Voronoi entropy for the random patterns and patterns demonstrating various elements of symmetry are calculated. The symmetric patterns are characterized by the values of the Voronoi entropy very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points, constituting the pattern. The extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables revealing of the elements of symmetry of the pattern.

Time evolution of the symmetry of symbols constituting alphabets rooted in the Phoenician script was investigated. A diversity of quantitative measures of symmetry of graphemes appearing in Phoenician, Western Greek, Etruscan from Marsiliana, Archaic Etruscan, Neo-Etruscan, Euclidian Greek, Archaic and Classical Latin, and Proto-Hebrew scripts, constituting the Phoenician script family, were calculated. The same measures were calculated for the Hebrew/Ashurit and English scripts. The Shannon-like measures of symmetry were calculated. The Shannon diversity index was calculated. The Shannon diversity index increased with time in a monotonic way for the scripts emerging from the Phoenician one. The diversity of symmetry groups inherent for alphabets emerging from the Phoenician one grows with time. We also introduced the symmetry factor of the alphabet. The symmetry factor quantifies the averaged level of symmetrization of the alphabet and the possible parsimony of graphical information necessary for the drawing of the entire set of graphemes, constituting the alphabet. The symmetry factor is decreased with time for the alphabets rooted in the Phoenician one. This means that the average level of symmetrization of the studied alphabet is increased with time. The parsimony of graphical information necessary for writing graphemes is increased with time. The values of the symmetry factor calculated for the addressed scripts are close one to another, with the pronounced exception of the Hebrew/Ashurit script. Our study supplies the arguments for the point of view, according to which the modern Hebrew/Ashurit script does not emerge from the Phoenician one.

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

The entropy models have been recently adopted in many studies to evaluate the distribution of the shear stress in circular channels. However, the uncertainty in their predictions and their reliability remains an open question. We present a novel method to evaluate the uncertainty of four popular entropy models, including Shannon, Shannon-Power Low (PL), Tsallis, and Renyi, in shear stress estimation in circular channels. The Bayesian Monte-Carlo (BMC) uncertainty method is simplified considering a 95% Confidence Bound (CB). We developed a new statistic index called as FREE_opt-based OCB (FOCB) using the statistical indices Forecasting Range of Error Estimation (FREE) and the percentage of observed data in the CB (N_in), which integrates their combined effect. The Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, had the highest certainty in the calculation of shear stress values in circular channels followed by traditional uniform flow shear stress and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy with much higher values of FOCB equal to 57.726 has less certainty in the estimation of shear stress than other models. Using the presented results in this study, the amount of confidence in entropy methods in the calculation of shear stress to design and implement different types of open channels and their stability is determined.

The Gaussian signaling strategy with power control for the Gaussian Z-interference channel with weak interference is reviewed in this paper. In particular, we study the various communication strategies that may arise at various points of the capacity region and identify the locations of the phase transitions between the various strategies. The Gaussian Z-interference channel with weak interference is known to have two critical points in its capacity region, where the slope of the region shows a sudden change. They occur at the points of the unconditional maximum rate for one of the users and the maximum rate that can be accommodated by the other user. In this paper, we discuss two additional critical points (locations of phase transitions) in the achievable region of this channel. At these points, we do not observe a discontinuous slope in the achievable rate region, but there is a discontinuity in the second derivative of the rate contour of the achievable region. This review paper is mainly based on some of our ITA (Information Theory and Applications Workshop, UCSD, San Diego, CA, USA) papers since 2011.

A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey number was established as R_trans (3,3)=5. Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits ζ=lim┬(N→∞)⁡〖N_g/N_r 〗, where N is the total number of green and red seeds, N_g and N_r, were found ζ=0.272±0.001 (Voronoi) and ζ= 0.47±0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as S= 1.690±0.001 and for the Poisson line tessellation as S =1.265±0.015.

