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We study the multistationarity for the reaction networks with one-dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states. We prove that if a network admits multistationarity, then…

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the…

This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the multilinear system under consideration involves a nonsingular…

We study the stationary states of networks consisting of weakly coupled bistable units. We prove the existence of a high multiplicity of stable steady states in networks with very general inter-unit dynamics. We present a method for…

We introduce a model of one-way language acceptors (a variant of a checking stack automaton) and show the following decidability properties: (1) The deterministic version has a decidable membership problem but has an undecidable emptiness…

Robustness is one of the key properties of nowadays networks. However, robustness cannot be simply enforced by design or regulation since many important networks, most prominently the Internet, are not created and controlled by a central…

In this paper we propose a unified way of analyzing a certain kind of greedy-type algorithms in Banach spaces. We define a class of the Weak Biorthogonal Greedy Algorithms that contains a wide range of greedy algorithms. In particular, we…

Concurrent accesses to databases are typically encapsulated in transactions in order to enable isolation from other concurrent computations and resilience to failures. Modern databases provide transactions with various semantics…

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…

Poly-PL kinetic systems are kinetic systems consisting of nonnegative linear combinations of power law functions. In this contribution, we analyze these kinetic systems using two main approaches: (1) we define a canonical power law…

Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…

For reaction networks arising in systems biology, the capacity for two or more steady states, that is, multistationarity, is an important property that underlies biochemical switches. Another property receiving much attention recently is…

We give a new proof of the fact that each weakly reversible mass-action system with a single linkage class is permanent.

In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…

In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions,…

The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary…

There exists a vast number of adversarial attacks and defences for machine learning algorithms of various types which makes assessing the robustness of algorithms a daunting task. To make matters worse, there is an intrinsic bias in these…

Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the…

We suggest to simulate evolution of complex organisms constrained by the sole requirement of robustness in their expression patterns. This scenario is illustrated by evolving discrete logical networks with epigenetic properties. Evidence…