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

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

The seminar features talks in Applied and Interdisciplinary Mathematics (AIM) by our own faculty as well as faculty from other departments at Northeastern and other Universities in the Boston Area. For additional information or to be added to the mailing list, please contact Robert McOwen.

### Future Talks

Date: November 25, 2014
Speaker: Scott Aaronson  (MIT)
TitleWhen Exactly Do Quantum Computers Provide a Speedup?

AbstractTwenty years after the discovery of Shor's factoring algorithm, I'll survey what we now understand about the structure of problems that admit quantum speedups.  I'll start with the basics, discussing the hidden subgroup, amplitude amplification, adiabatic, and linear systems paradigms for quantum algorithms.  Then I'll move on to some general results, obtained by Andris Ambainis and myself over the last few years, about quantum speedups in the black-box model.  These results include the impossibility of a superpolynomial quantum speedup for any problem with permutation symmetry, and the largest possible separation between classical and quantum query complexities for any problem.

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Date: December 2, 2014
SpeakerRamis Movassagh (Northeastern University)
Title:   Power law violation of the area law in quantum spin chains

Abstract: The sub-volume scaling of the entanglement entropy with the system's size, $n$, has been a subject of vigorous study in the last decade. The area law provably holds for gapped one dimensional systems and it was believed to be violated by at most a factor of $\log\left(n\right)$ in physically reasonable models such as critical systems.
In this paper, we generalize the spin$-1$ model of Bravyi et al to all integer spin-$s$ chains, whereby we introduce a class of exactly solvable models that are physical and exhibit signatures of criticality, yet violate the area law by a power law. The proposed Hamiltonian is local and translationally invariant in the bulk. We prove that it is frustration free and has a unique ground state. Moreover, we prove that the energy gap scales as $n^{-c}$, where using the theory of Brownian excursions, we prove $c\ge2$. This rules out the possibility of these models being described by a conformal field theory. We analytically show that the Schmidt rank grows exponentially with $n$ and that the half-chain entanglement entropy to the leading order scales as $\sqrt{n}$. Geometrically, the ground state is seen as a uniform superposition of all $s-$colored Motzkin walks. Lastly, we introduce an external field which allows us to remove the boundary terms yet retain the desired properties of the model. Our techniques for obtaining the asymptotic form of the entanglement entropy, the gap upper bound and the self-contained expositions of the combinatorial techniques, more akin to lattice paths, may be of independent interest.
(joint work with Peter W. Shor)

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Date: December 9, 2014
SpeakerMason A. Porter  (University of Oxford, U.K.)
TitleCascades and Social Influence on Networks

Abstract: I discuss "simple" dynamical systems on networks and examine how network structure affects dynamics of processes running on top of networks. I'll give an introduction to the idea of social ("complex") contagions, and I'll present a model for multi-stage complex contagions--in which fanatics produce greater influence than mere followers.  I'll also briefly discuss the use of ideas from topics like persistent homology to examine wavefront propagation versus the appearance of new contagion clusters, and I'll present a model (without network structure) for the adoption of applications on Facebook.
The last family of models illustrates how very different time-dependent dynamics can produce quantitatively similar long-time behavior, which poses both very serious challenges and exciting opportunities for the
modeling of complex systems.

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Date: January 27, 2015

Speaker:  Abhyudai Singh (University of Delaware)

Title: TBA

Date: February 10, 2015

Speaker Edoardo M. Airoldi (Department of StatisticsHarvard University)
Title: TBA

DateFebruary 17, 2015

Speaker:  Nayantara Bhatnagar (University of Delaware)

Title: TBA

Date: March 31, 2015

Speaker:  Lydia Bourouiba (Department of Mathematics, MIT)
Title: TBA

Past Talks

Date: November 18, 2014
Speaker: Francis Chung (University of Michigan)
Title:  Electromagnetic inverse problems with partial data

Abstract:  I will begin by describing an inverse problem for Maxwell's equations, which goes roughly as follows. Suppose we can measure the electromagnetic fields on the boundary of an object -- can we use this information to recover the electrical and magnetic parameters of the interior of the object?  In this talk I will consider the partial data version of this problem, where we can measure only on part of the boundary, and describe some recent results along these lines.

