Past Seminars Computational Applied Math Feb 18, 2009 11:00am, AMS Seminar Room Most oil is produced by pumping water in some wells and recovering oil in others. The injected water often contains suspended particles that penetrate the rock and are retained in the pores. The rock becomes less permeable, and the well may become useless. This is deep bed filtration with formation damage. It is modeled by two conservation laws describing transport and retention of particles, and Darcy's law. The model contains an empirical "filtration function" of the deposited concentration, which cannot be measured directly. It must be recovered from experimental data by solving and ill-posed inverse problem, in the form of a functional equation. We present a robust method for solving this inverse problem mathematically, which gives rise to a robust numerical procedure. We show some numerical applications for real data. Wednesday, March 11, 2009 10:30am, AMS Seminar Room, Math Tower 1-122 Hierarchical reconstruction for spectral volume and RKDG methods for solving hyperbolic conservation laws
In this talk, I will dicuss the recent development of hierarchical reconstruction (HR) [Liu etal., Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction. SIAM J. Numer. Anal., 45:2442-2467, 2007 and Xu et al., Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO type linear reconstruction and partial neighboring cells. J.C.P. (in press)] for limiting solutions computed by spectral volume and RKDG methods for solving hyperbolic conservation laws. HR is applied to a piecewise quadratic polynomial on two-dimensional unstructured grids as a limiting procedure to prevent spurious oscillations in numerical solutions. The key features of this HR are that the reconstruction on each element only uses adjacent neighbors, which forms a compact stencil set, and there is no truncation of higher degree terms of the polynomial. We explore a WENO-type linear reconstruction on each hierarchical level for the reconstruction of high degree polynomials. We demonstrate that the hierarchical reconstruction can generate essentially non-oscillatory solutions while keeping the resolution and desired order of accuracy for smooth solutions. Wednesday, March 18, 2009 12:00pm, AMS Seminar Room, Math Tower 1-122 The central scheme (Nessyahu and Tadmor '90) can be extended to staggered overlapping cells
on which the O(1/dt) dissipation error due to grid shifting can be removed while keeping
the benefit of using no flux function or Riemann solver. This strategy allows us Wednesday, April 1, 2009 12:00pm, AMS Seminar Room, Math Tower 1-122 Updating meshes on deforming domains via the target-matrix paradigm Mesh quality can impact simulation accuracy and efficiency, as
well as determine the time needed to create a mesh. Mesh Wednesday, April 22, 2009 12:00pm, AMS Seminar Room, Math Tower 1-122 Studying the physical and biological mechanisms of extracorporeal shock wave therapy (ESWT) requires modeling the propagation of strong shock waves through tissue and bone. Interfaces between different biological materials lead to reflections and focusing of shock waves and the creation of strong rarefaction zones and cavitation fields. I will discuss recent numerical work using high-resolution finite volume methods in which each grid cell is allowed to have distinct material properties. Sharp interfaces either occur at cell edges (if an appropriate geometry-conforming grid can be obtained) or are represented by averaging the material properties over grid cells on a Cartesian grid. In either case, logically rectangular grids with adaptive mesh refinement are used to efficiently deal with multiscale problems where the medium has heterogeneities at various length scales. Wednesday, June 24, 11:00am, AMS Seminar room, Math Tower 1-122 Title: Multi-scale simulations of multiphase flow and reactive transport in fractured and porous media. An SPH multiphase flow model was used to study the effects of pore-scale heterogeneity and anisotropy on infiltration/drainage cycles, entrapment and dissolution of non-wetting fluids and a pressure/saturation relationship. An SPH reactive transport model was used as a part of a multi-scale numerical and experimental study of mixing-induced reactions and mineral precipitation. In a laboratory experiment, solutions containing Na2CO3 and CaCl2 were each injected in different halves of a quasi two-dimensional flow cell filled with quartz sand. Pore-scale simulations were conducted to help understand the mechanism of precipitation layer formation. A meso-scale langevin model and a hybrid model were developed to bridge a gap between pore-scale and darcy-scale descriptions of transport processes. Wednesday, September 23rd, 10:30 am, AMS Seminar room, Math Tower 1-122 Title: The Common Component Architecture for Scalable Scientific Software Engineering Kostadin