Title: Boolean canalization in the micro and macro scales
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. 

In the early months of coronavirus pandemic, the first important achievement in medicine was including anticoagulant therapy in protocols of treatment that decreased percentage of deaths. Many aspects of blood coagulation are still to be understood in the future. 

Blood coagulation is an interesting object of investigation by mathematical models. It includes a nonlinear threshold system of activation, polymerization of fibrin leading to gelation, activation of blood cells and others. All this biochemical system works in a branched network of blood vessels with a variety of hydrodynamical conditions in them. This research is related to nonlinear dynamical systems and reaction-diffusion-convection models.

Title: Modeling of Emergent Patterns Within Stem Cell Colonies

Abstract: The differentiation of stem cell colonies into specified tissue types is possible through local and long-distance intercellular communication; however, it is unclear which mechanisms take priority in context-specific situations. Here we consider human induced pluripotent stem cells (hiPSCs) whose therapeutic potential arises from their ability to differentiate into all germ lineages. Prior work in the literature suggests that both cell-autonomous and non-autonomous (e.g. positional) mechanisms determine cell fate during the differentiation of hiSPCs, producing patterns and other system-level features in the process. Informed by experimental data, we develop a collection of agent-based models (ABMs) whose agents (i.e. cells) are each equipped with local rules that govern how the agents interact with their environment and with each other. The purpose of each ABM is to simulate the early differentiation of hiPSCs according to a different set of biological assumptions, with some ABMs using a Boolean network to model potential mechanisms of intercellular communication. We also extend an existing mathematical framework by M. Yereniuk and S.D. Olson which formalizes ABMs to estimate long-term model behavior with respect to time. Our extensions introduce the birth and death of agents into the framework, and our estimates aim to establish connections between local interactions and certain system-level observations. Thus, we study both the emergent behaviors of our ABMs and the dynamics of the local rules governing each agent in order to ascertain which modes of intercellular communication determine cell fate.

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.