27 papers · ranked by Valyu relevance
Tomoei Takahashi, Takashi Takahashi, Yoshiyuki Kabashima
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic transitions: the speciation transition, at which generated samples begin to capture…
Nuria Alina Chandra, Yucen Lily Li, Alan N. Amin, Alex Ali + 4 more
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 their shared goal, these models have disparate algorithms, theoretical…
Sanjukta Bhattacharya, Christian Gensbigler, Shaamil Karim, Jon Lees
Current generative modeling of single-cell transcriptomics relies on continuous latent representations, transforming inherently discrete and sparse gene counts into continuous space. We propose Discrete Cell Models (DCM), a diffusion-based framework that learns cellular representations directly in the discrete domain.…
Xiaochen Zhang, Shuangxi Wang, Ying Fang, Qiankun Zhang + 1 more
Recent advancements in denoising diffusion models have revolutionized image, text, and video generation. Inspired by these achievements, researchers have extended denoising diffusion models to the field of molecule generation. However, existing molecular generation diffusion models are not fully optimized according to…
Marcel Kollovieh, Sirine Ayadi, Stephan Günnemann
Discrete diffusion models form a powerful class of generative models across diverse domains, including text and graphs. However, existing approaches face fundamental limitations. Masked diffusion models suffer from irreversible errors due to early unmasking, while uniform diffusion models, despite enabling…
Grigory Bartosh, Teodora Pandeva, Sushrut Karmalkar, Javier Zazo
Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn the target process in a…
Ye Yuan, Weien Li, Rui Song, Zeyu Li + 18 more
Discrete denoising diffusion models (DDMs) have recently emerged as a compelling alternative to autoregressive (AR) modeling for discrete data, offering parallel generation and iterative global refinement capabilities. Unlike continuous diffusion, where the state space is fixed, DDMs are fundamentally shaped by how the…
Yuchen Liang, Lifeng Lai, Ness Shroff, Yingbin Liang + 5 more
Discrete diffusion models have become an important class of generative models for categorical data, yet their theoretical understanding remains largely limited to time-homogeneous noise schedules. In this work, we study uniform-rate discrete diffusion models with time-inhomogeneous continuous-time Markov chain forward…
Jing Liu, Yahao Wu, Limin Li
Deciphering the cellular composition of spatial spots in spatial transcriptomics (ST) data is fundamental for elucidating the heterogeneity of tissue spatial structures. However, existing models often require retraining for each new deconvolution task, reflecting limitations in both generalization performance and…
Liam J. Revell, Laura R. V. Alencar, Michael E. Alfaro, Jonathan Dain + 5 more
The practical utility of many modern phylogenetic comparative methods can depend on how accurately mathematical models capture the evolutionary process of traits. 4 described a new quantitative trait model for testing hypotheses about constraint on phenotypic character evolution: Brownian motion with reflective limits.…
Nartallo-Kaluarachchi, Ramón, Lambiotte, Renaud + 2 more
We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains. Using finite-volume approximations, we derive an approximate master equation…
Paul G. Blackwell
In spatial ecology, the concept of resource selection expresses the idea that for many animals, the distribution of an individual’s location is not uniform over the region available to them; instead, they spend time preferentially in some locations compared to others, in a way that can often be related to spatial…
Adarshkrishnan Rajakumar, Pascal R. Buenzli, Matthew J. Simpson
Understanding and predicting extinction risk is a central challenge in population biology. Mathematical models incorporating Allee thresholds are commonly used to understand population dynamics and to assess extinction risks. Inaccurate predictions can have serious consequences for conservation management. In this…
Authors not listed
Predicting how often molecules collide in dilute solution remains a long-standing challenge often with several orders of magnitude difference between theoretical values and experimental values also among different experimental values. Traditional frameworks from Smoluchowski and Langmuir rely on the formation of stable…
Neveen Ali Eshtewy, Ali Forootani, Zahra Ahangari Sisi
Mathematical modeling has become an indispensable tool for understanding, predicting, and controlling the spread of infectious diseases. Over the years, a wide variety of models have been developed to analyze disease dynamics and forecast epidemic trajectories. Deterministic and stochastic frameworks provide…
Lidia Mrad, Joceline Lega
This article introduces a computational method, called Recapture of Diffusive Agents & Particle Swarm Optimization (RDA-PSO), designed to estimate the dispersal parameter of diffusive insects in mark-release-recapture (MRR) field experiments. In addition to describing the method, its properties are discussed, with…
Yichao Yao, Minyu Feng, Matjaž Perc, J. Kurths
—Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the node count remains constant, instead prioritizing node growth. In this work, we…
Authors not listed
Designing molecules with specific target properties remains a fundamental challenge in computational chemistry. While existing approaches show promise, most rely on simplified representations like SMILES strings or 2D graphs that lack essential three-dimensional geometric information. We present EvoDiffMol, a…
Jordi Ripoll, Joan Saldaña
We study the random times between successive cases in a transmission chain of infectious diseases with asymptomatic carriers. We derive the probability distribution of this generation time (in days) from a discrete-time epidemic model with variable infectiousness both along elapsed times and across phases. The…
Shahak Kuba, Matthew J. Simpson, Pascal R. Buenzli
Many biological tissues grow at rates that depend strongly on the local geometry of the tissue interface, yet the cellular mechanisms underlying this dependence remain poorly understood. In this work, we develop a two-dimensional mathematical model of tissue growth to investigate how curvature-dependent growth emerges…
Authors not listed
Fragment-based drug design (FBDD) has become a key approach in structure-based drug discovery, allowing researchers to systematically develop molecular fragments into potent ligands. Although recent generative AI models, such as diffusion-based approaches, show great potential for designing new molecules, applying them…
Domenic P. J. Germano, Alexander E. Zarebski, Sophie Hautphenne, Robert Moss + 2 more
Multi-scale systems often exhibit a combination of stochastic and deterministic dynamics. In compartmental models, low occupancy compartments tend to exhibit stochastic dynamics while high occupancy compartments tend to follow deterministic dynamics. Representing both dynamics with existing methods is challenging.…
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A multi-fidelity Monte Carlo framework for molecular dynamics simulations of the diffusion coefficient of liquid water is presented. The model hierarchy is constructed based on the size of the simulation box, taking advantage of the well-known size effects that simulations of the diffusion coefficient suffer from.…
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Vertex models have been established as powerful tools for the cell-based simulation of epithelial tissues as they allow a detailed description of their mechanical development with respect to the properties of individual cells. Thus, they suit the challenges of simulating intestinal organoids which arise from the…
Madeline Jarvis-Cross, Andrew W. Bateman, Cole B. Brookson, Nicole Mideo + 1 more
Despite the impacts of within-host disease dynamics on disease outcomes in individual hosts and disease spread among-hosts, generic models of within-host population dynamics have received far less attention than their among-host counterparts. While a number of models have been proposed to explore theoretical…
Authors not listed
Metastable states and the conformational transitions in between them are key to understanding dynamical behaviour and function of large-scale molecular systems. By combining basic dimensionality reduction techniques with a state-of-the art approximation of the Koopman operator associated to molecular dynamics…
Authors not listed
Atomistic simulations provide essential mechanistic insights into chemical processes, yet many important phenomena in chemistry and materials science occur on timescales that are inaccessible to molecular dynamics. Existing computational approaches force a choice between atomic resolution on relatively short timescales…