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We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential decay in time of the space-derivatives of the semigroup…
Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analogue is a challenge as it involves an inverse Fourier transform of the spherical Hankel functions (and their…
Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy non-stationary signals. We systematically study the performance of different variants of the…
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
We present a general framework of detrending methods of fluctuation analysis of which detrended fluctuation analysis (DFA) is one prominent example. Another more recently introduced method is detrending moving average (DMA). Both methods…
Domain Adaptation(DA) for dense prediction tasks is an important topic, which enhances the dense prediction model's performance when tested on its unseen domain. Recently, with the development of Diffusion-based Dense Prediction (DDP)…
Diffusion models show promise for 3D molecular generation, but face a fundamental trade-off between sampling efficiency and conformational accuracy. While flow-based models are fast, they often produce geometrically inaccurate structures,…
Dynamic graph augmentation is used to improve the performance of dynamic GNNs. Most methods assume temporal locality, meaning that recent edges are more influential than earlier edges. However, for temporal changes in edges caused by random…
We introduce an inferential framework for a wide class of semi-linear stochastic differential equations (SDEs). Recent work has shown that numerical splitting schemes can preserve critical properties of such types of SDEs, give rise to…
A fractional advection-dispersion equation (fADE) has been advocated for heavy-tailed flows where the usual Brownian diffusion models fail. A stochastic differential equation (SDE) driven by a stable L\'{e}vy process gives a forward…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
Most visual generative models compress images into a latent space before applying diffusion or autoregressive modelling. Yet, existing approaches such as VAEs and foundation model aligned encoders implicitly constrain the latent space…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…
Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…
Statistical inference is central to many scientific endeavors, yet how it works remains unresolved. Answering this requires a quantitative understanding of the intrinsic interplay between statistical models, inference methods and data…
A standard model for the study of scalar dispersion through advection and molecular diffusion is a two-dimensional periodic flow with closed streamlines inside periodic cells. Over long time scales, the dispersion of a scalar in this flow…
Self-consistency boosts inference-time performance by sampling multiple reasoning traces in parallel and voting. However, in constrained domains like math and code, this strategy is compute-inefficient because it samples with replacement,…
Several methods have been proposed to identify which sensor sets are optimal for finding and localizing faults under different conditions for mechanical equipment. In order to preserve acceptable performance while minimizing costs, it is…
The aim of this paper is to shed light on the analysis of non-stationary time series by means of the method of diffusion entropy. For this purpose, we first study the case when infinitely many time series, as different realizations of the…