Damevski Abstract: In recent years, component technology has been a successful methodology for large-scale commercial software development. Component technology encapsulates a set of frequently used functions into a component and makes the implementation transparent to the users. Application developers typically use a group of components, connecting them to create an executable application. The Common Component Architecture (CCA) is a project whose goal is to use component technology in scientific computing to tame the software complexity required in coupling multiple disciplines, multiple scales, and/or multiple physical phenomena. The CCA is designed to fit the needs of the scientific computing community by imposing very low overhead, supporting parallel components, and enabling interoperability with legacy code. The CCA component model has already been used in several application domains, creating components for large simulations involving accelerator design, climate modeling, combustion, and accidental fires and explosions. These simulations are able to execute on sets of distributed memory machines spanning several computational and organizational domains. This talk will introduce the CCA and its associated tools and discuss some of the recent advancements made by this project. Wednesday, October 7, 10:30 am, AMS Seminar Room 1-122 Viktor Kilchyk Pressure-wave Amplification of Flame Area in Wave Rotor Channels Abstract Deformation of an interface between fluids with different densities following a shock passage is referred as Richtmyer-Meshkov instability. To characterize interface increase produced by the instability, perturbation amplitude growth is commonly studied. However, it is the area of the interface that is crucial to flame speed and burning rate predictions. Therefore, in our work we studied numerically the area increase of a flame following a shock or an expansion wave passage. Numerical solutions to the Navier-Stockes equations were obtained using an in-house second order CFD code. The code is specialized in handling ideal and real compressible fluids. An upwind finite-volume spatial discretization was used with an approximate Riemann solver adapted to the generalized form of the governing equations. It was found that the area of a sinusoidally perturbed flame increases almost linearly, for a time period significantly exceeding duration of growth of the perturbation amplitude. Opposite to the expected from the Richtmyer-Meshkov theory, for a given set of initial parameters, faster interface growth rates were observed in shock refractions where shock approached from the “hot” side of the interface (fast/slow refractions). More importantly, the computed interface growth rates produced by shocks and expansion waves showed nearly linear correlation with deposited circulation. Using an analytical solution for shock and expansion wave deposited circulation, contribution of the flame area increase to the overall burning rate variation was examined. The results showed that the flame area increase plays a dominant role in the burning rate change with relatively weak shocks and expansion waves. In the case of expansion waves, it was also shown that expansion wave-flame interaction may result in a burning rate increase temporarily; the negative chemical kinetic effect of expansion wave passage is offset by the flame area increase. Wednesday, October 21, 2009, 1:00 pm, AMS Seminar Room 1-122 Ravi Samtaney Title: Overcoming spatial and temporal stiffness in MHD simulations. Abstract: Magnetohydrodynamics (MHD) is arguably the most popular mathematical model for the macroscopic simulations of fusion plasmas. In this talk we will focus on the resistive single-fluid MHD equations, the solutions of which can exhibit near-singular layers (or even discontinuities in the absence of diffusion terms). We rely on locally adaptive structured mesh refinement (AMR) methods to mitigate the separation of spatial scales in MHD. We will present results from AMR simulations of MHD applications: (a) pellet injection, a proven method to refuel tokamaks; (b) magnetic reconnection which is a canonical problem in plasma physics involving thin current sheets; and (c) an example in MHD shock refraction where five or more For a tokamak fusion plasma, the presence of a large background field and toroidal geometry results in a large separation of temporal scales. Explicit time-stepping methods to simulatfusion plasmas become prohibitively expensive due to the CFL constraint on the time-step. To overcome the temporal stiffness associated with the fast compressive and Alfven waves in MHD, we have developed a nonlinearly implicit time stepping method using a Jacobian-Free Newton-Krylov approach (JFNK) and begun exploring nonlinear multigrid methods. At the heart of our JFNK method is a PDE-operator based preconditioner (exact for a 1D