Applied Math Seminar
Spring 2016
All talks are from 12:00-1:00 p.m. in the Seminar Room, unless otherwise specified.
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Apr29
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Naval S&T and Perception in the Undersea DomainJason StackOffice of Naval ResearchTime: 12:00 PM
View Abstract
This talk will briefly overview the Office of Naval Research (ONR) and the conduct of naval S&T across the research enterprise. It will then discuss current efforts and future research directions that are related to undersea warfare. Particular emphases will be on perception and its relation to autonomous unmanned systems in the warfare areas of mine countermeasures, explosive ordnance disposal, and naval special warfare.
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Apr20
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Aspects of Modeling and Simulation of Waves in Random MediaKnut SolnaUniversity of California, IrvineTime: 12:00 PM
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Tutorial on aspects of modeling and simulation of waves in random media.
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Apr18
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Beam Propagation and Focussing in Complex MediaKnut SolnaUniversity of California, IrvineTime: 03:45 PM
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See Math Colloquium listings.
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Apr01
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The Paraxial Wave and Vibrating Plate Equation ConnectionPeter McCoyUnited States Naval AcademyTime: 12:00 PM
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The Paraxial Wave Equation arises in modeling the propagation of a laser thru the atmosphere under ideal conditions. The solutions of this equation are complex-valued functions. Using a system analogous to Cauchy-Riemann equations, we show that the real and imaginary parts of these solutions solve the Vibrating Plate Equations. Conversely, one constructs solutions of the Paraxial Wave Equation from solution of the Vibrating Plate Equation of this system.
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Mar28
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A model reduction approach to inversionLiliana BorceaUniversity of MichiganTime: 03:45 PM
View Abstract
See Math Colloquium listings.
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Mar25
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Transition Matrix Model for Evolutionary Game DynamicsChristopher GriffinUnited States Naval AcademyTime: 12:00 PM
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We study an evolutionary game model based on a transition matrix approach, in which the total change in the proportion of a population playing a given strategy is summed directly over contributions from all other strategies. This general approach combines aspects of the traditional replicator model, such as preserving unpopulated strategies, with mutation-type dynamics, which allow for nonzero switching to an unpopulated strategy, in terms of a single transition function. Under certain conditions, this model yields an endemic population playing non-Nash-equilibrium strategies. In addition, a Hopf bifurcation with a limit cycle may occur in the generalized Rock-Paper-Scissors game, unlike the replicator equation. Nonetheless, many of the Folk Theorem results are shown to hold for this model. We will discuss new problems in control that may emerge from this model and discuss methods they might be solved. Discussion on control is entirely future work.
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Mar07
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Wolfram Technology in Education and ResearchAndy DorsettWolfram ResearchTime: 12:00 PM
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This talk illustrates capabilities in Mathematica 10 and other Wolfram technologies that are directly applicable for use in teaching and research on campus. Topics of these technical talks include: * Enter calculations in everyday English, or using the flexible Wolfram Language * Visualize data, functions, surfaces, and more in 2D or 3D * Store and share documents locally or in the Wolfram Cloud * Use the Predictive Interface to get suggestions for the next useful calculation or function options * Access trillions of bits of on-demand data * Easily turn static examples into mouse-driven, dynamic applications * Access 10,000 free course-ready applications * Get deep support for specialized areas including machine learning, time series, image processing, parallelization, and control systems, with no add-ons required * Compute with Mathematica in the Wolfram Cloud * Create multi-domain models and simulate them with Wolfram SystemModeler Current users will benefit from seeing the many improvements and new features of Mathematica 10 (http://www.wolfram.com/mathematica/new-in-10/), but prior knowledge of Mathematica is not required.
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Feb19
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Mathematical Modeling: Immune System Dynamics in the Presence of Cancer and Immunodeficiency in vivoThomas J. WesterMIDN 1/CTime: 12:00 PM
View Abstract
The Human Immunodeficiency Virus (HIV) targets CD4 T-cells which are crucial in regulating the immune systems response to foreign pathogens, including cancerous cell development. Furthermore, several studies link HIV infection with the proliferation of specific forms of cancer such as Kaposi Sarcoma and Non-Hodgkin's Lymphoma; HIV infected individuals can be several thousand times more likely to be diagnosed with cancer. However, much remains unknown about the dynamic interaction between cancer development and immunodeficiency. During HIV-1 primary infection, we know that the virus concentration increases, reaches a peak, and then decreases until it reaches a set point. In this project, we studied longitudinal data from 18 subjects identified as HIV positive during plasma donation screening to examine the dynamics of primary HIV infection. In doing so, we applied several nonlinear ordinary differential equation HIV infection models and analyzed the behavior of the system. In our future work, we seek to integrate cancer-immune models to examine the interaction of both cancer and immunodeficiency within the immune system.
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Jan14
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Topological pressure with applications to genomicsDavid KoslickiOregon State UniversityTime: 12:00 PM
View Abstract
Topological pressure is a well-known concept in Ergodic theory that measures the "weighted information content" of infinite strings of symbols. I will present an adaptation of topological pressure suitable for use on finite strings and apply this to the problem of determining regions of high coding sequence density in a given genome. The theoretical underpinnings of this approach (based on thermodynamic formalism) will also be presented and a justification given for the usage of tools from symbolic dynamics to the analysis of genomic data. This is joint work with Daniel J. Thompson.
