UB Applied Mathematics Seminar
All seminars take place on Tuesdays at 3:45 p.m.(Spring 2017) in Room 250 in Mathematics Building unless otherwise noted.
Year -
2017-2018,
2016-2017,
2015-2016,
2014-2015,
2013-2014,
2012-2013,
2011-2012,
2010-2011
Fall 2017
September 5 Jose Carrillo (Imperial College - London) - Talk starts at 3:30 pm
Title: Swarming, Interaction Energies and PDEs
Abstract: I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random particle simulations, flocks and mills, and their qualitative behavior. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. Compactly supported global minimizers determine the flock patterns whose existence is related to the classical H-stability in statistical mechanics and the classical obstacle problem for differential operators.
September 12 Vitali Vougalter (University of Toronto)
Title: On the solvability of some systems
of integro-differential equations with anomalous diffusion
Abstract: The work deals with the existence of solutions
of a system of integro-differential equations in the case of anomalous
diffusion with the Laplacian in a fractional power. The proof of
existence of solutions is based on a fixed point technique.
Solvability conditions for non Fredholm elliptic operators in unbounded
domains are used.
September 18, 19 and 20. Myhill Lecture Series by Guoliang Yu (Texax A & M)
September 26 Gourab Ghoshal (University of Rochester)
- Cancelled
October 3 Jie Sun (Clarkson University)
Title: Computational Network Inference from Data
Abstract: Understanding the dynamics and functioning of complex systems is one of the most challenging tasks faced in modern science. A central problem to tackle is to accurately and reliable infer the underlying cause-and-effect (i.e., causal) network from observational data, especially when the system consists of a large number of interacting components and the dynamics can be intrinsicaly nonlinear.
In this talk I will review my recent collaborative projects on optimal causation entropy (oCSE) as a general framework to reconstruct networks (whose edges are hidden) from data measured on the nodes. Depending on the context, the framework can be adapted to incorporate prior information of noise distributions, and also to accommodate both longitudinal and non-longitudinal data.
I will show results of applying oCSE to synthetic datasets (as benchmark) as well as real-world datasets in several different disciplines. Examples of application include discovering ``socialâ€ť interaction in swarming insects, detecting structural patterns and damages in bridges, as well as fitting Boolean functions to genotype-phenotype data. Time permits I will also discuss a few other related problems, including data fusion network reconstruction, uncertainty quantification, and visualization of bipartite network data.
October 10 Dane Taylor (UB)
Title: Centrality analysis and community detection for temporal and multilayer networks
Abstract: The social and biological sciences often give rise to datasets represented by multilayer networks in which different layers encode different types of interactions. In particular, many networks are time-varying and can be modeled as a temporal sequence of layers. Despite their commonality, the mathematical foundations for such data structures are not well established. I will present my recent work in this area for two network-analysis methodology classes. First, I will present a temporal generalization of eigenvector-based centrality measures (e.g., PageRank), giving a tunable framework to analyze the importances of network nodes over time. As case studies, we examine the fame of actors during the Golden Age of Hollywood and department prestige for academic institutions. We also conduct a singular perturbation analysis to provide insight toward 'time averaging' for this framework. Next, I will describe the detection of small-scale communities in temporal networks, which is a paradigmatic problem in cybersecurity for detecting anomalies such as fraud and intrusions. To provide theoretical guidance, we develop random-matrix theory to analyze phase transitions in which the dominant eigenvectors of modularity matrices localize onto the communities, thereby allowing their detection. We propose and address a foundational question by asking when is it beneficial to preprocess a temporal network by first aggregating the layers into time windows. We find that layer aggregation via summation and thresholding can be effectively used as a preprocessing filter to allow super-resolution detection of communities that are otherwise too small to detect. This work paves the way for further 'holistic' research that simultaneously considers the network-preprocessing and network-analysis steps.
October 17 Xudan Luo (UB)
Title: Soliton dynamics in the Korteweg-de Vries (KdV) equation with step boundary conditions
Abstract: The long time evolution of initial data consisting of solitons and a positive or negative step are considered for the Korteweg-de Vries (KdV) equation. The positive/negative step evolves into a rarefaction wave/dispersive shock wave that either transmits or traps the solitons within its interior. For the case of solitons passing through a step, the phase shift is calculated. Solitons can also become trapped, in this case the corresponding eigenvalues of the Schr\"odinger equation are embedded in the continuous spectrum.