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Date: November 4, 2014
Speaker: David R. Nelson (Lyman Laboratory of Physics, Harvard University)
Title: Dislocation-Mediated Elongation of Bacteria

Abstract: Recent experiments have revealed a remarkable growth mechanism for rod-shaped bacteria:  specialized proteins associated with cell wall elongation move at constant velocity in clockwise and counterclockwise directions
on circles around the cell circumference.  We argue that this machinery attaches to dislocations in the ordered peptidoglycan cell wall, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Unlike the dislocations typical in materials science, the motion is predominantly climb (glycan strand extension) instead of glide. The activated motion of these dislocations and the resulting dynamics within a simple kinetic model show surprising effects arising from the cylindrical geometry, with important implications for bacterial growth.   Recent experiments revealing plastic deformation of bacterial cell walls bent by a hydrodynamic flow will be presented as well.

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DateOctober 28, 2014

Speaker: Ken Duffy (Hamilton Institute, NUIM, Ireland)
Title: Inferring the average generation of a population of cells

Abstract: A fundamental quantity of interest in cell biology is the average number of divisions per cell since the initial progenitors, i.e. the average generation of presently living cells. It can, for example, be used to quantify dynamics and aging of the immune system, to better understand the evolution and risk of cancer, and to rank cell types in hierarchies of complex differentiation programs. Estimating average generation is a simple matter if, for example, the cells are directly observable with time-lapse microscopy or if one can stain progenitors with a division-diluting dye. For large numbers of generations and/or in vivo systems, as is necessary for several significant applications, no methodology is presently available.

In this talk we describe a scheme that we have developed to infer average generation. We shall introduce theorems regarding the average generation of an age-dependent branching process that enable us to relate its growth rate to an experimentally measurable quantity, the proportion of neutrally mutated cells. A genetic construct that enables the realization of this estimate, a version of which is presently being built by Ton Schumacher's group (Netherlands Cancer Institute), will be described. No prior biological knowledge will be assumed of the audience.

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Date: October 21, 2014
Speaker: Seth Lloyd (MIT)
Title: Quantum machine learning

Abstract:

Machine learning algorithms look for patterns in data.   Frequently, that data comes in the form of large arrays of high-dimensional vectors.   Quantum computers are adept at manipulating large arrays of high-dimensional vectors.  This talk presents a series of quantum algorithms for big data analysis.   The ability of quantum computers to perform Fourier transforms, find eigenvectors and eigenvalues, and invert matrices translates into quantum algorithms for clustering, principal component analysis, and for identifying topological features such as numbers of connected components, holes and voids.  These quantum algorithms are exponentially faster than their classical counterparts: complex patterns in datasets of size N can be identified in time O( log N).
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Date: October 14, 2014
Speaker: Steven G. Johnson (MIT)
Title: The mathematics of lasers: From nonlinear eigenproblems to linear noise

Abstract:
Lasers are ubiquitous in modern technology, but their theoretical description is a complicated mixture of quantum and classical electromagnetic phenomena.   Starting from a simple toy model of a laser as an oscillator with a nonlinear gain, we will review the basic description of laser physics.  In recent years, this description has evolved into the steady-state ab-initio laser theory (SALT) of Tureci, Stone, and others: a type of nonlinear eigenproblem. Although the SALT equations could initially only be solved in simple 1d and 2d geometries, we have now demonstrated that modern numerical methods can solve SALT for the lasing modes in general 3d systems, coupling the full vectorial Maxwell equations with the nonlinear gain of the lasing medium in complex inhomogeneous media.
This progress in computational solvers, in turn, has enabled purely analytical progress on the laser linewidth in the presence of noise.  Returning to the toy nonlinear-oscillator model of a laser, we review how the presence of noise induces a Brownian drift of the laser phase (described by a stochastic ODE) and causes its spectrum to be a finite-width peak.  The theoretical challenge is to derive the width of this peak in the context of complex laser geometries and dynamics, where the noise originates from quantum charge fluctuations (Johnson-Nyquist noise) in matter.  We show how, by linearizing the dynamics around the steady-state (noise-free) SALT solutions, we can obtain an analytical linewidth expression that encapsulates nearly all previous results (which were mostly derived in simplified 1d models; e.g. the Schawlow-Townes formula, the Petermann correction, and the Henry α correction) as special cases.

