We focus on the aspect of Hilbert Sixth Problem concerning the kinetic theory for gases. There are two parts to this Problem. The first part is the derivation of the Boltzmann equation from the Newtonian interacting particle systems, and the second part concerns the relation between the Boltzmann equation and the fluid dynamics. Both involves some form of averaging. The derivation of the Boltzmann equation is both philosophically and mathematically challenging and is historically important. For instance, it is not clear how the probabilistic element comes in and the scaling involved in the averaging is very subtle. The relation between the Boltzmann equation and the fluid dynamics is a rich subject; the Boltzmann equation is known to be able to explain observed phenomena that the traditional fluid equations such as Navier-Stokes cannot. We will discuss these topics, survey the recent progresses and raise open problems.

In solving unsteady PDEs in multi-dimensions, accuracy, stability, and efficiency are main concerns in constructing temporal discretization. Moreover, extra care has to be exercised in dealing with nonlinear, high-order, or stiff PDE systems. This minisymposium will focus on recent advances on a variety of time integration methods, such as operator splitting methods, integration factor methods, and alternating direction implicit methods. It intends to create a forum for researchers from different fields to discuss on challenging issues such as the stability improvement via by implicitly treating some subsystems, the computation efficiency of implicit schemes in multi-dimensions, and the spatial treatment of irregular domains/boundaries. Emphasis will be placed not only on computational algorithms and analysis, but also on their applications to emerging physical, engineering, and biological problems.

Lili Ju, University of South Carolina
Amanda Diegel, University of Tennessee
Zhu Wang, University of South Carolina
Chuan Li, University of Alabama, Tuscaloosa

Inverse Problems for differential equations play an important role in both pure and applied mathematics including areas such as hydrodynamics, optical fibers, dissipative processes, gas and oil exploration, to name a few. Mathematically, such problems come in different contexts while sharing the common feature that a cause for an observed effect needs to be determined. In recent years, a subtle link between coefficient recovery of PDEs and control theoretic concepts such as controlability has been established. We propose a session where new results from a variety of viewpoints are presented through a broad array of different mathematical methods and approaches, each tuned to a particular formulation of the inverse problem at hand.

Ricardo Weder, Universidad Nacional Autónoma de Mexico
Shitao Liu, Clemson University
Maxim Zinchenko, University of New Mexico, Albuquerque

Inverse and imaging problems arise in diverse areas of science, medicine, and engineering, etc. The mathematical studies of inverse and imaging problems pose significant analytical and computational challenges. This mini-symposium seeks to bring together researchers to promote exchange of ideas, and present recent developments on the mathematical analysis and novel computational methods in this area. We would like to organize two sessions, and the speakers listed below have confirmed to participate.

Yunmei Chen, University of Florida
Zuhair Nashed, University of Central Florida
Peijun Li, Purdue University
Daniel Onofrei, University of Houston

Biological systems are complex and span multiple scales. The mini-symposium includes new research on mathematical modeling of molecular networks, cellular phenotypes and organs in cancer. The speakers will introduce new models/equations, analysis schemes, and discuss how the mathematical analysis advances our understanding and practice of biology and medicine.

Nidhal Bouaynaya, Rowan University
Etienne Baratchart,, INRIA Bordeaux, France
Olivier Saut, INRIA Bordeaux, France
Dimah Dera, Rowan University

Conservation laws are important nonlinear PDEs arising from continuum mechanics. In this mini-symposium we bring together researchers working on theory and applications of these and related systems to exchange new results and new ideas, and to promote collaboration between them.

Robin Young, University of Massachusetts
Ralph Saxton, University of New Orleans
Yanni Zeng, University of Alabama at Birmingham
Geng Chen, Georgia Institute of Technology

Partial differential equations play a fundamental role in the mathematical modeling of many physical phenomena. Closed form solutions of such modeling equations are extremely rare. Hence, the primary mechanism for the realization of the mathematical model is the numerical approximation of the modeling partial differential equations. In this minisymposium we bring together active researchers in the numerical approximation of partial differential equations to present, and discuss, their current research in this field.

