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A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
In this paper, We study the problem of learning a controllable representation for high-dimensional observations of dynamical systems. Specifically, we consider a situation where there are multiple sets of observations of dynamical systems…
This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine…
When multiple forecasts are available for a probability distribution, forecast combining enables a pragmatic synthesis of the information to extract the wisdom of the crowd. The linear opinion pool has been widely used, whereby the…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…
Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
A wide variety of problems in combinatorics and discrete optimization depend on counting the set $S$ of integer points in a polytope, or in some more general object constructed via discrete geometry and first-order logic. We take a tour…
We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity…
Collective human behaviors are analyzed using the time series of word appearances in blogs. As expected, we confirm that the number of fluctuations is approximated by a Poisson distribution for very-low-frequency words. A non-trivial…
Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Entanglement can be distributed using a carrier which is always separable from the rest of the systems involved. Up to now, this effect has predominantly been analyzed in the case where the carrier-system interactions take the form of ideal…
Many cultural traits characterizing intelligent behaviors are now thought to be transmitted through statistical learning, motivating us to study its effects on cultural evolution. We conduct a large-scale music data analysis and observe…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
Distributed aggregation allows the derivation of a given global aggregate property from many individual local values in nodes of an interconnected network system. Simple aggregates such as minima/maxima, counts, sums and averages have been…
Angular observations, or observations lying on the unit circle, arise in many disciplines and require special care in their description, analysis, interpretation and visualization. We provide methods to construct concentric circular boxplot…