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The distribution of genetic polymorphisms in a population contains information about the mutation rate and the strength of natural selection at a locus. Here, we show that the Poisson Random Field (PRF) method of population-genetic…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
In this work, we describe a computational framework for the genome-wide identification and characterization of mixed transcriptional/post-transcriptional regulatory circuits in humans. We concentrated in particular on feed-forward loops…
Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
Feature selection is fundamental to robust data-centric AI, but most existing methods optimize predictive performance under a single data distribution. This often selects spurious features that fail under distribution shifts. Motivated by…
We introduce a novel method to screen the promoters of a set of genes with shared biological function, against a precompiled library of motifs, and find those motifs which are statistically over-represented in the gene set. The gene sets…
The conformational landscape of proteins is crucial to understanding their functionality in complex biological processes. Traditional physics-based computational methods, such as molecular dynamics (MD) simulations, suffer from rare event…
Classifier-Free Guidance (CFG) is a widely adopted technique in diffusion and flow-based generative models, enabling high-quality conditional generation. A key theoretical challenge is characterizing the distribution induced by CFG,…
Gene expression is controlled primarily by interactions between transcription factor proteins (TFs) and the regulatory DNA sequence, a process that can be captured well by thermodynamic models of regulation. These models, however, neglect…
The relation between rate distortion function (RDF) and Bayesian filtering theory is discussed. The relation is established by imposing a causal or realizability constraint on the reconstruction conditional distribution of the RDF, leading…
Classifier-Free Guidance (CFG) is a widely used technique for improving conditional diffusion models by linearly combining the outputs of conditional and unconditional denoisers. While CFG enhances visual quality and improves alignment with…
We present a novel factor analysis method that can be applied to the discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited…
We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have…
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…
Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types Galton-Watson forest is a random model of population growth without space or…
Transcription factor proteins bind specific DNA sequences to control the expression of genes. They contain DNA binding domains which belong to several super-families, each with a specific mechanism of DNA binding. The total number of…
Our aim is to predict how often genic and non-genic promoters fire within a cell. We first review a parsimonious pan-genomic model for genome organization and gene regulation, where transcription rate is determined by proximity in 3D space…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
Promoters and enhancers are cis-regulatory elements (CREs), DNA sequences that bind transcription factor (TF) proteins to up- or down-regulate target genes. Decades-long efforts yielded TF-DNA interaction models that predict how strongly an…