system of hyperbolic PDEs), to effectively solve the resulting large ill-conditioned linear system. Wednesday, October 28, 2009, 9:30 am, AMS Seminar Room 1-122 Speaker: Min Zhou Title: Petascale Adaptive Computational Fluid Dynamics Abstract: In this study, we identify and resolve several bottlenecks facing unstructured, adaptive, implicit finite element methods march toward petascale simulations. With those obstacles resolved, our method demonstrates its capabilities with strong scalability on large scale supercomputers and its ability to solve problems of interest requiring intensive numerical computations in a reasonable time frame. The performance of our implicit solver is improved by two algorithms developed in this work. The first algorithm, multiple compute-object partition improvement, incrementally improves the load balance, hence the scalability of both the equation formation and the equation solution of the finite element analysis (FEA). The second algorithm, data reordering, enables the effective usage of the memory subsystem by increasing the data locality, so as to accelerate the per-core performance of the FEA. We present excellent strong scaling for several applications performed on various supercomputers including IBM Blue Gene (BG/L and BG/P), Cray (XT3 and XT5) and Sun Constellation Cluster. The applications involve the flow simulations of a bifurcation pipe model with relatively small meshes and cardiovascular flow of an abdominal aorta aneurysm model with a much bigger mesh (more than 1 billion elements). The other application involves the blood flow in a ``whole'' body model composed of 78 arteries; from the neck to the toes. The effectiveness of our methodologies and the algorithms developed in this work are investigated in those applications. With the ability to solve real-world problems having complex geometry/physics in a realistic time, this work provides a reliable and efficient computation tool that can be used by researchers for design and development purpose. Computational Biology Friday, March 27, 2pm, AMS Seminar Room, Math Tower 1-122 The primary aim of our research is to understand how gene regulation generates precise spatial patterns in embryonic development. However, the chemical reactions and transport processes underlying pattern formation are subject to numerous sources of variability and noise. Extrinsic sources include variability in temperature, size and maternally-supplied factors. Intrinsic noise arises from the low concentrations of many biological molecules and the random aspects of cell shape, orientation and movement. For development to reliably form complex body plans, gene network dynamics must be robust to these disruptive influences. We use one of the genetically best characterized model systems for embryonic patterning, anterior-posterior (AP) segmentation in Drosophila. We combine quantified data acquisition, statistical extraction of trends and noise components, and stochastic and evolutionary modeling of gene networks. Such an integrated approach is required to properly characterize the different aspects of developmental noise (within an embryo, e.g. nucleus-to-nucleus) and variability (embryo-to-embryo), and to understand how these are controlled. Our long-term goal is to provide a mathematically quantified understanding of the interactions which give the robust spatial patterning underlying the development of complex body plans. Studying how networks maintain robustness, and how they lose it, should have direct bearing on heritable human diseases, particularly birth defects, which display variable outcome. Monday, April 13, 2009 10:30 AM, AMS Seminar Room, Math Tower 1-122 P. Therese Lang Although proteins populate ensembles of structures in solution, X-ray diffraction data are traditionally interpreted using a single dominant model. To detect ensembles of side chain motions in x-ray electron density, we developed a new computational method called Ringer. Using this approach, we have identified structural fluctuations in protein active sites and explored their effects on the biophysical properties of ligand binding. Using experimental density, Ringer identified unmodeled alternate rotamers in 5-15% of side chains, supporting the idea that the newly detected conformations are widespread. With this new method, we are exploring X-ray structures of calmodulin (CaM), a calcium signaling protein that recognizes approximately 200 different peptide sequences, to test the idea that free receptors contain structural fluctuations required for bound conformations. We have identified several, previously unmodeled alternate side chain conformations in the active site of apo-CaM structure necessary for diverse binding. We have also seen a correlation with NMR experiments that detect changes in side chain rotamers. The identified alternate conformations support