October 24 Matthew J. Hoffman (RIT)
Title: Estimating Hydrodynamic Flows through Data Assimilation and Tracking Plastic Pollution in the Great Lakes
Abstract: Numerical hydrodynamic forecasts similar to weather forecasts are used operationally in bodies of water such as the Chesapeake Bay and the Great Lakes to predict biogeochemical variables as well as transport. Achieving the best forecasts requires not just improving the numerical model, but combining the modeled output with observational data through data assimilation. I will talk about data assimilation and the application to operational forecasts in Chesapeake Bay and Lake Erie. Data assimilated products could also improve results of transport studies, such as a project of mine estimating the fate of plastic pollution in the Great Lakes. I will discuss our modeling of plastic input and transport through out the entire Great Lakes system.
October 31 Gino Biondini (UB)
Title: A unified approach to boundary value problems
Abstract: Over the last twenty years, a unified approach has been developed by
A.S. Fokas and collaborators to solve boundary value problems (BVPs) for
integrable nonlinear partial differential equations (PDEs). The
approach is a generalization of the inverse scattering transform (IST),
which was originally developed in the 1970's to solve initial value
problems for such PDEs.
Interestingly, however, the approach also provides a novel and powerful
way to solve BVPs for linear PDEs. This talk aims to provide an
introduction to this method for BVPs for linear PDEs. Specifically, I
will describe in detail the solution of BVPs for linear evolution PDEs
in one spatial and one temporal dimension. After presenting the method
in general, a few concrete examples will be considered. Time
permitting, two-point IBVPs, multi-dimensional PDEs and BVPs for linear
elliptic PDEs will also be discussed.
This talk is intended for a broad audience, and will contain no original
results.
November 7 Sonjoy Das (UB MAE)
- Cancelled
November 14 Gino Biondini (UB)
- Cancelled
November 22 - November 25 - UB Fall Recess
November 28 Katharine (Kate) Anderson (Carnegie Mellon University)
- Cancelled
Title: Skill networks and measures of complex human capital
Abstract: We propose a novel, network-based method for measuring worker skills. We demonstrate the method using data from an online free- lance website. Using the tools of network analysis, we divide skills into endogenous categories based on their relationship with other skills in the market. Workers who specialize in these different areas earn dramatically different wages. We then show that in this mar- ket, network-based measures of human capital provide more insight into wages than traditional human capital measures. In particular, we show that workers with diverse skills earn higher wages than those with more specialized skills. Moreover, we can distinguish between two different types of workers benefiting from skill diversity: jacks- of-all-trades, whose skills can be applied independently on a wide range of jobs, and synergistic workers, whose skills are useful in combination and fill a hole in the labor market. On average, workers whose skills are synergistic earn more than jacks-of-all-trades. This framework has the potential to reduce friction in online job markets, improve employer-employee matches, and guide worker training and marketing decisions.
Spring 2018
February 6 Jiwei Zhao (UB Biostatistics)
February 14 (Wed) 4pm - Weiran Sun (Simon Fraser University)
Title: Global Well-Posedness of the Non-Cutoff Boltzmann Equation
with Polynomial Decay Perturbations
Abstract: In this talk we will present our recent work on the global well-posedness of the non-cutoBoltzmann equation with hard potentials. The solution considered is near equilibrium where
the deviation has a polynomial decay. The main step is to show a closed energy estimate for
small data. This is achieved by combining methods of moment propagation, spectral analysis
of the linearized operator, and smoothness ect starting from data with weak regularity. This
is a joint work with Alonso, Morimoto, and Yang.
March 13 Guo Deng (UB)
UB Spring break, March 19 - March 24
April 3 Barbara Prinari (Univeristy of Colorado, Colorado Springs)
Title: Integrable systems, solitons and the inverse scattering transform
Abstract: The study of physical phenomena by means of mathematical
models often leads to a certain class of nonlinear differential
equations referred to as integrable systems. Over the last fifty
years, the study of these equations has attracted considerable
interest because it offers a unique blend of interesting mathematics
and concrete physical applications. Understanding the properties of
these equations, their solutions and their surprisingly rich
mathematical structure often requires a combination of techniques from
different branches of mathematics. After a brief introduction to the
subject, I will review some of my main results in this field.
