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The difference between the timelike and spacelike meson form factors is analysed in the framework of perturbative QCD with Sudakov effects included. It is found that integrable singularities appear but that the asymptotic behavior is the…
Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…
Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…
Hypersurfaces of arbitrary causal character embedded in a spacetime are studied with the aim of extracting necessary and sufficient free data on the submanifold suitable for reconstructing the spacetime metric and its first derivative along…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of…
We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all…
Temporally modulated optical media are important in both abstract and applied applications, such as spacetime transformation optics, relativistic laser-plasma interactions, and dynamic metamaterials. Here we investigate the behaviour of…
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…