Title: First-order Upwind Scheme for Solving the Adjoint Euler Equations

Abstract: A first-order upwind scheme based on matrix splitting is developed for solving the 2D adjoint Euler equations. We prove that the adjoint advection equation is a suitable model for the 1D adjoint Euler equations and use this knowledge to develop and study our proposed numerical scheme. Solution behavior is first discussed from a mathematical perspective and later demonstrated numerically for both the model equations and adjoint Euler equations.

Title:  Linearized Krylov subspace Bregman iteration with nonnegativity constraint

Abstract: Bregman-type iterative methods have attracted considerable attention
in recent years due to their ease of implementation and the high quality of the
computed solutions they deliver. However, these iterative methods may 
require alarge number of iterations and this reduces their attractiveness. This talk
describes a linearized Bregman algorithm defined by projecting the 
problem tobe solved into an appropriately chosen low-dimensional Krylov subspace. The projection reduces both the number of iterations and the computational  effort required for each iteration. A variant of this solution method, in which nonnegativity of each computed iterate is imposed, also is described. 
The talk presents joint work with A. Buccini and M. Pasha.

Title: Efficient control methods for stochastic Boolean networks

Abstract: The development of efficient methods for finding intervention strategies that can direct a system from an undesirable state into a more desirable state is an important problem in systems biology. The identification of potential interventions can be achieved through mathematical modeling by finding appropriate input manipulations that represent external interventions in the system. This talk will describe a stochastic modeling framework generalized from Boolean networks, which will be used to formulate an optimal control problem. The optimal control method requires a set of control inputs, each representing the silencing of a gene or the disruption of an interaction between two molecules. Several methods from Markov decision processes can be used to generate an optimal policy that dictates the action to be taken at each state. However, the computational complexity of these algorithms limits the applications of standard algorithms to small models. This talk will discuss alternate methods that can be used for large models.

Title: Enhancing mechanistic modeling with machine learning

Abstract: At their core, biological systems are information processing systems. In response to numerous environmental cues, the complex molecular interaction networks within human cells integrate these signals and orchestrate a number of intricate cellular behaviors. Verbal argument and intuition alone are insufficient to understand how these complex networks control cellular behaviors or to rationally design treatment, and it is beneficial to translate these molecular networks into realistic and predictive mathematical models. However, the development of such models faces several fundamental challenges: 1) the control network is complex and full of interacting feedbacks, 2) the kinetic constants characterizing the biological reactions are often unavailable, 3) it is often impossible to derive analytical solutions of these models, and 4) once the models become increasingly realistic and complex, they are often as difficult to understand as the original biological system. To address these above mentioned challenges, we have developed an integrated computational pipeline that combines Mechanistic modeling, Machine learning and nonlinear dynamical analysis. By integrating different methods with unique strength and limitations, this innovative pipeline can potentially overcome each other’s limitations. This novel, integrated pipeline has been applied to study several different biological systems, and the results have been verified experimentally. Based on our theoretical analysis and experimental confirmation, we propose that his novel pipeline can be generally applied to understand any complex and uncertain biological systems.

Title: Recovering data sparse in a frame
Abstract: In this talk, we will first review some classical results on compressed sensing, a subject about recovering sparse signals from undersampled linear measurements. The theory developed in compressed sensing is transformative as it has been applied to a broader class of data recovery problems such as matrix completion. Then we will focus on its generalization where signals are sparse in a redundant frame. We will discuss the challenges faced in this case, as well as some new results. A preliminary image inpainting application will also be addressed at the end of the talk.

Title: Information Theoretic Learning with Infinitely Divisible Kernels

Abstract: In this work, we introduce a framework for information theoretic learning based on an entropy-like functional defined on positive definite matrices. The proposed functional, which is based on Renyi's axiomatic definition of entropy, provides a quantity that can be estimated from data and applied as an objective function in different machine learning problems. As an application example, we derive a supervised metric learning algorithm using a matrix-based analogue to conditional entropy with results comparable with the state of the art.

Title: Particle collision model embedded into an optimization graph theory problem.

Abstract: The color reconnection model is used to explain and predict the production of particles in high energy collisions of hadrons.  According to this model, the colored partons produced in an event  can lose their original color quantum numbers and acquire new ones if this reduces a type of free energy. The computation of the  ground state of the free energy is combinatorially complex.  In this note, we demonstrate the limitations of traditional techniques for solving this problem and the possibility of using quantum solvers.   In particular, we present an Ising model formulation for quantum annealers and a gate-based formulation.

During my time at FermiLab, given by the MSGI-NSF program, I was able to jump in on this problem to help construct an optimal Hamiltonian for quantum annealers. I will be providing an introduction to the physics problem and my contribution in how we used AMPL to help us construct a Hamiltonian.

Title: Generative Adversarial Networks

Abstract: ​In 2014, Ian Goodfellow et al. proposed a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. In this talk, I will talk about the structure of such a framework, how we train it as well as some theoretical results and applications.

Title: Algebraic Data Science 

Abstract:  Data science has emerged as an important field for making decisions based on data collected from sectors as varied as health care and housing. Two important steps in a data-science pipeline are data collection strategies and predictive modeling.  In this talk, we introduce an algebraic-geometric platform for unifying experimental design for discrete data sets and model selection for polynomial dynamical systems.  We will illustrate the utility of the platform on a few biological systems.