solid theoretical foundation for nonlocal models and related numerical approximations."

September 12, 2016
Lili Ju and Zhu Wang are awarded a US Department of Energy grant

Lili Ju and Zhu Wang (IMI) are awarded a 3-year US DOE grant totaling $584,495 for their project: Grid Generation, Coupling Strategies, and Spatially-dependent Time Stepping for Ocean–tidal/Estuary Systems and other ESM Components. This is in collaboration with Max Gunzburger, John Burkardt and Janet Peterson of Florida State University.

"Multi-resolution meshes are an important feature of and a major contributor to gains in efficiency and fidelity in modern ESMs. We have already made significant contributions in this regard in that a centroidal Voronoi tessellation (CVT) meshing technology we developed is now used in the ocean component of MPAS and in the Felix-Stokes ice-sheet model we have developed and which will be incorporated into ACME. High quality, highly nonuniform meshes will be even more important for the seamless incorporation of tidal and estuary systems into ESMs under current development. Other needed improvements are in means for coupling different climate system components and the development of spatially-dependent time stepping strategies. The project addresses these issues that are crucial to the development of improvements in ACME components and in their coupling."

September 08, 2016
Czabarka and Szekely co-organize AMS-MRC Workshop on Crossing Numbers of Graphs
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In the framework of the Mathematics Research Communities program of the American Mathematical Society, a workshop "Beyond Planarity: Crossing Numbers of Graphs" will be held June 11–18, 2017 at Snowbird, Utah. Individuals within one to two years prior to the receipt of their PhDs, or up to five years after receipt of their PhDs, are welcome to apply. The MRC program is open to individuals who are U.S. citizens as well as to those who are affiliated with U.S. institutions. Women and underrepresented minorities are especially encouraged to apply. A few international participants may be accepted. Individuals who can cover their MRC participation costs from other sources of funding should contact AMS Senior Program Coordinator Steven Ferrucci at sxf@ams.org for instructions on how to apply. All applicants will be notified of their status by May 1, 2017.

We look for participants with interests in some of the following fields: graphs, planar graphs, combinatorial geometry, design and complexity of algorithms. Previous experience with crossing numbers is not required. The workshop will provide opportunities for the participants to build social and collaborative networks through which they can inspire and sustain each other in their work. For more information on the workshop, see:
http://www.ams.org/programs/research-communities/mrc-17
http://www.ams.org/programs/research-communities/2017MRC-2
The application website is: https://www.mathprograms.org/db/programs/455

The organizers are:
Éva Czabarka, University of South Carolina
Silvia Fernández-Merchant, California State University, Northridge
Gelasio Salazar, Universidad Autónoma de San Luis Potosí, Mexico
Marcus Schaefer, DePaul University
László A. Székely, University of South Carolina

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September 04, 2016
Ivanov and Petrushev publish article in IMI Preprint Series
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Kamen Ivanov and Pencho Petrushev published their article "Harmonic Besov and Triebel-Lizorkin Spaces on the Ball" in the IMI Preprint Series (2016:02). Please see the link above to the full article and visit Preprints to see other articles in this series.

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July 07, 2016
László Székely and Linyuan Lu are awarded a National Science Foundation grant

László Székely and Linyuan Lu (IMI) are awarded a 3-year NSF grant totaling $180,000 for their project: Extremal and Probabilistic Combinatorics with Applications II.

"The investigators continue their work on extremal graph, set, and hypergraph theory, in particular on Turan type problems, forbidden configurations in hypergraphs and matrices. They investigate connections between graph theory and geometry, on the one hand through studying Ricci curvature on graphs, on the other hand studying crossing numbers of graphs and related incidence problems. Understanding random structures is the way to understand typical behavior of discrete structures. One focus of the proposal is the spectral analysis of random hypergraphs, another is further use of the lopsided Lovasz Local Lemma for asymptotic enumeration. The investigators study graph and tree indices originating in chemical graph theory, and will apply combinatorial and probabilistic techniques to phylogenetics and to the theory of complex network."

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June 14, 2016
Yi Sun is awarded a National Science Foundation grant

Yi Sun (IMI) is awarded a 3-year National Science Foundation (NSF) grant totaling $165,741 for his research on: Hybrid Computational Methods and Algorithms for Complex Biological Systems.

