Related papers: Modeling Non-Stationary Processes Through Dimensio…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
In the recent literature dealing with spatial extensions of the continuous Ramsey model, the capital accumulation process via time and space is modeled as a linear parabolic partial differential equation. The process of capital movement…
In the context of model-based control of industrial processes, it is a common practice to develop a data-driven linear dynamical model around a specified operating point. However, in applications involving wider operating conditions,…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
The packing problem, also known as cutting or nesting, has diverse applications in logistics, manufacturing, layout design, and atlas generation. It involves arranging irregularly shaped pieces to minimize waste while avoiding overlap.…
Reinforcement learning (RL) agents typically assume stationary environment dynamics. Yet in real-world applications such as healthcare, robotics, and finance, transition probabilities or reward functions may evolve, leading to model drift.…
Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack…
We consider the dynamics of pattern formation in a system of point defects under sustained irradiation within the framework of the rate theory. In our study we generalize the standard approach taking into account a production of defects by…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
Ambient air pollution remains a critical issue in the United Kingdom, where data on air pollution concentrations form the foundation for interventions aimed at improving air quality. However, the current air pollution monitoring station…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
In these lecture notes we present different methods and concepts developed in statistical physics to analyze gradient descent dynamics in high-dimensional non-convex landscapes. Our aim is to show how approaches developed in physics, mainly…
Dynamic patterns are characterized by complex spatial and motion patterns. Understanding dynamic patterns requires a disentangled representational model that separates the factorial components. A commonly used model for dynamic patterns is…
An important task for many if not all the scientific domains is efficient knowledge integration, testing and codification. It is often solved with model construction in a controllable computational environment. In spite of that, the…
With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the…
We consider the three-dimensional Ising model in a half-space with a boundary field (no bulk field). We compute the low-temperature expansion of layering transition lines.
Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…
Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of…
Latent space is one of the key concepts in generative AI, offering powerful means for creative exploration through vector manipulation. However, diffusion models like Stable Diffusion lack the intuitive latent vector control found in GANs,…