# Applied and Interdisciplinary Mathematics (AIM) Seminar

# Meets Tuesdays, 11am to 12pm, 509 LA

### Organizers: Chris King, Robert McOwen, Adam Ding

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**Future Talks**

**Date**: September 23, 2014**Speaker**: Carlos Castillo-Chavez (Arizona State University)

**Title**: TBA

**Past Talks**

**Date**: March 25, 2014**Speaker**: Maxim Bichuch (Worcester Polytechnic Institute)

**Title**: Optimal Investment with Transaction Costs and Stochastic Volatility

**Abstract**: Two major financial market frictions are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when the cost is small. Under stochastic volatility, but with no transaction costs, the Merton problem under general utility functions can also be analyzed with asymptotic methods. Here, we look at the long-run growth rate problem when both frictions are present, using separation of time scales approximations. This leads to perturbation analysis of an eigenvalue problem. We find the first term in the asymptotic expansion in the time scale parameter, of the optimal long-term growth rate, and of the optimal strategy, for fixed small transaction costs. This is a joint work with Ronnie Sircar (Princeton).

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**Date**: March 18, 2014**Speaker**: Paul J. Atzberger (UC Santa Barbara)

**Title**: Mesoscale Methods for the Hydrodynamics of Microstructures: Applications in Soft Materials and Microfluidics

**Abstract**: Fluctuating hydrodynamic descriptions provide a promising approach for mesoscale simulations of elastic microstructures of soft materials and devices. The use of a fluctuating hydrodynamic description allows for capturing simultaneously such effects as the collective Brownian motion of hydrodynamically coupled microstructure as well as responses to external flows. The approach allows also for handling domains having arbitrary geometries and large systems through spatially adaptive discretizations. However, obtaining viable methods for simulations requires handling stochastic hydrodynamic equations (SPDEs) that are stiff in the sense of exhibiting a wide-range of dynamical time-scales and exhibit non-classical solutions (distributions). We show how viable stochastic spatial and temporal discretizations can be developed based on ideas from statistical mechanics and exponential time-step integration. We also perform stochastic mode analysis to obtain reduced descriptions tailored to specific physical regimes. We demonstrate for practical applications our computational methods for simulations of (i) particles within microfluidic devices, (ii) diffusion within lipid bilayer membranes, and (iii) the rheological responses of soft materials. We also discuss our open source software package Mango-Selm that aims to make our computational methods accessible to the wider scientific community.

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**Date**: February 11, 2014**Speaker**: Dima Krioukov (NU Physics)

**Title**: Random geometric graphs, Apollonian packings, number networks, and

**Abstract: **Random geometric graphs in hyperbolic spaces are shown to model well the structure and dynamics of some real networks, such as the Internet, social and biological networks. Due to the duality between hyperbolic and de Sitter spaces, random hyperbolic graphs are asymptotically identical to random de Sitter graphs, known as causal sets in quantum gravity where they represent discretizations of the global causal structure of an accelerating universe. Several connections between these random graphs, and Apollonian circle packings, Farey trees, divisibility network of natural numbers, and the Riemann hypothesis are also discussed.

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**Date**: January 14, 2014**Speaker**: Carina Curto (Univ of Nebraska)

**Title**: A geometric approach to understanding neural codes in recurrent networks

**Abstract:**Synapses in many cortical areas of the brain are dominated by local, recurrent connections. It has long been suggested, therefore, that cortical networks may serve to restore a noisy or incomplete signal by evolving it towards a stored pattern of activity. These “preferred” activity patterns are constrained by the excitatory connections, and comprise the neural code of the recurrent network. In this talk I will briefly review the permitted and forbidden sets model for cortical networks, first introduced by Hahnloser et. al. (Nature, 2000), in which preferred activity patterns are modeled as “permitted sets” - that is, as subsets of neurons that co-fire at stable fixed points of the network dynamics. I will then present some recent results that provide a geometric handle on the relationship between permitted sets and network connectivity. This allows us to precisely characterize the structure of neural codes that arise from a simple learning rule. In particular, we find “natural codes” that can be learned from few examples, and that closely mimic receptive field codes that have been observed in the brain. Finally, we use our geometric description of permitted sets to prove that these networks can perform error correction and pattern completion for a wide range of connectivities.

