24 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…
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…
Haoran Sun, Lijun Yu, Bo Dai, Dale Schuurmans + 1 more
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e., the score function, is not properly defined for discrete spaces. This makes it…
Pavel Avdeyev, Chenlai Shi, Yuhao Tan, Kseniia Dudnyk + 1 more
Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in many applications. Score-based generative stochastic differential equations…
Elliot J. Carr
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such transport processes are well established, they fail to account for randomness inherent…
Marvin van Aalst, Oliver Ebenhöh
dismo is a Python package for building and analysing discrete spatial models based on ordinary differential equations. Its primary purpose is to allow arbitrarily complex internal and transport processes to easily be mapped over multiple different regular grids. For this it features one, two and threedimensional…
Matthew J. Simpson, Keeley M. Murphy, Scott W. McCue, Pascal R. Buenzli
'Pascal R. Buenzli'] Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key…
Marco Nizama, Adam Gadomski
I study a lattice with periodic boundary conditions using a non-local master equation that evolves over time. I investigate different system regimes using classical theories like Fisher information, Shannon entropy, complexity, and the Cramér-Rao bound. To simulate spatial continuity, I employ a large number of sites…
Jixin Chen
Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing…
Matthew J. Simpson, Ruth E. Baker, Pascal R. Buenzli, Ruanui Nicholson + 1 more
Stochastic individual-based mathematical models are attractive for modelling biological phenomena because they naturally capture the stochasticity and variability that is often evident in biological data. Such models also allow us to track the motion of individuals within the population of interest. Unfortunately…
Anna M. Langmüller, Courtney C. Murdock, Philipp W. Messer
Ordinary differential equation models such as the classical SIR model are widely used in epidemiology to study and predict infectious disease dynamics. However, these models typically assume that populations are homogeneously mixed, disregarding possible variations in disease prevalence due to spatial heterogeneity. To…
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…
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…
Thomas Williams, James McCaw, James M. Osborne
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are…
Michael Alverson, Sterling Baird, Ryan Murdock, Taylor Sparks
The idea of materials discovery has excited and perplexed research scientists for centuries. Several different methods have been employed to find new types of materials, ranging from the arbitrary replacement of atoms in a crystal structure to advanced machine learning methods for predicting entirely new crystal…
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…
Rafael Bravo de la Parra, Luis Sanz-Lorenzo
The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could represent movements between spatial locations, changes of individual activities…
Stefan Hohenegger, Francesco Sannino
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state of the entirety of the population. However, the type and structure of the…
Jurgen Riedel, Chris P. Barnes
In this study we examine the emergence of complex biological patterns through the lens of reaction-diffusion systems. We introduce two novel complexity metrics, Diversity of Number of States (DNOS) and Diversity of Pattern Complexity (DPC), which aim to quantify structural intricacies in pattern formation, enhancing…
Junkil Park, Aseem Partap Singh Gill, Seyed Mohamad Moosavi, JIHAN KIM
The success of diffusion models in the field of image processing has propelled the creation of software such as Dall-E, Midjourney and Stable Diffusion, which are tools used for text-to-image generations. Mapping this workflow onto materials discovery, a new diffusion model was developed for the generation of pure…
Carolin Grumbach, Femke N. Reurik, Juan Segura, Daniel Franco + 1 more
'Frank M. Hilker'] Many populations occupy spatially fragmented landscapes. How dispersal affects the asymptotic total population size is a key question for conservation management and the design of ecological corridors. Here, we provide a comprehensive overview of two-patch models with symmetric dispersal and two…
Amit K. Chattopadhyay, Bidisha Kundu, Sujit Kumar Nath, Elias C. Aifantis
'Elias C. Aifantis'] Abstract Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved inter-sectoral mapping of techniques. Material mechanics has benefitted hugely from such interpolations from mathematical physics where dislocation patterning of platstically…
Authors not listed
As a prove of concept for experimental geochemistry, an advanced 3D numerical framework, here and after called Digital Twin (DT), of a diffusion experiment conducted at a synchrotron beamline, has been implemented using in-situ measurements data, physics-based modelling, a machine learning (ML) model, and parameter…
Tommaso Lorenzi, Kevin J. Painter, Chiara Villa
Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc. Clearly, the phenotypic distribution - and how this changes over time and space…