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Consider random matrices $A$, of dimension $m\times (m+n)$, drawn from an ensemble with probability density $f(\rmtr AA^\dagger)$, with $f(x)$ a given appropriate function. Break $A = (B,X)$ into an $m\times m$ block $B$ and the…
Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled Burgers-like model in one dimension (1d), a generalization of the Burgers model to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to MHD,…
In this brief, we try to develop a comprehensive framework to identify, quantify, isolate, and reduce the uncertainties in the original BHR model \citep {Besnard1992} for variable-density flows. Because the eigenspace perturbation of…
Machine learning classification methods usually assume that all possible classes are sufficiently present within the training set. Due to their inherent rarities, extreme events are always under-represented and classifiers tailored for…
We consider a two-parameter discrete generalized beta (DGB) distribution and propose its universal applications to study the size-distribution of the urban agglomerations across various countries in the world, where the urban agglomerations…
Floods are highly uncertain events, occurring in different regions, with varying prerequisites and intensities. A highly reliable flood disaster risk map can help reduce the impact of floods for flood management, disaster decreasing, and…
In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we consider the distribution of the ratio of persistence…
Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…
Scaling of the Reynolds stresses has been sought by many researchers, since it provides a template of universal dynamical patterns across a range of Reynolds numbers. Various statistical and normalization schemes have been attempted, but…
When analysing extreme values, two alternative statistical approaches have historically been held in contention: the block maxima method (or annual maxima method, spurred by hydrological applications) and the peaks-over-threshold. Clamoured…
We analyze the constituents stocks of the Dow Jones Industrial Average (DJIA30) and the Standard & Poor's 100 index (S&P100) of the NYSE stock exchange market. Surprisingly, we discover the data collapse of the histograms of the DJIA30…
This paper discusses and analyzes various models of binary correlated sources, which may be relevant in several distributed communication scenarios. These models are statistically characterized in terms of joint Probability Mass Function…
In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…
River networks serve as a paradigmatic example of all branching networks. Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we show that sub-branches are distributed…
Random systems of curves exhibiting fluctuating features on arbitrarily small scales ($\delta$) are often encountered in critical models. For such systems it is shown that scale-invariant bounds on the probabilities of crossing events imply…
This paper introduces the distributionally robust random utility model (DRO-RUM), which allows the preference shock (unobserved heterogeneity) distribution to be misspecified or unknown. We make three contributions using tools from the…