Specifically, I will discuss the following kinds of problems: (i)
development of the inverse scattering transform (IST) for scalar,
vector and matrix nonlinear Schrodinger (NLS) systems with non-zero
boundary conditions; (ii) soliton interactions in coupled NLS systems;
(iii) development of the IST for integrable systems in two spatial and
one temporal dimension.
April 12/19 Shi Jin (University of Wisconsin Madison)
Fall, 2016
Oct 4: Alethea Barbaro (Case Western Reserve University)
Title: A Phase Transition in a Model for Gang Territorial Development
Abstract: Spray-painting a gang's graffiti around the neighborhood is a job which is often relegated to the youngest members of the gang. However, this is one of the main ways for a gang to lay claim to an area. In this talk, we examine a model for territorial development based on this mechanism. We employ an agent-based model for two gangs, where each agent puts down graffiti markings and moves to a neighboring site, preferentially avoiding areas marked by the other gang. We observe numerically that the systems undergoes a phase transition from well-mixed to segregated territories as the intensity of the avoidance of the other gang's graffiti is varied. We then derive a system of macroscopic PDEs from the model and examine the phase transition in the context of the continuum system.
Oct 25: He Yang (Ohio State University)
Title: Inverse Problem and Optimization in Medical Imaging
Abstract: In the first part of the presentation, I will discuss an inverse problem of x-ray computed tomography (CT) with applications in radiation therapy. The inverse problem is about image reconstruction to compute the attenuation coefficients inside the human body. We investigated several three-dimensional image reconstructions under different system designs. By evaluating the quality of image reconstruction results based on image registrations, we picked the best design for an extremely rapid radiation therapy system.
In the second part of the presentation, I will discuss deep learning technique which is an optimization procedure to study the representations of medical images. In particular, we developed a deep convolutional neural network (CNN) and applied such CNN to thoracic CT images for the classification of lung nodules. I will present the architecture of our deep CNN as well as some results about comparative studies on different CT scan datasets.
Nov 3: Katharine (Kate) Anderson (Carnegie Mellon University)
- Cancelled
Nov 10: Pavel Lushnikov (University of New Mexico)
- Note that the seminar is on Thursday.
Title: Formation of limiting Stokes wave from non-limiting wave
Abstract: Stokes wave is the fully nonlinear periodic gravity wave parameterized by its height. Wave of greatest height has the limiting
form with 120 degrees angle on the crest as found by Stokes in 1880. We consider a conformal map of a free fluid surface of
Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. Stokes wave is fully characterized by
the complex singularities in the upper complex half-plane. The only singularity in the physical sheet of Riemann surface of
non-limiting wave is the square-root branch point located on the imaginary axis. Crossing corresponding branch cut defines the
second sheet of the Riemann surface, which has a singularity in lower complex half-plane. We found the infinite number of square
root singularities in infinite number of non-physical sheets of Riemann surface. Increase of the height of the Stokes wave means
that all these singularities simultaneously approach the real line from different sheets of Riemann surface and merge together
forming 2/3 power law singularity of the limiting wave. It was conjectured (Journal of Fluid Mechanics, v. 800, pp. 557-594 (2016)) that non-limiting
Stokes wave at the leading order consists of the infinite product of nested square root which form the infinite number of sheets
of Riemann surface.
Nov 15: Misun Min (Argonne National Lab)
Title: Scalable High-Order Simulations for PDEs and Applications
Abstract: I will present recent development and analysis on performance characteristics
that impact the scalability of electromagnetic and fluid simulations on large-scale parallel
computers including multi-GPU and many-core architectures.
Discussions include highly-tuned implementation and fast, efficient algorithms based on
high-order spectral element discretizations for solving convection-diffusion type equations
arising in semiconductor and ionic channel applications, as well as classical and quantum
mechanical modelling approaches for simulating electromagnetic systems such as quantum
dots for nanoscale devices and particle accelerators.