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Date: October 7, 2014
Speaker: Ken Kamrin (MIT)
Title: Continuum modeling of granular flow

Abstract:
Despite the ubiquity of granular matter in the world around us, the challenge of predicting the motion of a collection of flowing grains has proven to be a difficult one, from both computational and theoretical perspectives.  Grain-by-grain discrete element methods can be used, but these approaches become computationally unrealistic for large bodies of material and long times.   A broadly accurate continuum model would be ideal if it could be found, as it would provide a much more rapid means of calculating flows in real-world problems, such as those encountered in industrial design and geotechnical engineering.

With this challenge in mind, in this talk we propose a new constitutive relation for granular matter, which produces quantitatively accurate predictions for granular flow.  The model is constructed in a step-by-step fashion.  First we compose a local relation based on existing granular rheological approaches (i.e. the principle of  "inertial" rheology) and point out where the model succeeds and where it does not.  The clearest missing ingredient is shown to be the lack of an intrinsic length-scale.  To tie flow features more carefully to the characteristic grain size, we justify a nonlocal modification which takes the form of a size-dependent term in the rheology (with one new material parameter).  The nonlocal model is then numerically implemented with a custom-written User-Element in the Abaqus package, where it is shown to greatly improve flow predictions compared to the local model.  In fact, it is the first model to accurately predict all features of flows in `split-bottom cell' geometries, a decade-long open question in the field.  In total, we will show that this new model, using three material parameters, quantitatively matches the flow and stress data from over 160 experiments in several different families of geometries.  We close the talk by showing how the same model can be used to reconcile certain "strange" features of granular media that have been documented in the literature, such as the observation that thinner granular layers behave as if they are stronger, and the motion-induced "quicksand" effect wherein flow at one location reduces the yield limit everywhere.

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Date: September 23, 2014
Speaker: Carlos Castillo-Chavez (Arizona State University)
Title: Dispersal, Epidemics and Disease Evolution: Challenges and Opportunities in Computational, Mathematical and Theoretical Epidemiology
Abstract: I will briefly trace the history of the field of mathematical epidemiology with emphasis on the transmission and evolution of influenza. Emphasis will be placed on the role of multiple time scales and the study of long-term versus short-term dynamics. The role of dispersal will be briefly addressed and its relation to diseases that include Leprosy and Ebola. This presentation will be based on the work of former students and collaborators including Ana Luz Vivas Barber, Edgar Diaz and others.
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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.
In the cell, we will examine the translation machinery, in particular the genetic code and the ribosome, the engine of self-replication. The genetic code will be described in terms of a stochastic mapping whose basic features are governed by the topology of the mapped molecular spaces. Then we will look at the efficiency of the ribosome in carrying the mapping task, and especially the effective functional dimension. The analysis suggests a generic mechanism relevant for other molecular recognition systems.

At the lingual scale, we will discuss the notion of loops in linguistic structures, mainly in dictionaries. In a simplified view, a dictionary is a graph that links every word (vertex) to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions, one may loop back to the original word. We will examine possible links between such definitional loops and the emergence of new concepts during the evolution of language.

Savir Y et al.   The ribosome as an optimal decoder: a lesson in molecular recognition, Cell (2013)
Levary D et al.  Loops and Self-Reference in the Construction of Dictionaries, Phys Rev X (2012)
Savir Y et al. RecA-Mediated Homology Search as an Optimal Signal Detection System, Mol Cell (2010)
TT, A Colorful Origin for the Genetic Code, Phys Life Rev (2010)

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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.
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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.
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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.
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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 coecient 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 di erent 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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Date: October 23, 2012
SpeakerIvan Corwin (Clay Institute, Massachusetts Institute of Technology, Microsoft Research)
TitleBeyond 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.
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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.