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We use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes, or decision makers, interact strategically and with limited information. In such environments, which arise…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices. From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
Studying extreme events and how they evolve in a changing climate is one of the most important current scientific challenges. Starting from complex climate models, a key difficulty is to be able to run long enough simulations in order to…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
Computing the first few singular vectors of a large matrix is a problem that frequently comes up in statistics and numerical analysis. Given the presence of noise, exact calculation is hard to achieve, and the following problem is of…
In this paper we consider a recently developed distributed optimization algorithm based on gradient tracking. We propose a system theory framework to analyze its structural properties on a preliminary, quadratic optimization set-up.…
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap…
Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…