Center seminars are organized by the Mathematics Department and the College of Engineering. The Center gratefully acknowledges support from the UMassD Office of the Provost.
December 14, 2017
"Searching for stochastic gravitational waves using pulsar timing"
Abstract: In this talk, I will describe how scientists are using the ticks of Nature's most precise clocks (i.e., pulsars) to search for the background noise of gravitational waves produced by binary systems of supermassive black holes in the centers of distant galaxies. I will also provide an acoustical analogy of a pulsar timing array, which uses a pair of metronomes and a microphone to illustrate several techniques in real pulsar timing---the most important of which, for detecting gravitational waves, are correlations between the timing measurements for pairs of pulsars in the array.
"Computational Oncology: two approaches to obtain personalized cancer treatments"
Abstract: In this talk, I employ mathematical methods as well as computer science techniques to develop models for carcinogenesis. I will discuss some of my computational models for studying tumor evolutionary dynamics and designing novel therapeutic targets. In the first part, I will talk about modeling stem cell therapy for solid tumors. I will introduce a unique 4-compartmental stochastic model for cell dynamics in the colon and intestinal crypts to obtain the probability and the time of mutants’ progeny taking over or being washed out from crypts. The model predicts that if there are any immortal cells, normal stem cells alone are not able to cure the crypts, and the therapeutic strategies, which are based on transforming immortal cells to mortal ones, are needed. In the second part of the talk, I will show that killing cancer cells is not an optimal cancer treatment by developing a stochastic model for cell dynamics after conventional cancer treatments. Finally, I will introduce a bioinformatics technique to obtain personalized targeted therapies for cancer patients.
November 16, 2017
University Of Rhode Island
"From Nobel(s) to Neutron Stars: How gravitational waves are shaping 21st century astronomy"
Abstract: On September 14th 2015 the Laser Interferometer Gravitational wave Observatory (LIGO) made the first direct detection of gravitational waves (GWs) from the merger of two black holes. It was the culmination of a century of scientific effort, and it has been heralded as the beginning of a new era in observational astronomy. This discovery was so impactful that, just two years later, three of LIGO’s founders were awarded the 2017 Nobel Prize in physics for decisive contributions to the project. And a mere two weeks after the Nobel announcement, LIGO – in partnership with the Virgo GW detector and astronomers from some 70 astronomical observatories – announced another first: the detection of a merger of two neutron stars. But this discovery was unique as not only were GWs detected from the event, we saw light from it as well. These “multi-messenger” observations were the first of their kind, and with them we have begun to answer some of our most intriguing questions about the nature of our universe. In this talk, we will explore the events that have ushered us into this era of multi-messenger astronomy and discuss the exciting new insights into the cosmos that we have gleaned from them.
"Free-boundary minimal surfaces with connected boundary in the 3-ball by tripling the equatorial disc"
Abstract: Minimal surfaces are critical points (but necessarily honest minimizers) of the area functional on certain spaces of surfaces. A free-boundary minimal surface is a minimal surface with boundary constrained to lie on another given surface. I will describe a new construction that uses PDE techniques to glue together discs to produce the first examples of embedded free-boundary minimal surfaces with connected boundary lying on the unit sphere.
November 2, 2017
Harvard-Smithsonian Center For Astrophysics
"X-ray observations of GW170817: Behind the scenes at the beginning of multi-messenger astronomy"
Abstract: On September 14, 2015, the first detection of a gravitational waves from a binary black hole system kick-started the era of gravitational wave astronomy, and changed the face of physics and astronomy forever. Just over two years since the monumental first detection, we stand at the gateway to another new, and even more promising, era of astronomy. With the detection of both electromagnetic and gravitational waves from a binary neutron star system, GW170817 has started the age of multi-messenger astronomy off with a bang. In this talk I will give an introduction to the binary neutron star system of GW170817 and an overview of the wide range of information we gathered from this one detection. I will also discuss the basics of Chandra X-ray telescope, as well as the ins and outs of working on the science mission planning team. Following that, I will discuss the excitement, effort, and frustration that went on behind the scenes of our contribution to the multi-spectrum detection of GW 170817. Finally, I will give a quick overview of why GW170817 was labeled the worst kept secret in astronomy" and give a unique insider view of the controversy that has surrounded it to this day."
