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In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals…
Graph Neural Networks (GNNs) set the state-of-the-art in representation learning for graph-structured data. They are used in many domains, from online social networks to complex molecules. Most GNNs leverage the message-passing paradigm and…
Robots are still poor at traversing cluttered large obstacles required for important applications like search and rescue. By contrast, animals are excellent at doing so, often using direct physical interaction with obstacles rather than…
We present a dynamic algorithm for solving the Longest Common Subsequence Problem using Ant Colony Optimization Technique. The Ant Colony Optimization Technique has been applied to solve many problems in Optimization Theory, Machine…
This paper studies asynchronous message passing (AMP), a new paradigm for applying neural network based learning to graphs. Existing graph neural networks use the synchronous distributed computing model and aggregate their neighbors in each…
We develop a model-based methodology for integrating gene-set information with an experimentally-derived gene list. The methodology uses a previously reported sampling model, but takes advantage of natural constraints in the…
Two classical stochastic processes are considered, the Ehrenfest process, introduced in 1907 in the kinetic theory of gases to describe the heat exchange between two bodies and the Engset process, one of the early (1918) stochastic models…
Known results on the moments of the distribution generated by the two-locus Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical methods…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
The recently introduced path-star task is a minimal task designed to exemplify limitations to the abilities of language models (Bachmann and Nagarajan, 2024). It involves a path-star graph where multiple arms radiate from a single starting…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the…
Enormous progress have been made in the last 20 years since the publication of our review \cite{csk05polrev} in this journal on transport and traffic phenomena in biology. In this brief article we present a glimpse of the major advances…
Timely recognition of plant pests from field images is significant to avoid potential losses of crop yields. Traditional convolutional neural network-based deep learning models demand high computational capability and require large labelled…
Ant Colony Optimization algorithm is a magnificent heuristics technique based on the behavior of ants. Parallel computing is a means to achieve the desired results in commensurable execution time. Parallelization of Ant Colony Optimization…
Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed…
It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in…
The Moran process, as studied by [Lieberman, E., Hauert, C. and Nowak, M. Evolutionary dynamics on graphs. Nature 433, pp. 312-316 (2005)], is a stochastic process modeling the spread of genetic mutations in populations. In this process,…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…