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Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…
Entanglement generation in long-distance quantum networks is a difficult process due to resource limitations and the probabilistic nature of entanglement swapping. To maximize success probability, existing quantum routing algorithms employ…
A Procedure is outlined that may be used as a starting point for a perturbative treatment of theories with permanent confinement. By using a counter term in the Lagrangian that renormalizes the infrared divergence in the Coulomb potential,…
The renewal contact process is a non-Markovian variant of the classical contact process in which recoveries are governed by independent renewal processes with interarrival distribution $\mu$. We establish new sufficient conditions ensuring…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect…
Efficient and biologically plausible alternatives to backpropagation in neural network training remain a challenge due to issues such as high computational complexity and additional assumptions about neural networks, which limit scalability…
We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…
A new form of the Wilson renormalization group equation is derived, in which the flow equations are, up to linear terms, proportional to a gradient flow. A set of co\"ordinates is found in which the flow of marginal, low-energy, couplings…
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…
A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully…
The paper presents efficient approaches for evaluating convergence rate in total variation for finite and general linear Markov chains. The motivation for studying convergence rate in this metric is its usefulness in various limit theorems.…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
We explore the convergence rate of the Ka\v{c}anov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference…
A collection of quantile curves provides a complete picture of conditional distributions. Properly centered and scaled versions of estimated curves at various quantile levels give rise to the so-called quantile regression process (QRP). In…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…