Title: A Self-consistent-field Iteration for Orthogonal Canonical Correlation Analysis

Abstract: We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a useful criterion for visualization, pattern recognition and feature extraction, existing methods for solving OCCA problem are either numerically unstable by relying on a deflation scheme, or less efficient by directly using generic optimization methods. In this paper, we propose an alternating numerical scheme whose core is the sub-maximization problem in the trace-fractional form with an orthogonality constraint. A customized self-consistent-field (SCF) iteration for this sub-maximization problem is devised. It is proved that the SCF iteration is globally convergent to a KKT point and that the alternating numerical scheme always converges. We further formulate a new trace-fractional maximization problem for orthogonal multiset CCA and propose an efficient algorithm with an either Jacobi-style or Gauss-Seidel-style updating scheme based on the SCF iteration. Extensive experiments are conducted to evaluate the proposed algorithms against existing methods, including real-world applications of multi-label classification and multi-view feature extraction. Experimental results show that our methods not only perform competitively to or better than the existing methods but also are more efficient.

Abstract: Canalization is a property of Boolean automata that characterizes the extent to which subsets of inputs determine (canalize) the output. In this presentation, I describe the role of canalization as a determinant of the dynamical character of Boolean networks (BN). I consider two different measures of canalization introduced by Marques-Pita and Rocha, namely 'effective connectivity' and 'input symmetry,' in a three-pronged approach. First, we show that the mean 'effective connectivity,' a measure of the true mean in-degree of a BN, is a better predictor of the dynamical regime (order or chaos) of random BNs with homogeneous connectivity than the mean in-degree. Next, I combine effective connectivity and input symmetry in a single measure of 'unified canalization' by using a common yardstick of Boolean hypercube “dimension” — a form of fractal dimension. I show that the unified measure is a better predictor of dynamical regime than effective connectivity alone for BNs with large in-degrees. Finally, I introduce 'integrated effective connectivity' as a macro-scale extension of effective connectivity that characterizes the canalization present in BNs coarse-grained in time obtained by iteratively composing a BN with itself. I show that the integrated measure is a better predictor of long-term dynamical regime than just effective connectivity for a small class of BNs known as the elementary cellular automata. The results also help partly explain the chaotic properties of Rule 30 and why it makes sense to use it as a random number generator.

Title: Statistics, Topology and Data Analysis

Abstract: In this talk, I will discuss how statistics and topological data analysis are beautifully complement each other to solve real data problems. As a paradigm, I will discuss supervised learning, and present a classification approach using a novel Bayesian framework for persistent homology. An application to materials science will be discussed.

Bio: Vasileios Maroulas is a Professor of Mathematics with joint appointments at the Business Analytics and Statistics, and the Bredesen Center’s Data Science Engineering at the University of Tennessee, Knoxville (UTK). He is a Senior Research Fellow at the US Army Research Lab, an Elected Member of the International Statistical Institute, and an Editor-in-Chief of Foundations of Data Science published by AIMS.  Following his PhD graduation from the Statistics Department at the University of North Carolina at Chapel Hill in 2008, he continued as a Lockheed Martin Postdoctoral Fellow at the IMA at the University of Minnesota for two years until he joined UTK in 2010 as an Assistant Professor. Maroulas was also a Mathematical Sciences Leverhulme Trust Fellow at the University of Bath, UK during 2013-2014. His research interests span from computational statistics and machine learning to applied probability and computational topology and geometry with applications in data analysis and quantum computing. His methods have found applications in chemistry, neuroscience, materials science, and biology. His work has been funded by several federal agencies, including AFOSR, ARO, DOE, and NSF; by national labs and private foundations, including ARL, ORNL, the Simons Foundation, and the Leverhulme Trust in the UK; as well as by industry, including Eastman, and Thor Industries.

Title: Mathematical modelling of blood coagulation system

Abstract: Blood is an important liquid organ performing transport functions. Any injury may lead to dangerous blood loss, but fortunately we have a reliable emergency blood coagulation system that quickly reacts to injuries and prevents massive blood loss. Disorders in blood coagulation may induce thrombosis, stroke, myocardial infarction and other complications, including lethal ones. 

Title: Improved Training of Generative Adversarial Network

Abstract: The original Generative Adversarial Network was introduced by Ian Goodfellow et al. in 2014, together with a discriminator loss function, called binary cross-entropy. Later, other discriminator loss functions were developed: WGAN loss, hidge loss, Dragan loss, etc. We introduce a new family of discriminator loss functions. Experiments validated the effectiveness of our loss functions on unconditional image generation task.

Title: Designing multistability with AND gates

Abstract: Systems of differential equations have been used to model biological systems such as gene and neural networks. A problem of particular interest is to understand and control the number of stable steady states. Here we propose conjunctive networks (systems of differential equations equations created using AND gates) to achieve any desired number of stable steady states. Our approach uses combinatorial tools to easily predict the number of stable steady states from the structure of the wiring diagram.

Title: Mechanisms of stabilization and development in early multicellular evolution

Abstract: The evolution of life on Earth is marked by a few biological innovations that profoundly changed downstream evolutionary trajectories. John Maynard Smith and Eörs Szathmáry termed these innovations Major Evolutionary Transitions and among others, they include the evolution of multicellular organisms from unicellular ancestors. Although the fossil record is scarce to understand what happened in the early evolution of multicellularity, we can conduct experiments in the laboratory to evolve primitive multicellular organisms. Using an experimental model of multicellularity, called ‘snowflake yeast', and some theoretical tools, we asked: how is multicellularity stabilized over evolutionary time? and, how simple developmental rules can lead to an increase in multicellular size? The understanding of multicellular evolution can inform us about the mechanisms underlying other major evolutionary transitions, and more generally, this research can deepen our understanding of the evolution of biological complexity.