This paper reveals some properties of the cumulative entropy of consecutive k-out-of-n:F system's lifetime. First, we introduce a method for calculating the cumulative entropy of their lifetime and explore its preservation properties using established stochastic orders. Ad- ditionally, we obtain useful bounds that can used in situations where the distribution function of the system's component lifetimes are complicated or systems have large components. To support practical applications, we present two nonparametric estimators for the cumulative entropy of these systems. The efficiency and performance of these estimators are illustrated with simulated datasets and further validated with real data sets.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-diffusion; (iv)~hydrodynamic fully developed turbulence, and (v)~plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon Permutation Entropy ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

Recently, there has been growing interest in alternative measures of uncertainty, including cumulative residual entropy. In this paper, we consider a mixed system consisting of n components, assuming that all components are operational at time t. We use the system signature to calculate the cumulative residual entropy of the mixed system’s remaining lifetime. This measure is a useful criterion for assessing the predictability of a system’s lifetime. We study several results related to the cumulative residual entropy of mixed systems, including expressions, limits, and order properties. These results shed light on the behavior of the measure and provide insights into the predictability of mixed systems. In addition, we propose a criterion for selecting a preferred system based on the relative residual cumulative entropy. This criterion is closely related to the parallel system and provides a practical way to choose the best system configuration. Overall, the present study of cumulative residual entropy and the proposed selection criterion provide valuable insights into the predictability of mixed systems and can be applied in various fields.

Recent developments, begun by the ascending spiral of the anticipated endless prospects of ChatGPT, promote artificial intelligence (AI) as an indispensable tool and commodity whose time has come. Yet the sinister specter of a technology that has hidden and unmanageable attributes that might be harmful to society looms in the background. As well as the likelihood that it will never deliver on the purported promise of artificial general intelligence (AGI). Currently the prospects for the development of AI and AGI are more a matter of opinion than based on a consistent methodological approach. Thus the need to take a step back to develop a general framework from which to evaluate current AI efforts, which also permits the determination of the limits to its future prospects as AGI. To gain insight into the development of a general framework, a key question that needs resolution is, what is the connection between human intelligence and machine intelligence? This is the question that needs a response because humans are at the center of AI creation and realize that without an understanding of how we become what we become, we have no chance of finding a solution. This work proposes infoautopoiesis, the self-referential, recursive and interactive process of self-production of information, as the needed general framework. Infoautopoiesis shows how the key ingredient of information is fundamental to an insightful resolution to this crucial question and allows predictions as to the present and future of AGI.

The world is now undergoing through a global emergency due to COVID-19 which needs immediate remedies in order to strengthen the healthcare facility to save the nations. Looking towards to the remedies, research on different aspects including the genomic and proteomic level characterizations of the SARS-CoV2 are necessarily important. In this present study, the spatial representation/composition of twenty amino acids across the primary protein sequences of SARS-CoV2 have been looked into through different parameters viz. Shannon entropy, Hurst exponent in order to fetch the autocorrelation and amount of information over the spatial representations. Also frequency distribution of each of the amino acids over the protein sequences have been chalked out.

In 2020, the pandemic caused by the Coronaviruses (CoV) that are a large family of viruses that cause illness ranging from the common cold to more severe diseases such as Middle East Respiratory Syndrome (MERS-CoV) and Severe Acute Respiratory Syndrome (SARS-CoV2). The Coronavirus disease (COVID-19) is a new strain that was discovered in 2019 and has not been previously identified in humans. It is the high time to investigate the quantitative and/or qualitative genomic informations of the virus SARS-CoV2 in order to strengthen the healthcare facility to fight against this viral disease. In this article, a through quantitative understanding of the purine and pyrimidine spatial distribution/organization of all 89 complete sequences of SARS-CoV (available as on date in the NCBI virus database, is made using different parameters such as fractal dimension, Hurst exponent, Shannon entropy and GC content of the nucleotide sequences of the genome of SARS-CoV2. Also a cluster among all the the SARS-CoV sequences of nucleotide have been made based on their phylogeny made through their closeness (Hamming distance) based on respective purine-pyrimidine distribution.

