相关论文: Best matching Barenblatt profiles are delayed
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…
Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed…
The large time behavior of entropy solution to the compressible Euler equations for polytropic gas (the pressure $p(\rho)=\kappa\rho^{\gamma}, \gamma>1$) with time dependent damping like $-\frac{1}{(1+t)^\lambda}\rho u$ ($0<\lambda<1$) is…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…
We consider asynchronous versions of the first and second order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be…
I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with…
We study the problem of discovering joinable datasets at scale. This is, how to automatically discover pairs of attributes in a massive collection of independent, heterogeneous datasets that can be joined. Exact (e.g., based on distinct…
We deal with the problem of separation of time-scales and filamentation in a linear drift-diffusion problem posed on the whole space $\mathbb{R}^2$. The passive scalar considered is stirred by an incompressible flow with radial symmetry. We…
Two time scale stochastic approximation algorithms emulate singularly perturbed deterministic differential equations in a certain limiting sense, i.e., the interpolated iterates on each time scale approach certain differential equations in…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
In general, comprehension of any type of complex system depends on the resolution used to examine the phenomena occurring within it. However, identifying a priori, for example, the best time frequencies/scales to study a certain system…
We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent…
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations…
Local scale-invariance for ageing systems without detailed balance is tested through studying the dynamical symmetries of the critical bosonic contact process and the critical bosonic pair-contact process.Their field-theoretical actions can…
Generating a dissimilarity matrix is typically the first step in big data analysis. Although numerous methods exist, such as Euclidean distance, Minkowski distance, Manhattan distance, Bray Curtis dissimilarity, Jaccard similarity and Dice…