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Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…

We realize autonomous Boolean networks by using logic gates in their autonomous mode-of-operation on a field-programmable gate array. This allows us to implement time-continuous systems with complex dynamical behaviors that can be…

We study a genetic regulatory network model developed to demonstrate that genetic robustness can evolve through stabilizing selection for optimal phenotypes. We report preliminary results on whether such selection could result in a…

Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…

Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with…

We analyze pattern formation on a network of cells where each cell inhibits its neighbors through cell-to-cell contact signaling. The network is modeled as an interconnection of identical dynamical subsystems each of which represents the…

Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive…

Style transfer describes the rendering of an image semantic content as different artistic styles. Recently, generative adversarial networks (GANs) have emerged as an effective approach in style transfer by adversarially training the…

A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the…

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node…

We are interested in the design of generative networks. The training of these mathematical structures is mostly performed with the help of adversarial (min-max) optimization problems. We propose a simple methodology for constructing such…

Recently, research has increasingly focused on developing efficient neural network architectures. In this work, we explore logic gate networks for machine learning tasks by learning combinations of logic gates. These networks comprise logic…

A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean nets and are proposed as on extended approach to genetic…

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…

This paper proposes methods for identification of large-scale networked systems with guarantees that the resulting model will be contracting -- a strong form of nonlinear stability -- and/or monotone, i.e. order relations between states are…

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Generative Adversarial Networks (GAN) are generative neural networks which can be trained to implicitly model the…

In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input-output dynamic of the system under control. Robust satisfaction of input and output constraints and recursive…