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**Date**: November 26, 2013**Speaker**: Ramis Movassagh (NU Math)

**Title**: Optical Bernoulli Forces

**Abstract:**By Bernoulli's law, an increase in the relative speed of a fluid around a body is accompanied by a decrease in the pressure. Therefore, a rotating body in a fluid stream experiences a force perpendicular to the motion of the fluid because of the unequal relative speed of the fluid across its surface. It is well known that light has a constant speed irrespective of the relative motion. Does a rotating body immersed in a stream of photons experience a Bernoulli-like force? We show that, indeed, a rotating dielectric cylinder experiences such a lateral force from an electromagnetic wave. In fact, the sign of the lateral force is the same as that of the fluid-mechanical analog as long as the electric susceptibility is positive, but for negative-susceptibility materials (e.g., metals) we show that the lateral force is in the opposite direction. Because these results are derived from a classical electromagnetic scattering problem, Mie-resonance enhancements that occur in other scattering phenomena also enhance the lateral force.

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**Date**: November 19, 2013**Speaker**: Silas Alben (University of Michigan)

**Title**: Optimizing snake locomotion in the plane

**Abstract:**Snake locomotion has recently drawn interest from biologists, engineers and applied mathematicians. Snakes propel themselves by a variety of gaits including slithering, sidewinding, concertina motion and rectilinear progression. We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we show that retrograde traveling waves are optimal. We give an asymptotic analysis showing that the optimal wave amplitude decays as the -1/4 power of the coefficient of transverse friction. This result agrees well with the numerical optima. At the other extreme, zero coefficient of transverse friction, we propose a triangular direct wave which is optimal. Between these two extremes, a variety of complex, locally optimal, motions are found. Some of these can be classified as standing waves (or ratcheting motions).

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**Date**: November 12, 2013**Speaker**: Emanuel Lazar (University of Pennsylvania)

**Title**: Dynamical Cell Structures: Evolution and Statistics

**Abstract:**Countless natural structures are cellular in nature -- soap foams, biological tissue, and polycrystalline metals are but a few examples that we frequently encounter in our everyday lives. In many of these systems, energetic factors force the geometry and topology of these structures to evolve in a continuous manner so as to drive the system towards more stable configurations. We use computer simulations to study how mean curvature flow shapes cell structures in two and three dimensions and how this can be measured in a statistical manner. This research lightly touches on discrete geometric flows, combinatorial polyhedra and their symmetries, and the quantification of topological features of large cellular systems.

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**Date**: November 5, 2013**Speaker**: Tsvi Tlusty (Institute for Advanced Study)

**Title:**Geometry and dimension in living information systems

**Abstract:**Life relies on efficient and accurate information processing. We will discuss living information systems that range between two extremes: the molecular scale of cellular codes and the much larger scale of human cortex and social interaction where languages evolve. The leitmotif of the discussion will be the common notion of geometry, topology and dimension, which appears to be essential to the understanding of how these systems emerge and evolve.

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**Date**: October 29, 2013**Speaker**: Pavlo Pylyavskyy (University of Minnesota)

**Title**: Inverse problems in cylindrical electrical networks

**Abstract:**The inverse Dirichlet-to-Neumann problem in electrical networks asks one to recover the combinatorial structure of a network and its edge conductances from its response matrix. For planar networks embedded in a disk, the problem was studied and effectively solved by Curtis-Ingerman-Morrow, de Verdière-Gitler-Vertigan and Kenyon-Wilson. I will describe how the problem can be solved for a large class of networks embedded in a cylinder. Our approach uses an analog of the R-matrix for certain affine geometric crystals. It also makes use of Kenyon-Wilson's groves. This is joint work with Thomas Lam.

**Date**: October 22, 2013**Speaker**: Mustafa Kesir (NU Math)

**Title**: A Mathematical Model of Redox/Methylation Metabolism in SY5Y Cells

**Abstract:** A mathematical model for glutathione (GSH) and folate metabolism in hepatic cells was previously developed (Reed et al. 2008)*, and was used to explore basic metabolic features and to understand changes occurring in autism and Down syndrome. The model predicted responses of liver cells to changing conditions and gave new insights into glutathione metabolism. However, redox/methylation metabolism can differ between tissues. We developed a similar model of the same metabolic pathways for neuronal cells, taking into account important differences between the two cell types, like low concentrations of cysteine and GSH and limited transsulfuration in neuronal cells. This makes cysteine uptake more critical for redox regulation in neuronal cells. In addition, an important role for selenoproteins has been added to our model. Sensitivity of cysteine uptake to IGF, TNF-α and morphine treatment adds a new dimension to our model. In this talk, methods and some details about developing such a model will be discussed. We will also talk about some practical implications of our findings.

