Related papers: How complex is a random picture?
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of…
The complexity of visual stimuli plays an important role in many cognitive phenomena, including attention, engagement, memorability, time perception and aesthetic evaluation. Despite its importance, complexity is poorly understood and…
Information entropy is applied to the state of knowledge of reaction amplitudes in pseudoscalar meson photoproduction, and a scheme is developed that quantifies the information content of a measured set of polarization observables. It is…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
We revisit the long-standing question of the relation between image appreciation and its statistical properties. We generate two different sets of random images well distributed along three measures of entropic complexity. We run a…
How much does a single image reveal about the environment it was taken in? In this paper, we investigate how much of that information can be retrieved from a foreground object, combined with the background (i.e. the visible part of the…
We define the relevant information in a signal $x\in X$ as being the information that this signal provides about another signal $y\in \Y$. Examples include the information that face images provide about the names of the people portrayed, or…
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays. The size of the smallest bounded…
We study a simple model of the stochastic information filtering, in a randomly organized information system. For simplest versions of the model it appears to be possible to describe the filtering dynamics in terms of the master equations.…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods for estimating uncertainties are poorly calibrated, computationally expensive,…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
By using finite resolution measurements it is possible to simultaneously obtain noisy information on two non-commuting polarization components of a single photon. This method can be applied to a pair of entangled photons with polarization…