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We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…

We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…

A popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent. This paper generalizes the random effects model to a conditional dependence model which allows…

This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no…

We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…

It is "well known" that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of…

We demonstrate the advantages of feedforward loops using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical behaviors of network embedded feedback and…

Controlling complex networked systems to a desired state is a key research goal in contemporary science. Despite recent advances in studying the impact of network topology on controllability, a comprehensive understanding of the synergistic…

We consider populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. In the case of sex- ual populations, we are able to derive models close to existing mod- els in theoretical biology, from a…

We define a minimal model of traffic flows in complex networks containing the most relevant features of real routing schemes, i.e. a trade--off strategy between topological-based and traffic-based routing. The resulting collective behavior,…

Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the…

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…

Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…

We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…

Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random…

Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their…

Many algorithms and observed phenomena in deep learning appear to be affected by parameter symmetries -- transformations of neural network parameters that do not change the underlying neural network function. These include linear mode…

Controllability of complex networks arises in many technological problems involving social, financial, road, communication, and smart grid networks. In many practical situations, the underlying topology might change randomly with time, due…

This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate…

The minimum number of inputs needed to control a network is frequently used to quantify its controllability. Control of linear dynamics through a minimum set of inputs, however, often has prohibitively large energy requirements and there is…