"An application of persistent homology to 3D spectral approximations of stenotic vascular flows"
Abstract: Vascular disease is a leading cause of death world wide and therefore the treatment thereof is critical. Understanding and classifying the types and levels of stenosis can lead to more accurate and better treatment of vascular disease. In this talk, we propose to use persistent homology as a tool to aid in the classification of vascular data. Persistent homology is a method of computing various topological features based on a simplicial complex. We use the 3D spectral approximation data of stenotic vascular flows to obtain better results than with lower order approximations. We then apply persistent homology to the spectral data and find Betti numbers in various dimensions. To make this approach work, we propose the spherical projection method. With the spherical projection the 3D spectral data is projected to n-dimensional sphere and Betti numbers are found in each dimension. In this talk, we briefly explain persistent homology first and then provide some results with stenotic vascular flows with and without stent installation.
"Steady and Traveling Wave Solutions in a Chain of Periodically Forced Couple Nonlinear Oscillators"
Abstract: Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts and annihilation of radial ones. Finally, we show that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.
Abstract: 2017 has been a landmark year for astrophysics. In this talk we will discuss recent astrophysical developments over an extraordinary range in time and space. We will journey from our own solar system, to distant stars and galaxies, and the cosmos as a whole. From our own sun, to Proxima Centauri B, Tabby's Star, LIGO rumors, fast radio bursts, ultralight dark matter, and cosmological controversies, we will undertake a tour of the latest and most exciting developments in astrophysics. This is a joint Physics seminar.
"Pattern Detection in Computer Networks Using Robust Dimension Reduction"
Abstract: In this talk, we will discuss theory and algorithms for detecting weak, distributed patterns in computer network data. Our focus is on detecting weak patterns in computer networks where the nodes (terminals, routers, servers, etc.) are sensors that provide measurements (of packet rates, user activity, CPU usage, IDS logs, etc.). In particular, we use robust principal component analysis to detect distributed patterns that are not discernible at the level of individual sensors. Robust principal component analysis is an extension of classic principal component analysis that aims to recover low dimensional subspaces corrupted by sparse outliers, and in this talk, we will demonstrate that such methods, when properly phrased, hold promise for anomaly detection during cyber network attacks. The approaches we propose are applicable to many other types of sensor networks including wireless networks, mobile sensor networks, and social networks where anomalous phenomena are of interest.
"Asymptotically Well-posed Boundary Conditions for Partitioned Fluid-Structure Algorithms"
Abstract: A new partitioned algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with elastic structures undergoing finite deformations. The new algorithm, referred to as the Added-Mass Partitioned (AMP) scheme, overcomes the added-mass instability that has for decades plagued partitioned FSI simulations of incompressible flows coupled to light structures. Within a Finite-Difference framework, the AMP scheme achieves fully second-order accuracy and remains stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The stability and accuracy of the AMP scheme is validated through mode analysis and numerical experiments. Aiming to extend the AMP scheme to a Finite-Element framework, we also develop an accurate and efficient Finite-Element Method for solving the Incompressible Navier-Stokes Equations with high-order accuracy up-to the boundary.
April 25, 2017
Air Force Research Laboratory
"MULTI-SCALE AND MULTI-PHYSICS SIMULATIONS USING THE MULTI-FLUID PLASMA MODEL"
Abstract: The multi-fluid plasma model represents electrons, multiple ion and neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. There is a broad range of timescales in the plasma model mainly due to the large mass ratio between the electrons and the ions, but also due to necessity to resolve the plasma frequency and the speed of light. To address this challenges a blended continuous and discontinuous Galerkin method (BFEM) is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutral physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. Distribution A: Approved for public release; distribution unlimited AFTC/PA clearance No. 16221.
Abstract: Neutron star mergers are among the most violent events in the Universe. Gravitational wave, electromagnetic, and neutrino signals from these mergers encode important aspects of the physics and astrophysics of neutron stars, which cannot be inferred from terrestrial laboratory experiments. For example, on the nature of the short-range interaction between nucleons, which is imprinted in the neutron star equation of state. However, harnessing these imminent detections will only be possible by combining the observational data with reliable theoretical predictions. The formers, in turn, rely on the availability of high-precision simulations. In this talk, I will review the current state-of-the art in the modeling of neutron star mergers and discuss future challenges and possibilities in this field.
