|Professor: Prof. Sergei. Avdonin, Univ. of Alaska, Fairbanks|
|Title: Control and Inverse Problems for Differential Equations on Graphs|
|Abstract: Quantum graphs are metric graphs with differential equations defined on the edges. Recent interest in control and inverse problems for quantum graphs is motivated by applications to important problems of classical and quantum physics, chemistry, biology, and engineering.In this talk we describe some new controllability and identifiability results
for partial differential equations on compact graphs. In particular, we consider graph-like networks of inhomogeneous strings with masses attached at the interior vertices. We show that the wave transmitted through a mass is more regular than the incoming wave. Therefore, the regularity of the solution to the initial boundary value problem on an edge depends on the combinatorial distance of this edge from the source, that makes control and inverse problems for such systems more difficult.
We prove the exact controllability of the systems with the optimal number of controls and propose an algorithm recovering the unknown densities of the strings, lengths of the edges, attached masses, and the topology of the graph.
The proofs are based on the boundary control and leaf peeling methods de-
|Lecturer: Dr. Yonggang Yao, SAS Institute Inc.|
|Time and location: 2:00-4:45 pm, Friday 141 (Please note this NEW location)|
Course Description: If you ever worry about the validity of the common variance or other parametric distribution assumptions for your data analysis, quantile regression might be a relief for you because quantile regression is a distribution-agnostic methodology. Whereas generalized linear regression models the conditional means via link functions, quantile regression enables you to more fully explore your data by modeling conditional quantiles, tail distributions, or the entire conditional distributions. Quantile regression is particularly useful when your data are heterogeneous and when you cannot assume a parametric distribution for the response. This tutorial provides an overview and a set of intuitive examples of the quantile regression methodology. From the basic concepts and comparison to linear regression to more advanced applications and research topics, this tutorial demonstrates the benefits and potentials of using quantile regression methods and introduces computing tools for quantile model fitting, quantile predictions, conditional distribution estimation, conditional percentage estimation, and other inferences and hypothesis testing. The attendees are assumed to be familiar with basic probability distributions, linear algebra, and linear regression.
The first lecture covers:
The second lecture covers:
ComputingSoftware: Neither personal computer nor pre-installed software are required in classroom. This short course will present SAS outputs for relevant example programs. You are welcome to try the programs on SAS 9.22 or later release including the free SAS University Edition.
Short Biography: Dr. Yonggang Yao is a principal research statistician at SAS Institute Inc. He joined SAS in 2008 after obtaining his PhD in statistics from The Ohio State University. Dr. Yao has developed several SAS quantile-regression procedures for standard and distributed computing environments including PROC QUANTSELECT and PROC HPQUANTSELECT. He is also the key supporting developer for two other SAS procedures: PROC QUANTREG for quantile regression and PROC ROBUSTREG for robust regression. Dr. Yao has taught tutorials on quantile regression at SAS Global Forums, the Joint Statistical Meetings, and for the ASA traveling courses.
|Registration: To ensure your seat and order a hard copy of the lecture notes, please email Professor Yanqing Sun at firstname.lastname@example.org using email subject “Lecture Registration for Applied Quantile Regression” or “Lecture Registration and Ordering Notes for Applied Quantile Regression”. There is a $20 fee for each hard copy of the lecture notes (cash or check).|
Parking: Visitor parking is available inEast Deck 1.
|Professor: Valery, Romanovski, Center for Applied Mathematics and Theoretical Physics, University of Maribor|
|Title: Some problems in the theory of polynomial ordinary differential equations|
|Abstract: In addition to their theoretical interest systems of ordinary differential
equations whose right hand sides are polynomials have wide practical application. In this talk we will describe significant problems that arise in studying the behavior of solutions of polynomial differential equations and techniques of analysis that are used to attack them.
|Professor: Min Ru, Professor, Department of Mathematics, University of Houston, USA|
|Title: Results related to F.T.A. in number theory, complex analysis and geometry
|Abstract: The fundamental theorem of algebra (F.T.A.) states that for every complex polynomial P, the equation P(z)=0 always has d solutions on the complex plane, counting multiplicities, where d is the degree of P.
