Search

The response of a biological network to ligand binding is of crucial importance for regulatory control in various cellular biophysical processes that is achieved with information transmission through the different ligand-bound states of such networks. In this work, we address a vital issue regarding the link between the information content of such network states and the experimentally measurable binding statistics. Several fundamental networks of cooperative ligand binding, with the bound states being adjacent in time only and in both space and time, are considered for this purpose using the chemical master equation approach. To express the binding characteristics in the language of information, a quantity denoted as differential information index is employed based on the Shannon information. The index, determined for the whole network, follows a linear relationship with (logarithmic) ligand concentration with a slope equal to the size of the system. On the other hand, the variation of Shannon information associated with the individual network states and the logarithmic sensitivity of its slope are shown to have generic forms related to the average binding number and variance, respectively, the latter yielding the Hill slope, the phenomenological measure of cooperativity. Furthermore, the variation of Shannon information entropy, the average of Shannon information, is also shown to be related to the average binding. [ABSTRACT FROM AUTHOR]

Triangular γ -graphyne has a special carbon–carbon bonding arrangement, which results in outstanding electrical characteristics. It is a potential material for semiconductors and conductors in nanoelectronic devices. The number of vertices at a distance of 2 from a vertex is known as the connection number (CN) of that vertex. In this paper, we computed Zagreb-type indices based on connection numbers. In order to give us a better knowledge of the structural properties of molecules or networks, these indices are calculated. Following the computation of these indices, we investigated their use in computing entropy, providing important new information about the thermodynamic characteristics and complexity of the understudied systems. We used Python language to find the Pearson correlation coefficient between indices and entropy and show its heat map. [ABSTRACT FROM AUTHOR]

Chaotic systems are often used as random sequence generators due to their excellent pseudo-randomness, but there is limitation that the discretization of complex chaotic systems requires a long computational time. Therefore, a parallel discretization method for chaotic system, and an accelerated chaotic image secure communication system based on the Zynq-7000 platform are proposed in this paper. Firstly, a 3-dimensional (3-D) chaotic system is constructed to generate random sequence, which has high Shannon entropy (SE) complexity. Then, chaotic system is parallelly discretized through finite state machine, which sequences are combined with scrambling and diffusion algorithms to construct an accelerated chaotic image secure communication system. Finally, the secure communication process based on the Zynq-7000 platform is completed, and the analysis of hardware experimental results shows that the system has safe performances, simple structure and excellent operational efficiency. [ABSTRACT FROM AUTHOR]

In the current age of chemical science, chemical graph theory has significantly advanced our understanding of the characteristics of chemical compounds. To simulate the mathematical, chemical, and physical aspects of networks, a topological index, a numerical measure obtained from the graph of a chemical network, employed. Recent work has explored the topological properties of boron oxide using chemical graph theory. In this work, we conduct a Pearson correlation analysis of boron oxide to assess the correlations between the Van and S indices and entropy metrics. We analyze the Pearson correlation coefficients between the entropy values and the calculated indices using a heatmap. In this article, a significant positive correlation between the Van, and S indices, and entropy values, which is represented by the heatmap of the strong linear correlations. To avoid duplication, a dimensionality reduction technique should be used for highly connected variables. Additionally, this study gives a detailed explanation of the link between the indices and entropy, which will form the basis of further statistical investigations. [ABSTRACT FROM AUTHOR]

The Odd Weibull‐G (OWG) family of distributions has been discussed earlier in the literature. This family of distributions provides a "better fit" in certain practical situations. In a similar fashion, the OWG family of distributions is defined in this article. A method of moments estimator based on the maximum entropy principle is proposed for the discrimination of two members of the OWG family of distributions. [ABSTRACT FROM AUTHOR]