"Algebraic Multigrid Methods for Computing Diffusion-Based Metrics on Graphs"
Abstract: Recently, diffusion-based metrics have been developed for protein-protein interaction networks and used for protein function prediction. In this talk, we focus on the challenges in computing these diffusion-based metrics, especially for large-scale networks. By exploring the algebraic properties of the distance metrics, we reformulate the computation of distances into solving a series of graph Laplacians systems. In particular, we develop algebraic multilevel methods for solving the resulting linear systems efficiently. Applications to the protein-protein networks will be presented and possible generalizations will be discussed.
April 10, 2017
Scripps Inst. Of Oceanography
"Satellite observations of interactions between atmospheric convection and surface Winds"
Abstract: Satellite scatterometers measure surface winds over the global oceans, but these observations have historically been limited by rain-related errors. We have recently developed techniques to circumvent these rain-related errors, allowing for direct observational study of convection-wind coupling over the ocean.
We use these corrected wind data to detect cool downdrafts from mesoscale convective systems (MCSs) for the first time. These wind observations are validated against surface buoys and satellite observations of cloud-top temperature.
Building on this study, we utilize satellite wind and rainfall observations to examine coupling between the land-sea breeze and the diurnal cycle of rainfall in the Bay of Bengal. Observations show co-propagation of surface convergence and rainfall anomalies from the eastern coast of India into the bay; surface convergence leads the rainfall anomalies by several hours, implying that the land breeze forces the diurnal cycle of convection over the bay.
"Measure transport for Bayesian inference: theory and applications."
Abstract: Measure transport is a valuable tool for characterizing, sampling and manipulating multivariate non-Gaussian target distributions [1,2,3]. This method has a broad range of applications -- e.g., the solution of Bayesian inverse problems, as well as filtering and smoothing of dynamical systems. The transport maps framework seeks a deterministic parametric map that pushes forward a tractable reference distribution to a potentially complex target distribution of interest. The construction of high-dimensional maps may be challenging due to the curse of dimensionality. In many cases, though, one can leverage a number of sources of low-dimensional structure: marginal independence, smoothness, separability, conditional independence , to just name a few. In this seminar we will outline the transport map framework and some of the key ingredients useful to tackle high-dimensional problems. The presentation will be accompanied by examples of Bayesian inference problems in geophysics and finance.
 El Moselhy, T. a., Marzouk, Y. M. (2012). Bayesian inference with optimal maps. Journal of Computational Physics, 231(23), 7815–7850.
 Parno, M., Marzouk, Y. (2014). Transport map accelerated Markov chain Monte Carlo. ArXiv:1412.5492
 Marzouk, Y., Moselhy, T., Parno, M., Spantini, A. (2016). Sampling via Measure Transport: An Introduction. In R. G. Ghanem, D. Higdon, H. Owhadi (Eds.), Handbook of Uncertainty Quantification (pp. 1–41). Cham: Springer International Publishing.
 Spantini, A., Bigoni, D., Marzouk, Y. (2017). Inference via low-dimensional couplings.
April 4, 2017
University Of Southern California
"Software Development in Alzheimer’s Research"
Abstract: ccording to Alzheimer’s Association, Alzheimer Disease(AD) is the 6th leading cause of death in the United States that cannot be prevented or cured. A person suffering from AD shows different symptoms of memory loss to language disability (In later stage). To help millions of people and advance in the research of AD, Alzheimer’s Therapeutic Research Institute (ATRI) is an institute committed to advancing the development of new treatments for AD through innovation in clinical trials.
Software development, nowadays has become a vital factor in all research fields and I would like to introduce how it plays its role in Alzheimer’s Research. ATRI has been responsible in organizing more than 50 clinical trials and the Informatics team actively develops and maintains a secure data capture system to record and analyze the data received from trials. Being a software developer at ATRI, I would also like to share my experiences of different concepts and best programming practices that I have learnt.