Yanzhi Zhang, Missouri University of Science and Technology
Feng Bao, Oak Ridge National Laboratory
Hong Wang, University of South Carolina
Song Chen, University of Wisconsin at La Crosse

This minisymposium includes theoretical and numerical methods applied to optimal control, optimization, inverse problems and applications. A non exhaustive list of topics includes: well-posedness and stability of complex systems, optimal control of ODEs and PDEs, linear and nonlinear optimization, parameter estimation, and advanced numerical methods with applications.

Xiang Wan, University of Virginia
Stephen Guffey , Western Kentucky University
Catalin Trenchea , University of Pittsburgh
Mehdi Vahab, Florida State University

Statistical learning theory is an interdisciplinary area at the intersection of mathematics, statistics, and machine learning. It deals with the problem of finding predictive functions based on data. As modern technologies allows to collect data much easier, big data processing and high dimensional data analysis becomes central to knowledge discovery and play essential roles in many fields of modern sciences. This has driven a lot of research in the context of variable selection, dimension reduction, and online learning. In this symposium, we would like to take this opportunities to exchange research ideas, report current advances, and discuss existing challenges in statistical learning theory. The topics will cover functional regression, online learning, interactive component modeling.

Jun Fan, University of Wisconsin-Madison
Yiming Ying, University at Albany, State University of New York
Ning Zhang, Middle Tennessee State University

This session will provide opportunities to present and exchange ideas on new tensor methods based on optimization and probability for established application areas in signal and image processing as well as in new application areas in machine learning, compressed sensing and big data science.

Christina Glenn, University of Alabama at Birmingham
Shuchin Aeron, Tufts University
Xiaofei Wang, Northeast Normal University, China and University of Alabama at Birmingham

Variational method has become an important tool for constructing models to accomplish different tasks in image processing. During the last twenty years, quite a few high order variational models have been proposed to fulfill even more advanced imaging tasks. In these models, curvature of curves or surfaces was often incorporated to constitute an appropriate regularizer, which makes these models very intractable numerically. The aim of this minisymposium is to provide a forum to stimulate discussions and establish collaborations for further developments in both the modeling and numerical methods of variational models, especially curvature based ones, in mathematical imaging.

SungHa Kang, Georgia Institute of Technology
Xiaojing Ye, Georgia State University
Daozhi Han, Florida State University
Wei Zhu, University of Alabama, Tuscaloosa

James L. Moseley, West Virginia University, "The Discrete Agglomeration Model:The Moment Problem for the Autonomous Quadratic Kernel"
Israel Ncube, Alabama A & M University, "Stability in a distributed delay differential equation"
Howard Richards, Marshall University, "Metastable Decay of Nearest-Neighbor Ising Ferromagnets in the Hyperbolic Plane"
Tomer Lancewicki, University of Tennessee, "Multi-target shrinkage estimation for covariance matrices"

Caleb Moxely, University of Alabama at Birmingham
Christina Glenn, University of Alabama at Birmingham
Alzaki Fadlallah, University of Alabama at Birmingham

Supercomputers, capable of performing 10^16 floating-point operations per second (34 PFlops), connect millions of computing cores by complex networks. In the case of the Tianhe-2, 3.12 million cores require networking. In 2019 when Exascale systems emerge, more than 100 million cores will need to be connected and the traditional intuition with simple networks will unlikely survive to produce scalable systems. To advance, we must leverage on the, active and young, graph theory, conceptually and computationally, to seek for new breakthrough in network topologies and routing protocols.

