# Applied Math Seminar

## Applied Math Seminar

**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.

## Applied Math Seminar

**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.

## Applied Math Seminar

**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.

## Applied Math Seminar

## Applied Math Seminar

## Applied Math Seminar

## Applied Math Seminar

## Applied Math Seminar

## Applied Math Seminar

**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.

## Applied Math Seminar

**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.