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(Abbr.) We consider a direct representation of a periodic time-function by means of its zero-crossings. The use of the zero-crossings as the describing parameters is made possible by a singular model of a strongly nonlinear electrical…

The representations of conditional entropy and conditional mutual information are significant in explaining the unique effects among variables. While previous studies based on conditional contrastive sampling have effectively removed…

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…

In this note we introduce a representation of simple undirected graphs in terms of polynomials and obtain a unique code for a simple undirected graph.

Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…

These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly…

This paper presents an approach for learning to translate simple narratives, i.e., texts (sequences of sentences) describing dynamic systems, into coherent sequences of events without the need for labeled training data. Our approach…

Building on recent advances in scientific machine learning and generative modeling for computational fluid dynamics, we propose a conditional score-based diffusion model designed for multi-scenarios fluid flow prediction. Our model…

Typically, real-world stochastic processes are not easy to analyze. In this work we study the representation of any stochastic process as a memoryless innovation process triggering a dynamic system. We show that such a representation is…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…

A \emph{double extrema form} of the calculus of variations is put forward in which only the smallest one of the finite differences is physically meaningful to represent the variational derivatives defined on the discrete points. The most…

We study the design of optimal incentives in sequential processes. To do so, we consider a basic and fundamental model in which an agent initiates a value-creating sequential process through costly investment with random success. If…

The evaluation of probabilistic forecasts plays a central role both in the interpretation and in the use of forecast systems and their development. Probabilistic scores (scoring rules) provide statistical measures to assess the quality of…

A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A…

We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example (i) crossing events for level or…

In the classic scoring rule setting, a principal incentivizes an agent to truthfully report their probabilistic belief about some future outcome. This paper addresses the situation when this private belief, rather than a classical…

Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…

We present a computer simulation model that is a one-to-one copy of a quantum eraser experiment with photons (P. D. D. Schwindt {\sl et al.}, Phys. Rev. A 60, 4285 (1999)). The model is solely based on experimental facts, satisfies…