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We offer an improved method for using a nuclear-magnetic-resonance quantum computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to the application of the NMRQC are exponential diminishment of density-matrix elements with…
Neural operators have shown promise in solving many types of Partial Differential Equations (PDEs). They are significantly faster compared to traditional numerical solvers once they have been trained with a certain amount of observed data.…
This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a connected matrix Lie group. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…
Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior…
This paper proposes a finitely terminating algorithm to solve reach-and-stay control problems for nonlinear systems. The algorithm is guaranteed to return a control strategy if the specification is robustly realizable. Such a feature is…
Dantzig-Wolfe decomposition (DWD) is a classical algorithm for solving large-scale linear programs whose constraint matrix involves a set of independent blocks coupled with a set of linking rows. The algorithm decomposes such a model into a…
In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria.…
We consider a nonlinear filtering problem for a signal-observation system driven by a Volterra-type Gaussian rough path, whose sample paths may exhibit greater roughness than those of Brownian motion. The observation process includes a…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…
The current algorithms are based on linear model, for example, Precision Time Protocol (PTP) which requires frequent synchronization in order to handle the effects of clock frequency drift. This paper introduces a nonlinear approach to…
We study fundamental problems in linear algebra, such as finding a maximal linearly independent subset of rows or columns (a basis), solving linear regression, or computing a subspace embedding. For these problems, we consider input…
There is an increasing body of literature proposing new and efficient persistent versions of concurrent data structures ensuring that a consistent state can be recovered after a power failure or a crash. Their correctness is typically…
Integrating deep learning with latent state space models has the potential to yield temporal models that are powerful, yet tractable and interpretable. Unfortunately, current models are not designed to handle missing data or multiple data…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
In this paper, we introduce the online and streaming MAP inference and learning problems for Non-symmetric Determinantal Point Processes (NDPPs) where data points arrive in an arbitrary order and the algorithms are constrained to use a…
Despite remarkable successes achieved by modern neural networks in a wide range of applications, these networks perform best in domain-specific stationary environments where they are trained only once on large-scale controlled data…
Autonomous systems often must predict the motions of nearby agents from partial and noisy data. This paper asks and answers the question: "can we learn, in real-time, a nonlinear predictive model of another agent's motions?" Our online…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…