Related papers: Reaction Diffusion TAP
We investigate solutions to the TAP equation, a phenomenological implementation of the Theory of the Adjacent Possible. Several implementations of TAP are studied, with potential applications in a range of topics including economics, social…
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
Two alternative views of an economy are combined and studied. The first view is that of technological evolution as a process of combinatorial innovation. Recently a simple mathematical model (TAP) was introduced to study such a…
The notion of the "adjacent possible" has been advanced to theorize the generation of novelty across many different research domains. This study is an attempt to examine in what way the notion can be made empirically useful for innovation…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
Diffusion models achieve strong generative performance but remain slow at inference due to the need for repeated full-model denoising passes. We present Token-Adaptive Predictor (TAP), a training-free, probe-driven framework that adaptively…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
Generative tabular augmentation is appealing in data-scarce domains, yet the prevailing focus on distributional fidelity does not reliably translate into better downstream models. We formalize a fidelity-utility gap: common generative…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
The behavior of many complex systems, from nanostructured materials to animal colonies, is governed by local transitions that, while involving a restricted number of interacting units, may generate collective cascade phenomena. Tracking…
Diffusion processes in a social system are governed by external triggers and internal excitations via interactions between individuals over social networks. Underlying mechanisms are crucial to understand emergent phenomena in the real…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
We have previously discussed the one-dimensional multitrap system of finite range and found the somewhat unexpected result that the larger is the number of imperfect traps the higher is the transmission through them. We discuss in this work…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local…
Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction…
Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out…