March 3 - 5, 2013
We investigate the dynamic response of a recurrent neural network to inputs under reward modulated learning rules. The inputs combine distinct features (A, B and X, Y respectively) of the stimulus, and are grouped in pairs (A, X), (A, Y), (B, X), (B, Y). The learning task is defined by a pair-association paradigm. It leads to specific changes in the synaptic weight connectivity matrix that further influences the recurrent network internal dynamics.
I describe a sequence of polynomials $p_n(x)inmathbb{Z}_2[x]$ such that the order of $p_n(x)=d_n$ and $p_n(x)q_n(x)=1+x^{d_n}$ with the property that the proportion of $1$'s among the coefficients of $q_n(x)$ goes to 1 as $ntoinfty$.
We determine the spectrum and essential spectrum as well as resolvent estimates for a class of integral operators $T_{mu,nu}f(z)=z^{mu-1}(1-z)^{-nu}int_{0}^{z}f(w)w^{-mu}(1-w)^{nu-1}dw$ acting on either analytic besov spaces or other Banach spaces of analytic functions on the unit disk, including the classical Hardy and weighted Bergman spaces as well as certain generalized Bloch spaces.
Georgia Benkart earned her B.S. degree summa cum laude and with distinction in mathematics from The Ohio State University and her M.Phil. and Ph.D. degrees in mathematics from Yale University. She serves as the E. B. Van Vleck Professor Emerita of Mathematics at the University of Wisconsin, Madison, where 21 students have completed doctoral degrees under her direction. Her research focuses on algebra, specifically on representation theory, Lie theory, ring theory, and algebraic combinatorics. She has held visiting positions at the Aspen Center for Physics, the Institute for Advanced Study, and the Mathematical Sciences Research Institute (MSRI) at Berkeley and now serves on the MSRI Board of Trustees. In 2012, she was elected a fellow of the American Mathematical Society (AMS). From 2000 to 2002 she was the George Pólya Lecturer of the Mathematics Association of America. Having served as president of the Association for Women in Mathematics from 2009 to 2011, she currently is an associate secretary of the American Mathematical Society and was recently elected to the U.S. National Committee for Mathematics of the National Academy of Sciences.
Erica Klampfl leads the Strategy and Sustainability Analytics group at Ford Research and Advanced Engineering. Her research interests include the application of mathematics to sustainability, strategic planning, marketing, and manufacturing. Many of these applications have been deployed as corporate systems or used to inform corporate strategy on complex decisions across Ford business units. She received her Ph.D. degree in computational and applied Mathematics from Rice University. Klampfl is an active member of INFORMS, serving as chair of the 2012 INFORMS Business Analytics & Operations Research Conference and the 2011 INFORMS Prize Committee. In addition, she has served periodically as Ford’s INFORMS Roundtable representative. Klampfl is on the advisory boards of industrial and operations engineering at the University of Michigan and the master’s program in industrial mathematics at Michigan State University. She also serves on the Board of Governors for the Institute for Mathematics
Irina Mitrea is, by training, a Harmonic Analyst working at the interface between Harmonic Analysis, PDE, Functional Analysis and Geometric Measure Theory. She has pursued her graduate studies in the School of Mathematics at the University of Minnesota, where she earned a Ph.D. degree under the direction of Carlos Kenig and Mikhail Safonov. Currently Mitrea is a
faculty member in the Department of Mathematics at Temple University.
To date, she has 40 research articles that have appeared or have been accepted for publication and has co-authored two research monographs published by Springer-Verlag and Birkhauser.
Over the years her research has been supported through an NSF CAREER
Grant, a 2008 Ruth Michler Memorial Prize from the Association of Women in
Mathematics, a Sloan Dissertation Fellowship, and a Liftoff Fellowship from the Clay Mathematics Institute. Mitrea currently serves on the Executive Committee of the Association for Women in Mathematics and as an editor for the American Mathematical Monthly.
