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This review article provides an overview of recent work in the modeling and analysis of recurrent events arising in engineering, reliability, public health, biomedicine and other areas. Recurrent event modeling possesses unique facets…

The concept of correlation appears straightforward: measurement outcomes coincide, and patterns emerge. For any record of events, the coefficients are uniquely determined. Thus, if correlations change spontaneously, as seen in quantum…

This paper shows that characterizing co-occurrence between events is an important but non-trivial and neglected aspect of discovering potential causal relationships in multimedia event streams. First an introduction to the notion of event…

Identifying the salience (i.e. importance) of discourse units is an important task in language understanding. While events play important roles in text documents, little research exists on analyzing their saliency status. This paper…

Children can use the statistical regularities of their environment to learn word meanings, a mechanism known as cross-situational learning. We take a computational approach to investigate how the information present during each observation…

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

This paper collects some reflections about an apparent incongruity between the usual (third-person) understanding of the probability of an event calculated for an extended period of time in the future (e.g., the expected probability of a…

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

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…

Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g. in terms of pairwise dependences) - as in statistical learning - or because they capture the…

In these notes we review emergent phenomena in complex systems, emphasizing ways to identify potential underlying universal mechanisms that generates complexity. The discussion is centered around the emergence of collective behavior in…

The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory…

The decoherent (consistent) histories formalism has been proposed as a means of eliminating measurements as a fundamental concept in quantum mechanics. In this formalism, probabilities can be assigned to any description which satisfies a…

Language technologies that accurately model the dynamics of events must perform commonsense reasoning. Existing work evaluating commonsense reasoning focuses on making inferences about common, everyday situations. To instead investigate the…

Herein we consider various concepts of entropy as measures of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do…

We consider the problem of assessing whether, in an individual case, there is a causal relationship between an observed exposure and a response variable. When data are available on similar individuals we may be able to estimate prospective…

In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate…

The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…

As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…

We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…