Related papers: Regional exponential general observability in diff…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
Recent advancements in diffusion models have significantly advanced text-to-image generation, yet global text prompts alone remain insufficient for achieving fine-grained control over individual entities within an image. To address this…
We present a general theory of spontaneous emission at exceptional points (EPs)---exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light--matter interaction described by the local density…
An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized…
The exponentially repulsive EXP pair potential defines a system of particles in terms of which simple liquids' quasiuniversality may be explained [A. K. Bacher et al., Nat. Commun. 5, 5424 (2014); J. C. Dyre, J. Phys. Condens. Matter 28,…
Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…
In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary…
This work extends previous 1D irreversible port-Hamiltonian system (IPHS) formulations to boundary-controlled ND distributed parameter systems describing conduction-diffusion fluid phenomena. Within a unified and thermodynamically…
Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…
This paper is concerned with the concepts of regional controllability for the Riemann-Liouville time fractional diffusion systems of order $\alpha\in(0,1)$. The characterizations of strategic actuators to achieve regional controllability…
In this communication, we prove some important limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability…
This paper deals with a distributed state estimation problem for jointly observable multi-agent systems operated over various time-varying network topologies. The results apply when the system matrix of the system to be observed contains…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…