Evelyn Sander earned her BS degree with distinction and honors in mathematics from Northwestern University and earned her MS and PhD degrees from the University of Minnesota - Twin Cities. After a postdoc at Georgia Tech, she joined the faculty at George Mason University, where she has been ever since, recently earning the rank of Professor. She has advised a PhD student, is advising three current PhD students, as well as three masters students, and six undergraduate research theses. She has held a visiting position at the Institute for Mathematics and Its Applications (IMA) in Minneapolis. Her research focuses on numerical and theoretical methods for dynamical systems and differential equations, with an interest in materials, biological, and chemical applications. Having served as Editor-in-Chief and Section Chief Editor of Tutorials for DSWeb, as well as SIAM Dynamical Systems Activity Group secretary/treasurer, she is currently an associate editor for the journal SIADS and for the Research Spotlights Section of the SIAM Review. She is a member of the development committee for the Juergen Moser Chehrzad (Cheri) Shakiban earned a B.S. degree in mathematics from the National University of Iran in 1973, an M.S. degree from Harvard University in 1975, and a Ph.D. from Brown University in 1979. She has been a professor of mathematics at the University of St. Thomas since 1983, where she served as chair of the department for eight years (1996–2004) and has been engaged in undergraduate research with students resulting in several presentations and publications. She has also severed as an associate director of the IMA since 2006, promoting diversity. Her current research focuses on applications of differential geometry to computer vision and object recognition.
Chehrzad (Cheri) Shakiban earned a B.S. degree in mathematics from the National University of Iran in 1973, an M.S. degree from Harvard University in 1975, and a Ph.D. from Brown University in 1979. She has been a professor of mathematics at the University of St. Thomas since 1983, where she served as chair of the department for eight years (1996–2004) and has been engaged in undergraduate research with students resulting in several presentations and publications. She has also severed as an associate director of the IMA since 2006, promoting diversity. Her current research focuses on applications of differential geometry to computer vision and object recognition.
The bacteria, Myxococcus xanthus, are known to exhibit collective motion, but the details of their organized motility is not fully understood. Mathematical modeling can be used to understand complex biological processes such as bacteria swarming. I will present a parallel implementation of a subcellular element model of M. Xanthus. The parallelization of this model allows for thousands of bacteria cells to be modeled so questions pertaining to collective motion may now be studied. This model is used to analyze the clusters of bacteria that form when M. Xanthus swarm in a vegetative state. In particular, we investigate how a cell’s flexibility, adhesive properties, and reversal period contribute to cluster formation. These findings lead to predictions that can be tested experimentally.
We analyze the positive solutions to a steady state reaction diffusion equation with Dirichlet boundary conditions on a bounded domain. In particular, we consider a model which describes the steady states of phosphorus cycling in stratified lakes. It can also describe the colonization of barren soils in drylands by vegetation. We discuss the existence of multiple positive solutions for certain parameter ranges leading to the occurrence of an S-shaped bifurcation curve. We outline the proof of our results using the method of sub-super solutions. Also, we look at the one-dimensional case using the quadrature method.
Goldman and Turaev defined a Lie bialgebra structure on the vector space generated by nontrivial free homotopy classes of loops on an oriented surface. The Goldman bracket and Turaev cobracket give lower bounds on the minimal intersection and self-intersection numbers of loops in given free homotopy classes, respectively. Chas showed that these bounds are not equalities in general. Andersen, Mattes, and Reshetikhin defined a Lie bracket that generalizes Goldman's. We show that their bracket gives a formula for the minimal intersection number. We also define an operation that generalizes Turaev's cobracket in the same way that the Andersen-Mattes-Reshetikhin bracket generalizes Goldman's bracket, and show this operation gives a formula for the minimal self-intersection number.
Recently there have been a lot of modifications to the classic Markowitz mean-variance analysis for finance portfolio constructions. Among which those methods, the methods introduce estimator shrinkage, although introduce some bias at the same time, deliver lower out-of-sample portfolio variance and higher Sharpe ratios in the U.S. equity market. However it is unclear if similar shrinkage can improve portfolio performance in foreign exchange market. We apply the newly developed inverse covariance matrix shrinkage method, graphical lasso, to the portfolio construction in currency market and examine if these shrinkage would improve the behavior of portfolios based on Sharpe ratio. We take a look at the out-of-sample performance of minimum-variance portfolios and the out-of-sample performance of portfolios based on economic utility function.
