Applied and Interdisciplinary Mathematics (AIM) Seminar
Meets Tuesdays, 11am to 12pm, 509 LA
Organizers: Chris King, Robert McOwen
The seminar features talks in Applied and Interdisciplinary Mathematics (AIM) by our own faculty as well as faculty fromother departments at Northeastern and other Universities in the Boston Area. For additional information or to be added to the mailing list, please contact Chris King .
Next Talk
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.
Future Talks
None scheduled at this time.
Past Talks
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
Speaker: Ivan Corwin (Clay Institute, Massachusetts Institute of Technology, Microsoft Research)
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.
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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.