predictions about which residues within the binding site can influence recognition selectively by modulating the ensemble of side motions. These studies have the potential to provide new tools to explore the underpinnings of ligand specificity in CaM and other systems. Operations Research Thursday, March 19, 11:30am, AMS Seminar Room, Math Tower 1-122 Monday, March 23, 4:00pm, AMS Seminar Room, Math Tower 1-122 Tuesday, May 5, 11:00 am, AMS Seminar Room, Math Tower 1-122 Evdokia Nikolova How do we get to the airport on time? Ideally we would like to take the shortest path, however in the presence of uncertain traffic what does that mean? Is that the path with smallest expected travel time, or should we minimize the path variance or some other metric? One natural objective is to choose the path which maximizes our probability of arriving on time. This turns out to be equivalent to a non-convex optimization problem, for which no efficient algorithms are available. We develop algorithms that bridge stochastic, nonconvex and combinatorial optimization. In fact, our algorithms extend to solve a much more general framework of stochastic optimization that incorporates risk, beyond shortest paths. In an alternative route planning model, we seek adaptive algorithms which tell us where to go at every node along the way, given the realized edge values so far and the edges adjacent to our current position. This problem, called the Canadian traveler problem, turns out very challenging even with simple linear objectives which aim to minimize the expected route length. We provide the optimal policies (adaptive algorithms) for a class of graphs based on Markov Decision Processes and conclude with intriguing open problems. Quantitative Finance February 19, 2009, 4:00pm, AMS Seminar RoomTitle: Quantitative Challenges in Algorithmic Execution Professor Robert Almgren of NYU Courant Institute Thursday, March 19th, 4pm, AMS Seminar Room, Math 1-122 After a brief review of the development of US mortgage market, a widely-used Mortgage Backed Securities (MBS) pricing procedure, consisting of Option Adjusted Spread (OAS) analysis and prepayment modeling, is introduced. Then we discuss some challenges in pricing MBS, including evaluation of prepayment risk, interest rate modeling, and analysis of loans with different characteristics. In the end, several key factors causing the current subprime mortgage credit crisis are examined and recommendations are provided to improve the pricing models for MBS. Tuesday, April 21, 2009 4:00pm, AMS Seminar Room, Math Tower 1-122 The Capital Asset Pricing Model (CAPM) was a fundamental contribution to the field of financial economics, relating the sensitivity of an asset's return to the stock market return. This sensitivity (or slope), referred to as beta, is ubiquitous in modern finance. An assumption of CAPM is that there is a linear relationship between asset returns and market returns, but this does not always hold in practice. We consider a continuous-time CAPM model where beta is not constant, but rather is piecewise constant. This allows us to introduce regime-switching dynamics while keeping things tractable. When the market level crosses below a given threshold, an additive term increases the slope, resulting in a higher sensitivity of asset returns to market returns. We develop the price of an equity option using this approach. Along the way, several interesting quantities appear, such as the occupation time of a Brownian motion in an interval, and Brownian local time. One of the future goals of this research will be to introduce a calibration technique for the slope in each regime based on estimated option price parameters of both the asset and the market index. Monday, May 4, 2009, 1:00pm, AMS Seminar Room, Math Tower 1-122 Monday, June 8, 11:30am, AMS Seminar room, Math Tower 1-122 American Options: Free-Boundary-Value Problems in Finance Qiang Zhang A vanilla option is a right to buy or sell an underlying security at a fixed price. Exotic options have more complicated payoff structures and depend on more state variables. It is well known that, in a simple setting, the prices of European options that can only be exercised on the maturity date are given by the Black-Scholes formulae. However, most of options traded in the market are American type that can be exercised any time before and on the maturity date. So far, except in a few special cases, no close-form expressions for American options have been found and numerical computation is the main method for pricing American options. The difficulty is due to the fact that the American options are free-boundary-value problems, namely at what critical price of the underlying one should exercise the options? In this talk we will discuss the theoretical properties of American options and analytical approximations for the solutions of American options