Mathematics Colloquium Schedule
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----------------------------| Spring 2013 |----------------------------
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January 25, 2013 (10 -11 AM, FO3-200A), Professor I-Liang Chern, Department of Mathematics, National Taiwan University
Title: Exploring Ground States and Excited States of Spin-1 Bose-Einstein Condensates
Abstract: In this talk, I will first give a brief introduction to the spinor Bose-Einstein condensates. Then I will present two recent results, one is numerical, the other is analytical.
In 1925, Bose and Einstein predicted that massive bosons could occupy the same lowest-energy state at low temperature and formed the so-called Bose-Einstein condensates (BECs). It was realized on several alkali atomic gases in 1995 by laser cooling technique.
In the numerical study of spinor BEC, a pseudo-arclength continuation method (PACM) was proposed and employed to compute the ground state and excited state solutions of spin-1 BEC. Numerical results on the wave functions and their corresponding energies of spin-1 BEC with repulsive/attractive and ferromagnetic/antiferromagnetic interactions are presented. Furthermore, it is found that the component separation and population transfer between the different hyperfine states can only occur in excited states due to the spin-exchange interactions.
In the analytical study, the ground states of spin-1 BEC are characterized. For ferromagnetic systems, we show the validity of the so-called single-mode approximation (SMA). For antiferromagnetic systems, there are two subcases. When the total magnetization M ≠ 0, the corresponding ground states have vanishing zeroth (m_F = 0) components, thus are reduced to two-component systems. When M = 0, the ground states are also reduced to the SMA, and there are one parameter families of such ground states. The key idea is a redistribution of masses among different components, which reduces kinetic energy in all situations, and makes our proofs simple and unified.
Finally, a fast algorithm based on the above analytic result is provided. It is shown that the new method is about 10 to 20 faster than an old method of Bao-Lim's continuous normalized gradient method.
The numerical part is a joint work with Jen-Hao Chen and Weichung Wang, the fast algorithm part is with Weizhu Bao and Yanzhi Zhang, whereas the analytical part is jointly with Liren Lin.
February 1, 2013 (12 noon-1PM, FO3-200A), Professor Ali Nadim, Claremont Graduate University
Title: Digital Microfluidics via Electrowetting.
Abstract: Electrowetting actuation of individual liquid droplets on a solid surface, known as digital microfluidics, has a variety of interesting applications. These include liquid lenses without mechanical moving parts (www.varioptic.com), novel displays for consumer electronics (www.liquavista.com), and liquid handling without the need for channels, pumps or valves (www.liquid-logic.com). In this talk, we review our group's progress in this area and describe some of the mathematical models we have developed that help us estimate the magnitudes of forces and speeds that can be achieved by electrowetting. Our models focus on the problem of electrowetting actuation of individual sessile drops on a patterned array of electrodes with a thin dielectric coating. For both the case when the drop is electrically grounded from below and when it is floating, we compute the electric field in the vicinity of the drop over a range of frequencies and use the traction derived from the Maxwell stress tensor to calculate the effective electrowetting force on the drop. At low frequencies when the drop behaves like a perfect conductor, the results are compared with previously derived lumped parameter models for the electrowetting force.
February 15, 2013 (12 noon-1PM, FO3-200A), Professor Muge Kanuni, Bogazici University, Istanbul, Turkey
Title: Incidence Algebras
Abstract: In his celebrated paper of 1964, "On the foundations of combinatorial theory I: Theory of Möbius Functions" Gian-Carlo Rota defined an incidence algebra as a tool for solving combinatorial problems.
Incidence algebra is a specific ring of functions defined on the ordered pairs of a given partially ordered set to a given ring, moreover incidence ring is equipped with a module action by this ring. Möbius function is an element of an incidence algebra, besides with the appropriate choice of the partially ordered set, Möbius function of this incidence algebra coincides with the well-known Möbius function of number theory. A product of copies of a ring and upper triangular matrices are typical examples of incidence algebras. In the following papers of Rota with his co-authors, and papers of other contemporary authors incidence algebras are investigated as an algebraic object, as a tool in algebraic topology. After a general view of the above research, I will summarize what I study in the algebraic context of incidence algebras.
