Related papers: Large systems of random linear equations with non-…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
Replication studies estimate the replicability rate of scientific results by aggregating binary verdicts of experiments. Exact replications are rarely attainable, so most replication sequences are non-exact. Experiments differ in ways that…
We show that if the nearly-linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations…
We discuss first order transitions for systems in the Ising universality class. The critical long distance physics near the endpoint of the critical line is explicitly connected to microscopic properties of a given system. Information about…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
The dynamics of a binary system with non conserved order parameter under a plain shear flow with rate $\gamma $ is solved analytically in the large-N limit. A phase transition is observed at a critical temperature $T_c(\gamma)$. After a…
We present an analytic formalism describing structural properties of random uncorrelated networks with arbitrary degree distributions. The formalism allows to calculate the main network characteristics like: the position of the phase…
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…
We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…
The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…
In this paper, we focus on the problem of existence and computing of small and large stable models. We show that for every fixed integer k, there is a linear-time algorithm to decide the problem LSM (large stable models problem): does a…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
We study an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is constantly perturbed by weak measurements of the spin component in a random…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
Gram's Law describes a pattern that frequently occurs in the distribution of the non-trivial zeros of the Riemann zeta function along the critical line. Whenever Gram's Law holds true, it reduces the difficulty of computing the…