Related papers: Outliers, Dynamics, and the Independence Postulate

We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…

In this paper we present, in the context of Diaconis' paradigm, a general method to detect the cutoff phenomenon. We use this method to prove cutoff in a variety of models, some already known and others not yet appeared in literature,…

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…

The Fluctuation Theorem gives an analytical expression for the probability of observing second law violating dynamical fluctuations, in nonequilibrium systems. At equilibrium statistical mechanical fluctuations are known to be ensemble…

We address the question of why particular laws were selected for the universe, by proposing a mechanism for laws to evolve. Normally in physical theories, timeless laws act on time-evolving states. We propose that this is an approximation,…

We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…

As a direct result of ongoing efforts to detect more exoplanetary systems, an ever-increasing number of multiple-planet systems are being announced. But how many of these systems are truly what they seem? In many cases, such systems are…

Existing studies on identifying outliers in wind speed-power datasets are often challenged by the complicated and irregular distributions of outliers, especially those being densely stacked yet staying close to normal data. This could…

We provide theoretical and experimental evidence of statistical outliers in random laser emission that are not accounted for by the, now established, power-law tailed (L\'evy) distribution. Such outliers manifest themselves as single, large…

Large deviation theory quantifies the occurence of events that deviate from the average behavior of a system. Such events arise from non-typical trajectories of the dynamics. In this note we derive the time evolution of these rare…

This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction,…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…

Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…

We show that singularities necessarily occur when a boundary of causality violating set exists in a space-time under the physically suitable assumptions except the global causality condition in the Hawking-Penrose singularity theorems.…

We prove an existence result for a quasilinear elliptic equation satisfying natural growth conditions. As a consequence, we deduce an existence result for a quasilinear elliptic equation containing a singular drift. A key tool, in the…

Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can…

Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…

In this paper we consider the two major computational effects of states and exceptions, from the point of view of diagrammatic logics. We get a surprising result: there exists a symmetry between these two effects, based on the well-known…