"This project aims to develop new hybrid computational methods and algorithms to study complex biological systems and problems arising in biomaterials and tissue engineering. Two thrusts are focused: (a) cellular aggregate fusion via cell self-assembly; (b) bacterial patterns formation in biofilm growth. For the thrust (a), recent experimental evidence in the fusion processes suggests that adhesion molecules like cadherins can also function as signaling molecules, triggering intracellular actomyosin activities and thereby inducing mechanical polarization among interfacial cells. The PI proposes to investigate how these factors effect the fusion processes by integrating hybrid models for molecular signaling pathways with those for mechanical motion. In particular, 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. Whereas, mechanical motion of the cellular system is described by an on-lattice model based on the kinetic Monte Carlo (KMC) algorithm. Communication between the lattice model and the continuum scale RDs is carried out via a suite of multiscale protocols.
For the thrust (b), the PI proposes to study three major factors that effect the formation of bacterial patterns in biofilms: bacterial chemotaxis, bacterial motility, and direct interaction between bacteria. In the proposed hybrid model, each of bacteria is characterized by an individual off-lattice particle or an elongated rod shape with its location, orientation, and its state of stress exerted by local environment, while the dynamics of extracellular polymeric substances (EPS) in the environment is described by continuously changing fields. The hybrid model is described by a system of partial differential equations (PDEs)."

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March 14, 2016
Cooper on WACH FOX 57!

On Pi day, March 14th, Joshua Cooper represented the University of South Carolina on "Good Day Columbia," a local TV morning show on WACH FOX 57. To see the recorded segment, please visit: http://wach.com/news/local/good-day-columbia-solves-an-equation-using-pi

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March 04, 2016
Temlyakov is awarded a National Science Foundation grant

Vladimir Temlyakov (IMI) is awarded a 1-year National Science Foundation (NSF) grant totaling $26,298 for his project: Constructive Approximation and Harmonic Analysis.

"This proposal requests funding from the National Science Foundation to support the Intensive Research Program "Constructive Approximation and Harmonic Analysis" to be held at the Centre de Recerca Matematica (CRM) in Barcelona, Spain, during the period March-July, 2016. This Research Program will concentrate on the area of Harmonic Analysis and Approximation Theory. The emphasis will be put on constructive high-dimensional methods of approximation and representation. Recently, driven by applications in engineering, biology, medicine and other areas of science new challenging problems have appeared. The common feature of these problems is high, really high, dimensions. Classical methods do not work for such dimensions. It is a hot rapidly developing area of mathematics and numerical analysis where researchers try to understand which new approaches may work. The aim of the Program is to bring together several groups of mathematicians working in several areas of analysis and numerical analysis to try to make a breakthrough in high-dimensional problems and to establish fruitful collaborations in the future. The Program activity will impact the signal/image processing community; the numerical mathematics, in particular the approximation theory, community; the learning theory community; and the optimization theory community."

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February 29, 2016
Czabarka and Szekely are plenary speakers at IntersectionFest: The Workshop on Interesecting Set Systems

Eva Czarbarka and Laszlo Szekely (IMI) are among six plenary speakers at IntersectionFest: The Workshop on Intersecting Set Systems, hosted by Virginia Commonwealth University on March 7 - 9, 2016. This workshop, supported in part by the Simons Foundation, is organized by Glenn Hurlbert and Vikram Kamat, Department of Mathematics and Applied Mathematics, VCU.

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January 26, 2016
Wang invited to present a colloquium at the University of North Carolina, Greensboro
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Qi Wang is invited to present a Joint JSNN and Department of Mathematics & Statistics Colloquium at the University of North Carolina, Greensboro, on Thursday, February 4, 2016. His talk on "Active matter and complex biological systems" begins at 4:00 PM. For details, download the colloquium poster.

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January 05, 2016
Shen, Zhao, Fuente-Núñez, Wang, Hancock, Roberts, Ma, Wang and Haapasalo publish article in IMI Preprint Series
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Ya Shen, Jia Zhao (IMI), César de la Fuente-Núñez, Zhejun Wang, Robert E. W. Hancock, Clive R. Roberts, Jingzhi Ma, Qi Wang (IMI) and Markus Haapasalo published their article "Development and Experimental Validation of a Model for Oral Multispecies Biofilm Recovery after Chlorhexidine Treatment" in the IMI Preprint Series (2016:01). Please see the link above to the full article and visit Preprints to see other articles in this series.

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