Related papers: On the temporal resolution limits of numerical sim…
In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a class of time-homogeneous Markov processes, by…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two…
Efficient simulation of quantum dynamics with time-dependent Hamiltonians is important not only for time-varying systems but also for time-independent Hamiltonians in the interaction picture. Such simulations are more challenging than their…
We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…
As control systems grow in complexity, abstraction-based methods have become essential for designing controllers with formal guarantees. However, a key limitation of these methods is their reliance on discrete-time models, typically…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…
Anisotropic barostats are employed to carry out Molecular Dynamics simulations where the volume is allowed to fluctuate with no constraints on the shape of the simulation cell. Most of these algorithms are based on second-order differential…
Analog and digital quantum simulators can efficiently simulate quantum many-body systems that appear in natural phenomena. However, experimental limitations of near-term devices still make it challenging to perform the entire process of…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
Quantum chaotic and integrable systems are known to exhibit a characteristic $1/f$ and $1/f^{2}$ noise, respectively, in the power spectrum associated to their spectral fluctuations. A recent work [R. Riser, V. A. Osipov, and E. Kanzieper,…
We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…
This paper addresses the secure state estimation problem for continuous linear time-invariant systems with non-periodic and asynchronous sampled measurements, where the sensors need to transmit not only measurements but also sampling…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…
A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range…
Realistic multi-qubit noise processes often result in error mechanisms that are not captured by the probabilistic, Markovian error models commonly employed in circuit-level analyses of quantum fault-tolerance. By working within an…
Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…