In this work, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced bilattice of four vertices. We use the logarithmic function of the Shannon entropy H_(s) to construct the paraconsistent equations and thus adapt a probabilistic model for representations in quantum physics. Through analyses of the interlaced bilattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, quantum entanglement, wave functions, and equations that determine the energy levels of the layers of an atom. At the end of this article, we use the hydrogen atom as a basis of the representation of the PAL2v model, where the values of the energy levels in six orbital layers are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.

In this paper, the Shannon entropy measure was used to assess changes in precipitation and temperature conditions. Due to the short, low-volume sequences of precipitation and temperature data analysed, a bootstrap method was used in the procedure for calculating Shannon entropy. The analysis used minimum and maximum values of monthly precipitation totals and monthly mean temperatures for 377 catchments distributed across the globe. A 110-year data series from 1901 to 2010 was analysed. Entropy values for the estimated parameters of the generalised extreme value distribution (GEV) were calculated for the adopted data. Entropy value calculations were performed for the left-hand constraint, based on minimum values, and for the right-hand constraint, based on maximum values. The applicability of Shannon's entropy measure in the analysis of climate change was demonstrated by allowing the degree of disorder and complexity of the distributions describing climate variables in the form of precipitation and temperature to be measured. This made it possible to obtain information on the directions of changes occurring with regard to minimum and maximum values in the field of monthly precipitation and mean temperatures in the analysed catchments. The study demonstrated the existence of Shannon entropy trends. The evaluation of entropy trends for precipitation and temperature sequences was performed using non-parametric tests. Mann -Kendall tests at the 5% significance level were used for trend analyses. The Pettitt test was performed to determine the point of change in trend for the rainfall and temperature data. The performed analysis was supported by graphical presentations.

For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure.

Most existing flexible count regression models allow only approximate inference. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under- and overdispersion). The new method, referred as “balanced discretization”, consists in discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation in terms of the continuous distribution. For illustrative purposes, we have developed the family of balanced discrete gamma distributions which can model equi-, under- and overdispersed count data. This family of count distributions is appropriate for building flexible count regressionmodels because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we have shown that under equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersion, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data is Poisson distributed.

Big data is considered to be the solution to many complex problems, but its application appears to be relegated to the problems that are factorable (e.g., the tensor-like operations which reflect separable elements), not the non-factorable data from teamwork, team intelligence, and possibly not individual consciousness. In contrast, the quantum likeness of interdependence is set apart from the standard science of teams by recognizing a measurement problem between a team and its individual teammates, and between individual beliefs and actions. Teams that concern us are based on artificial intelligence (AI) and machine learning (ML) systems, which we find lacking for two reasons. First, neither AI nor ML models the human's timeless need for debate to solve a problem at the social level when facing uncertainty or complexity, where the debate of proposed actions serves to establish the boundaries of a problem in reality, no matter how complex nor uncertain. Second, at the individual level exists the illusion of a unified reality propagated by a bifurcated brain that we assume is split to determine a context with narrative and bounded spaces. We hypothesize that the quantum-likeness of interdependence applied to autonomous human-machine teams suggests that at the social level, debate models an individual's bifurcated brain, providing advantages for human-machine teams in freer systems over those oppressed by command and control systems (e.g., authoritarian regimes). Human-machine teams are coming, but they are not yet available, forcing us to rely on data from human systems. We close with plans for future research.