Spring 2017
Feb 7 Greg Forest (University of North Carolina at Chapel Hill) - Cancelled
Feb. 14
Jun Zhuang (UB Industrial and Systems Engineering)
Title: Applied Mathematics, Game Theory and Disaster Management
Abstract: Society is faced with a growing amount of property damage and casualties from man-made and natural disasters. Developing societal resilience to those disasters is critical but challenging. In particular, societal resilience is jointly determined by federal and local governments, private and non-profit sectors, and private citizens. We will present a sequence of applied mathematical game models among players such as federal, local, and foreign governments, private citizens, and adaptive adversaries. In particular, the governments and private citizens seek to protect lives, property, and critical infrastructure from both adaptive terrorists and non-adaptive natural disasters. The federal government can provide grants to local governments and foreign aid to foreign governments to protect against both natural and man-made disasters; and all levels of government can provide pre-disaster preparation and post-disaster relief to private citizens. Private citizens can also, of course, make their own investments. The tradeoffs between protecting against man-made and natural disasters, specifically between preparedness and relief, efficiency and equity, and between private and public investment, will be discussed.
Feb 21 Kazuo Yamazaki (University of Rochester)
Title: Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model
Abstract: This talk concerns the speaker's collaborative work with Prof. Xueying Wang of Washington State University. Cholera is an infectious disease caused by the bacterium Vibrio cholerae. Its spread and consequence in countries of Africa, Southeast Asia, Haiti and central Mexico are well-known and indicates the need for an efficient mathematical model to control the spread of such a disease. In dynamics of population biology, an important disease threshold is called the basic reproduction number R0, which measures the expected number of secondary infections caused by one infectious individual during its infectious period in an otherwise susceptible population. In this talk, we discuss our recent result which showed that R0 serves as a parameter that predicts whether cholera will persist or become globally extinct. Specifically, when R0 is beneath one, the disease-free-equilibrium is globally attractive while if it exceeds one, then in the case the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, the uniform persistence can be proven as well as the existence of an endemic equilibrium. We also make remarks on previous results on similar models (e.g. malaria, dengue fever, avian influenza) and discuss remaining difficult open problems.
Feb 28 Matthew J. Hoffman (RIT)
- Cancelled
March 7 Sean Nixon (SUNY Geneseo)
Title: Parity-Time Symmetry in Optical Lattices
Abstract: Parity-Time-Symmetry gained notoriety as a way to extend quantum mechanics to non-Hermitian potentials. PT-symety allows for complex systems which still exhibit an all real spectrum (real energy levels in QM). Since then, the concept has been applied to optics, electronic circuits, Bose-Einstien condensates and other physical systems where a complex potential can be realized by adding gain and loss. In the presence of nonlinearity, these PT-symmetric systems exhibit phenomena which are incredibly rare in dissipative systems, including continuous families of solitons, stabilization nonlinear modes in unstable regimes, and unique evolution dynamics. And recently, the study of PT-symmetry has also involved searching for other complex systems with the same or similar properties.
March 14 Michael Langberg (UB Electrical Engineering) - Cancelled due to weather
Title: Can one network edge make a difference: The edge removal problem
Abstract: The "edge removal problem" addresses the loss in communication rate (i.e., capacity) when a single edge is removed from a given network. For example, one can ask whether removing a single cable of a given capacity C from the internet can have impact larger than C on the internet as a whole. Remarkably, this problem remains unsolved. That is, if we compare the capacity of a given network to the capacity of the same network after the removal of a single edge, it is currently unknown how much the network capacity can change. In this talk I will study the edge removal problem through the lens of reduction. Specifically, I will give an overview of several intriguing reductive connections that have emerged recently between the edge removal problem and seemingly unrelated problems in network communication.
(to be confirmed) Carina Curto (Penn State University)
Mar 28 Ferdinand Schweser (UB Department of Neurology)
Title: Mathematical Problems of the Quantification of Brain Tissue Composition and Integrity With Phase MRI
Abstract: The noninvasive tomographic quantification of physical properties of biological tissues has been a perpetual quest in the field of biomedical imaging. I will present recent developments toward this goal in the field of phase-based magnetic resonance imaging (MRI), a special variant of MRI that employs the phase of the complex-valued resonance signal. We have developed efficient direct and numerical methods to solve several inverse problems of computing magnetic and electric tissue properties from the tissues's interactions with the externally applied electromagnetic fields in the MRI scanner. These problems include large-scale 3D source separation and deconvolution problems.