Frequency functions, monotonicity formulas, and the thin obstacle
problemMarch 4, 2013
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Monotonicity formulas play a pervasive role in the study of
variational inequalities and free boundary problems. In this talk we will
describe a new approach to a classical problem, namely the thin obstacle (or
Signorini) problem, based on monotonicity properties for a family of
so-called frequency functions.
Donatella Danielli is a Professor of Mathematics at Purdue
University. She received a Laurea cum Laude in Mathematics from the
University of Bologna, Italy (1989), and a Ph.D. degree in Mathematics from
Purdue University (1999) under the direction of Carlos Kenig. Her research
areas are partial differential equations, harmonic analysis, and
sub-Riemannian geometry. She has been the recipient of an NSF CAREER Award,
a Purdue University Teaching for Tomorrow Award, and a Ruth and Joel Spira
Award for Graduate Teaching. Before joining the Purdue University faculty in
2001, she held positions at The Johns Hopkins University and at the Institut
Mittag-Leffler in Sweden. She is the author of 40 published papers and 2
monographs. She is the creator and organizer of the Symposia on Analysis and
PDEs and the Women in Mathematics Days, both at Purdue University.
This panel discussion is centered around the challenges and rewards of developing a
research program and professional leadership skills early on in the career, starting as
a graduate student. During this session we shall think strategically and offer advise
of practical nature for some of the key aspects of initiating a thriving research program.
This includes: making time for research, writing your PhD thesis and your first research
papers, establishing collaborations, applying for your first job, attending and organizing
conferences and scientific events in your area, and seeking funding.
We will cover some of the basics of preparing yourself for a job search or a transition within your chosen career area, including access to materials on resume and interview preparation as well as building a strong online “brand.” However, the main focus of this talk will be on helping you begin to 1) focus on your strengths and a career that is truly a fit for you. If you do this it will make going to work something you look forward to most days. And, 2) begin to actively develop your own network of colleagues, friends, and leaders in your field so that you can continue to find career opportunities throughout the balance of your professional life.
Laurie Derechin is the executive director of the Minnesota Center for Financial and Actuarial Mathematics (MCFAM), School of Mathematics, University of Minnesota. Derechin is responsible for overall MCFAM operations, including student recruiting, external relations, internship and job placements, and developing partnerships with and support from the financial and actuarial mathematics sector. Derechin has more than 25 years of business experience in a variety of industry sectors. She has been a hiring manager for many years and has experience identifying talented employees and helping them progress in their careers. Her expertise includes new product and organizational development, revenue and customer growth in highly competitive markets, and cross functional teamwork to improve customer satisfaction and company profitability. She was one of the founders and senior officers of Xcel Energy’s wholly owned broadband subsidiary which grew to 47,000 customers in six years and was sold. She founded and was president and CEO of a Minnesota broadband company, Great River Communications Corp. Derechin was also an adult education teacher in Spain and has an MBA from ESADE in Barcelona, Spain, a B.A. degree in political science from the University of Wisconsin, Madison, and a teaching certification from Oxford, Cambridge, and RSA.
The Benjamin-Ono equation describes long internal waves in a stratified medium of infinite depth. In this work we investigate unique continuation properties of solutions to the initial value problem associated to the Benjamin-Ono equation in weighted Sobolev spaces. More precisely, we prove that the uniqueness property based on a decay requirement at three times cannot be lowered to two times even by imposing stronger decay on the initial data.
Evolutionary Dynamics of CancerMarch 3, 2013
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Cancer initiation, progression, and treatment can be described as a complex evolutionary process occurring at the level of cells in the body. Mathematical models of this process can yield useful insights into the mechanisms causing cancer and also suggest possible treatment strategies. In this talk, I will introduce some basic mathematical models of cancer evolution and describe some applications to the design of treatment strategies.