For a regular graph of N vertices each with k edges, we note it as Nkk , e.g., for a regular graph with N=32 vertices each with k=5 edges, we note it as 32k5. After discovering a series of perfectly optimized (in terms of the graph diameter and average vertex-vertex edge distances) regular graphs with N=4,8,16,32 for the appropriate corresponding node degrees we embed them to generate much larger composite hierarchical graphs, e.g., 16k432k5 or 8k316k4 32k5. These embedded graphs, with tens of thousands of vertices, are used to design supercomputer interconnection networks. With the metrics we introduced to measure the network-performance-relevant properties of graphs, we compare our quasi-optimal embedded graphs with many widely adopted networks for supercomputers.

In solving unsteady PDEs in multi-dimensions, accuracy, stability, and efficiency are main concerns in constructing temporal discretization. Moreover, extra care has to be exercised in dealing with nonlinear, high-order, or stiff PDE systems. This minisymposium will focus on recent advances on a variety of time integration methods, such as operator splitting methods, integration factor methods, and alternating direction implicit methods. It intends to create a forum for researchers from different fields to discuss on challenging issues such as the stability improvement via by implicitly treating some subsystems, the computation efficiency of implicit schemes in multi-dimensions, and the spatial treatment of irregular domains/boundaries. Emphasis will be placed not only on computational algorithms and analysis, but also on their applications to emerging physical, engineering, and biological problems.

Yingjie Liu , Georgia Institute of Technology
Wei Guo, Michigan State University
Taras Lakoba, University of Vermont
Xinfeng Liu, University of South Carolina

Inverse Problems for differential equations play an important role in both pure and applied mathematics including areas such as hydrodynamics, optical fibers, dissipative processes, gas and oil exploration, to name a few. Mathematically, such problems come in different contexts while sharing the common feature that a cause for an observed effect needs to be determined. In recent years, a subtle link between coefficient recovery of PDEs and control theoretic concepts such as controlability has been established. We propose a session where new results from a variety of viewpoints are presented through a broad array of different mathematical methods and approaches, each tuned to a particular formulation of the inverse problem at hand.

Ian Knowles, University of Alabama at Birmingham
Roberto Triggiani, University of Memphis
Sergey Avdonin, University of Alaska, Fairbanks

Inverse and imaging problems arise in diverse areas of science, medicine, and engineering, etc. The mathematical studies of inverse and imaging problems pose significant analytical and computational challenges. This mini-symposium seeks to bring together researchers to promote exchange of ideas, and present recent developments on the mathematical analysis and novel computational methods in this area. We would like to organize two sessions, and the speakers listed below have confirmed to participate.

Sung Ha Kang, Georgia Institute of Technology
Jianfeng Cai, University of Iowa
Yuanchang Sun, Florida International University
Lars Ruthotto, Emory University

This minisymposium will focus on computational strategies for systems that involve multiple length/time scales and multiple physics. The complexity of structure and phenomena of these systems have had significant impacts on many scientific disciplines. This minisymposium brings together researchers from PDEs, analysis, mathematical physics, numerical analysis, and scientific computing to address the difficult challenges that are presented by these issues. To address the importance of approaches and exciting new developments, we will focus on multiscale modeling and simulations in atmosphere and ocean sciences, dynamical systems, inverse problems in seismology including heterogeneous multiscale methods, domain decomposition methods, and many other methods.

Yoonsang Lee, New York University
Christina Frederick, Georgia Institute of Technology
Duk-soon Oh, Rutgers University
Seong Jun Kim, Georgia Institute of Technology

Biological systems are complex and span multiple scales. The mini-symposium includes new research on mathematical modeling of molecular networks, cellular phenotypes and organs in cancer. The speakers will introduce new models/equations, analysis schemes, and discuss how the mathematical analysis advances our understanding and practice of biology and medicine.

Elizabeth Scribner, University of Alabama at Birmingham
Pedro Lowenstein, University of Michigan
Thierry Colin, Bordeaux INP and INRIA, France
Hassan Fathallah-Shaykh, University of Alabama at Birmingham

Conservation laws are important nonlinear PDEs arising from continuum mechanics. In this mini-symposium we bring together researchers working on theory and applications of these and related systems to exchange new results and new ideas, and to promote collaboration between them.

Shuang Miao, University of Michigan
Huihui Zeng, Harvard University and Tsinghua University
Yilun Wu, Indiana University
Kun Zhao, Tulane University
Tao Luo, Georgetown University

Partial differential equations play a fundamental role in the mathematical modeling of many physical phenomena. Closed form solutions of such modeling equations are extremely rare. Hence, the primary mechanism for the realization of the mathematical model is the numerical approximation of the modeling partial differential equations. In this minisymposium we bring together active researchers in the numerical approximation of partial differential equations to present, and discuss, their current research in this field.

Javier Ruiz-Ramirez, Clemson University
Lunji Song, Lanzhou University
Hans-Werner van Wyk, Florida State University
Shuhan Xu, Clemson University

This minisymposium includes theoretical and numerical methods applied to optimal control, optimization, inverse problems and applications. A non exhaustive list of topics includes: well-posedness and stability of complex systems, optimal control of ODEs and PDEs, linear and nonlinear optimization, parameter estimation, and advanced numerical methods with applications.

Cécile Dobrzynski, Institut Polytechnic of Bordeaux
Chaoxu Pei, Florida State University
Yongjin Lu, Virginia State University

This session will provide opportunities to present and exchange ideas on new tensor methods based on optimization and probability for established application areas in signal and image processing as well as in new application areas in machine learning, compressed sensing and big data science.

Luke Oeding, Auburn University
Shannon Starr, University of Alabama at Birmingham
Alexandra Fry, University of Alabama at Birmingham
Carmeliza Navasca, University of Alabama at Birmingham

Alzaki Fadlallah, University of Alabama at Birmingham, "Linear elliptic systems with nonlinear boundary conditions without Landesman-Lazer conditions"
Mohammad H Akanda, Auburn University, "A few model problems as symmetric positive systems"
Muhammad Mohebujjaman, Clemson University, "Numerical analysis and testing of a fully discrete, decoupled algorithm for MHD in Elsasser variable"
Rachel Grotheer, Clemson University, "Application of the Reduced Basis Method to the Forward Problem of Hyperspectral Diffuse Optical Tomography"
Ali Darwish, University of Alabama at Birmingham, "Method for Comparing Saliency Maps in Computer Vision"
Serdar Cellat, Florida State University, "Towards a Diagnostic Tool for Facial Dysmorphia"

Sirani M. Perera, Daytona State College, "Signal Flow Design Approach to Orthogonal Radix-2 DCT-DST Algorithms"
Nguyen Hoang, University of West Georgia, "A fast algorithm for computing integration matrices for spectral methods"
Hyunju Kim, North Greenville University,"Computation of Energy Release Rate Using Non-Uniform Rataional B-Spline Geometrical Mapping Method with Multiple Patches"
Mahmoud DarAssi, Princess Sumaya University for Technology, Sedimentation and Thermophoresis Effects in the Presence of Convection in Colloidal Suspensions"

Orhan Akal, Florida State University, "Agent Based Modeling for Stock Markets"
Mohammad H. Akanda, Auburn University, "Variants of linear poroelasticity equation as symmetric positive systems"
Alexandra Fry, University of Alabama at Birmingham, "Compressed sensing in a multilinear sparse system of genomic interactions"
Christina Glenn, University of Alabama at Birmingham, "Symmetric Tensor Outer Product Decomposition"
Ingyu Lee, Troy University, "A Recursive Iterative Preconditoner for Conjugate Gradient Algorithm"
Yaobin Ou, Renmin University of China, "Global classical solutions to the vacuum free boundary problem of 1-D full Navier-Stokes equations with large initial data"
Duc Nguyen, University of Alabama, Tuscaloosa, "Time-domain matched interface and boundary methods for transverse electric modes with complex dispersive interfaces"
Mohamed Selim, University of Alabama at Birmingham, "An Unstructured Cell-Center Finite Volume Approach for Structural Dynamics"
John Vastola, University of Central Florida, "Solving Differential Equations via An Exotic Integral Transform"

Xiang Wan, University of Memphis, "Global Well-Posedness and Uniform Stability of a Nonlinear Thermo-Elastic PDE System"
Javier Ruiz Ramirez, Clemson University, "Darcy fluid flow with deposition"
Etienne Baratchart, INRIA Bordeaux, France, "Modeling of in vivo experiments of metastatic initiation and tumor-tumor spatial interactions"
Amanda Diegel, University of Tennessee, "Analysis of a Second-Order in Time Mixed Method for the Cahn-Hilliard Equation"

An appearance of flutter in oscillating structures is an endemic phenomenon. Most common causes are vibrations induced by the moving flow of a gas (air, liquid) which is interacting with a structure. Typical examples include: turbulent jets, vibrating bridges, oscillating facial palate in the onset of apnea. The intensity of the flutter depends heavily on the speed of the flow (subsonic, transonic or supersonic regimes). Thus, reduction or attenuation of flutter is one of the key problems in aeroelasticity with application to a variety of fields including aerospace engineering, structural engineering, medicine and life sciences.

Mathematical models describing this phenomenon involve coupled systems of partial differential equations (Euler Equation and nonlinear plate equation) with interaction at the interface - which is the boundary surface of the structure. The aim of this talk is to present a mathematical theory describing: (1) qualitative properties of the resulting dynamical systems (existence, uniqueness and robustness of weak solutions), (2) asymptotic stability and associated long time behavior that includes the study of global attractors, (3) feedback control strategies aiming at the elimination or attenuation of the flutter.

Since the properties of the flutter depend heavily on the speed of the flow (subsonic, transonic or supersonic), it is natural that the resulting mathematical theories will be very different in the subsonic and supersonic regimes. In fact, supersonic flows are known for depleting ellipticity from the corresponding static model. Thus, both wellposedness of finite energy solutions and long time behavior of the model have been open questions in the literature. The results presented include: (1) Existence, uniqueness and Hadamard wellposedness of finite energy solutions; (2) Existence of global and finite dimensional attracting sets for the elastic structure in the {absence of any mechanical dissipation}; (3) Strong convergence to multiple equilibria for the subsonic model subjected to a frictional damping imposed on the structure. As a consequence, one concludes that the supersonic flow alone (without any dissipation added to the elastic structure) provides some stabilizing effect on the plate by reducing asymptotically its dynamics to a finite dimensional structure. However, the resulting "dynamical system" may be exhibiting a chaotic behavior. In the subsonic case, instead, a feedback control which provides a sufficient damping of the structure eliminates asymptotically the flutter.

Linear systems that arise in large scale inverse problems are very challenging to solve. In addition to the problem being large scale, the underlying mathematical model is often ill-posed, which results in highly ill-conditioned coefficient matrices. Noise and other errors in the measured data can be highly magnified in computed solutions. Regularization methods are often used to overcome this difficulty. In this talk we describe hybrid regularization approaches, which combine matrix factorization methods with iterative solvers that can be efficient for large scale problems. Applications from image processing will be used to illustrate the effectiveness of hybrid methods.

In solving unsteady PDEs in multi-dimensions, accuracy, stability, and efficiency are main concerns in constructing temporal discretization. Moreover, extra care has to be exercised in dealing with nonlinear, high-order, or stiff PDE systems. This minisymposium will focus on recent advances on a variety of time integration methods, such as operator splitting methods, integration factor methods, and alternating direction implicit methods. It intends to create a forum for researchers from different fields to discuss on challenging issues such as the stability improvement via by implicitly treating some subsystems, the computation efficiency of implicit schemes in multi-dimensions, and the spatial treatment of irregular domains/boundaries. Emphasis will be placed not only on computational algorithms and analysis, but also on their applications to emerging physical, engineering, and biological problems.

Xiaofeng Yang, University of South Carolina
Yanzhi Zhang, Missouri University of Science and Technology
Yulong Xing, University of Tennessee
Shan Zhao, University of Alabama, Tuscaloosa

Inverse Problems for differential equations play an important role in both pure and applied mathematics including areas such as hydrodynamics, optical fibers, dissipative processes, gas and oil exploration, to name a few. Mathematically, such problems come in different contexts while sharing the common feature that a cause for an observed effect needs to be determined. In recent years, a subtle link between coefficient recovery of PDEs and control theoretic concepts such as controlability has been established. We propose a session where new results from a variety of viewpoints are presented through a broad array of different mathematical methods and approaches, each tuned to a particular formulation of the inverse problem at hand.

Roger Nichols, University of Tennessee at Chattanooga
Alexander Bukhgeym, Wichita State University
Rudi Weikard, University of Alabama at Birmingham

This session concerns computation, application of nonlinear differential equations.

Jerry L. Bona, University of Illinois at Chicago
Hongqiu Chen, University of Memphis
Ohannes Karakashian, University of Tennessee
Hassan Fathallah-Shaykh, University of Alabama at Birmingham

Conservation laws are important nonlinear PDEs arising from continuum mechanics. In this mini-symposium we bring together researchers working on theory and applications of these and related systems to exchange new results and new ideas, and to promote collaboration between them.

Kasia Saxton, Loyola University
Allen Tesdall, CUNY Staten Island
Alexey Miroshnikov, University of Massachusetts
Greg Lyng, University of Wyoming

Partial differential equations play a fundamental role in the mathematical modeling of many physical phenomena. Closed form solutions of such modeling equations are extremely rare. Hence, the primary mechanism for the realization of the mathematical model is the numerical approximation of the modeling partial differential equations. In this minisymposium we bring together active researchers in the numerical approximation of partial differential equations to present, and discuss, their current research in this field.

Zhu Wang, University of South Carolina
Hoang Tran, Oak Ridge National Laboratory
Jinhong Jia, Shandong University
Su Yang, University of South Carolina

This minisymposium includes theoretical and numerical methods applied to optimal control, optimization, inverse problems and applications. A non exhaustive list of topics includes: well-posedness and stability of complex systems, optimal control of ODEs and PDEs, linear and nonlinear optimization, parameter estimation, and advanced numerical methods with applications.

Philippe Laval, Kennesaw State University
Thomas Robacker , East Tennessee State University
Ana-Maria Croicu, Kennesaw State University

Koffi Fadimba, University of South Carolina Aiken, "Error Estimates for a Regularization of a Formulation of the Porous Medium Equation"
Thinh Kieu, University of North Georgia, "Two-phase Generalized Forchheimer Flows in Porous Media"
Jonas Holdeman, "On the Physics of Incompressible Fluids"
Khalid Alammar, King Saud University, "Effect of Round Cavities on Flow and Heat Transfer Characteristics in Converging Pipes: A Numerical Study"

Daniel Fong, U.S. Merchant Marine Academy, "Modeling of Ischemia Reperfusion and Postconditioning"
Emre Esenturk, University of Warwick, "On the Coffee Stain Problem"
Mikhail Khenner, Western Kentucky University, "Mathematical model of electromigration-driven evolution of the surface morphology and composition for a bi-component solid film"
Nick Kirby, Austin Peay State University, "Step-flow model stability in the presence of electromigration during evaporation"

James Lambers, University of Southern Mississippi, "High-Order Time-Stepping through Rapid Estimation of Block Gaussian Quadrature Nodes"
Ogugua Onyejekwe, Indian River State College, "The Application of Homotopy Analysis Method for the Solution of Time-Fractional Diffusion Equation with A Moving Boundary"
Hashim Saber, University of North Georgia, "A Model Reduction Algorithm for Simulating Sedimentation Velocity Analysis"