I will begin the presentation with a brief introduction to the basics of MRI. We will then discuss some of the inverse problems and their practical relevance for biomedical imaging research and clinical routine. I will conclude with an overview of significant problems that remain unsolved.
April 4:
Matt Tranter (Loughborough University),
Department of Mathematical Sciences, Loughborough University,
Loughborough, LE11 3TU, UK
Title: Scattering of strain solitary waves in delaminated waveguides
Abstract:
In this talk I will discuss the dynamics of long longitudinal bulk strain solitary waves in
bonded elastic bars with delamination. We have developed direct and semi-analytical nu-
merical methods for these types of problems. The semi-analytical method is based on the
weakly nonlinear solution of the problem.
Firstly I will consider a symmetric perfectly bonded layered bar with delamination, showing
that the direct and semi-analytical results for the full scattering problem are in agreement.
Furthermore, ssion of an incident solitary wave can occur in the delaminated region of the
bar [1, 2]. The approach is extended to the case of a layered bar with a soft bonding layer,
described by a system of coupled Boussinesq equations supporting radiating solitary waves
[3]. The modelling indicates that a delamination of a given length can be detected by the
behaviour of the waves [4]. This is joint work with K. R. Khusnutdinova.
References
[1] K. R. Khusnutdinova, A. M. Samsonov, Fission of a longitudinal strain solitary wave in
a delaminated bar, Phys. Rev. E, 77 (2008) 066603.
[2] K. R. Khusnutdinova and M. R. Tranter, Modelling of nonlinear wave scattering in a
delaminated elastic bar, Proc. Roy. Soc. A, 471 (2015) 20150584.
[3] K. R. Khusnutdinova, A. M. Samsonov and A. S. Zakharov, Nonlinear layered lattice
model and generalized solitary waves in imperfectly bonded structures, Phys. Rev. E, 79
(2009) 056606.
[4] K. R. Khusnutdinova and M. R. Tranter, On radiating solitary waves in bi-layers with
delamination and coupled Ostrovsky equations, Chaos (in press) (2017).
April 6 James Boyle (UB) - This talk is on Thursday
Title: Horizon Annealing: A co-NP Problem in Creating an Ordinal Composite from Paleontological Data
Abstract: In the Earth's history there is an underlying true and unique sequence of appearances and extinctions of organisms because each organism arises only once and once extinct never reappears. If it were reliably known, scientists could use this ordered sequence of events as a proxy for time in their study of events in Earth history. However, the record of events is full of gaps and biases that obscure and mislead. What we are left with in the fossil record is a set of incomplete, fractured, and sometimes contradictory, local collections of fossil specimens. In order to try and estimate the true, or at least most consistent, order of events in Earth history more accurately, geologists have developed several quantitative methods by which to extract useful information from these imperfect data.
The Horizon Annealing (HA) approach that we employ to order events uses data collected from measured columns of layered rock at particular geographic sites where the order of occurrences within each layer is known. These are known as local sections. Typically, older rocks are found at the bottom of a column because they were laid down first. Older specimens appear lower in local sections, younger specimens at the top. However, each section does not have the complete range of all species. Many are missing and most are truncated, so the local range is less than, or at most equal to, the global range of a species.
In the HA process, the individual collections from each measured section are allowed to shuffle up and down at random relative to those in other sections, while preserving their internal orders. Occurrences from all of the collections are then combined to form a global ordering of events that minimizes the number of gaps within an organism's span of the composite sequence. Data sets often consist of several hundred sections, each containing tens of samples that record the presence of one or more of the several hundred species that existed during the interval examined. The data are often very noisy and the number of possible solutions scales exponentially with the size of the dataset. The solution space is expected to be complex and there are likely to be multiple equally optimal solutions for even modest datasets. Despite the difficulty in knowing whether the true answer has been found, a proposed solution can easily be rejected if its calculated score is higher than the best solution known, making this a co-NP problem. Nonetheless, it can be difficult to avoid having searches become trapped in a local minimum by particularly large or densely sampled local sections that were placed unfortunately in initial runs.
