Related papers: Path integral approach to generating functions for…

Generative methods for graphs need to be sufficiently flexible to model complex dependencies between sets of nodes. At the same time, the generated graphs need to satisfy domain-dependent feasibility conditions, that is, they should not…

Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…

In this paper we propose a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) with oscillating covariance functions through systems of stochastic partial differential equations (SPDEs). We discuss how to build…

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the…

This work introduces the generative fractional diffusion model for protein generation (ProT-GFDM), a novel generative framework that employs fractional stochastic dynamics for protein backbone structure modeling. This approach builds on the…

Graph generation poses a significant challenge as it involves predicting a complete graph with multiple nodes and edges based on simply a given label. This task also carries fundamental importance to numerous real-world applications,…

Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation…

Deep generative models have been shown powerful in generating novel molecules with desired chemical properties via their representations such as strings, trees or graphs. However, these models are limited in recommending synthetic routes…

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…

Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements…

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically; and the frequency spectrum of this chemical fluctuation carries valuable information about the mechanism and the dynamics of the intracellular…

Fact verification (FV) is a challenging task which aims to verify a claim using multiple evidential sentences from trustworthy corpora, e.g., Wikipedia. Most existing approaches follow a three-step pipeline framework, including document…

Generative artificial intelligence (AI) has made unprecedented advances in vision language models over the past two years. During the generative process, new samples (images) are generated from an unknown high-dimensional distribution.…

We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low…

Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory…

Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as…

Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…

Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for…

We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution…

Discovering genes with similar functions across diverse biomedical contexts poses a significant challenge in gene representation learning due to data heterogeneity. In this study, we resolve this problem by introducing a novel model called…