(*:Theor Biol Med Model. 2008 Apr 28, A mathematical model of glutathione metabolism. Reed MC, Thomas RL, Pavisic J, James SJ, Ulrich CM, Nijhout HF.)

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**Date**: October 8, 2013**Speaker**: Rifat Sipahi (NU MIE)

**Title**: Delays in Dynamical Systems - Stability Analysis and Control Design for Linear Time-Invariant Systems

**Abstract:**Time delays appear in many disciplines, from engineering to physics, and from economics and biology to operations research. In this talk, I will first give an overview of various applications, and explain how delay arises in real-world systems. Next, using stability theory, I will demonstrate how delays can be detrimental and in some cases beneficial to render certain dynamic behavior in linear time-invariant dynamical systems. I will then present some results in which delays, network graphs, and stability cross-couple with each other, and which we apply on an experimental system to explore the validity of the theory.

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**Date**: October 1, 2013**Speaker**: Matt Kahle (Ohio State)

**Title**: Configuration spaces of hard spheres

**Abstract:**Configuration spaces of points are well-studied spaces in algebraic topology, geometric group theory, and combinatorics. Give the particles thickness, and you have what physicists might describe as phase space for a hard spheres gas. When the points are points, the topology of the configuration space is well understood but hardly anything is known when points have thickness. Changes in the topology as the thickness of the particles varies could be thought of as topological phase transitions. I will report on recent work understanding these kinds of changes in topology theoretically and experimentally, including joint work with Baryshnikov and Bubenik, and with Carlsson, Gorham, and Mason. I will also report on some work in progress, joint with MacPherson.**__________________________________________**

**Date**: September 17, 2013

**Speaker**: Leonid Petrov (NU Math)

**Title**: Integrable Stochastic Models for Highway Traffic in 1+1 Dimension

**Abstract:**Since the end of 1990's there has been a significant progress in understanding the long time nonequilibrium behavior of certain integrable (1+1)-dimensional interacting particle systems and random growth models in the KPZ universality class. Some of these systems have an interpretation as models of traffic on a one-lane highway.

**I will give a survey of integrable (1+1)-dimensional models, and present recent results on the most general of them (to date), including q-TASEP and q-PushASEP. The latter particle system is an especially nice traffic model. The miracle of integrability in most cases (with the notable exception of the partially asymmetric simple exclusion process) can be traced to an extension of the stochastic evolution to a suitable (2+1)-dimensional random growth model whose remarkable properties yield the solvability.**

**Based on joint works with Alexei Borodin, Ivan Corwin, and Tomohiro Sasamoto.**

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**Date**: September 11, 2013, 11:00-12:00 pm (Special Wednesday seminar)

**Speaker**: Anima Anandkumar (UC Irvine)

**Title**: Fast and Guaranteed Learning of Overlapping Communities via Tensor Methods

**Abstract:**Detecting hidden communities in networks is an important problem. A community refers to a group of related nodes. For instance, in a social network, it can represent individuals with shared interests or beliefs; in a gene network, it can represent genes with common regulatory mechanisms, and so on. Most previous approaches assume non-overlapping communities where a node can belong to at most one community. In contrast, we provide a guaranteed approach for detecting overlapping communities, when the network is generated from a class of probabilistic mixed membership models. Our approach is based on fast and scalable tensor decompositions and linear algebraic operations. We provide guaranteed recovery of community memberships and carry out a finite sample analysis of our algorithm. Additionally, our results match the lower bounds on scaling requirements (up to poly-log factors) in the special case of the stochastic block model (with non-overlapping communities).

**We have deployed the algorithm on GPUs, and our code design involves a careful optimization of GPU-CPU storage and communication. Our method is extremely fast and accurate on real datasets consisting of facebook network (about 20,000 nodes), yelp reviews (about 40,000 nodes) and dblp co-authorship network (about 120,000 nodes). For instance, on dblp dataset, our method takes under 2 hours to run to convergence. Thus, our approach is fast, scalable and accurate for detecting overlapping communities.**

**Bio:**Anima Anandkumar is a faculty at the EECS Dept. at U.C.Irvine. Her research interests are in the area of large-scale machine learning and high-dimensional statistics with a focus on learning probabilistic graphical models and latent variable models. She is the recipient of the Microsoft Faculty Fellowship, ARO Young Investigator Award, NSF CAREER Award, IBM Fran Allen PhD fellowship, and paper awards from the ACM SIGMETRICS and IEEE Signal Processing societies. She has been a visiting faculty at Microsoft Research New England and a postdoctoral researcher at the Stochastic Systems Group at MIT. She received her B.Tech in Electrical Engineering from IIT Madras and her PhD from Cornell University.**__________________________________________**