March 22, 2013 (12 noon-1PM, FO3-200A), Jacquelyn Rische, PhD Student, Department of Mathematics, University of California, Irvine
Title: Mathematical Modeling of Language
Abstract: In this talk, we will look at mathematical modeling of language using computer simulations. Using these models, we study how individuals with language spread through a population of individuals without language. We consider a population without language on one- and two-dimensional grids. Language will appear in the population through a genetic mutation. To study how the language group will grow, we focus on the effects of talking and movement. If two individuals with language are next to each other on the grid, they can communicate. We consider their ability to talk to be advantageous, giving them a higher reproduction rate. Individuals are also able to move around on the grid and reproduce within a certain radius, called the jump radius. We are looking at how these affect the time it takes for the individuals with language to invade the population. We find that, for a two-dimensional grid, a jump radius that is too small or too large will increase the time it takes to invade. For a one-dimensional grid, we do not see the same effect. The time to invasion decreases as the jump radius increases.
April 12, 2013 (12 noon-1PM, FO3-200A), Professor Demla Senturk, Department of Biostatistics, University of California, Los Angeles
Title: Cardiovascular Event Risk Dynamics Over Time in Older Patients on Dialysis: A Generalized Multiple-Index Varying Coefficient Model Approach
Abstract: Among patients on dialysis, cardiovascular disease and infection are leading causes of hospitalization and death. Although recent studies have found that the risk of cardiovascular events is higher after an infection-related hospitalization, studies have not fully elucidated how the risk of cardiovascular events changes over time for patients on dialysis. In this work, we characterize the dynamics of cardiovascular event risk trajectories for patients on dialysis via multiple time indices:(1) time since the start of dialysis, (2) time since the pivotal initial infection-related hospitalization and (3) the patient's age at the start of dialysis, by developing generalized multiple-index varying coefficient (GM-IVC) models. The proposed GM-IVC models utilize a multiplicative structure and one-dimensional varying coefficient functions along each time and age index to capture the cardiovascular risk dynamics before and after the initial infection-related hospitalization.We develop a two-step estimation procedure for the GM-IVC models based on local maximum likelihood. We report new insights on the dynamics of cardiovascular events risk using the United States Renal Data System database, which collects data on nearly all patients with end-stage renal disease in the U.S.
April 19, 2013 (12 noon-1PM, FO3-200A), Cynthia Northrup, PhD Student, Department of Mathematics, University of California, Irvine
Title: Using Forcing to Obtain a Model of the Continuum Hypothesis
Abstract: Forcing is a method used to extend a transitive model M by adjoining a new set G in order to obtain a larger transitive model M[G]. Our choice of partial order, or notion of forcing, determines what is true in M[G]. We will consider the forcing introduced by Paul Cohen in proving the independence of the Continuum Hypothesis. The Diamond Principle, introduced by Jensen in 1972, can be thought of as a strengthening of the Continuum Hypothesis. From a diamond sequence of length k we can read off all of the subsets of k. We are interested in using an iteration involving Radin forcing in order to obtain a model of the failure of Diamond.
April 26, 2013 (12 noon-1PM, FO3-200A), Professor Ami Radunskaya, Pomona College
This talk has been cancelled.
Title: Coming Soon
Abstract: Coming Soon
May 3, 2013 (12 noon-1PM, FO3-200A), Triet Pham, PhD Student, Department of Mathematics, University of Southern California
Title: A brief overview of financial mathematics
Abstract: The financial crisis in 2007-2008 has sparked renewed interest on financial mathematics. Since most of the tradings on Wall Street are performed based on sophisticated mathematical models, one would naturally question to what extent they are to blame for the crisis. However, I believe that it is not the models, but the model-users who are at fault in this situation. Robert Merton, Nobel laureate in economics wrote in a recent article in Harvard Business Review: A model is unreliable if the person using it does not understand it or its limitations." But to understand a specific model and its limitation, one first needs to understand the field and the subject area. In this talk, I will introduce the fundamental concepts of financial mathematics, as well as the fundamental questions it tries to answer. New areas of research will also be mentioned, as well as other branches of mathematics that are related to math finance. We will see a very basic model for pricing a financial instrument, and how misunderstandings of this model can potentially lead to a crisis, as mentioned in the quote above. This talk is intended for the general audience, no background in finance is required.
