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We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…

Tools that effectively analyze and compare sequences are of great importance in various areas of applied computational research, especially in the framework of molecular biology. In the present paper, we introduce simple geometric criteria…

In the field of connectomics, neuroscientists seek to identify cortical connectivity comprehensively. Neuronal boundary detection from the Electron Microscopy (EM) images is often done to assist the automatic reconstruction of neuronal…

We analyze the structure of DNA molecules of different organisms by using the additive Markov chain approach. Transforming nucleotide sequences into binary strings, we perform statistical analysis of the corresponding "texts". We develop…

We describe and analyze a simple and effective algorithm for sequence segmentation applied to speech processing tasks. We propose a neural architecture that is composed of two modules trained jointly: a recurrent neural network (RNN) module…

Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it…

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…

The goal of metagenomics is to study the composition of microbial communities, typically using high-throughput shotgun sequencing. In the metagenomic binning problem, we observe random substrings (called contigs) from a mixture of genomes…

This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based…

We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…

It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…

Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy…

The ability to extrapolate gene expression dynamics in living single cells requires robust cell segmentation, and one of the challenges is the amorphous or irregularly shaped cell boundaries. To address this issue, we modified the U-Net…

Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…

We develop randomized modifications of Markov chains and apply these modifications to the routing chains of customers in Jacksonian stochastic networks. The aim of our investigations is to find new rerouting schemes for non standard Jackson…

At the core of high throughput DNA sequencing platforms lies a bio-physical surface process that results in a random geometry of clusters of homogenous short DNA fragments typically hundreds of base pairs long - bridge amplification. The…

We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…

Linear recurrent neural networks have emerged as efficient alternatives to the original Transformer's softmax attention mechanism, thanks to their highly parallelizable training and constant memory and computation requirements at inference.…

Within the field of instance segmentation, most of the state-of-the-art deep learning networks rely nowadays on cascade architectures, where multiple object detectors are trained sequentially, re-sampling the ground truth at each step. This…

Selecting input variables or design points for statistical models has been of great interest in adaptive design and active learning. Motivated by two scientific examples, this paper presents a strategy of selecting the design points for a…