**Date**: September 10, 2013

**Speaker**: Ting Zhou (MIT)

**Title**: Quantitative Thermo-Acoustic Tomography (TAT)

**Abstract:**TAT is an example of a coupled-physics modality, which combines the high contrast of a physical phenomenon (here the electrical properties of tissues) with the high resolution of another phenomenon (here ultrasound). Thermo-acoustic imaging may be decom- posed into two steps. The rst step aims at reconstructing an amount of electromagnetic radiation absorbed by tissues from boundary measurements of ultrasound signals gener- ated by these radiations. We assume this rst step done. Quantitative thermo-acoustics then consists of reconstructing the conductivity coecient in the equation from the now known absorbed radiation. This second step is the problem of interest in this work.

**Mathematically, quantitative thermo-acoustics consists of reconstructing the conduc- tivity in time-harmonic Maxwell's equations from available internal data that are linear in the conductivity and quadratic in the electric eld. We consider inverse problems of this type with applications in thermo-acoustics. In this framework, we obtain uniqueness and stability of the reconstruction for a scalar model of time-harmonic wave propaga- tion, by choosing appropriate illuminations known as complex geometric optics (CGO) solutions for the equation. At last but not least, we consider the full system models of Maxwell's equations and see a dierent avor of analysis of uniqueness and stability using CGO solutions.**

**These are joint works with Guillaume Bal, Kui Ren and Gunther Uhlmann.**

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**Date**: April 2, 2013

**Speaker**: Mark Alber (University of Notre Dame)

**Title**: Multi-scale Modeling in Biology and Medicine

**Abstract:**A three-dimensional multi-scale modeling approach will be described for studying fluid–viscoelastic cell interaction during blood clot formation, with cells modeled by subcellular elements (SCE) coupled with Navier-Stokes fluid flow sub model. Using this method, motion of a viscoelastic platelet in a shear blood flow was simulated and compared with experiments on tracking platelets in a blood chamber. It will be shown that complex platelet-flipping dynamics under linear shear flows can be accurately recovered with the SCE model [1]. The structural features and mechanical properties of different types of fibrin networks grown in microfluidic devices will be also described including networks formed from normal plasma with and without cells, and from plasma from a hemophilic patient [2]. The mechanical model based on the microstructures within the network will be used to calculate the bulk properties of the network.

**In the second half of the talk, population of bacteria P. aeruginosa, main infection in hospitals, will be shown to propagate as high density waves that move symmetrically as rings within swarms towards the extending tendrils. Biologically-justified cell-based multi-scale model simulations suggest a mechanism of wave propagation as well as branched tendril formation at the edge of the population that depend upon competition between the changing viscosity of the bacterial liquid suspension and the liquid film boundary expansion caused by Marangoni forces [3,4]. P. aeruginosa efficiently colonizes surfaces by controlling the physical forces responsible for expansion of thin liquid films and by propagating towards the tendril tips. Therefore, P. aeruginosa can efficiently colonizes surfaces by controlling the physical forces responsible for expansion of thin liquid films and by propagating towards the tendril tips. The model predictions of wave speed and swarm expansion rate as well as cell alignment in tendrils were confirmed experimentally.**

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**Date**: February 26, 2013

**Speaker**: Aidong Ding (Math Dept)

**Title**: A Class of Discrete Transformation Survival Models with Application to Default Probability Prediction**Abstract:** Accurate corporate default probability prediction is very important for banking capital reservation calculation. While the corporate default can be naturally considered as a survival event, the survival analysis theory and techniques were not used for this application until last decade. In this talk, we discuss some distinct features of corporate bankruptcy from the traditional survival analysis model, and apply a discrete transformation family of survival analysis to corporate default risk predictions. We show using the default data of the US companies from 1980-2006 that a transformation parameter different from the popular Shumway's model and the proportional hazards model is needed for default prediction. The predicted corporate default probabilities on this data set show that the distressed company stocks did not receive full risk premium as speculated by the famous Fama and French's (1996) conjecture.