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----------------------------| Fall 2012 |----------------------------
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September 21, 2012 (12 noon-1PM, FO3-200A), Professor Gung-Min Gie, Department of Mathematics, UC Riverside
Title: Motion of Fluids in the Presence of a Boundary
Abstract: In most practical applications of fluid mechanics, it is the interaction of the fluid with the boundary that is most critical to understanding the behavior of the fluid. Physically important parameters, such as the lift and drag of a wing, are determined by the sharp transition the air makes from being at rest on the wing to flowing freely around the airplane near the wing. Mathematically, the behavior of such flows are modeled by the Navier-Stokes equations. In this talk, I will discuss the asymptotic behavior of solutions to the Navier-Stokes equations at small viscosity under various boundary conditions.
September 28, 2012 (12 noon-1PM, FO3-200A), Professor Robert Mena, Department of Mathematics and Statistics, CSU Long Beach
Title: A Little Big Problem in Graph Theory
Abstract: This introductory talk presents two problems in graph theory, one from the fifties and one from the seventies—at first glance seemingly unrelated. It will present the almost complete solution, although there is an unsolved intriguing case. The talk will only use elementary matrix theory (as well as some graph theory which will be explained). Any junior or more advanced student should be able to follow.
October 19, 2012 (12 noon-1PM, FO3-200A), Professor James Kelliher, Department of Mathematics, UC Riverside
Title: Fluids and Boundaries
Abstract: The behavior of a fluid as it encounters a boundary produces interesting and challenging physical phenomena, which to this day are only imperfectly understood. I will explain what the fundamental obstacle to understanding is, and give a little idea of what is known about certain of these phenomena.
November 9, 2012 (12 noon-1PM, FO3-200A), Professor Ming Ji, Graduate School of Public Health, San Diego State University
Title: Statistical Challenges in Molecular Diagnostics
Abstract: Diagnostic tests are of critical importance in medicine and public health. Traditional statistical methods in diagnostic tests include sensitivity, specificity, predictive values of positive and negatives and the ROC curve. The revolution in genetics (SNPs, microarrays, proteomics and DNA sequencing) has created new biological measurement tools and excitement for molecular diagnostics. This technology advancement, however, leads to great challenges to statistical sciences for providing adequate methods of evaluating new diagnostic tests from high-dimensional data. In this talk, I will use proteomic measurements of autoimmune response in lupus to illustrate the difficulties and challenges for developing new diagnostic tests. Various statistical methods have been applied in this case study including normalization, dimension reduction, multiple comparison adjustment, optimal linear combination of multiple markers and ROC curves. I will also introduce other statistical methods such as partial least squares, genetic algorithms, random forests, regularized discriminant analysis as well as other challenges such as sampling, reliability and validation in molecular diagnostics. .
November 16, 2012 (11am- 12:00 noon, FO3-200A), Professor Thomas Laurent, Department of Mathematics, UC Riverside
Please note the special time for this seminar, starting at 11:00am instead of the usual 12:00 noon.
Title: Machine learning, Balance cut and Total variation
Abstract: Machine Learning is the branch of Artificial Intelligence which is devoted to the design and study of algorithms that learn patterns from large data sets in order to make intelligent decisions. In this talk we will be concerned with the problem of partitioning a large and high dimensional data set into groups of data having ``similar behavior''. One successful approach is to construct a graph from the data and then to cut this graph in a sensible way. Here we will present a fast algorithm, based of total variation optimization technique recently developed in image processing, that accomplish this task.
November 30, 2012 (12 noon-1PM, FO3-200A), Professor Shadnaz Asgari, Department of Computer Engineering and Computer Science, CSU Long Beach
Title: Biomedical signal processing for the improvement of health care of patients with brain-related disorders
Abstract: Despite the existence of various advanced monitoring devices in the modern intensive care units (ICU) that enables measurement of several physiological signals, the ability to analyze these data for real-time clinical care remains intuitive and primitive. This presentation provides an overview on the statistical, mathematical and informatics tools that have been applied to the large volume of clinical physiological data routinely monitored at UCLA Neuro-ICU with the goal of identifying better biomarkers of brain-related adverse events and providing clinicians with improved ability to target specific goals in the management of patients with acute neurological conditions such as traumatic brain injury or stroke.