We used the complete set of convex pentagons enabling filing the plane without any overlaps or gaps (including the Marjorie Rice tiles) as generators of Voronoi tessellations. Shannon entropy of the tessellations was calculated. Some of the basic mosaics are flexible and give rise to a diversity of Voronoi tessellations. The Shannon entropy of these tessellations varied in a broad range. Voronoi tessellation, emerging from the basic pentagonal tiling built from hexagons only, was revealed (the Shannon entropy of this tiling is zero). Decagons and hendecagon did not appear in the studied Voronoi diagrams. The most abundant Voronoi tessellations are built from three different kinds of polygons. The most widespread is the combination of pentagons, hexagons and heptagons. The most abundant polygons are pentagons and hexagons. No Voronoi tiling built only of pentagons was registered. Flexible basic pentagonal mosaics give rise to a diversity of Voronoi tessellations, which are characterized by the same symmetry group; however, the coordination number of the vertices is variable. These Voronoi tessellations may be useful for the interpretation of the iso-symmetrical phase transitions.

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links are considered. Shannon-entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. Introduced Shannon entropy is insensitive to the exact shape of the graph, but it is sensitive to the distribution of monochromatic polygons in a given graph. The introduced Shannon Entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph, Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon Entropy is suggested. Various measures quantifying the Shannon Entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon Entropies are discussed.

A precise understanding of the genes and associated genomes of SARS-CoV2 is important for various reasons such as discovering origin of the virus and virulence and so on. A thorough descriptive understanding of the SARS-CoV2 genomes and other coronavirus of the beta-coronavirus genus is primarily important. In this article, a set of ten genomes of four CoVs and their associated genes are considered for this present study. A spatial representations of nucleotide bases including purine-pyrimidine representations of the different genes of the corresponding genomes are quantified using Hurst exponent, Shannon entropy and density estimation of different nucleotides including GC content, in order to draw a comparison and contrast among the ten genomes of different types of CoVs which include MERS, SARS-CoV, HKU1 (Human Coronavirus) and associated their genes.

The time’s arrow of macroscopic physical phenomenon is reflected by irreversible physical process, which essentially occurs from small probability state to high probability state. In this paper, simplified models are proposed to understand the macroscopic physical process. In order to describe the information of a physical system, we defined the full self-information as "information height" to describe the complexity or difficulty of a macrostate of physical system. In this way, the direction of macroscopic physical process is from high information height to low information height. We can judge the direction of physical process by the information height. If we want the macroscopic physical process to evolve from the low information height state to the high information height state, the system need to add extra information and corresponding energy to increase the information height.

Sierra Madre Mountain Range (SMMR) is the backbone of Luzon Islands that contains high concentration of highly important ecological resources distributed among the 68 protected areas therewith. The present study aimed to assess the tree species composition and diversity in a secondary forest within the SMMR. A 2.25-km transect with 10 900-m2 was established to record tree species with a diameter at breast height of at least 10 cm. The findings revealed 148 individuals of trees from 38 morphospecies, 28 genera, and 20 families. Importance values unveiled the Aurora endemic Macaranga stonei Whitmore as the most important species in terms of the relative values of its abundance, frequency, and dominance. The area was also found to be home for 33 natives, 12 endemics, five IUCN threatened species, and nine Philippine threatened trees. Furthermore, the study site was also found to have a considerably high diversity with Shannon Weiner Index value of 3.269 and a relatively even distribution of individuals among species supported by the Simpson’s Evenness index value of 0.9453. Significant correlational relationships were also found among species richness, Shannon Weinder index, and Simpson’s Evenness index with correlation coefficients ranging from 0.881 to .934 all significant at p < .001. Lastly, the study was able to produce a distribution map necessary in implementing targeted conservation strategies. These findings provided valuable implications for future research and implementation of targeted and participatory biodiversity conservation and protection strategies.

Information theory is widely used in various disciplines, and effective calculation of Shannon mutual information is typically not an easy task for many practical applications, including problems of neural population coding in computational and theoretical neuroscience. Asymptotic formulas based on Fisher information may provide accurate approximations to mutual information but this approach is restricted to continuous variables because the calculation requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations based on Kullback-Leibler divergence and Rényi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding, and these asymptotic formulas hold true for discrete variables as there is no requirement for differentiability. In particular, one of our approximation formulas has consistent performance and good accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating mutual information between the discrete variables or stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.