Jasmine Foo has been an Assistant Professor of mathematics at the University of Minnesota since 2011. She received an Sc.B. in math/physics (2002) and a Ph.D. (2008) from Brown University in applied mathematics. She did postdoc work at the Sloan Kettering Institute and Harvard. Her research has been in mathematical biology, cancer evolution, stochastic processes, and numerical analysis. She has been a recipient of a Department of Energy graduate fellowship, National Cancer Institute Young Investigator Award, and McKnight Land Grant Professorship.
Eaton Corporation is a premier, diversified industrial manufacturer with two global business sectors—industrial and electrical. Eaton successfully maintains global leadership in power quality, distribution, and control; hydraulics components, systems, and services for industrial and mobile equipment; hydraulics, fuel, and pneumatic systems for commercial and military aircraft; intelligent truck drive train systems for safety and fuel economy; and automotive engine air management systems, power train solutions, and specialty controls for performance, fuel economy, and safety. The Eaton Innovation Center is a corporate function specifically tasked with introducing new technologies in the Eaton product family. The mission of the Innovation Center is to provide research and advanced technology concepts that lead to breakthrough opportunities for Eaton’s growth. Scientists and research engineers provide expertise in several key areas, including decision and control algorithm development; electrical, software, and communication architecture; wireless communications; and material science, chemistry, noise vibration, and harshness. The talk will provide an overview of Eaton’s businesses and products as well as enabling technologies from the Innovation Center.
Ankur Ganguli has been with Eaton Corporation since 2003 and currently serves as Director of Engineering for Control Systems & Solutions department at Innovation Center. In her current role she is leading a group of scientists & engineers involved in creating, evaluating & validating innovative product ideas based on breakthrough technologies in the area of automated controls & intelligent systems.
She began her career in Eaton as an engineer, fresh out of graduate school. After spending few years honing her technical expertise as an engineer, she progressed to take on roles with increasing impact and responsibilities - first as a project leader, then as a program manager coordinating & managing multi-disciplinary globally distributed teams and currently as the department leader.
Ankur is a mutli-faceted professional who combines technical depth with organizational strategy & management. She has a MS & PhD in Automatic Controls from department of Mechanical Engineering at University of Minnesota (2003).
We present here a very accurate fast algorithm to solve the inhomogeneous
Biharmonic equation with different boundary conditions in the interior of a
unit disk of the complex plane. The fast algorithm is based on the
representation of the solution in terms of Green functions, fast Fourier
transform and some recursive relation derived in the Fourier space. The fast solver is derived through exact analyses and properties of convolution of
integrals using Greens function and hence is very accurate.
The numerical evaluation of the double integrals has been optimized giving
an asymptotic operation count $O(ln N)$ per point on the average and
requires no additional memory storage except the initial data. It has been
implemented, validated and applied to solve several interesting applied
problems from fluid mechanics and electrostatics.
This study focuses on the simulation of compressible multifluid flows with strong shocks. To solve the hyperbolic-elliptic Euler equations for compressible flows, quasi-BGK scheme is suggested. The proposed scheme can be oscillation-free through material interfaces. The scheme is applied to typical shock flows and the results are compared with exact solutions. These demonstrate that the gas-kinetic BGK scheme is an excellent shock-capturing method for supersonic flows in aerospace applications such as scramjets and re-entry vehicles.
Conservation Laws for BeginnersMarch 4, 2013
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Research in quasilinear hyperbolic partial differential equations (i.e., “conservation laws”) presents formidable challenges. It is a subject where technical difficulties dominate, and where even the most basic questions (like existence of solutions) have not yet been answered, or have unsatisfactory answers. In this talk, I will try to paint a different picture. In fact, some simple and elegant principles underlie many aspects
of the theory, and new and surprising results are always appearing.