December 7, 2012 (12 noon-1PM, FO3-200A), Professor Antonella Sciortino, Department of Civil Engineering and Construction Engineering Management, CSU Long Beach
Title: Numerical Modeling of Transport Processes in the Subsurface
Abstract: This presentation is an overview of three research topics that I have been working on before and after I joined CSULB. All three projects focus on numerical modeling of contaminant transport in the subsurface, which includes both the vadose and saturated zone.
The first topic involves an inverse modeling procedure to locate DNAPL pool sources in groundwater. The model is based on the Levenberg-Marquardt method and on analytical solutions to describe DNAPL dissolution in groundwater. DNAPLs (Dense Non-Aqueous Phase Liquids) are organic hydrocarbons used in the manufacturing and dry-cleaning industry. The most common types are chlorinated solvents. These compounds are slightly soluble in water and fairly volatile. Once spilled, they will act as an effectively permanent source of groundwater pollution. The solubility of these highly toxic compounds is much greater than the maximum allowed concentrations allowed and they pose a serious threat to human health. Thus remedial strategies must be developed to restore or at least improve the groundwater quality. Such strategies must begin with source identification and removal.
The second topic focuses on the impact of ethanol-blended fuels on the hydraulic properties of the vadose zone. Ethanol and ethanol-blended fuels are being widely promoted to reduce the emission of harmful chemicals into the atmosphere. Water flow and contaminant transport in the vadose zone will be impacted by spillage and leakage of ethanol or ethanol-blended fuels due to changes in surface tension and viscosity. The completely miscible ethanol also causes modifications of the dielectric properties of the soil solution leading to shrinking/swelling and flocculation/dispersion of soil colloids. The hydraulic conductivity of soils with appreciable amounts of clay may therefore be significantly altered by ethanol. An existing numerical code for unsaturated flow and transport was modified to account for the dependency of vadose zone properties on ethanol concentration.
The third topic focuses on modeling contaminant transport in dual-permeability or dual-porosity media. These are media where the pore space is partitioned into two flow domains such as inter- and intra-aggregate pore space in aggregated soils or fractures and matrix in a rock formation. A variety of simplified models have been developed in order to derive an analytical solution to describe contaminant transport in these soils: I. simple advection-dispersion equation (ADE) with one effective flow domain, II. mobile-immobile model (MIM) with water flow only in the mobile region and solute exchange between the mobile and immobile regions, III. dual-advection dispersion equation (DADE) with different flow but equal dispersivity in both regions and solute transfer between the regions, and IV. stream-tube model (STM) with flow according to the ADE in both domains but no solute exchange between them. We used a benchmark numerical model to assess the performance of the simplifying assumptions using synthetic data and experimental data collected for an Andisol.
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----------------------------| SPRING 2012 |----------------------------
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January 27, 2012 (12 noon-1PM, FO3-200A), Professor Juhi Jang, UC Riverside
Title: Stability theory of polytropic gaseous stars
Abstract: I'll discuss stability theory of Lane-Emden equilibrium stars under Euler-Poisson or Navier-Stokes-Poisson system. A linear stability can be characterized by the adiabatic exponent. A nonlinear instability will be also discussed.
February 3, 2012 (12 noon-1PM, FO3-200A), May Mei, PhD Student, UC Irvine
Title: An Introduction to Non-integer Dimensions
Abstract: We know that a line has one dimension and we can measure its length. We know that a box has two dimensions and we can measure its area. However, one does not have to look hard to find instances where our intuition fails us. What happens when we come across an object whose dimension appears to lie between two integers? This talk will explore fractals in mathematics and nature, and introduce two different ways to measure the dimension of fractals.
February 17, 2012 (12 noon-1PM, FO3-200A), Todd CadwalladerOlsker, Department of Mathematics, CSU Fullerton
Title: Does a Statement of Whether Order Matters in Counting Problems Affect Students' Strategies?
Abstract: Counting problems ask students to compute the number of ways a certain set of requirements can be satisfied, and they are important in such mathematical subjects as probability, combinatorics, and abstract algebra, among others. Students are often taught to solve counting problems by looking for specific clues to help categorize the problems and identify solution strategies. In a recent study, we investigate how the wording of certain counting problems, specifically whether or not "order matters", affects students' solution strategies.
February 24, 2012 (12 noon-1PM, FO3-200A), Jeremy Jankans, PhD Student, UC Irvine
Title: How to Distinguish a Football from a Basketball Mathematically
Abstract: How different is a football from a basketball? This is the question that we want to answer. While this is a geometric problem, we will use algebra to solve it. The tool that we will us is called the algebraic variety. We can also use the algebraic variety to answer other geometric questions such as smoothness and irreducibility.