Hyperspectral images are an important tool to assess ecosystem biodiversity both on terrestrial and benthic habitats. To obtain more precise analysis of biodiversity indicators that agree with indicators obtained using field data, analysis of spectral diversity calculated from images have to be validated with field based diversity estimates. The plant species richness is one of the most important indicators of biodiversity. This indicator can be measured in hyperspectral images considering the Spectral Variation Hypothesis (SVH) which states that the spectral heterogeneity is related to spatial heterogeneity and thus to species richness. The goal of this research is to capture spectral heterogeneity from hyperspectral images for a terrestrial neo tropical forest site using Vector Quantization (VQ) method and then use the result for prediction of plant species richness. The results are compared with that of Hierarchical Agglomerative Clustering (HAC). The validation of the process index is done calculating the Pearson correlation coefficient between the Shannon entropy from actual field data and the Shannon entropy computed in the images. Terrestrial dry forest and marine coastal hyperspectral images with different resolutions have been used for spectral diversity feature validation.

Species diversity has been shown to be influenced by environmental factors, but the mechanism underlying their relationship remains unclear across spatial scales. Based on field investigation data collected from 3,077 sample plots in temperate forest ecosystems, we compared tree species richness, evenness and dominance at 10 km × 10 km, 30 km × 30 km and 90 km × 90 km spatial scales. Then, we detected the scale dependence of changes in tree species composition on climate, topography and forest structure using variation partitioning and quantified their contribution to tree diversity with gradient boosted models (GBMs) and fitted their relationships. The magnitude of tree richness, evenness and dominance significantly increased with spatial scale. Ecological factors jointly accounted for 24.3%, 26.5% and 38.5% of the variation in tree species composition at the three spatial scales, respectively. Annual mean temperature had a strong impact on tree richness, evenness and dominance and peaked at an intermediate scale. Tree evenness and dominance increased with the variation of temperature but had upper and lower limits. Tree richness obviously increased with annual precipitation on multiple scales and decreased with annual sunshine duration at large spatial scale. Tree richness, evenness and dominance obviously increased with the variation elevation and diameter at breast height at large scales and small scales, respectively. Tree dominance decreased with tree height in a hump at small scale. The dependence of tree diversity on ecological factors increased with spatial scales. Furthermore, different factors exert various controls on tree diversity at different spatial scales, representing a comprehensive mechanism regulating tree diversity.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

In this paper, we concentrate on the study of the properties of residual Tsallis entropy for order statistics. Order statistics have an important role in reliability structural engineering for example for modelling lifetimes of series and parallel systems. The residual Tsallis entropy of ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of ith order statistics from a uniform distribution is investigated. In a mathematical framework, a method to express the residual Tsallis entropy of the ith order statistic from a continuous distribution in terms of the residual Tsallis entropy of the ith order statistic from a uniform distribution is provided. This approach may provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. Further, we study the monotonicity properties of the residual Tsallis entropy of order statistics under dierent conditions. By studying these properties, deeper understanding of the relationship between the position of order statistics and the resulting residual Tsallis entropy is gained.

Perception and motor interaction with physical surroundings can be analyzed by the changes in probability laws governing two possible outcomes of neuronal activity, namely the presence or absence of spikes (binary states). Perception and motor interaction with physical environment are accounted partly by the reduction in entropy within the probability distributions of binary states of neurons in distributed neural circuits, given the knowledge about the characteristics of stimuli in physical surroundings. This reduction in the total entropy of multiple pairs of circuits in networks, by an amount equal to the increase of mutual information among them, occurs as sensory information is processed successively from lower to higher cortical areas or between different areas at the same hierarchical level but belonging to different networks. The increase in mutual information is partly accounted by temporal coupling as well as synaptic connections as proposed by Bahmer and Gupta [1]. We propose that robust increases in mutual information, measuring the association between the characteristics of sensory inputs and neural circuits connectivity patterns, are partly responsible for perception and successful motor interactions with physical surroundings. It is also argued that perception from a sensory input is the result of networking of many circuits to a common circuit that primarily processes the given sensory input.