and the free boundaries. We show that this approximation method is applicable to both American type vanilla and exotic options. We will also discuss free-boundary-value problems in other types of financial products. Wednesday, September 9, 2009, 3:50 pm, AMS Seminar Room, Math Tower 1-122 David Cru Abstract: Portfolio Selection as introduced by Harry Markowitz laid the foundation for Modern Portfolio Theory. However, the assumption that underlying asset returns follow a normal distribution and that investors are indifferent to skew and kurtosis are not practically suited for the hedge fund environment. Additionally, the Lockup and Notice provisions built into hedge fund contracts make portfolio rebalancing difficult and justify the need for dynamic allocation strategies. Market conditions are dynamic therefore rebalancing constraints in the face of changing market environments can have a severe impact on return generation. There is a need for sophisticated yet tractable solutions to the multi-period problem of hedge fund portfolio construction and rebalancing. We Generalize the hedge fund asset return distribution to a Multivariate K-mean Gaussian Mixture Distribution; cast the multi-period hedge fund allocation problem as a constrained optimization problem; and propose practical rebalancing strategies that represent a convergence of literature on Hedge Fund investing, Regime Switching and Dynamic Portfolio Optimization Wednesday, September 16, 2009, 3:50PM to 5PM, AMS Seminar Room, Math Tower 1-122 Andrew P. Mullhaupt, Ph.D. Dr. Mullhapt recently retired as Director of Research and Portfolio Manager at SAC Meridien Fund, a systematic hedge fund. Dr. Mullhaupt has worked at Renaissance Technologies as a Senior Research Analyst and at Morgan Stanley. He has held various academic posts at SUNY Buffalo, the University of New Mexico and the Courant Institute. Dr. Mullhaupt received his Ph.D. in Applied Mathematics from the Courant Institute and his B.S. from Stevens Institute of Technology. Wednesday, September 30, 2009, 3:50 - 5:10 pm, Math Common Room 4-125 Speaker: Michael Driscoll, Ph.D. Title: Challenges in Assessing Credit Risk in Today's Financial Crisis Abstract: In the current environment, the financial services industry and its regulators are concerned about exposure to credit risk. The distribution of financial losses due to changes in the credit quality of a counterparty to a financial agreement. Credit risk pervades virtually all financial transactions. The rise in the complexity and globalization of financial services has contributed to stronger linkages between counterparties. While higher connectivity facilitates economic growth through credit allocation and risk diversification, it also increases the potential for disruptions to spread throughout the system. Financial engineering further enabled risk transfers that were not fully accounted for by regulators or by the institutions themselves, thereby complicating the assessment of counterparty risk, risk management, and policy responses. The current crisis highlights how systemic linkages can arise not just from financial institutions’ solvency concerns but also from the lack of market liquidity and other stress events. At the center of the issue is the quantification of the probability of a default; an event resulting from a complex decision process. This process is affected by the intricate network of business relations between firms, and in turn, the default decision of a single firm affects the entire system. Corporate defaults aggregate and is induced by the correlation among firms. It is driven by individual firm sensitivity to common economic factors such as interest rates or inflation, but also from the feedback of an individual firm event to the entire system. -Forecasting of individual defaults, All facets of credit risk assessment face a wide range of challenges ranging from the availability of historical events to measure and calibrate models to the transparency of risk within the system and the uncertainty of available information. Michael Driscoll is a Managing Director at Cogent Partners, specializing in capital markets and risk management advisory services in Private Equity and Alternative Investments. Dr. Driscoll has been a Principal and Global Head of Risk Management for Allianz (ART Group) and a member of their Underwriting, Risk and Investment Management Committees. He began his career in the research division of AT&T Bell Laboratories and received his Ph.D, M.S. and B.S. degrees from SUNY Stony Brook where he was elected to Sigma Xi and Tau Beta Pi. Dr. Driscoll also serves a member of the Stony Brook Center for Quantitative Finance Advisory Board. Wednesday, October 7th, 3:50pm - 5:10PM , AMS Seminar room 1-122 Speaker: Michael Driscoll, Ph.D. Title: Challenges in Assessing Credit Risk in Today's Financial Crisis Abstract: In