April 13, 2012 (12 noon-1PM, FO3-200A), Daniel Reich, Operations Research Analyst, Ford Motor Co. Research & Advanced Engineering
Title: Helping Ford’s Fleet Customers Reach Their Sustainability Goals Through Optimization
Abstract: Sustainability and environmental impact are areas of growing importance to many of Ford’s fleet customers. In recent years, many new green vehicle technologies have emerged, which present organizations with an opportunity to increase the fuel economy of their fleets. “Fleet Purchase Planner (FPP)” (patent pending) is a software system we’re developing to assist Ford’s fleet customers in planning their purchases. This talk will introduce FPP, the modeling framework we use and the underlying mathematics.
April 20, 2012 (12 noon-1PM, FO3-200A), Chiu-Yen Kao, Department of Mathematics and Computer Science, Claremont Mckenna College
Title: Shape optimization problem involving principal eigenvalue in population dynamics
Abstract: In this talk, an efficient rearrangement algorithm is introduced to the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. The method proposed is based on Rayleigh quotient formulation of eigenvalues and rearrangement algorithms which can handle topology changes automatically. Using the efficient rearrangement strategy, the new proposed method is more efficient than classical level set approaches based on shape and/or topological derivatives. The optimal results are explored theoretically and numerically under different geometries and boundary conditions.
May 4, 2012 (12 noon-1PM, FO3-200A), Arlo Caine, Department of Mathematics & Statistics, Cal Poly Pomona
Title: Mathematics and Astronomy, Kepler's Laws of Planetary Motion
Abstract: In the early 1600's, the German mathematician-astronomer Johannes Kepler analyzed the volumes of astronomical data recorded to that day in attempt to discover mathematical laws governing the motion of the planets. After nearly a decade of work, building on the ideas of Galileo, Copernicus, and others, he proposed the first two of his three empirical laws concerning planetary motion. Nearly three quarters of a century later, the Calculus was used to deduce these laws of motion as a consequence of Sir Isaac Newton's theory of gravity, permanently cementing the bond between mathematics and physics. This presentation will illustrate how geometry is used by astronomers to make precise observations of the night sky, allowing us to bring mathematics to bear on the study of this aspect of nature. We will then follow Kepler's empirical analysis which led to his laws of motion, often celebrated as one of the greatest performances of retroductive reasoning.
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----------------------------| PRIOR YEARS |----------------------------
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------------------------------| FALL 2011 |------------------------------
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October 7, 2011 (12 noon-1PM, FO3-200A), Shane Ryerson , PhD Student, UC Irvine
Title: How Quantum Computers Ruin Everything
Abstract: Almost all forms of communication on the internet are initiated and obfuscated by a method of public key cryptography. Perhaps the most important among these are credit card transactions. This talk will discuss why public key cryptography is considered safe enough for those transactions and how quantum computers are a threat to those methods.
October 14, 2011 (12 noon-1PM, FO3-200A), Ron Tani, Industry
Title: Life as an Actuary
Abstract: In this talk, I'll talk about (1) how to become an actuary out of school, (2) the career opportunities and paths available to actuaries, including the types of work done, and (3) the relevant skill sets for career success. I'll try to relate to my own 25-year career and the relevance of my CSULB education. This talk is accessible to students of all backgrounds and levels.
October 28, 2011 (12 noon-1PM, FO3-200A), Ami Radunskaya, Department of Mathematics, Pomona College
Title: Mathematical Challenges in the Treatment of Cancer
Abstract: What can mathematics tell us about the treatment of cancer? Cancer is a myriad of individual diseases, with the common feature that an individual's own cells have become malignant. It is believed that a healthy individual keeps potentially cancerous cells from developing into a threatening tumor through a complicated network of immune response and mechanisms built into the cell cycle that recognize aberrant cells and control their proliferation. Thus, the treatment of cancer poses great challenges, since an attack must be mounted against cells that are nearly identical to normal cells. Mathematical models that describe tumor growth in tissue, the immune response, and the administration of different therapies can suggest treatment strategies that optimize treatment efficacy and minimize negative side-effects. However, the inherent complexity of the immune system and the spatial heterogeneity of human tissue gives rise to mathematical models that pose unique analytical and numerical challenges. These include modeling behavior over vastly different time scales, incorporating delays into the model, optimization in high-dimensional spaces, and fitting large sets of dependent parameters to data.