Barbara Lee Keyfitz is the Dr. Charles Saltzer Professor of Mathematics at The Ohio State University, which she joined in January 2009 after 21 years at the University of Houston and four and a half years as director of the Fields Institute. She received her undergraduate education at the University of Toronto and her M.S. and Ph.D. degrees from the Courant Institute, New York University. Her research area is nonlinear partial differential equations. She has contributed to the study of nonstrictly hyperbolic conservation laws. With Herbert Kranzer, she developed the concept of singular shocks, which occur in some types of systems. With Suncica Canic and others, she was a pioneer in the mathematical theory of self-similar solutions of multidimensional conservation
laws. Keyfitz was named fellow of SIAM, AAAS, and AMS, and the recipient of the 2012 SIAM Award for Distinguished Service to the Profession. In 2012, she was the Noether lecturer at the Joint Mathematics Meetings and the Kovalevsky lecturer at the SIAM Annual Meeting. She has received the 2005 Krieger-Nelson Prize of the Canadian Mathematical Society and an honorary Doctor of Mathematics degree from the University of Waterloo. Before joining the faculty of the University of Houston, Keyfitz was a faculty member in engineering at Columbia and Princeton and in mathematics at Arizona State University. She has also held visiting positions at the University of Nice, Duke University, University of California, Berkeley, the IMA, the Fields Institute, and Brown University. She was president of AWM (2005-2006) and currently serves as vice president of AMS and president of the International Council on Industrial and Applied Mathematics.
Dinner and Networking at the Tea HouseMarch 3, 2013
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Image Modeling with Undergraduates and IndustryMarch 4, 2013
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Kathryn Leonard received her Ph.D. degree in mathematics from Brown University and joined the California State University, Channel Islands (CI), faculty after postdoctoral work at the California Institute of Technology and a visiting position at Pomona College. Her awards include an NSF CAREER Award and an MAA Henry L. Alder Award for Distinguished Teaching. She is currently a codirector of the NSF-funded Center for Undergraduate Research in Mathematics and the director of the CI Center for Integrative Studies.
This talk will cover one of my first multi-disciplinary projects that I worked on at Boeing. I will discuss the several ways that the Applied Math group contributed to a NASA contract to design a hypersonic vehicle. Along with the mathematics, I will share what I have learned during my transition to a career as an industrial mathematician.
Laura Lurati joined Boeing Research & Technology as a mathematician in 2008. She received her Ph.D. in applied mathematics from Brown University. Prior to joining Boeing, she was an Industrial Postdoctoral fellow at the IMA. Her current research centers around multidisciplinary optimization and design under uncertainty.
Localization of vibrations is one of the most intriguing
features exhibited by irregular or inhomogeneous media. A striking
(but certainly not unique) example is the so called 'Anderson
localization' of quantum states by a random potential, that was
discovered by Anderson in 1958 and that brought him the Nobel Prize in
1977. Anderson localization is one of the central topics in condensed
matter physics, producing hundreds of papers each year. Yet, there
exists up to now no theoretical framework able to predict exactly what
triggers localization, where it happens and at which frequency.
We present a fundamentally new mathematical approach that explains how
the system geometry and the differential operator intervening in the
wave equation interplay to give rise to a ``landscape" that reveals
weakly coupled subregions inside the system, and how these regions
shape the spatial distribution of the vibrational eigenmodes.
This is joint work with Marcel Filoche.
Svitlana Mayboroda is an Associate Professor at the School of
Mathematics at the University of Minnesota. Her research interests
include elliptic partial differential equations, harmonic analysis,
and geometric measure theory. She graduated from the University of
Missouri in 2005 and held positions at the Ohio State University,
Brown University, Australian National University, and Purdue
University before coming to Minnesota. Svitlana Mayboroda has been a
recipient of the Alfred P. Sloan Fellowship and NSF CAREER award. She
is the creator of the Workshop for Women in Analysis and PDEs.
Keywords of the presentation: crowd, crowd behavior, emergency, exit, social interactions.