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**Date & Time**: 4:30-5:30 pm, Monday, February 4, 2013 (Note unusual day & time)

**Speaker**: Christopher Genovese (Statistics, Carnegie Mellon)

**Title**: Estimating Manifolds: Methods and Surrogates**Abstract:** Spatial data and high-dimensional data, such as collections of images, often contain high-density regions that concentrate around some lower dimensional structure. In many cases, these structures are well-modeled by smooth manifolds, or collections of such manifolds. For example, the distribution of matter in the universe at large scales forms a web of intersecting clusters (0-dimensional manifolds), filaments (1 dimensional manifolds), and walls (2-dimensional manifolds), and the shape and distribution of these structures have cosmological implications.

**I will discuss a new theory and methods for the problem of estimating manifolds (and collections of manifolds) from noisy data in the embedding space. The noise distribution has a dramatic effect on the performance (e.g., minimaxrates) of estimators that is related to but distinct from what happens in measurement-error problems. Some variants of the problem are "hard'' in the sense that no estimator can achieve a practically useful level of performance. I will show that in the "hard'' case, it is possible to achieve accurate estimators for a suitable surrogate of the unknown manifold that captures many of the key features of the object. And I will describe efficient methods for estimating surrogates and characterizing "hyper-ridges'' in many dimensions.**

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**Date**: January 29, 2013

**Speaker**: Dagmar Sternad (Biology, ECE, & Physics, Northeastern)

**Title**: Sensorimotor Skill: Analysis of Variability as a Window into Control (Part 2)

**Date**: January 15, 2013

**Speaker**: Dagmar Sternad (Biology, ECE, & Physics, Northeastern)

**Title**: Sensorimotor Skill: Analysis of Variability as a Window into Control

**Abstract**: Motor skills such as throwing a ball, dancing, or drinking a cup of coffee are key to functional behavior. Optimizing the acquisition and preventing or reverting the degradation of skill requires a rigorous quantitative understanding. Our approach analyzes how task dynamics constrains performance of sensorimotor skills and their change with practice. Our analysis focuses on the structure of variability, both in its distribution in high-dimensional task space and its temporal evolution. I will review experimental work on two model tasks where we showed how human skill learning is understood as one of navigating solution space. One task is a throwing task with accuracy demands, the second one simulates the interactive task of carrying a cup of coffee, i.e. manipulation of an object with an internal degree of freedom. Both tasks are implemented in a virtual environment that affords complete analytical understanding of the task and its solutions. I will focus on some open mathematical problems that may be of interest to scientists working on biological problems.

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**Date**: November 27, 2012

**Speaker**: Hoai-Minh Nguyen (University of Minnesota)

**Title**: Approximate cloaking using transformation optics and negative index materials

**Abstract**: Cloaking recently attracts a lot of attention from the scientific community due to the progress of advanced technology. There are several ways to do cloaking. Two of them are based on transformation optics and negative index materials. Cloaking based on transformation optics was suggested by Pendry and Leonhardt using transformations which blow up a point into the cloaked regions. The same transformations had previously used by Greenleaf et al. to establish the non-uniqueness for Calderon's inverse problem. These transformations are singular and hence create a lot of difficulty in analysis and practical applications. The second method of cloaking is based on the peculiar properties of negative index materials. It was proposed by Lai et al. and inspired from the concept of complementary media due to Pendry and Ramakrishna. In this talk, I will discuss approximate cloaking using these two methods. Concerning the first one, I will consider the situation, first proposed in the work of Kohn et al., where one uses transformations which blow up a small ball (instead of a point) into cloaked regions. Many interesting issues such as finite energy and resonance will be mentioned. Concerning the second method, I provide the (first) rigorous analysis for cloaking using negative index materials by investigating the situation where the loss (damping) parameter goes to 0. I will also explain how the arguments can be used not only to establish the rigor for other interesting related phenomena using negative index materials such as superlense and illusion optics but also to lighten the mechanism of these phenomena.

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**Date**: November 13, 2012

**Speaker**: Alain Karma (Physics, Northeastern)

**Title**: Physics of Cracking

**Abstract**: Most engineering, biological, and geological materials ultimately fail under large enough forces, as exemplified by catastrophic airplane failure, broken bones, and earthquakes. Even though crack propagation is the most common mode of failure, predicting the path of a crack in a material has remained a major challenge. This challenge stems from the fact that cracking is controlled by phenomena on multiple length and time scales from the elastic deformation of the material on a macroscopic scale to the breaking of atomic bonds on submicrometer to angstrom scales. I will present recent progress made to understand how cracks propagate in a three-dimensional material through computational and experimental studies. Computational studies exploit a new class of continuum fracture models that naturally bridge short and large scales of this problem. The results shed light on the fundamental mechanism by which the combination of tension and tearing leads to a widely observed and intriguing fragmentation of a planar crack into multiple daughter crack segments or ”fracture lances”. They also highlight the need for a short-scale regularization of standard crack propagation laws in three dimensions to avoid unphysical ultraviolet divergences that have until recently escaped notice of the fracture community.