Over the past decade and a half, dynamic functional imaging has revolutionized the neuroimaging field. Since 2009, it has revealed low dimensional brain connectivity measures, has identified potential common human spatial connectivity states, has tracked the transition patterns of these states, and has demonstrated meaningful alterations in these transition and spatial patterns in neurological disorders, psychiatric disorders, and over the course of development. Recently, researchers have begun to analyze this data from the perspective of dynamic system and information theory in the hopes of understanding how these dynamics support less easily quantified processes, such as information processing, cortical hierarchy, and consciousness. Consciousness, in particular, appears to be strongly linked to entropy production in the brain. Little attention has been paid to the effects of psychiatric disease on entropy production in the human brain, however. Even disorders characterized by substantial changes in conscious experience have not been widely analyzed from this perspective. We begin to rectify this by examining the complexity of subject trajectories in state space through the lens of information theory. Specifically, we identify a basis for the dynamic functional connectivity state space and track subject trajectories through this space over the course of the scan. The dynamic complexity of these trajectories is assessed along each dimension of the proposed basis space. Using these estimates, we demonstrate that schizophrenia patients display substantially simpler trajectories than demographically matched healthy controls, and that this drop in complexity concentrates along specific dimensions. We also demonstrate that entropy generation in at least one of these dimensions is linked to cognitive performance. Overall, results suggest great value in applying dynamic systems theory to problems of neuroimaging and reveal a substantial drop in the complexity of schizophrenia patients’ brain function.

We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere [1], but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of $\pi$. If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer's eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously performs a conversion between information and energy, or else as a feedback-controlled device that is operated by an external agent. We derive generalized second laws of thermodynamics for both pictures. We illustrate our model with numerical simulations, as well as analytical calculations in a particular, exactly solvable limit.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

This paper shows that by applying the Nyquist-Shannon sampling theorem, the spatial and temporal resolution of a simulation can be no more than half the resolution of the simulating reality. This has significant implications for not only the values of the observables in the simulation but also its physical laws. This progressive halving of nested simulations coupled with the minimum resolution compatible with the production of a simulation also sets a limit to the nestedness of a lineage of simulations (it is by no means infinite). The limit of nestedness is then used to calculate the probability that we are living in a simulation assuming a single base reality. This will be shown to be significantly lower than popular expectation. A Kardashev-like scale, with three variants, is also developed to gauge the technological advancement of a civilization in relation to the extent to which it can extract information from space and time.

Detailed evaluation is provided for the likelihood statistics intrinsic to interlocking Sequential Bayes analysis, which allows estimation of evidential support for dendrograms charting the macroevolution of taxa. It involves complexity functions, such as fractal evolution, to generate well-supported evolutionary trees. Required are data on trait changes from ancestral species to descendant species, which is facilitated by reduction of large genera to monothetic groups (one ancestral species each), most conveniently named as separate genera. Assigning each species one Shannon informational bit per new trait, then adding the traits as sequential Bayesian analysis (each posterior probability used as the prior for the next iteration of Bayes Formula), then interpretation with an odds chart, provides a posterior probability that the ancestor-descendant order is correct, that is, entirely follows evolutionary theory involving adaptation and rarity of total trait reversals. The key fact is that the most recently acquired traits of the ancestral species are selectively inviolate and passed on without change to each descendant species. The details of sequential Bayesian analysis were clarified by calculation of likelihood ratios and Bayes factors that compare optimal models with the next most likely model. Such analysis demonstrated that the optimum arrangement of ancestor and descendant species leads to high support values for fitting evolutionary theory, comparable to statistical support levels reported for molecular evolutionary trees. The fact that phylogenetic analysis does not offer an ancestor-descendant model in is found to be conducive of precision at the expense of accuracy, and leads to wrong ancestor-free models with likelihoods explaining data at high credible levels. The number of advanced traits in the outgroup as a Bayesian prior greatly enhances posterior probability. The method is simple, free of special computer analysis, and well-suited to standard taxonomic practice.

