Where: CSIC 4122

Speaker: Professor Jian-Guo Liu, Duke University, Physics and Mathematics

Abstract: In this talk, I will present some mathematical results for a coagulation-fragmentation model used to study animal group-size statistics. There is no detailed balance for this coagulation-fragmentation model and hence the current mathematical theory can not be usedto study this problem. Based on the complete Bernstein function theory, we establish global existence, convergence to the steady solution, asymptotic behavior, and completely monotonicity property of the steady solution

for this coagulation-fragmentation model.

This is a joint work with Pierre Degond and Bob Pego.

Where: CSIC 4122

Speaker: Professor Bo Li, University of California, San Diego, Department of Mathematics

Abstract: The structure and dynamics of biomolecules such as DNA and proteins determine the functions of underlying biological systems. Modeling biomolecules is, however, extremely challenging due to their enormous complexity. Recent years have seen the initial success of variational implicit-solvent models (VISM) for biomolecules. Central in VISM is an effective free-energy functional of all possible solute-solvent interfaces, coupling together the solute surface energy, solute-solvent van der Waals interactions, and electrostatic contributions. Numerical relaxation by the level-set method of such a functional determines biomolecular equilibrium conformations and minimum free energies. Comparisons with experiments and molecular dynamics simulations demonstrate that the level-set VISM can capture the hydrophobic hydration, multiple dry and wet states, and many other important solvation properties. This talk begins with a description of the level-set VISM and continues to present new developments around the VISM. These include: (1) the coupling of solute molecular mechanical interactions in the VISM; (2) the effective dielectric boundary forces; and (3) the solvent fluid fluctuations. Mathematical theory and numerical methods are discussed, and applications are presented. This is joint work mainly with J. Andrew McCammon, Li-Tien Cheng, Joachim Dzubiella, Jianwei Che, Zhongming Wang, Shenggao Zhou, and Zuojun Guo.

Where: CSIC #4122

Speaker: Prof. Anna Mazzucato, Department of Mathematics, Penn State University

Abstract: We construct explicit approximate Green's functions for time-dependent, linear Fokker-Planck equations in terms of Dyson series, Taylor expansions, and exact commutator formulas. Under a uniform parabolicity condition on the operator, the associated approximate solution to the initial-value problem is accurate in terms of Sobolev norms to arbitrary order in time in the short-time limit. Bootstrap allows to extend the construction to large time. The algorithm works well also for certain types of degenerate equations with vanishing and unbounded coefficients, such as those arising in pricing of contingent claims. The advantage of this method is that it requires only numerical integration and appears very stable numerically.

This is joint work with Victor Nistor and Wen Cheng.

Where: CSIC #4122

Where: CSIC #4122

Speaker: Prof. Pedro Lowenstein, Department of Neurosurgery and Department of Cell and Developmental Biology, University of Michigan School of Medicine

Abstract: Malignant brain tumors are rapidly progressive and fatal. Even though they do not metastasize outside the brain, following neurosurgical resection, radiotherapy and chemotherapy, tumors inevitably recur. Glioma genomes are highly unstable, with elevated genomic mutations and chromosomal abnormalities. However, genomic subtype classifications have been slow to provide increased understanding or effective treatments. We propose a new approach to understanding glioma tumors. Namely, by characterizing glioma growth patterns we aim to determine how glioma tumors can grow in a tissue with no extracellular space while causing minor symptoms for long times, and how individual growth patterns determine response to treatments.

Glioma cells can grow on blood vessels, myelin fibers, subpially, perineuronally and through interstitial space. The molecular basis of such growth patterns remains unknown. We are currently characterizing growth patterns of individual rodent and human glioma cells, and glioma stem cell like cells. We identified a series of cells (both rodent and human) which grow exclusively along blood vessels. We have characterized their detailed growth patterns, and determined the microenvironmental basis which determines glioma growth. Understanding glioma cell behavior has allowed us to uncover how cellular growth patterns determine the progression, microenvironmental interactions with the innate and adaptive immune systems, and the responses to antiangiogenic treatment.

In the long run we are interested in building abstract mathematical models to capture the behavioral specificity and variability of glioma growth, and use mathematical models to help us predict tumor progression and treatment response.

Where: CSIC #4122

Speaker: Prof. Richard Tsai, Department of Mathematics and Institute for Computational Engineering and Sciences, University of Texas at Austin

Abstract: We present new numerical algorithms for solving Poisson's and Helmholtz equations on domains with smooth boundaries. Using either signed distance function or the closest point mapping to the domain boundaries, we formulate and solve the corresponding integral equations which are defined in a thin tubular neighborhoods of the domain boundaries. Our algorithms are suitable for computing interfaces whose dynamics are derived from the solutions of such PDEs in the enclosed set. We shall also present new algorithms for integration over open curves and surfaces using point clouds sampled from these geometrical objects.

Where: CSIC #4122

Speaker: Prof. Dejan Slepcev, Department of Mathematics, Carnegie Mellon University

Abstract: Nonlocal-interaction equations serve as one of the basic models of biological aggregation. The interaction between individuals is typically attractive at large distances and repulsive at short distances. We will discuss several phenomena appearing in such systems: the variety of patterns that stable steady states exhibit, rolling traveling waves in heterogeneous environments, and phase separation (flock / empty space) in systems with nonlinear diffusion. In addition new structures appearing in systems where the long range interaction is attenuated by the crowdedness will be discussed.

We will introduce the gradient flow structure of the above systems and indicate how it can be used to prove well-posedness of equations, study the nonlinear stability of steady states, establish the interfacial behavior and study new models that take the crowdedness into account.

Where: CSIC #4122

Speaker: Prof. Alina Chertock, Department of Mathematics, North Carolina State University

Abstract: In this talk, I will present a numerical method for solving tracking-type optimal control problems subject to scalar nonlinear hyperbolic balance laws in one and two space dimensions. The approach is based on the formal optimality system and requires numerical solutions of the hyperbolic balance law forward in time and its nonconservative adjoint equation backward in time. To this end, we develop a hybrid method, which utilizes advantages of both the Eulerian finite-volume scheme (for solving the balance law) and the Lagrangian discrete characteristics method (for solving the adjoint transport equation). Experimental convergence rates as well as numerical results for optimization problems with both linear and nonlinear constraints and a duct design problem will also be presented and discussed.

Where: CSIC #4122

Speaker: Prof. Vladislav Panferov, Department of Mathematics, CA State University (CSUN)

Abstract: Dynamics of particles with self‐propulsion, in the simplest case expressed by the condition of constant speed, has received a lot of attention in recent years due to applications in emergent self‐organized behavior such as flocking and swarming. In situations when the number of particles becomes large a continuum description becomes possible, in which a system may be described by a coarse‐grained density and direction fields. The lack of the momentum conservation in such systems presents specific difficulties in applying known approaches from kinetic theory. I will discuss results of analysis and numerics concerning the problem of validation of hydrodynamic equations for systems of self‐propelled particles with various types of interactions.

Where: CSIC #4122

Speaker: Prof. Giovanni Russo, Department of Mathematics, Università di Catania

Abstract: The purpose of this talk is to present some recent results on the development of semilagrangian high order method for some kinetic equations. Two particular applications are considered, namely Vlasov-Poisson system and BGK model.

For the VP system, high order semilagrangian methods are obtained by tracing back the characteristics form each grid node in phase space, by solving (backward) their evolution equation in a self-consistent electric field. The solution at the foot of the characteristic at time tn is reconstructed by WENO interpolation in space and velocity.

For the BGK model, high order semilagrangian schemes are obtained by integrating the equation along the characteristics (in the forward direction). Since there is no drift, the characteristics are known, and the solution at time tn at the foot of the characteristic is obtained by WENO interpolation in space. Implicit schemes are used to avoid restriction on the time step in case of small relaxation time. Because of the special structure of the collision operator of BGK, the implicit equation can be explicitly solved. Two family of schemes are considered and compared: implicit Runge-Kutta and BDF.

Both approaches described above (for VP and BGK) are non-conservative in nature.

The third part of the talk is devoted to a general technique that can be used to make the method conservative. The approach is a conservative correction that can be applied to a non-conservative method. Examples of conservative schemes constructed by this techniques are illustrated in various contexts. When applied to semilagrangian schemes, the technique suffers from CFL-type stability restriction. Stability analysis is performed to understand the instability due to time discretization, however the contribution of space discretization has not yet been analyzed.

Where: Math 3206

Speaker: Dr. Jacob Bedrossian, Courant Institute, New York University

Abstract: We prove asymptotic stability of shear flows close to the planar, periodic Couette flow in the 2D incompressible Euler equations. That is, given an initial perturbation of the Couette flow small in a suitable regularity class, specifically Gevrey space of class smaller than 2, the velocity converges strongly in L2 to a shear flow which is also close to the Couette flow. The vorticity is asymptotically mixed to small scales by an almost linear evolution and in general enstrophy is lost in the weak limit. The strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with Landau damping in the Vlasov equations. Joint work with Nader Masmoudi.

Where: CSIC #4122

Speaker: Prof. Ben Adcock, Department of Mathematics, Purdue University

Abstract: Compressed sensing is an area of applied mathematics, engineering and computer science that deals with the recovery of objects - e.g. images and signals - from seemingly highly incomplete sets of data. To achieve this, it relies on three key principles: (i) sparsity of the object to be recovered in some appropriate basis or frame (ii) incoherence between the sparsity system and the sampling system and (iii) uniform random subsampling of the measurement space. Subject to these conditions, the now well-established theory of compressed sensing shows that one can reconstruct objects using near-optimal numbers of measurements.

Unfortunately, in many practical problems (e.g. MRI) incoherence is lacking. Whilst compressed sensing techniques have often been applied successfully in such areas, there is no theory to explain why. In this talk I will present a mathematical framework for compressed sensing that explains such empirical results. In this theory, the concepts of sparsity, incoherence and uniform random subsampling are relaxed to three new principles: asymptotic sparsity, asymptotic incoherence and multilevel random subsampling. As I demonstrate, these new concepts are more realistic in applications. In particular, sparsity is too crude a model to explain the reconstruction quality seen in practice in such applications. The new theory shows that compressed sensing is possible under these more general conditions, and in several important settings (including MRI) it is possible to get near-optimal recovery guarantees. Finally, I will discuss a number of interesting consequences of this new theory.

This is joint work with Anders C. Hansen, Clarice Poon and Bogdan Roman.

Where: CSIC #4122

Speaker: Prof. Siddhartha Mishra, Seminar für Angewandte Mathematik, ETH Zurich

Abstract: We propose a shock capturing spacetime Discontinuous Galerkin (DG) methods for multi-dimensional systems of conservation laws. We show that that these methods are (formally) arbitrarily high-order accurate, satisfy a discrete version of the entropy inequality and converge to entropy measure valued solutions. We present preconditioners that enhance the efficiency of the method and highlight the ability of space-time DG methods to compute all speed flows and allow for spacetime adaptivity. A large number of numerical experiments, illustrating the method, are also presented. The talk is based on joint work with Andreas Hiltebrand (ETH Zurich).

Where: CSIC #4122

Speaker: Dr. Emil Wiedemann, University of British Columbia, Department of Mathematics

Abstract: Young measures are an important tool in the calculus of variations and nonlinear elasticity theory, where they are used e.g. to describe microstructures in crystals. A realistic mathematical model for the deformation of a solid should, however, not allow the deformation to collapse the solid's volume to zero, or to reverse orientation. It has therefore been an important open question to characterize those Young measures which arise from such physically admissible deformations. I will present such a characterization, which is achieved by the so-called method of convex integration, along with several applications. Joint work with K. Koumatos (Oxford) and F. Rindler (Warwick).

Where: CSIC #4122

Speaker: Prof. Wojciech Czaja, University of Maryland, Department of Mathematics

Abstract: The problem of data integration and fusion is a longstanding problem in the remote sensing community. It deals with finding effective and efficient ways to integrate information from heterogeneous sensing modalities. In this talk we shall present a completely deterministic approach which exploits fused representations of certain well known data-dependent operators, such as, e.g., graph Laplacian and graph Schroedinger operators. It is through the eigendecomposition of these operators that we introduce the notion of fusion/integration of heterogeneous data, such as hyperspectral imagery (HSI) and LIDAR, or spatial information. We verify the results of our methods by applying them to HSI classification.

Where: CSIC #4122

Speaker: Dr. Lin Lin, Computational Research Division, Lawrence Berkeley National Laboratory

Abstract: Kohn-Sham density functional theory (KSDFT) is the most widely used electronic structure theory for molecules and condensed matter systems. Although KSDFT is often stated as a nonlinear eigenvalue problem, an alternative formulation of the problem, which is more convenient for understanding the convergence of numerical algorithms for solving this type of problem, is based on a nonlinear map known as the Kohn-Sham map. The solution to the KSDFT problem is a fixed point of this nonlinear map. The simplest way to solve the KSDFT problem is to apply a fixed point iteration to the nonlinear equation defined by the Kohn-Sham map. This is commonly known as the self-consistent field (SCF) iteration in the condensed matter physics and chemistry communities. However, this simple approach often fails to converge. The difficulty of reaching convergence can be seen from the analysis of the Jacobian matrix of the Kohn-Sham map, which we will present in this talk. The Jacobian matrix is directly related to the dielectric matrix or the linear response operator in the condensed matter community. We will show the different behaviors of insulating and metallic systems in terms of the spectral property of the Jacobian matrix. A particularly difficult case for SCF iteration is systems with mixed insulating and metallic nature, such as metal padded with vacuum, or metallic slabs. We discuss how to use these properties to approximate the Jacobian matrix and to develop effective preconditioners to accelerate the convergence of the SCF iteration. In particular, we introduce a new technique called elliptic preconditioner, which unifies the treatment of large scale metallic and insulating systems at low temperature. Numerical results show that the elliptic preconditioner can effectively accelerate the SCF convergence of metallic systems, insulating systems, and systems of mixed metallic and insulating nature. (Joint work with Chao Yang)

Where: CSIC #4122

Speaker: Prof. Elana Fertig, Johns Hopkins University, Department of Oncology

Abstract: Matrix factorization techniques are essential to infer dominant patterns related to temporal processes in big data, such as time course genomics. However, the orthogonality constraint in standard pattern-finding algorithms, including notably principal components analysis (PCA), confounds inference of simultaneous biological processes. Non-negative matrix factorization (NMF) techniques were initially introduced to find non-orthogonal patterns in data, making them ideal techniques for inference of patterns that distinguish concurrent processes. We introduce a Markov chain Monte Carlo NMF algorithm, CoGAPS, which uses an atomic prior to naturally model biological sparsity and correlation structure of data matrices. Comparisons to gradient-based NMF algorithms show that CoGAPS yields more robust and biologically relevant patterns related to biochemical perturbations to cancer cells.

Where: CSIC #4122

Speaker: Prof. Thierry Goudon, INRIA Sophia Antipolis Research Centre

Abstract: We introduce a new scheme for 2*2 systems of conservation laws, typically barotropic Euler equations. The design of the scheme is motivated by its application to the

simulation of "multifluid flows" where models involve an intricate constraint on the divergence of the velocity field. The scheme works on staggered grids and numerical fluxes have the flavor of kinetic fluxes.

We analyze the stability properties: positivity of the density, decay of

entropy.

Where: CSIC #4122

Speaker: NO SEMINAR

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Where: CSIC #4122

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Where: CSIC #4122

Speaker: Prof. Vladimir Temlyakov, Department of Mathematics, University of South Carolina

Abstract: The talk is devoted to theoretical aspects of sparse approximation and

optimization. The main motivation for the study of sparse approximation is

that many real world signals can be well approximated by sparse ones. Sparse

approximation automatically implies a need for nonlinear approximation, in

particular, for greedy approximation. We will discuss greedy approximation

in dierent settings: with respect to bases and redundant dictionaries, in

Hilbert and in Banach spaces.

We also discuss sparse approximate solutions to convex optimization

problems. It is known that in many engineering applications researchers

are interested in an approximate solution of an optimization problem as a

linear combination of a few elements from a given system of elements. There

is an increasing interest in building such sparse approximate solutions using

dierent greedy-type algorithms. The problem of approximation of a given

element of a Banach space by linear combinations of elements from a given

system (dictionary) is well studied in nonlinear approximation theory. At

a rst glance the settings of approximation and optimization problems are

very dierent. In the approximation problem an element is given and our

task is to nd a sparse approximation of it. In optimization theory an energy

function is given and we should nd an approximate sparse solution to the

minimization problem. It turns out that the same technique can be used for

solving both problems. We discuss how the technique developed in nonlinear

approximation theory, in particular the greedy approximation technique can

be adjusted for nding a sparse solution of an optimization problem.

Where: CSIC #4122

Speaker: TBA

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Where: CSIC #4122

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Where: CSIC #4122

Speaker: Prof. Manuel Tiglio, CSCAMM and Department of Physics, University of Maryland

Abstract: I will present a program effort aimed at predicting and evaluating gravitational waves from binary black hole collisions on mobile devices instead of months of supercomputer time. The effort is based on an offline-online decomposition of the problem, reduced bases, surrogate models and fast online real-time analysis (from 100 days to within a few hours). This is an effort to be able to do real science within the advanced network of gravitational wave detectors, worth billions of dollars.

The effort is a medium size, interdisciplinary one, in collaboration with Pablo Perez De Angelis (LVK Labs) Harbir Antil (GMU), Jonathan Blackman (Caltech), Priscilla Canizares (Cambridge, UK), Sarah Caudill (UWM), Scott Field (UMD), Jonathan Gair (Cambridge, UK), Chad Galley (Caltech), Jason Kaye (Brown Univ), Jan Hesthaven (EPFL, Switzerland), Frank Herrmann (London, UK), Andres Pagliano (LVKLabs), Ricardo Nochetto (UMD), Evan Ochsner (UWM), Vivien Raymond (Caltech), Rory Smith (Caltech), Bela Szilagyi (Caltech)

Where: CSIC #4122

Speaker: TBA

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Where: CSIC #4122

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Where: CSIC #4122

Speaker: Prof. Govind Menon, Division of Applied Mathematics, Brown University

Abstract: In the early days of scientific computing, Goldstine and Von Neumman suggested that it would be fruitful to study the "typical" performance of Gaussian elimination on random data. This approach lay dormant for decades until Alan Edelman's 1989 thesis on the distribution of condition numbers of random matrices. Since then numerical linear algebraists have made basic contributions to random matrix theory and the study of condition numbers of random matrices has proven to be a rich subject.

We approach the symmetric eigenvalue problem from a similar viewpoint. The underlying mathematical issue is to analyze the number of iterations required for an eigenvalue algorithm to converge. Our study focuses on the QR algorithm, the Toda algorithm and a version of the matrix-sign algorithm. All three algorithms have intimate ties with completely integrable Hamiltonian systems. Our results stress an empirical discovery of "universality in computation". We also show that this problems admits an elegant mathematical formulation and suggests interesting new questions in integrable systems, kinetic theory and random matrix theory. Very little background in these areas will be presumed, and the talk will be self-contained.

This is joint work with Percy Deift (Courant Institute) and Christian Pfrang (JP Morgan).

Where: CSIC #4122

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Where: CSIC #4122

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Where: CSIC #4122

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Where: CSIC #4122

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Where: CSIC #4122

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