Evacuation process is a set of actions, engaged to ensure human safety in an emergency situations. The main purpose of evacuation is to have people moved from risky locations to safe ones, in a minimum amount of time. Since catastrophes cannot be predicted, the challenge is in anticipating problems that may occur, especially those related to human behavior. Many evacuation models have been developed, in order to help minimize the evacuation time and maximize the number of rescues. To reach these goals, there are many factors that should be taken into account when developing such models. Among these factors are occupant’s characteristics and types of relation among them, building architecture (characteristics) and nature or type of emergency. We will see how a variation on one (or many) of these factors would affect the outcome of the evacuation (evacuation time, number of rescues). Therefore, it will help us to develop suitable evacuation models for a variety of buildings.
Joint work with Henry Hexmoor
The Travelers Companies is a property-casualty insurance company that offers a wide variety of insurance and surety products and risk management services to businesses, organizations, and individuals. A unique challenge in the insurance industry is that a company cannot know the cost of insuring a customer when the policy is sold. It is impossible to know which customers will experience a loss or how severe that loss will be. Since losses directly impact profit, insurance companies need to be able to predict expected losses for cohorts of insureds to determine the price they will charge. Historically, this has been done primarily through actuarial techniques. Recently, however, property-casualty insurance companies, such as Travelers, have embraced predictive modeling and advanced analytics as a strategic tool for competing in the marketplace. The current analytics community at Travelers is a large and diverse network of people holding Ph.D., master’s, and bachelor’s degrees in disciplines such as mathematics, statistics, physics, actuarial science, computer science, and business. Travelers is committed to growing their analytic community, particularly through the Actuarial and Analytics Leadership Development Program (AALDP), a five-year rotational program for new employees. This talk will provide information on the analytics career path and opportunities through the AALDP at Travelers.
Catherine (Katy) A. Micek is a senior consultant in analytics and research at Travelers. She holds a Ph.D. degree in applied mathematics from the University of Minnesota. In her Ph.D. thesis, Micek developed mathematical models for polymer gels used in artificial bone implants and drug-delivery devices. Prior to joining Travelers, she taught mathematics at Augsburg College and also worked as a visiting professor at Adventium Labs, a research and development lab focused on cyber security, system engineering, and automated reasoning problems.
Modeling of Trace Gas SensorsMarch 3, 2013
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Trace gas sensors are based on optothermal detection and use a modulated laser source and a quartz tuning fork amplifier to detect small amounts of gases for disease diagnosis
via breath analysis and monitoring of atmospheric pollutants and greenhouse gases. We introduce the first mathematical model of a resonant optothermoacoustic sensor. The model is solved via the finite element method and couples heat transfer and thermoelastic deformation to determine the strength of the generated signal.
Sue Minkoff is a professor of mathematical sciences and an affiliated professor in the Department of Geosciences at the University of Texas, Dallas. Her research interests include geoscience modeling and photonics. She received her Ph.D. degree in computational and applied mathematics from Rice University in 1995. From 1995 to 1997, she was an NSF industrial postdoc at the University of Texas at Austin and British Petroleum. From 1997 to 2000 she held a von Neumann fellowship in the Mathematics Department at Sandia National Laboratories in Albuquerque, NM. In 2000, she was promoted to senior member of the technical staff in the Geophysics Department at Sandia. From 2000 to 2012, she served on the faculty in the Department of Mathematics and Statistics at the University of Maryland, Baltimore County.
While content courses for future educators can be some of the most intimidating to develop, they greatly benefit both student and instructor. This presentation focuses on the creation, implementation, reflection and revision of a problem solving course for future middle grades educators at the University of Kentucky. In addition to the course’s structure and content, student feedback, examples of student work, motivation for each task and lessons learned by the instructor are presented.
Breast cancer is one of the most common types of cancer among women in the world and one of the primary causes of death. Black women below 40years have higher incidence and lower 5-year mortality rates than white women. Low income African American women without health insurance and those with no usual source of health care have lowest screening rates; are less likely to screen repeatedly.
