Related papers: Fluctuation-driven Turing patterns
The macroscopic fluctuation theory provides a complete hydrodynamic description of non-equilibrium classical diffusive systems. As a first step towards a diffusive theory of open quantum systems, we show how to construct a microscopic open…
In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…
Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the…
Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…
The understanding of the large-scale structure formation requires the resolution of coupled nonlinear equations describing the cosmic density and velocity fields. This is a complicated problem that, for the last decade, has been essentially…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…
Noise is often used in the study of open systems, such as in classical Brownian motion and in Quantum Dynamics, to model the influence of the environment. However generalising results from G\"{o}del and Chaitin in mathematics suggests that…
Adapting neural networks to new tasks typically requires task-specific fine-tuning, which is time-consuming and reliant on labeled data. We explore a generative alternative that produces task-specific parameters directly from task identity,…
The mechanism of production of a large number of universes is considered. It is shown that universes with parameters suitable for creation of life are necessarily produced as a result of quantum fluctuations. Fractal structures are formed…
The microscopic origin of dissipation of a driven quantum many body system is addressed in the framework of a parametric banded random matrix approach. We find noticeable violations of the fluctuation-dissipation theorem and we observe also…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…
The problem of morphogenesis and Turing instability are revisited from the point of view of dimensionality effects. First the linear analysis of a generic Turing model is elaborated to the case of multiple stationary states, which may lead…
One of the bottlenecks in robotic intelligence is the instability of neural network models, which, unlike control models, lack a well-defined convergence domain and stability. This leads to risks when applying intelligence in the physical…