Colloquia
Department of Mathematics and Statistics
Texas Tech University
In many applications in science and engineering, there is a high demand for fast and accurate computational methods that can simulate complex multi-physical processes and their interactions taking place at a wide range of time scales. A prominent example of such an application is numerical weather prediction (NWP) and climate modeling, which rely on computational solution of primitive equations used to predict the behavior of the atmosphere, oceans, land surface, etc. Numerical solutions of such multiphysics problems remain a challenging task due to the presence of multiple time scales in the system where different processes take different amounts of time to complete. For instance, acoustic and gravity waves travel much faster than advection/convection processes, thereby preventing the use of longer time steps which poses difficulties for real-time simulation of weather conditions. With the significantly increased computational power in recent years, the challenge will increase with modern simulations which include more physical processes (e.g., adding smaller scales) in an attempt to capture higher-order modeling effects that were omitted from earlier models. As such, developing fast and accurate time integration methods is crucial for a wide range of applications that rely on large-scale simulations of complex systems. In this talk, I will introduce new advanced exponential and multirate time integration methods that I developed recently and showcase their performance across several applications in visual computing, NWP, and computational biology.
This Departmental Colloquium may be attended Monday the 8th at 3:00 PM CST (UT-6) via this Zoom link.
Meeting ID: 937 6778 1313
Mathematical modeling from experimental data is an important and challenging problem in diverse applications in science and engineering. In this talk, we introduce the "Finite Expression Method" (FEX), a deep symbolic learning technique, to discover interpretable and explicit mathematical models with finitely many operators from observed data. FEX is a flexible framework with a wider range of applications, higher accuracy, and better noise robustness than many existing symbolic learning approaches. In the context of mathematical modeling on complex networks, a fast training algorithm based on stochastic sampling is proposed to accelerate the training of FEX, improving the computation cost to a much smaller scale. Various numerical and theoretical results will be provided to justify the performance of FEX. A future agenda of FEX for general scientific machine learning problems will also be discussed.
This Departmental Colloquium may be attended Tuesday the 9th at 3:00 PM CST (UT-6) via this Zoom link.
Meeting ID: 912 1286 4145
In many applications in science and engineering, there is a high demand for fast and accurate computational methods that can simulate complex multi-physical processes and their interactions taking place at a wide range of time scales. A prominent example of such an application is numerical weather prediction (NWP) and climate modeling, which rely on computational solution of primitive equations used to predict the behavior of the atmosphere, oceans, land surface, etc. Numerical solutions of such multiphysics problems remain a challenging task due to the presence of multiple time scales in the system where different processes take different amounts of time to complete. For instance, acoustic and gravity waves travel much faster than advection/convection processes, thereby preventing the use of longer time steps which poses difficulties for real-time simulation of weather conditions. With the significantly increased computational power in recent years, the challenge will increase with modern simulations which include more physical processes (e.g., adding smaller scales) in an attempt to capture higher-order modeling effects that were omitted from earlier models. As such, developing fast and accurate time integration methods is crucial for a wide range of applications that rely on large-scale simulations of complex systems. In this talk, I will introduce new advanced exponential and multirate time integration methods that I developed recently and showcase their performance across several applications in visual computing, NWP, and computational biology.
This Departmental Colloquium is hosted by the Applied Mathematics seminar group and may be attended Thursday the 18th at 3:30 PM CST (UT-6) in Chemistry 113.
In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the Black-Scholes equation supplied by new intervals for the underlying stock and \ new initial and boundary conditions for option prices. The Black-Scholes equation was solved in the positive direction of the time variable. This ill-posed initial boundary value problem was solved by the so-called Quasi-Reversibility Method (QRM). This approach with an added trading strategy was tested on the market data for 368 stock options and good forecasting results were demonstrated. In the current paper, we use the geometric Brownian motion to provide an explanation of that effectivity using computationally simulated data for European call options. We also provide a convergence analysis for QRM. The key tool of that analysis is a Carleman estimate.
Candidate's CV pdf
This Departmental Job Colloquium may be attended at 4 PM CST (UT-6) via this Zoom link. Meeting ID: 915 0439 8414
Dr. Conover recently retired after 50 years as a Professor of Statistics at Texas Tech, more than 40 years of this as a Paul Whitfield Horn Professor. During this time he served on many Horn Professor selection committees. In this lecture he describes what those committees looked for in their selection.
This Departmental Colloquium is sponsored by the Statistics seminar group.
Ever since Poincare' times, understanding the qualitative behavior of a system is one of the main goals of Dynamical Systems' theory. The points with the simplest dynamics are those belonging to periodic orbits. The concept of 'periodic' was then generalized to 'recurrent' (a point x is recurrent if its orbit gets arbitrarily close to x as t->infinity), 'non-wandering' (a point x in non-wandering if, arbitrarily close to x, there are orbits that get back close to x for t->infinity) and more sophisticated types. Since Smale showed that the non-wandering set decomposes into basic 'pieces', each piece being the analogue of a 'periodic orbit', the decomposition of the non-wandering set became an important ingredient of the qualitative study of a dynamical system. This decomposition, though, does not say anything about the behavior of points outside of the non-wandering set. In this talk Jim Yorke and I present a complementary ingredient to encode the full behavior of a dynamical system into a graph. The nodes of the graph are the pieces of the decomposition above; its edges describe the dynamics of all other points. The exposition will be mainly based on examples and pictures.
This Departmental Colloquium is sponsored by the Applied Math seminar group and may be attended Wednesday the 31st at 4:00 PM CST (UT-6) via this Zoom link.
Meeting ID: 944 4492 2197
Passcode: applied
Colloquium abstracts
This Departmental SIAM Colloquium may be attended Tuesday the 9th at 3:00 PM CDT (UT-5) via this Zoom link.
Meeting ID: 987 1274 9015
Passcode: SIAM
Afternoon Schedule
3:00 - 3:25 Nathan Holtman A Differential Game Model for Optimal Management of Wolf-Livestock Conflict
3:30 - 3:55 Boluwatife Awoyemi Simulation and Latin Hypercube Sampling of Comparable Mixed-Time Models in a Consumer-Resource Relationship
4:00 - 4:25 Md Mahmudul Bari Hridoy Investigating Infectious Disease Dynamics with Seasonal Stochastic Epidemic Models
The topic of the talk was originally motivated by the Floquet-Bloch theory of Schroedinger equations with periodic potential and other problems in Mathematical Physics. The ordered eigenvalues of families of self-adjoint matrices are not smooth at points corresponding to repeated eigenvalues (called diabolic points or Dirac points). Generalizing the notion of critical points as points for which the homotopical type of (local) sub-level set changes after the passage through the corresponding value, in the case of the generic family we give an effective criterion for a diabolic point to be critical for those branches and compute the contribution of each such critical point to the Morse polynomial of each branch, getting the appropriate Morse inequalities as a byproduct of the theory. Remarkably, the non-smooth contribution to the Morse polynomial turns out to be universal: it depends only on the size of the eigenvalue multiplicity and the relative position of the eigenvalue of interest and not on the particulars of the operator family. These contributions are expressed in terms of the homologies of Grassmannians. The talk is based on the joint work with Gregory Berkolaiko
This Departmental Colloquium is sponsored by the Probability, Differential Geometry and Mathematical Physics seminar group.