Eligible study participants were African American, Hispanic and Caucasian low income adult women who attend local churches, health fairs, and other gatherings in their local communities who agree to participate, as well as women who belong to not-for-profit organizations that provide breast health outreach education and screening services. The self-administered survey consists of approximately 50 questions the major themes being general health and utilization of health care for prevention, screening and health care; knowledge, attitudes and behavior with regard to breast health and breast cancer screening among others.
Of the respondents, 50% had family history of breast cancer, about 9% of which have the disease. More than 80% of respondents believe mammogram is important and have considered having one. Knowledge of breast self-exam is significantly (p less than 0.05) associated with doing the exam.
Our findings suggest the importance in understanding more carefully the link between knowledge, attitudes and behaviors as well as behavioral intentions with regards to breast health and their perceptions and utilization of screening and preventive health care in general and breast health in particular.
I show that the Tate cohomology ring of a finite dimensional Hopf algebra A is a direct summand of its Tate-Hochschild cohomology ring. This result extends the analogous cohomology relation of A to negative degrees. I will provide a computational example for the Sweedler algebra H_4. As an application, I will describe the decomposition of the Tate-Hochschild cohomology of a finite group algebra and introduce a product formula with respect to this decomposition. All necessary definitions will be given in the poster.
Sea-ice algae is a prominent part of ice-covered ecosystems. Alterations to the arctic algal life cycle, due to changes in annual ice patterns, has uncertain consequences. Understanding how algae is best modeled leads to further understanding, and eventually prediction, of the physical system. Additionally, a conceptual understanding of the small and large scale processes which control algal growth/death is vital to interpreting and validating larger models and limited observations.
A minimal complexity conceptual model of sea-ice algae is derived and analyzed. The model incorporates sea ice concentration, light, nutrients and ice-ocean brine dynamics. The model arises directly from conservation equations which allows direct analysis of individual components. The model is optimized over a large parameter space. We consider the relative merits of several alternative modeling choices, parameter values, and nutrient levels.
I will share my perception of some of these challenges and opportunities, illustrate with an extended mathematical example drawn from my own career, and offer some unsolicited advice.
Jill Pipher is Professor of Mathematics at Brown University, and Director of the Institute for Computational and Experimental Research in Mathematics (ICERM). She received her Ph.D. from UCLA in 1985, spent five years at the University of Chicago as Dickson Instructor and then Assistant Professor, and came to Brown as an Associate Professor .
Her research interests include harmonic analysis, partial differential equations and cryptography. She has published papers in each of these areas of mathematics, coauthored an undergraduate cryptography textbook, and jointly holds four patents for the NTRU encryption and digital signature algorithms. She was a co-founder of Ntru Cryptosystems, Inc, now part of Security Innovation, Inc. Her awards include an NSF Postdoctoral Fellowship, NSF Presidential Young Investigator Award, Mathematical Sciences Research Institute Fellowship, and an Alfred P. Sloan Foundation Fellowship. In February 2011, she became the President of the Association for Women in Mathematics.
The nephron in the kidney regulates its fluid capacity, in part, by a
negative feedback mechanism known as the tubuloglomerular feedback (TGF)
that mediates oscillations in tubular fluid pressure and flow, and NaCl
concentration. Single-nephron tubular flow oscillations found in
spontaneously hypertensive rats (SHR) can exhibit highly irregular
resembling deterministic chaos. In this study, we developed a mathematical
model of short-looped nephrons coupled through their TGF system to study
the extent to which internephron coupling contributes to the emergence of
regular or irregular flow oscillations. For a bifurcation analysis, we
derived a characteristic equation obtained via linearization from the TGF
model equations. An analysis of that characteristic equation revealed a
number of parameter regions, indicating the potential for different model
dynamic behaviors. The model results suggest that internephron coupling
tends to increase the likelihood of LCO. Some model behaviors exhibit a
degree of complexity that is consistent with our hypothesis for the
emergence of irregular oscillations in SHR.