the current environment, the financial services industry and its regulators are concerned about exposure to credit risk. The distribution of financial losses due to changes in the credit quality of a counterparty to a financial agreement. Credit risk pervades virtually all financial transactions. The rise in the complexity and globalization of financial services has contributed to stronger linkages between counterparties. While higher connectivity facilitates economic growth through credit allocation and risk diversification, it also increases the potential for disruptions to spread throughout the system. Financial engineering further enabled risk transfers that were not fully accounted for by regulators or by the institutions themselves, thereby complicating the assessment of counterparty risk, risk management, and policy responses. The current crisis highlights how systemic linkages can arise not just from financial institutions’ solvency concerns but also from the lack of market liquidity and other stress events. At the center of the issue is the quantification of the probability of a default; an event resulting from a complex decision process. This process is affected by the intricate network of business relations between firms, and in turn, the default decision of a single firm affects the entire system. Corporate defaults aggregate and is induced by the correlation among firms. It is driven by individual firm sensitivity to common economic factors such as interest rates or inflation, but also from the feedback of an individual firm event to the entire system. All facets of credit risk assessment face a wide range of challenges ranging from the availability of historical events to measure and calibrate models to the transparency of risk within the system and the uncertainty of available information. Michael Driscoll is a Managing Director at Cogent Partners, specializing in capital markets and risk management advisory services in Private Equity and Alternative Investments. Dr. Driscoll has been a Principal and Global Head of Risk Management for Allianz (ART Group) and a member of their Underwriting, Risk and Investment Management Committees. He began his career in the research division of AT&T Bell Laboratories and received his Ph.D, M.S. and B.S. degrees from SUNY Stony Brook where he was elected to Sigma Xi and Tau Beta Pi. Dr. Driscoll also serves a member of the Stony Brook Center for Quantitative Finance Advisory Board. Wednesday, October 14th, 3:50PM - 5:10PM, AMS Seminar room, Math Tower 1-122 Speaker: Greg Van Inwegen, Ph.D. Title: "Risk Management in a Non Transparent and Non Linear World: Perspectives and Challenges from a Fund of Hedge Funds" Abstract: Multi-Factor Risk Modeling & Stress Testing Dr. Van Inwegen is a Managing Director and Chief Investment Risk Officer at Ivy Asset Management, where he has worked since 2004. He chairs the Investment Risk Management Committee at Ivy and leads the Risk Management and Quantitative Research team at this Hedge Fund of Funds. His professional career started at Syracuse University, where he taught Finance as an Assistant Professor before moving to Wall St. He has worked at Verizon, Paine Webber, Bankers Trust, Deutsche Bank, and a hedge fund start up. In addition to risk management, he as been involved in a number of elements of the asset management business, including stock selection models, asset allocation, enhanced indexing and high frequency statistical arbitrage models. Dr. Van Inwegen has degrees from the University of California at Berkeley, the Sloan School at MIT; and the Wharton School at the University of Pennsylvania. Wednesday, October 28th, 3:50PM - 5:10PM, Physics Tower S-240 Speaker: Ann Tucker, Ph.D. Title: Momentum and the Financial Crisis Abstract: The momentum factor is a well documented market anomaly that continues to exhibit strength well after it was first documented in the academic literature. There is evidence that momentum exposure, or long exposure to assets with good recent performance and short exposure to assets with poor recent performance, is especially widespread within the hedge fund community. The extent of the exposure became painfully clear during the second half of 2008 when Lehman’s bankruptcy triggered a global unwinding of risk in almost every asset class. This talk explores the contribution of momentum-related strategies in equities, commodities, interest rates and foreign exchange to the buildup of risk in the global financial system and the chaos that ensued when the great reversal occurred. In addition, the roles played by the U.S. dollar and the Japanese yen as carry currencies of choice during this period are examined in the context of the momentum environment, possible intervention of the Chinese in the currency markets, and the unwinding of the aforementioned carry trades. Statistics No scheduled seminars |