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As observers of the universe we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
The last 20 years have seen an explosion in our understanding of the large-scale distribution and motions of galaxies in the nearby universe. The field has moved from a largely qualitative, morphological description of the structures seen…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
The field of astronomy is experiencing a data explosion driven by significant advances in observational instrumentation, and classical methods often fall short of addressing the complexity of modern astronomical datasets. Probabilistic…
In the modern quantum mechanics of cosmology observers are physical systems within the universe. They have no preferred role in the formulation of the theory nor in its predictions of third person probabilities of what occurs. However,…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong…
Numerical simulations play a key important role in modern cosmology. Examples are plenty including the cosmic web - large scale structure of the distribution of galaxies in space - which was first observed in N-body simulations and later…
Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…
Large-scale structure of Universe includes galaxy clusters connected by filaments. Voids occupy the rest of cosmic volume. The search of any dependencities in filament structure can give answer to more general questions about origin of…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of shapes without causing a possibly large loss of information. Dictionary learning and sparse coding allow us to reduce the high dimensional…
The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy -- the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy…
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…