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Elementary particles, i.e. the basic constituents of nature, are characterized by quantum recurrences in time. The flow of time of every physical system can be therefore decomposed in elementary cycles of time. This allows us to enforce the…
A fast algorithm to study one-dimensional self-gravitating systems, and, more generally, systems that are Lagrangian integrable between collisions, is presented. The algorithm is event-driven, and uses a heap-ordered set of predicted future…
This article examines large time behaviour of finite state mean-field interacting particle systems. Our first main result is a sharp estimate (in the exponential scale) on the time required for convergence of the empirical measure process…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
Finite-range interacting spin models are the simplest models to study the effect of beyond nearest-neighbour interactions and access new effects caused by the range of the interactions. Recent experiments have reached the regime of dominant…
The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity…
We investigate the recoverable robust single machine scheduling problem under interval uncertainty. In this setting, jobs have first-stage processing times p and second-stage processing times q and we aim to find a first-stage and…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
The reachability analysis of recursive programs that communicate asynchronously over reliable FIFO channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability…
A critical problem in the emerging high-throughput genotyping protocols is to minimize the number of polymerase chain reaction (PCR) primers required to amplify the single nucleotide polymorphism loci of interest. In this paper we study PCR…
Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…
In this paper we introduce randomized branching as a tool for parameterized approximation and develop the mathematical machinery for its analysis. Our algorithms improve the best known running times of parameterized approximation algorithms…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6\leq N\leq12$ hard spheres that are "sticky", i.e. they interact…
In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable…
Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…
In the classical context, it is well known that, sometimes, if the search does not find its target, it is better to start the process anew again, known as resetting. The quantum counterpart of resetting also indicates speeding up the…
We consider a large family of branching-selection particle systems. The branching rate of each particle depends on its rank and is given by a function $b$ defined on the unit interval. There is also a killing measure $D$ supported on the…