This is the third in a series of NSF sponsored workshops. The two day meeting will highlight research problems in industrial and interdisciplinary mathematics through talks by researchers in academia and industry and through a poster session. Additionally, the meeting will present a roundtable discussion on applied mathematics and a joint session with the Arizona Mathematics Undergraduate Conference on mathematical career choices in industry.
Title: Stochastic Modeling and the Theoretical Epidemic: Spatial Heterogeneity and Time to Extinction
Title: Linking Functional And Structural Brain Images With Multivariate Network Analyses: Description And
Application Using The Partial Least Square Method
Title: MANUFACTURING, ROBOTICS AND COMPUTATIONAL GEOMETRY
Abstract: This Lecture features examples of the dominating influence of geometry in the automotive manufacturing process. The lecture begins with the design and manufacture of sheetmetal components that motivated advances in mathematical applications for Computer Aided Design. After a discussing the mathematics developed for the geometric aspects of this manufacturing process, the lecture examines an application of the same mathematics to robotics. The next topic relates the previous geometric constructions with the analysis of automotive components for fatigue, stress and strain. The lecture ends with the award winning video tape "Ballet Robotique".
Title: Cross-shipping and Meeting Demand
Abstract: In this talk, results of simulations involving two manufacturing lines, manufacturing similar products, will be presented. Two very similar manufacturing lines with slightly different total manufacturing time will be considered. The main focus will be on the need for cross-shipping at different levels of the manufacturing process to meet short and long term demands.
Title: Computations of Multivalued Solutions of Nonlinear PDEs
Abstract:Many physical and industrial problems arising from high frequency waves, dispersive waves, Hamiltonian systems, traffic models and supply chains require the computations of multivalued solutions which cannot be described by the viscosity methods. In this talk I will review several recent numerical methods for such problems, including the moment methods, kinetic equations and the new level set method with S. Osher, H. Liu and R. Tsai. Applications to the semiclassical Schroedinger equation and Euler-Piosson equations with applications to modulated electron beams in Klystrons will be discussed.
Title: Some Mathematical Ideas for Attacking the
Brain Computer Interface Problem
Abstract: The Brain Computer Interface (BCI) Problem has become a topic of interest both to academic researchers and their industrial counterparts. The ability to interpret or classify rational thought from its measurements is, to say the least, intriguing. While there are currently no BCI products available on the market many companies are planning to introduce new devices and it appears that this is just the beginning. It is unknown whether computers will ever be mind readers and we will not attempt to answer this question! However, we will describe the BCI research efforts at Colorado State University and some mathematical ideas being considered.
Title: Modeling and control of manufacturing systems
Abstract:When considering the problem of supply chain management in semiconductor industry, a prerequisite is to use the simplest model that still contains sufficient information to answer all of the relevant questions. One of the problems of interest is how to ramp from zero production to full production in the shortest time possible. Roughly three classes of models for manufacturing systems have been studied in the literature so far: discrete event models, queueing theory and fluid models. Each of these models have its shortcomings. Discrete event models suffer from state explosion, queuing theory establishes only steady state results, and fluid models do not incorporate flow times (also called throughput times, cycle times or sojourn times). Therefore, we use a new class of flow models in which we assume that the flow of products can be considered as a compressible fluid flow. This new class of flow models yields computationally feasible, dynamic models that incorporate both throughput and cycle time. Even though discrete event models suffer from state explosion, they can be used for validation of the proposed PDE-models. Once the PDE-models have been validated, the ramp-up control problem can be studied.
Title: Optimization-based design of multisine signals for "plant-friendly"
identification of highly interactive process systems
Abstract:Highly interactive systems are ill-conditioned and as a consequence are very sensitive to model uncertainty; this imposes fundamental limitations to achievable closed-loop performance. We present an identification testing framework meaningful to highly interactive process systems based on the application of multivariable multisine input signals possessing specialized harmonic characteristics. "Plant-friendliness" in the design procedure is accomplished by using advanced optimization solvers that minimize an objective function while imposing constraints on the overall span, move size, and variability of both input and output signals. Objective functions of interest include minimizing crest factor (which results in signals that are evenly distributed at their high and low limits) and maximizing the geometric distribution of the output over a region in the state-space. The latter objective is particularly meaningful for data-centric estimation techniques such as Model-on-Demand. This signal design procedure is applied to a 2-by-2 multivariable model representing the simplified dynamics of high-purity distillation, which represents a class of systems exhibiting challenging interaction and gain directionality properties. The signals obtained from this approach are shown to possess significant fundamental and practical properties in comparison to classical designs.
