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In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
Both natural and engineered supply networks exhibit universal structural patterns, such as the formation of loops, yet the principles governing optimal structures remain unclear. These patterns can be interpreted as solutions of…
The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
The paper deals with the verification of reachability properties in a commonly used state transition model of communication protocols, which consists of finite state machines connected by potentially unbounded FIFO channels. Although simple…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
This paper introduces a conception that any weighted directed network topology is almost decouplable, which can help to transform the topology into a similar form being composed of uncoupled vertices, and thus reduce the complexity of…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform…
We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a…
We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a…
Contextuality was originally defined only for consistently connected systems of random variables (those without disturbance/signaling). Contextuality-by-Default theory (CbD) offers an extension of the notion of contextuality to…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system…
When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is…
Stability with respect to a given scheduling policy has become an important issue for wireless communication systems, but it is hard to prove in particular scenarios. In this paper two simple conditions for stability in broadcast channels…
This paper focuses on the issue of network connectedness (NC) in security-constrained optimal transmission switching problems, which is complicated by branch contingencies and corrective line switching. Two criteria are firstly proposed…