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Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Liquid drops slide more slowly over soft, deformable substrates than over rigid solids. This phenomenon can be attributed to the viscoelastic dissipation induced by the moving wetting ridge, which inhibits a rapid motion, and is called…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…
Data attribution methods trace model behavior back to its training dataset, offering an effective approach to better understand ''black-box'' neural networks. While prior research has established quantifiable links between model output and…
Methods in the field of quickest change detection rapidly detect in real-time a change in the data-generating distribution of an online data stream. Existing methods have been able to detect this change point when the densities of the pre-…
Numerous Optimization Algorithms have a time-varying update rule thanks to, for instance, a changing step size, momentum parameter or, Hessian approximation. In this paper, we apply unrolled or automatic differentiation to a time-varying…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
Statistics on migration flows are often derived from census data, which suffer from intrinsic limitations, including costs and infrequent sampling. When censuses are used, there is typically a time gap - up to a few years - between the data…
In the study of Heisenberg's error-disturbance relation, it is commonly believed that the non-unitary change of states hinders us from deducing the information encoded in original states about subsequently measured observable. However, we…
Discrete diffusion models are increasingly competitive for language modeling, yet it remains unclear how their denoising objectives organize learning. Although these objectives target the full data distribution, we show that the exact…
We present a simple result in which the distance gradient along a stream can be used to derive the transverse velocity (i.e. proper motion) along it, if the line-of-sight velocity is also known. We show its application to a mock orbit to…
Understanding what information neural networks capture is an essential problem in deep learning, and studying whether different models capture similar features is an initial step to achieve this goal. Previous works sought to define metrics…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site…
Word meaning change can be inferred from drifts of time-varying word embeddings. However, temporal data may be too sparse to build robust word embeddings and to discriminate significant drifts from noise. In this paper, we compare three…
The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the…
For a transition between two stable states, the committor is the probability that the dynamics leads to one stable state before the other. It can be estimated from trajectory data by minimizing an expression for the transition rate that…
We consider a discrete-time process adapted to some filtration which lives on a (typically countable) subset of $\mathbb{R}^d$, $d\geq 2$. For this process, we assume that it has uniformly bounded jumps, is uniformly elliptic (can advance…
When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…