Title: A Constrained Filtered Least Squares Method Applied to a Problem in
Title: Computational Biosciences Masters at ASU
Title: An Introduction to Inverse Problems
Abstract:The scope of this talk is basic. I hope to introduce and make concrete the concept and ideas that arise in the study of inverse problems. Several simple examples will demonstrate common difficulties arising in the study of inverse problems. These examples will be drawn from inverse problems of elliptic, parabolic and hyperbolic PDEs.
Title: Applications of Wavelets in Signal Processing: Introduction to
Abstract:Abstract: This talk introduces the audience to wavelets by describing what wavelets are (and are not), what their properties are (and are not), and what you can do with them (and can not). A brief history of the early development of wavelets is given to provide motivation for their existence, i.e. they were created on purpose as opposed to being discovered by accident. Specific examples of how wavelets are used in current applications and how they might be used in the future are discussed.
Title: Overview of our effort in using computer simulation to understand
the turbulence in the stratosphere
Abstract:Understanding the turbulence in the stratosphere is important as it affects aviation and light propagation. There are three major sources of turbulence in the stratosphere : (1) turbulence may be generated at the edge of the jet stream due to shear, (2) convection in the troposphere may overshoot into the stratosphere, (3) gravity waves generated in the troposphere may propagete upward and in turns create turbulence in the middle or upper stratosphere. The dynamics of the turbulence is goverened by the Navier-Stokes equation. Substituting different parameters and models into the equation, we are able to simulate computationally the turbulence generated from all three circumstances. Some features of our results, e.g. separation of mechanical and thermal layers, length scale of the turbulence, etc, will be presented.
Title: Reverse engineering gene networks
Abstract: We present a scheme to reverse-engineer gene networks on a genome-wide scale using a relatively small amount of gene expression data from microarray experiments. It uses singular value decomposition to construct a family of solutions and then identify the unique solution by robust regression. Our algorithm has $O(\log N)$ sampling complexity and $O(N^4)$ computational complexity. We test and validate our approach in a series of numerical experiments on model gene networks.
Title: Optimal Velocity Profiles for the Migration Flights of Swans
Abstract: Members of the two swan species that are native to North America, Tundra and Trumpeter swans, undertake long migratory journeys as long as 6,000 km twice yearly. These migrations are carried out as a series of hops and stops. For Tundra swans, hops of approximately 500 kilometers are followed by stops of several days during which flight-depleted fat stores and muscle mass are restored. In order to model migration flights it can be reasonably assumed that a swan will choose a velocity profile that minimizes energy expenditure over the course of the flight, and that its mass and frontal body area decrease during flight due to fat store depletion. Utilizing an equation describing power requirements for level flight published by Pennycuick (1989), optimal velocity profiles and resultant mass profiles were obtained by solving a constrained optimization problem with the calculus of variations. Swan mass over the course of migration can be described by a dynamical system that when coupled with optimal mass profiles obtained from the model yields a tool for predicting the length of a refueling stop based on the length of a preceding migratory hop. The model predictions can then be tested using satellite tracking data.
Title: Population movement of ladybeetles;
model evaluation of mechanisms causing ladybeetle aggregation in resource patches
Abstract:The presentation focuses on the analysis of an experiment in which areas in an alfalfa crop were sprayed with sucrose solution. Sucrose (table sugar) is a useful resource for ladybeetles (like for many insects), and it acts as an indicator for the presence of aphids because aphids excrete a waste product, honeydew, that is rich in sugars. Following sucrose application, it is observed that ladybeetle densities increase by a factor of 10-20 within a couple of hours. It is unknown whether this aggregation occurs by: (1) directional immigration by flight into sugar-sprayed areas (presumably guided by volatile chemical cues) (2) decreased emigration by flight by beetles who have (possibly by chance) entered the sugar sprayed area (3) decreased motility of walking beetles in sugar sprayed canopy, compared to unsprayed canopy (area restricted search) In the field experiment, strips of alfalfa of 2, 5 and 10 m width were sprayed with sugar, and ladybeetle densities on transects across those plots were measured at three times after sugar spray. Different spatially explicit models are fitted to the data to determine which of the above three candidate explanations for aggregation are operating.