Related papers: An efficient algorithm to estimate the potential b…
The paper presents an analytical approach for predicting the safe basins (SB) in a plane of initial conditions (IC) for escape of classical particle from the potential well under harmonic forcing. The solution is based on the approximation…
For the enhancement of the transient stability of power systems, the key is to define a quantitative optimization formulation with system parameters as decision variables. In this paper, we model the disturbances by Gaussian noise and…
With the introduction of machine learning in high-stakes decision making, ensuring algorithmic fairness has become an increasingly important problem to solve. In response to this, many mathematical definitions of fairness have been…
We identify a fundamental phenomenon of heterogeneous one dimensional random walks: the escape (traversal) time is maximized when the heterogeneity in transition probabilities forms a pyramid-like potential barrier. This barrier corresponds…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
Outdoor shooting ranges are subject to noise regulations from local and national authorities. Restrictions found in these regulations may include limits on times of activities, the overall number of noise events, as well as limits on number…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
Minimizing the empirical risk is a popular training strategy, but for learning tasks where the data may be noisy or heavy-tailed, one may require many observations in order to generalize well. To achieve better performance under less…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a…
Many techniques originally developed in the context of deterministic control theory have been recently applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask…
In many randomized experiments, the treatment effect of the long-term metric (i.e. the primary outcome of interest) is often difficult or infeasible to measure. Such long-term metrics are often slow to react to changes and sufficiently…
We consider the problem of designing almost optimal predictors for dynamical systems from a finite sequence of noisy observations and incomplete knowledge of the dynamics and the noise. We first discuss the properties of the optimal (Bayes)…
The Fermat distance has been recently established as a useful tool for machine learning tasks when a natural distance is not directly available to the practitioner or to improve the results given by Euclidean distances by exploding the…
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world…
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
We consider the problem of optimal zero-delay coding and estimation of a stochastic dynamical system over a noisy communication channel under three estimation criteria concerned with the low-distortion regime. The criteria considered are…
We describe and expand upon the scalable randomized benchmarking protocol proposed in Phys. Rev. Lett. 106, 180504 (2011) which provides a method for benchmarking quantum gates and estimating the gate-dependence of the noise. The protocol…
We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, $d\rightarrow \infty$. We prove that the optimal scaling…
Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…