As we cannot be certain whether a solution is the true solution, measures of uncertainty are desirable. We have developed jackknife approach in which one local section is removed at a time, and a new solution is found. The relative movement of collections among successive jackknifed solutions serves as a proxy for uncertainty in placement. This process is time-consuming, computationally expensive, and suffers the same pitfalls as for the general HA search, noted above. As datasets have become increasingly large, the current implementation of HA becomes unworkable and more efficient algorithms or approaches are needed.
April 18
Yang Yang (Michigan Tech)
Title: Local discontinuous Galerkin methods for chemotaxis model
Abstract: In this talk, we will focus on local discontinuous Galerkin methods for
Keller-Segel chemotaxis model, which might yield blow-up solutions. We first give the
error estimates based on two different finite element spaces, and then
proceed to the positivity-preserving technique to obtain positive numerical
approximations. Finally, we will numerically demonstrate how to find the
blow-up time.
April 25 Antonio Moro (Northumbria University)
Title: Dressing networks: towards an integrability approach to collective and complex phenomena
Abstract: A large variety of real world systems can be naturally modelled by networks, i.e. graphs whose nodes represent the components of a system linked (interacting) according to specific statistical rules. A network is realised by a graph typically constituted by a large number of nodes/links. Fluid and magnetic models in Physics are just two among the many classical examples of systems which can be modelled by using simple or complex networks. In particular "extreme" conditions (thermodynamic regime), networks, just like fluids and magnets, exhibit a critical collective behaviour intended as a drastic change of state due to a continuous change of thermodynamic parameters.
Using an approach to thermodynamics, recently introduced to describe a general class of van der Waals type models and magnetic systems in mean field approximation, we analyse the integrable structure of corresponding networks and use the theory of nonlinear conservation laws to provide an analytical description of the system outside and inside the critical region.
April 27 Michael Langberg (UB Electrical Engineering) - This talk is on Thursday.
Title: Can one network edge make a difference: The edge removal problem
Abstract: The "edge removal problem" addresses the loss in communication rate (i.e., capacity) when a single edge is removed from a given network. For example, one can ask whether removing a single cable of a given capacity C from the internet can have impact larger than C on the internet as a whole. Remarkably, this problem remains unsolved. That is, if we compare the capacity of a given network to the capacity of the same network after the removal of a single edge, it is currently unknown how much the network capacity can change. In this talk I will study the edge removal problem through the lens of reduction. Specifically, I will give an overview of several intriguing reductive connections that have emerged recently between the edge removal problem and seemingly unrelated problems in network communication.
May 2 Ming Yan (Michigan State University)
Title: A New Primal-dual Operator Splitting Scheme and its Applications
Abstract: In this talk, I will introduce a new primal-dual algorithm for minimizing f(x) + g(x) + h(Ax), where f, g, and h are convex functions, f is differentiable with a Lipschitz continuous gradient, and A is a bounded linear operator. This new algorithm has the Chambolle-Pock and many other algorithms as special cases. It also enjoys most advantages of existing algorithms for solving the same problem. Then I will show some applications including fused lasso, image processing, and decentralized consensus optimization.
May 9 Kanika Bansal (UB Math)
Title: Data-driven models of brain dynamics to predict cognitive performances
Abstract: Humans show individual differences in cognitive performance and the origin of this variability is not completely understood. How important is the basic structural skeleton of the brain in explaining and predicting individual differences in cognition?
In this talk, I will discuss our work with a data-driven computational brain network model. By emphasizing differences in the underlying structural connectivity, this model serves as a powerful tool to differentiate individual performances in cognitively demanding tasks.
Motivated by experimental data on three language related tasks, we perform computational experiments in which we stimulate the left inferior frontal gyrus and quantify the spread of the stimulation both within the global brain network and throughout the task specific sub-networks
across a cohort of individuals. We then relate the patterns of activation to individual performance across three tasks and find that task performance correlates with the activation of either local or global circuitry depending on the complexity of the task.
(to be confirmed) Joint seminar with UB SIAM Student Chapter