We will introduce the notion of categorification and discuss several examples. In particular, we will focus on Khovanov homology and chromatic homology theories categorifying the chromatic polynomial for graphs and relations between them. We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined algebra and show how to lift various operations on polynomials to the categorified setting. This construction generalizes to categorification of orthogonal polynomials, including Chebyshev polynomials and the Hermite polynomials
The Glezer lab at Georgia Tech has found that vorticity produced by vibrated reeds can improve heat transfer in electronic hardware. Vortices enhance forced convection by boundary layer separation and thermal mixing in the bulk flow. In this work, we propose a simplified model by simulating flow and temperature in a 2-D channel. We simulate periodically steady-state solutions. We classify three types of the vortex street and determine how the global Nusselt number is increased, depending on the vortices' strengths and spacings, in the parameter space of Reynolds and Peclet numbers. We find a surprising spatial oscillation of the local Nusselt number due to the vortices.
A quantum graph is a metric graph along with a differential
operator defined on edges and matching conditions defined at vertices. We
analyze the quantum graph equipped with the magnetic Schrodinger operator.
We consider the eigenvalues of this graph as functions of magnetic
potential (or equivalently, magnetic flux) and look for critical points, as
well as the corresponding Morse indices. We will prove that zero magnetic
flux is a critical point whose Morse index is directly related to the
number of zeros of the corresponding eigenfunction. A main tool in this
proof is cutting each cycle of the graph and analyzing the critical points
(and corresponding Morse indices) on the resulting tree. These will then
be related to eigenvalues on our original graph via an intermediate (third)
quantum graph which has imaginary magnetic flux.
Building Diversity in Mathematical SciencesMarch 5, 2013
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- Talk Slides(pptx)
Pamela J. Williams will talk about her past experience as a computational scientist at Sandia National Laboratories and as a supply chain management consultant with LMI.
Pamela J. Williams is a member of the Supply Chain Management group at LMI, a not-for-profit consulting firm. Her analyses and research include enterprise business systems, mathematical forecasting, and mathematical modeling tools. She also is an adjunct professor in the Science Technology and Business Department at Northern Virginia Community College. Prior to joining LMI, Williams worked at Sandia National Laboratories from 1998 to 2008. There she developed software to solve simulation-based optimization problems and conducted uncertainty quantification analyses for the Department of Energy’s Hydrogen Macro-System Model. Dr. Williams has a bachelor’s degree in mathematics from the University of Kentucky as well as a master’s degree and PhD in computational and applied mathematics from Rice University.
Developing efficient and accurate simulations of complex physical systems present numerous challenges. Numerical methods, software development, and computer science must come together with the driving science or engineering application in order to produce a truly usable simulation tool. In this presentation, I will discuss the mission of the US Department of Energy and overview a typical mathematician’s job at a DOE laboratory. I will include results from research and software code development in subsurface flow, core collapse supernova, magnetic fusion, crystal dislocations, and power grid modeling. In each case, I will outline the roles of the mathematicians in the work and how they fit into the overall goals of the project.
Carol Woodward is a computational scientist in the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory. She leads the Nonlinear Solvers and Differential Equations Project within CASC and is PI or co-PI on research projects in methods for dislocation dynamics, power grid modeling, and scientific code verification. Carol has been a computational scientist with CASC since 1996. Prior to that time, Carol attended Rice University where she received her PhD in Computational Science, and Engineering. Previous to graduate school, Carol attended Louisiana State University where she received a B.S. in Mathematics in 1991.
Motile cilia play a large role in fluid motion across the surface of ciliated tissue. We present an experimental and theoretical study involving a single rigid cilium rotating in a viscous fluid about one of its ends in contact with a horizontal no-slip plane. Experimentally tracked three dimensional Lagrangian trajectories are compared with theoretical trajectories computed using a properly imaged slender body theory. The addition of planar bend to the rod geometry is shown to break symmetry and create large scale nested tori in the Lagrangian particle trajectories. Three dimensional PIV measurements are presented which help to explain the origin of the large scale tori and compared directly with the slender body theory.