In this talk I will present an overview of work that I have done in this area over the last ten years, with the help of many collaborators, highlighting the various approaches we have taken to tackle these mathematical challenges. No knowledge of biology will be assumed.
November 4, 2011 (12 noon-1PM, FO3-200A), Joseph Tao-yi Wang, Department of Economics, National Taiwan University
Title:Experimental Implementations and Robustness of Fully Revealing Equilibria in Multidimensional Cheap Talk
Abstract: We design experiments that capture the essence of the theoretical environments studied in multidimensional cheap talk. Two senders transmit information to a receiver over a 2x2 state space. Interests between the senders and the receiver are misaligned under the two-dimensional state space, but common interests can be found along its single dimensional components, which are different for each sender and exploited in equilibrium for full revelation. Observed frequencies of receivers identifying the state are significantly higher in two-sender games than in the control game with one sender, in a manner consistent with the respective fully and partially revealing equilibria. By manipulating message/state space to control for out-of-equilibrium beliefs, we investigate the robustness of the fully revealing equilibrium and observe significantly lower adherence when the equilibrium requires support of "implausible beliefs." Introducing a fraction of non-strategically truthful senders to the equilibrium model rationalizes our findings.
This talk is accessible to senior math majors and graduate students.
November 18, 2011 (12 noon-1PM, FO3-200A), Angel Pineda, Department of Mathematics, CSU Fullerton
Title: Mathematical Research by Students at the CSU: Mentoring and Mathematics
Abstract: Mentoring students in research at the California State University system requires a shift in perspective from what most faculty members experienced at the research universities where they did their dissertation and/or postdoctoral research. The large variability in the student’s backgrounds and broad interests require a reformulation of the often specialized topics which mentors typically study in their research. The large financial strains on students and heavy teaching loads for mentors lead to an unusually high need for external support. The student-faculty interactions involved in mentoring research require a measure of success which is not only measured by publications and acceptance into PhD programs. The success needs to be measured both in terms of the student growth and the new mathematics produced.
This talk will describe my involvement in mentoring two graduate students and eight undergraduate students over the last four years at California State University. It will have a component targeted at students emphasizing opportunities for summer research experiences for undergraduates (REUs) and the new results in statistical estimation in magnetic resonance imaging (MRI) obtained by my students. For the faculty members, this talk will have an overview of various mentoring models for student research in terms of length of the project (summer, academic year), team or individual projects and graduate or undergraduate.
December 2, 2011 (12 noon-1PM, FO3-200A), Cindy Wyels, Department of Mathematics, CSU Channel Islands
Title: Graph parameters: a rich source of open questions
Abstract: Graph theory constitutes an engaging area of research with myriad open problems, some of which are relatively accessible, yet still demanding and intriguing. Many graph parameters have been defined – some for use in modeling physical situations, others to extend mathematical ideas. I’ll share several research questions regarding different graph parameters that I’ve collaborated on with students and others. Throughout, I’ll share ideas for creating additional research questions in fields ranging beyond graph theory.
December 9, 2011 (12 noon-1PM, FO3-200A), Zac Faubion, PhD Student, UC Irvine
Title: Limitations in Mathematics and the Search for New Axioms
Abstract: : In the study of mathematics we are interested in determining the truth of mathematical
statements. We want to answer questions such as: Are there positive integers a; b; c and n such that an + bn = cn?, and How big are the real numbers?. Furthermore we need a method which we can rely on to give true answers, and answer all mathematical questions.
In 1920, David Hilbert proposed his program to find a complete axiomatization of mathematics which can prove its own consistency. Then in 1931 Kurt Godel proved that this was impossible with his famous incompleteness theorem. In this talk we will explore these ideas and how Godel proposed to strengthen our methods (through the use of larger infinities) to be able to answer more questions.
