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The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…
This article proposes a fundamental methodological shift in the modelling of policy interventions for sustainability transitions in order to account for complexity (e.g. self-reinforcing mechanism arising from multi-agent interactions) and…
This study proposes a new model based on a classic S-curve that describes deployment and stabilization at maximum capacity. In addition, the model extends to the post-growth plateau, where technological capacity is renewed according to the…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Diffusion Models generate data by reversing a stochastic diffusion process, progressively transforming noise into structured samples drawn from a target distribution. Recent theoretical work has shown that this backward dynamics can undergo…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
Uncertainty persists over how and why some countries become democratic and others do not, or why some countries remain democratic and others 'backslide' toward autocracy. Furthermore, while scholars generally agree on the nature of…
We study a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our system models a competition relationship that one species escape from the region of high population density of their competitors in…
This technical report presents a diffusion model based framework for face swapping between two portrait images. The basic framework consists of three components, i.e., IP-Adapter, ControlNet, and Stable Diffusion's inpainting pipeline, for…
The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently,…
In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the…