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Characterization of the differences between biological and random networks can reveal the design principles that enable the robust realization of crucial biological functions including the establishment of different cell types. Previous…

Networks are fundamental building blocks for representing data, and computations. Remarkable progress in learning in structurally defined (shallow or deep) networks has recently been achieved. Here we introduce evolutionary exploratory…

Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the…

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…

Modeling biological networks serves as both a major goal and an effective tool of systems biology in studying mechanisms that orchestrate the activities of gene products in cells. Biological networks are context specific and dynamic in…

High-throughput experiments are shedding light on the topology of large regulatory networks and at the same time their functional states, namely the states of activation of the nodes (for example transcript or protein levels) in different…

The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean…

Imperfect molecular detection in single-cell experiments introduces technical noise that obscures the true stochastic dynamics of gene regulatory networks. While binomial models of molecular capture provide a principled description of…

In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…

Regulatory gene networks contain generic modules like those involving feedback loops, which are essential for the regulation of many biological functions. We consider a class of self-regulated genes which are the building blocks of many…

We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…

Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting…

This paper addresses the decomposition of biochemical networks into functional modules that preserve their dynamic properties upon interconnection with other modules, which permits the inference of network behavior from the properties of…

Network inference approaches are now widely used in biological applications to probe regulatory relationships between molecular components such as genes or proteins. Many methods have been proposed for this setting, but the connections and…

This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon the existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we…

Biological regulatory networks depend upon chemical interactions to process information. Engineering such molecular computing systems is a major challenge for synthetic biology and related fields. The chemical reaction network (CRN) model…

We study the dynamics of supervised on-line learning of realizable tasks in feed-forward neural networks. We focus on the regime where the number of examples used for training is proportional to the number of input channels N. Using…

Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…

Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics and engineering. In some previous work, we introduced dynamical structure functions as a tool for posing and solving the…