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----------------------------| SPRING 2011 |----------------------------
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May 13 (12 noon-1PM, FO3-200A), Michael Borghese, Department of Mathematics and Statistics, California State University, Long Beach
Image Segmentation using the Mumford-Shah Functional
Abstract: With the advent of digital photography, problems existing within the field of image processing can now be approached via numerical methods. One common issue within this field is the problem of segmentation, wherein an object within the image is distinguished from the background. Multiple approaches have been taken to address this problem including statistical, graph theory, and PDE based techniques. This talk, directed towards students, will discuss one such PDE based method developed by Esodoglu & Tsai. This method, referred to as Threshold Dynamics of the Piecewise-Constant Mumford-Shah Functional, is based upon a variation of the energy functional of Mumford & Shah. Included in this talk will be an introduction to the theory of image processing and the segmentation issue, as well as a discussion of the Threshold Dynamics approach and examples of applications.
May 6 (12 noon-1PM, FO3-200A), Prof. Federico Toschi, Department of Physics, Department of Mathematics and Computer Science, Eindhoven University of Technology
Particles in turbulence
Abstract: Particulate matter gets transported by turbulent flows in oceans, in the atmosphere as well as in industrial processes. The dynamics of particles in turbulence, their preferential accumulation, as well as their encounter rates depend on both turbulent statistics as well as on particles properties. We will review the methods and recent results from state-of-the-art numerical investigation of particles dynamics in turbulence. In particular we will discuss the limitations of the point particle approach to study the dynamics of finite-size particles in simple homogeneous and isotropic turbulence velocity fields. Comparison against experimental results will be discussed.
April 29 (12 noon-1PM, FO3-200A), Dr. Silvia Heubach, California State University Los Angeles
Nim, Wythoff and beyond – Let’s Play!
Abstract: I will introduce two-player impartial combinatorial games via the games of Nim and Wythoff. Both Nim and Wythoff consist of stacks of tokens. In the game of Nim, two players alternatively select one of the stacks of tokens and then remove at least one token (and as much as all the tokens) from that stack. The game of Wythoff has only two stacks, and a move consists of selecting one of the two stacks and removing any number of tokens, or to take the same number of tokens from both stacks. In both games, the last player who can make a move wins the game. A typical question in the theory of combinatorial games is whether there is a strategy for one of the two players that allows this player to win no matter how the other player plays. This question is answered by determining the set of losing positions.
I will give (known) results on the set of losing positions for Nim and Wythoff (with a surprise appearance of Phi, the reciprocal of the Golden Ratio) before introducing a generalization of these two games. For this more general family of games, we conjecture that a structural result for the losing positions similar to the one for the game of Wythoff holds. I'll give proofs for the cases for which we have established the conjecture.
This talk does not assume knowledge about combinatorial games and is accessible to students who have had a proof course.
February 11 (12 noon-1PM, FO3-200A), Dr. Carol Jacoby, Jacoby Consulting
Infinite groups and infinitary logic
Abstract: How can you get your arms around infinite groups? How much richer is the language of first order logic if we add infinitely many conjunctions and disjunctions? These two questions, one from algebra and one from logic, seem unrelated. Yet we will see that each field casts light on the other. We have developed numerical invariants that completely determine a large class of abelian groups up to partial isomorphism, a “finite lens” through which to examine these unwieldy groups. The infinitary logical language L-infinity-omega makes this possible. Group theory then reveals some of the limitations of this language.
February 4 (12 noon-1PM, FO3-200A), Prof. Erica Flapan, Department of Mathematics, Pomona College
Intrinsic Properties of Graphs Embedded in R^3
Abstract: Knot theory is the study of the topology of embeddings of simple closed curves in R^3. A natural extension of knot theory is the study of the topology of embeddings of graphs in R^3. However, in contrast with knots, the structure of a graph can be complex, and this can affect all of its embeddings. If every embedding of a graph has a particular property, then we say that property is intrinsic to the graph. For example, a graph is said to be intrinsically knotted if every embedding of the graph in R3 contains a knot. In this talk we will discuss intrinsic knotting and other intrinsic properties of graphs.
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------------------------------| FALL 2010 |------------------------------
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December 3 (12 noon-1PM, FO3-200A), Dr. Joshua Sack, School of Computer Science, Reykjavik University
Counting special inversions in permutations
Abstract: Counting occurrences of patterns in permutations is a young subject, approximately 30 years old, that has grown in popularity due to its applications to computer science and its connection to other topics in combinatorics. One is often concerned with counting the number of permutations with a certain number of occurrences of a pattern. This talk will provide some background on patterns, and will focus on a certain type of pattern, the inversion, and will discuss some results concerning a variety of types of inversions that come from joint work with Henning Ulfarsson. This talk aims to be accessible to upper division undergraduates.
