Related papers: On polynomial recurrence for reliability system wi…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series of recent results…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
We identify two recursively defined polynomial conditions for FI-modules in the literature. We characterize these conditions using homological invariants of FI-modules (namely the local degree and regularity, together with the stable…
Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to…
Cold standby 1-out-of-n redundant systems are well-established models in system reliability engineering. To date, reliability analyses of such systems have predominantly assumed exponential, Erlang, or Weibull failure distributions for…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…
We present the explicit construction of a stable queue with several servers and impatient customers, under stationary ergodic assumptions. Using a stochastic comparison of the (multivariate) workload sequence with two monotonic stochastic…
The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems,…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…
We consider a polling model with multiple stations, each with Poisson arrivals and a queue of infinite capacity. The service regime is exhaustive and there is Jacksonian feedback of served customers. What is new here is that when the server…
We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of…
Model selection is a cornerstone of statistical inference, where information criteria are widely employed to balance model fit and complexity. However, classical likelihood-based criteria are often highly sensitive to contamination,…
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively…
Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…