"A ROM-HPC framework with analysis for stochastic wave propagation models"
Abstract: We consider a class of wave propagation models with aleatoric and epistemic uncertainties. Using mathematical analysis-based, shape-independent, a priori parameter estimates, we develop offline/online strategies to compute statistical moments of a key quantity of interest in such models. We present an efficient reduced order model (ROM) and high performance computing (HPC) framework with analysis for quantifying aleatoric and epistemic uncertainties in the propagation of waves through a stochastic media comprising a large number of three dimensional particles. Simulation even for a single deterministic three dimensional configuration is inherently difficult because of the large number of particles. The aleatoric uncertainty in the model leads to a larger dimensional system involving three spatial variables and additional stochastic variables. Accounting for epistemic uncertainty in key parameters of the input probability distributions leads to prohibitive computational complexity. Our hybrid ROM and HPC framework can be used in conjunction with any computational method to simulate a single particle deterministic wave propagation model.
March 29, 2017
"New Bernstein-Bezier bases for the finite element exact sequence on tetrahedra"
Abstract: We present a set of new Bernstein-Bezier bases, with a local exact sequence property, for the finite element exact sequence on tetrahedra.
Abstract: Nonlocal models have been developed and received lot of attention in recent years to model systems with important scientific and engineering applications. While it is established that the nonlocal formulations can often provide more accurate descriptions of the systems, the nonlocality also increases the computational cost compared to conventional models based on PDEs. The goal is to combine the accuracy of nonlocal models with the computational and modeling efficiency of local PDEs.
In this talk, I will introduce a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with respect to the energy norms induced by the nonlocal diffusion kernels as well as the L2 norm, and it satisfies the maximum principle. A finite difference approximation is used to discretize the coupled system, which inherits the property from the continuous formulation. Furthermore, we design a numerical example which shows the discrepancy between the fully nonlocal and fully local diffusions, whereas the result of the coupled diffusion agrees with that of the fully nonlocal diffusion.
"Exploiting Low-Dimensional Structures for Sensing and Control of Fluids via Data-Driven Reduced-Order Modeling"
Abstract: Many applications in engineering and the sciences generate large-amounts of data to describe physical systems, e.g., via high-dimensional approximation or experimental measurements. Fortunately, the underlying dynamics of a complex system is often of much lower dimension than the data volume suggests. Thus, much progress has been made in deriving reduced-order models from system equations to enable (or speed up) engineering tasks such as control and optimization. Data-driven reduced-order modeling complements these intrusive, equation-based methods, and offers new pathways to work with real system data.
In this talk, I will discuss recent work on indoor airflow sensing through reduced-order models and the compressed sensing method to detect flow phenomena. We use simulated data to derive a low-dimensional basis for the fluid system via dynamic mode decomposition (DMD). We then extend the basis to account for time series of measurements, making the sensing method more robust. Results based-on a two dimensional Boussinesq equation are presented.
Building on this work, I will discuss recent results on control of parameter varying systems, where the physical parameters are uncertain and unknown. In this setting, we learn reduced-order models from system data that can then be used for reduced-order feedback control. The derived data-driven controllers successfully stabilize the considered convection-diffusion equation
"Wave breaking and modulational instability in full-dispersion shallow water models"
Abstract: In the 1960s, Benjamin and Feir, and Whitham, discovered that a Stokes wave would be unstable to long wavelength perturbations, provided that (the carrier wave number) x (the undisturbed water depth) > 1.363.... In the 1990s, Bridges and Mielke studied the corresponding spectral instability in a rigorous manner. But it leaves some important issues open, such as the spectrum away from the origin. The governing equations of the water wave problem are complicated. One may resort to simple approximate models to gain insights. \n I will begin by Whitham's shallow water equation and wave breaking conjecture, and move to modulational instability, the effects of surface tension and constant vorticity, turbulent bores, and I will indicate where numerical investigation may help for further understanding. I will discuss wave breaking and modulational instability in other related equations. I will say a few words about higher order corrections, extension to bidirectional propagation and two-dimensional surfaces, if time permits. This is based on the joint works with Jared Bronski (Illinois), Mat Johnson (Kansas), Ashish Pandey (Illinois), and Leeds Tao (UC Riverside).