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Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…

This paper introduces a stochastic hybrid system (SHS) framework in state space model to capture sensor, communication, and system contingencies in modern power systems (MPS). Within this new framework, the paper concentrates on the…

The proposed feature selection method builds a histogram of the most stable features from random subsets of a training set and ranks the features based on a classifier based cross-validation. This approach reduces the instability of…

In this paper we introduce a new model of random spanning trees that we call choice spanning trees, constructed from so-called choice random walks. These are random walks for which each step is chosen from a subset of random options,…

Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is…

Recurrent Neural Networks (RNNs) have long been recognized for their potential to model complex time series. However, it remains to be determined what optimization techniques and recurrent architectures can be used to best realize this…

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…

Euclidean Steiner trees are relevant to model minimal networks in real-world applications ubiquitously. In this paper, we study the feasibility of a hierarchical approach embedded with bundling operations to compute multiple and mutually…

A random number generator is proposed based on a theorem about existence of chaos in fixed point iteration of x= cot2(x). Digital computer simulation of this function iteration exhibits random behavior. A method is proposed to extract…

This paper presents an efficient algorithm for the incremental construction of a minimal acyclic sequential transducer (ST) for a dictionary consisting of a list of input and output strings. The algorithm generalises a known method of…

Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a…

Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons…

Stein's method is a powerful technique for proving central limit theorems in probability theory when more straightforward approaches cannot be implemented easily. This article begins with a survey of the historical development of Stein's…

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…

Providing theoretical guarantees for parameter estimation in exponential random graph models is a largely open problem. While maximum likelihood estimation has theoretical guarantees in principle, verifying the assumptions for these…

This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest…

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…

Based on sketching techniques, we propose two randomized algorithms for tensor ring (TR) decomposition. Specifically, by defining new tensor products and investigating their properties, we apply the Kronecker sub-sampled randomized Fourier…

Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some…