The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory, and exobiology. Many measures of these quantities, either rely on a statistical notion of information, are difficult to compute, or can only be applied to strings. Based on assembly theory, we propose the notion of a \textit{ladderpath}, which describes how an object can be decomposed into a hierarchical structure using repetitive elements. From the ladderpath two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origins of life. The ladderpath approach provides a novel characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.

Brain-Computer Interface (BCI) systems can assist physically challenged people to interact with their surroundings and improve the quality of their lives. Decoding human thoughts is a powerful technique that can assist paralyzed people who have lost their speech production ability. Speaking is a combined process involving synchronizing the brain and the oral articulators. This paper proposed a high-accuracy brain wave pattern recognition based on inner speech using a novel feature extraction method. Only eight EEG electrodes were used in this study, and they were set on selected spots on the scalp. Support Vector Machine (SVM) was employed to decode the recorded EEG dataset into four internally spoken words which are: Up, Down, Left, and Right. The proposed approach achieved overall classification accuracy that ranges between 96.20% to 97.5%. In addition, more performance evaluation metrics were estimated to test the reliability of classifying the EEG-based inner speech data, and we obtained 97.61%, 97.50%, and 97.73% for F1-score, recall, and precision respectively. Furthermore, the Area Under Curve of the Receiver Operating Characteristic (AUC-ROC) proved the strength of the proposed approach for classifying the specified inner speech commands by achieving a macro-average amount of 99.32%. The inner speech classification method using electroencephalography proposed in this work can clinically help improve communication for patients with problems including speech disorder, mutism, cognitive development, executive function, and psychopathology.

The Rényi entropy functional was optimised for the novel findings of this investigation under various conditions. Their research's findings suggest that the complete spectrum of Lévy stable distributions is covered by generalised t-distributions. Additionally, an exposition was undertaken to prove that the Lévy distribution generalizes Tsallisian distribution, rather than the reverse. The current study is a strong generalization of an existing research work in the literature.

Black hole temperature T_BH = T_P/2πd as a function of its Planck length real diameter multiplier d is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured d = 1/2π describes primordial Big Bang singularity as in this case T_BH = T_P. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -c² if all its vertices have black hole gravitational potential of -c²/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier d. It is shown that black holes feature wave-particle duality only if d ≤ 8π, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.

There are currently around 78 Nuclear Power Plants (NPP) in the world based on Boiling Water Reactors (BWR). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature

Computationally modelling a nuclear reactor startup core for a benchmark against the existing models is highly desirable for an independent assessment informing nuclear engineers and energy policymakers. This work presents a startup core model of the UK’s first Evolutionary Pressurised Water Reactor (EPR) based on Monte Carlo simulations of particle collisions using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup code. Coupling between neutronics and thermal-hydraulic conditions with the fuel depletion is incorporated into the multi-dimensional branches, obtaining the thermal flux and fission rate (power) distributions radially and axially from the three dimensional (3D) single assembly level to a 3D full core. Shannon entropy is employed to characterise the convergence of the fission source distribution, with 3 billion neutron histories tracked by parallel computing. Source biasing is applied for the variance reduction. Benchmarking the proposed Monte Carlo 3D full-core model against the traditional deterministic transport computation suite used by the UK Office for Nuclear Regulation (ONR), a reasonably good agreement within statistics is demonstrated for the safety-related reactivity coefficients, which creates trust in the EPR safety report.