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We prove the first polynomial separation between randomized and deterministic time-space tradeoffs of multi-output functions. In particular, we present a total function that on the input of $n$ elements in $[n]$, outputs $O(n)$ elements,…
Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable.…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
This paper considers the Cauchy problem for the nonlinear dynamic string equation of Kirchhoff-type with time-varying coefficients. The objective of this work is to develop a time domain discretization algorithm capable of approximating a…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Problem for the first order differential equation with an unbounded operator coefficient in Banach space and integral nonlocal condition is considered. An exponentially convergent algorithm is proposed and justified for the numerical…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An…
Although the laws of classical physics are deterministic, thermodynamics gives rise to an arrow of time through irreversible processes. In quantum mechanics the unitary nature of the time evolution makes it intrinsically reversible, however…
We address the problem of Bayesian inference for parameters in ordinary differential equation (ODE) models based on observational data. Conventional approaches in this setting typically rely on numerical solvers such as the Euler or…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
When facing time-variant problems in analog computing, the desirable RNN design requires finite-time convergence and robustness with respect to various types of uncertainties, due to the time-variant nature and difficulties in…
In this paper, we introduce a probabilistic approach to risk assessment of robot systems by focusing on the impact of uncertainties. While various approaches to identifying systematic hazards (e.g., bugs, design flaws, etc.) can be found in…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…