November 19 (12 noon-1PM, FO3-200A), Dr. Prasad Perlekar, Department of Physics, Department of Mathematics and Computer Science,
and J.M. Burgerscentrum, Eindhoven University of Technology
Life at High Reynolds Number
Abstract: Population dynamics deals with the study of birth, death and growth processes of biological species. These processes are severely affected by the local ecosystems, by the presence of nutrients, and by the local population density. Turbulence is normally known to increases mixing and diffusion; but, remarkably, population dynamics in a turbulent environment shows the localization (e.g. patchy regions of planktons on the ocean surface). We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field. The mixing of the populations in turbulent environment is characterized by the local carrying capacity. We investigate the complex interplay between turbulent dynamics and population evolution equation leads to pseudo-localization of population concentration. The statistical properties of the concentration field are investigated and quantitied. Most important we demonstrated numerically that the limit of negligibly small growth rates is nonsingular.
November 12 (12 noon-1PM, FO3-200A), Dr. Daniel Reich, Postdoctoral Fellow, Universidad Adolfo Ibáñez
Risk-Return Trade-Off with the Scenario Approach for Chance Constrained Programming
Abstract: We consider a naive portfolio optimization model with a single chance constraint and review an established sampling approach that can be used to identify feasible solutions. To improve solution quality while maintaining feasibility, we propose and compare two constraint removal procedures: one greedy and the other randomized. We present detailed computational results and discuss how and why these results may be generalizable to other chance constrained problems. (This talk will include a brief introduction to linear and mixed-integer programming for those unfamiliar with these optimization methods.)
November 5 (12 noon-1PM, FO3-200A), Paul Sobaje, Ph.D. Student, USC
Representations of Finite Groups in Characteristic p
Abstract: We will look at representations of a finite group G acting on a k-vector space V, with our primary attention on what happens when the characteristic of k divides the order of G. This question has a long history dating back to early work done by Richard Brauer, whose results were particularly useful in the classification of finite simple groups. We will define everything as we go, and give lots of examples.
October 15 (12 noon-1PM, FO3-200A), Dr. Kathryn Leonard, CSUCI
The mathematics of skeletal shape models
Abstract: The need for good models to represent 2D shape arises in several applications, including image analysis. A skeletal model was first suggested by Blum in the late 60s that now bears his name, the Blum medial axis. The Blum axis has several beautiful mathematical properties as well as good properties as a model for shape. We will define the Blum axis, explores its strengths, and compare its efficiency as a shape model with the boundary curve of the shape. We will also discuss related work-in-progress for a generalization of the Blum axis, as well as a few related research projects involving undergraduates.
September 24 (12 noon-1PM, FO3-200A), Dr. Mario Micheli, Department of Mathematics, UCLA
The geometry of the Riemannian manifold of Landmark points, with applications to Image Processing
Abstract: In the past few years there has been a growing interest, in diverse scientific communities, in endowing shape spaces with Riemannian metrics, so to be able to measure similarities between shapes and perform statistical analysis on data sets (e.g. for object recognition, target detection and tracking, classification, and automated medical diagnostics). The geometry of such spaces has started to emerge only very recently; in this talk we will explore the sectional curvature for the Riemannian manifold of landmark points (which is one of the simplest, in that it is finite-dimensional) and discuss its effects on applications.
September 10 (12 noon-1PM, FO3-200A), Alex Chen, Department of Mathematics, UCLA
Mathematical Morphology of Landscapes
Abstract: The evolution of a landscape is affected by many different factors such as grade of slope, surrounding vegetation, wind, soil quality, etc. Previous geological models have often added many parameters in order to measure the morphology of a landscape as accurately as possible. These laws can be quite accurate for processes near steady state, but they cannot track evolution on a longer time scale. We seek to reduce the number of parameters in order to examine qualitatively the formation of common features observed in nature. The model consists of a coupled system of three PDE based on the most important factors from previous landscape evolution models as well as conservation laws. Using these conservation laws allows for operation under longer time scales. Evaluation of the model is based on whether the formation of features such as rivers, canyons and lakes is observed and plausible.