In this talk, I’ll discuss the results related to F.T.A. in number theory, complex analysis and geometry. In particular, I’ll describe the integer solutions of the Fermat’s equation (Faltings’ theorem), and related Diophantine equations (Diophantine approximation); the Little Picard theorem in complex analysis (viewed as a generalization of F.T. A.)
and overall so-called Nevanlinna theory; how the Nevanlinna theory is related to Diophantine approximation. Finally, I’ll discuss the study of Gauss map of minimal surfaces as part of application of the Nevanlinna theory.
|Dr. Daniel Massatt, University of Minnesota|
|Title:Electronic Structure of Relaxed Incommensurate 2D Heterostructures|
Abstract: 2D materials have extensive potential application in optics and electronics due to their unique mechanical and electric properties. How to numerically simulate electronic properties is well understood for periodic atomistic lattices, but has been unknown for materials that are stacked with misalignment that breaks the periodicity of the ensemble, i.e., incommensurate materials. The previous approach has been to artificially strain the layers to be able to use the theory and computational methods for periodic systems.
We show how to rigorously define the electronic density of states (DOS) for two-dimensional incommensurate layered structures, where Fourier-Bloch theory does not apply, and efficiently approximate it using a novel configuration space representation and locality technique. We have also been able to apply our configuration space approach to obtain mechanical relaxation patterns using a continuum elasticity model coupled with a stacking energy model. We combine these two models together to form an electronic structure calculation for an incommensurate system with atomistic relaxation.
|Professor: Daniel Onofrei, Department of Mathematics, University of Houston|
|Title:Active manipulation of scalar wave fields and applications|
|Abstract: In this talk we will describe our recent results about the characterization of continuous boundary data (i.e., pressure or normal velocity) on active single sources or arrays for the approximation of different prescribed scalar wave field patterns in given exterior (bounded or unbounded) regions of space. We will present the theoretical ideas behind our results as well as numerical simulations with applications in scattering cancellation, field synthesis and inverse source problems.|
|Professor: Leonid Koralov, Department of Mathematics, University of Maryland|
|Title: Large Time Behavior of Randomly Perturbed Dynamical Systems|
| Abstract: We will discuss several asymptotic problems for randomly perturbed flows
(and related problems for Markov chains with rare transitions). One class of flows (with regions where a strong flow creates a trapping mechanism) leads to a new class of elliptic and parabolic boundary value problems with
non-standard boundary conditions. The same boundary value problems appear as a limiting object when studying the
asymptotic behavior of diffusion processes with pockets of large diffusivity.
We will also discuss how large-deviation techniques can be used
to study the asymptotic behavior of solutions to quasi-linear parabolic equations with a small parameter at the
second order term and the long time behavior of the corresponding diffusion processes.
|Professor: Yi Sun, Department of Mathematics, University of South Carolina|
|Title: Kinetic Monte Carlo Simulations of Multicellular Aggregate Self-Assembly in Biofabrication|
|Abstract: We present a 3D lattice model to study self-assembly of multicellular aggregates by using kinetic Monte Carlo (KMC) simulations. This model is developed to describe and predict the time evolution of postprinting structure formation during tissue or organ maturation in a novel biofabrication technology–bioprinting. Here we simulate the self-assembly and the cell sorting processes within the aggregates of different geometries, which can involve a large number of cells of multiple types.|
|Professor:Jae Woo JEONG, Department of Mathematics, Miami University|
|Title:Numerical Methods for Biharmonic Equations on non-convex Domains|
|Abstract: Several methods constructing C1-continuous basis functions have been introduced for the numerical solutions of fourth-order partial differential equations. However, implementing these C1-continuous basis functions for biharmonic equations is complicated or may encounter some difficulties. In the framework of IGA (IsoGeometric Analysis), it is relatively easy to construct highly regular spline basis functions to deal with high order PDEs through a single patch approach. Whenever physical domains are non convex polygons, it is desirable to use IGA for PDEs on non-convex domains with multi-patches. In this case, it is not easy to make patchwise smooth B-spline functions global smooth functions.In this talk, we propose two new approaches constructing C1-continuous basis functions for biharmonic equation on non-convex domain: (i) Firstly, by modifying Bezier polynomials or B-spline functions, we construct hierarchical global C1-continuous basis functions whose imple- mentation is as simple as that of conventional FEM (Finite Element Methods). (ii) Secondly, by taking advantages of proper use of the control point, weights, and NURBS (Non-Uniform Rational B-Spline), we construct one-patch C1-continuous geometric map onto an irregular physical domain and associated C1-continuous basis functions. Hence, we can avoid the difficulties aris- ing multi patch approaches. Both of the proposed methods can be easily extended to construct highly smooth basis functions for the numerical solutions of higher order partial differential equations.|