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Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…
The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in…
Learning about density functional approximations (DFAs), or approximations for the exchange-correlation functional, can be intimidating. Density Functional Theory is now one of the primary simulation tools for the practicing chemist or…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
Robustness is often regarded as a critical future challenge for real-world applications, where stability is essential. However, as models often learn tasks in a similar order, we hypothesize that easier tasks will be easier regardless of…
Conformance checking techniques allow us to quantify the correspondence of a process's execution, captured in event data, w.r.t., a reference process model. In this context, alignments have proven to be useful for calculating conformance…
To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By…
The excess power, energy and intensity of a random electromagnetic field above a high threshold level are characterized based on a Slepian--Kac model for upcrossings. For quasi-static fields, the probability distribution of the excess…
A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices…
As medical devices become more complex, they routinely collect extensive and complicated data. While classical regressions typically examine the relationship between an outcome and a vector of predictors, it becomes imperative to identify…
Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…
A central challenge in the study of complex systems is the quantification of emergence -- understood as the ability of the system to exhibit collective behaviours that cannot be traced down to the individual components. While recent work…
In this paper, a class of statistics based on high frequency observations of oscillating and skew Brownian motion is considered. Their convergence rate towards the local time of the underlying process is obtained in form of a functional…
One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. An extension of his approach is…
Since its publication in 1949, Langbein's formula has been applied ubiquitously in both research documents and national guidelines concerning frequency analyses (FAs) of hydrologic extremes. Given a time series of independent…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Functional data covers a wide range of data types. They all have in common that the observed objects are functions of of a univariate argument (e.g. time or wavelength) or a multivariate argument (say, a spatial position). These functions…
Upper limits and confidence intervals are a convenient way to present experimental results. With modern experiments producing more and more data, it is often necessary to reduce the volume of the results for convenient distribution. A…
We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting…