25 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…
Natalie Tkachenko, John D. Weissmann, Wesley P. Petersen, George Lake + 3 more
'George Lake' 'Christoph P. E. Zollikofer' 'Simone Callegari' 'Naoki Masuda'] Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and…
Lucy Henley, Owen D. Jones, Fiona Mathews, Thomas E. Woolley
We propose a novel approach for modelling bat motion dynamics and use it to predict roost locations using data from static acoustic detectors. Specifically, radio tracking studies of Greater Horseshoe bats demonstrate that bat movement can be split into two phases: dispersion and return. Dispersion is easily understood…
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…
Kai Trepka
Building models of organismal growth enables predictions of natural variability and responses to perturbations. Complex systems such as animal pattern development and bacterial colonies can be modeled numerically using a reaction-diffusion system with relatively few factors and yield qualitatively accurate results…
Wang Jin, Haolu Wang, Xiaowen Liang, Michael S Roberts + 1 more
Mathematical models are often applied to describe cell migration regulated by diffusible signalling molecules. A typical feature of these models is that the spatial and temporal distribution of the signalling molecule density is reported by solving a reaction–diffusion equation. However, the spatial and temporal…
Stuart T. Johnston, Ruth E. Baker, D. L. Sean McElwain, Matthew J. Simpson
'Matthew J. Simpson'] Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based description of the birth, death and movement of individuals. The model distinguishes…
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…
Paul B. Dieterle, Ariel Amir
Scientists have observed and studied diffusive waves in contexts as disparate as population genetics and cell signaling. Often, these waves are propagated by discrete entities or agents, such as individual cells in the case of cell signaling. For a broad class of diffusive waves, we characterize the transition between…
Mohammad Azimi, Yousef Jamali, Mohammad R. K. Mofrad, Nic D. Leipzig
Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the…
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…
Shin-Ichiro Ei, Hiroshi Ishii, Makoto Sato, Yoshitaro Tanaka + 2 more
'Miaoxing Wang' 'Tetsuo Yasugi'] In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using…
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…
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…
Sabeeha Hasnain, Upendra Harbola, Pradipta Bandyopadhyay
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move from history. At each step, particle can take right, left or stay moves which is…
Priyanka Saha, Nandadulal Bairagi
In this paper we analyze a continuous-time epidemic model and its discrete counterpart, where infection spreads both horizontally and vertically. We consider three cases: model with horizontal and imperfect vertical transmissions, model with horizontal and perfect vertical transmissions, and model with perfect vertical…
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…
Stephen Coleman
This research examines the geographical distributions of several historical epidemics in the United States and investigates whether they reached a geographical equilibrium, however briefly. An equilibrium distribution over a geographical area, as the end state of a diffusion or spatial contagion process, has definitive…
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…
Tamara A. Tambyah, Ryan J. Murphy, Pascal R. Buenzli, Matthew J. Simpson
In this study, we couple intracellular signalling and cell–based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction–diffusion equations are derived to…
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…
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…
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…
Alberto Berretti, Simone Ciccarone
Mobile computing platforms (from simple featurephones to smartphones to tablets) are becoming ubiquitous and ever more capable, and they are slowly eroding the predominance of the personal computer, especially at the notebook level. As they are becoming more capable and more common, they become the target of malware…