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**Date**: November 6, 2012

**Speakers**: Burak Erem and Dana Brooks (Electrical and Computer Engineering, Northeastern)

**Title**: Some applications of a differential geometric approach to multielectrode signal processing problems in cardiac bioelectricity

**Abstract**: There are many situations in which measurements of bioelectric signals from an array of electrodes are of clinical or research interest, especially in the contexts of cardiology and neuroscience. Cardiac electrical signals in particular are measured clinically on the body surface or with electrodes on the inner heart surface and/or in the cardiac chambers. These signals lead to a variety of signal processing problems including signal averaging, wavefront arrival estimation, filtering, and inverse reconstruction of cardiac signals from body surface or intra-chamber measurements. Typically the measurements are treated as a collection of temporal waveforms. However the relevant biophysics imposes strong constraints on spatial variation in the temporal dynamics of these waveforms. In this work we treat such signals as trajectories on a low-dimensional dynamic manifold. We use that perspective to develop embedding approaches for several relevant problems, including the classical signal processing problem of signal averaging, identification of complex physiological behavior in the context of controlled ischemia studies, and the long-sought goal of clinically useful electrocardiographic inverse reconstructions. We will present results on several sets of measured data from canine experiments and human subjects. If time permits we will also suggest potential applications of this perspective to electroencephelogram signals.

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**October 23, 2012****Date**:

**Ivan Corwin (Clay Institute, Massachusetts Institute of Technology, Microsoft Research)****Speaker**:

**Title**: Beyond the Gaussian Universality Class

**Abstract**: The Gaussian central limit theorem says that for a wide class of stochastic systems, the bell curve (Gaussian distribution) describes the statistics for random fluctuations of important observables. In this talk I will look beyond this class of systems to a collection of probabilistic models which include random growth models, polymers,particle systems, matrices and stochastic PDEs, as well as certain asymptotic problems in combinatorics and representation theory. I will explain in what ways these different examples all fall into a single new universality class with a much richer mathematical structure than that of the Gaussian.

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**Date**: October 9, 2012

**Speaker**: Ramis Movassagh (Mathematics, Northeastern)

**Title**: Quantum Many-Body Systems and Their Ground States

**Abstract**: Study of quantum many-body systems (QMBS) encompasses the study of all aspects of matter. Properties of matter not adequately described by classical physics has gained a lot of attention in quantum information science and condensed matter physics. The non-classcality is mostly attributed to "entanglement", which can be utilized for quantum computing and yet makes the study of QMBS on classical computers so difficult. Two interesting features of QMBS are locality of interaction and that they often are in the their lowest energy states. In this talk we discuss the interface of quantum information science and condensed matter physics through QMBS research. We will then discuss the ground state properties of quantum spin chains with generic interactions. We then introduce a new spin chain model (measure zero) whose ground state is the uniform superposition of all "Motzkin walks" and whose gap can be calculated using a new technique based on mixing times of Markov chains. This model is the first example of a spin-1 'frustration free' quantum spin chain with signatures of criticality. Lastly, we will show the generalization of this model to integer spin-s and discuss open problems.**__________________________________________**

**Date**: September 25, 2012

**Unusual Time and Place:**3:00pm - 4:00pm in 335 Shillman Hall (SH)

**Speaker**: A.J. Devaney (Electrical and Computer Engineering, Northeastern)

**Title**: Theory and practice of Imaging, Tomography and Wavefield Inversion

**Abstract**: In this talk the speaker will review a number of applications that employ wavefields to probe the inner structure of three dimensional objects with the goal of deducing their inner structure. Examples include geophysical acoustic and elastic wave tomography, optical imaging and tomography, electromagnetic and ultrasound imaging and tomography, imaging of proteins and other micro structures using coherent X-rays, and radar target identification in military applications. All of these applications admit a unified formulation of the inverse problem that is readily solved using well developed methods drawn from the physics and mathematics communities. This talk will review this generalized formulation and its solution for a number of applications with special emphasis devoted to electromagnetic and optical tomography and ultrasound imaging. The talk will include both simulated as well as real data examples.