The process of microencapsulation and the development of microparticle-based drug formulations have gained increased pharmaceutical interest, particularly for drug delivery and bacterial-encapsulation purposes for probiotic delivery. Existing studies have examined microcomposite (MC) responses to gastrointestinal (GI) conditions with the aim of controlling disintegration, and thus release, across the small and large bowel. However, the delivery of MCs which remain intact, without degrading, could act as bacterial growth scaffolds or materials providing a prebiotic support, conferring potentially beneficial GI health properties. This present study employs prilling as a method to produce a portfolio of MCs using a variety of biopolymers (alginate, chitosan, pectin and gellan gum) with a range of MC diameters and density compositions. Fluorescent probes are co-encapsulated within each MC to enable flow-cytometry directed release profile assessments following exposure to chemical simulated gastric and intestinal digestion conditions. We observe that MC size, gel-strength, density, and biopolymer material all influence response to gastric and intestinal conditions. Gellan gum (GG) MCs demonstrated complete resistance to disintegration throughout GI-simulation in the stomach and small intestine. Considering these MCs could reach the colon intact, we then examined how such MCs, doped with prebiotic growth supporting carboxymethyl cellulose (CMC) polymers, could impact microbial communities using a bioreactor model of the colonic microbiome. Following supplementation with GGCMC MCs, mucosal bacterial diversity (using 16 s rRNA sequencing and Shannon entropy and observed feature diversity metrics) and taxonomic composition changes were observed. Concentrations of short chain fatty acid (SCFA) metabolites were also found to be altered. This is the first study to comprehensivelyexamine how MC physicochemistry can be manipulated to tailor MCs to have the desired GI release performance and subsequently, how GI-resistant MCs could have influential microbial altering properties and be adopted in novel prebiotic strategies. [Display omitted] • The physicochemistry of hydrogel microcomposites (MCs) are manipulated to tailor gastrointestinal (GI) release. • Commonly used MC formulation materials significantly impacted the intestinal microbiota. • MCs that are inert to GI degradation act as prebiotics. • Carboxymethylcellulose/Gellan Gum MCs improve the growth of beneficial intestinal bacteria. [ABSTRACT FROM AUTHOR]

The investigation of correlations in Monte Carlo power iteration has long been dominated by the question of generational correlations and their effects on the estimation of statistical uncertainties. More recently, there has been a growing interest in spatial correlations, prompted by the discovery of neutron clustering. Despite several attempts, a comprehensive framework concerning how Monte Carlo sampling strategies, population control, and variance reduction methods affect the strength of such correlations is still lacking. In this work, we propose a set of global and local (i.e., space-dependent) tallies that can be used to characterize the impact of correlations. These tallies encompass Shannon entropy, pair distance, normalized variance, and Feynman moment. In order to have a clean yet fully meaningful setting, we carry out our analysis in a few homogeneous and heterogeneous benchmark problems of varying dominance ratio. Several classes of collision sampling strategies, population control, and variance reduction techniques are tested, and their relative advantages and drawbacks are assessed with respect to the proposed tallies. The major finding of our study is that branchless collisions, which suppress the emergence of branches in neutron histories, also considerably reduce the effects of correlations in most of the explored configurations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate several extremal combinatorics problems that ask for the maximum number of copies of a fixed subgraph given the number of edges. We call problems of this type Kruskal–Katona-type problems. Most of the problems that will be discussed in this paper are related to the joints problem. There are two main results in this paper. First, we prove that, in a 3-edge-colored graph with R red, G green, B blue edges, the number of rainbow triangles is at most 2 R G B , which is sharp. Second, we give a generalization of the Kruskal–Katona theorem that implies many other previous generalizations. Both arguments use the entropy method, and the main innovation lies in a more clever argument that improves bounds given by Shearer's inequality. [ABSTRACT FROM AUTHOR]

The enhancing risk from human action and multi‐hazard interaction has substantially complicated the hazard–society relationship. The underlying vulnerabilities are crucial in predicting the probable impact to be caused by multi‐hazards. Thus, the evaluation of social vulnerability is decisive in inferring the driving factor and preparing for mitigation strategies. The Himalayan landscape is prone to multiple hazards as well as possesses a multitude of vulnerabilities owing to changing human landscape. Thus, an attempt has been made to inquire into the underlying socioeconomic factors enhancing the susceptibility of the region to multi‐hazards. The social vulnerability index (SVIent) has been introduced, consisting of 13 indicators and 33 variables. The variables have been standardized using the maximum and minimum normalization method and the relative importance for each indicator has been determined using Shannon entropy methods to compute SVIent. The findings revealed that female population, population above 60 years old, net irrigated area, migrant population, dilapidated house, nonworkers, bank, and nonworkers seeking jobs were found to be relatively significant contributors to the vulnerability. The western part of the study area was classified as the highly vulnerable category (SVI > 0.40628), attributed to high dependence, and higher share of unemployed workers and high poverty. The SVIent was shown to have positive correlation between unemployment, socioeconomic status, migration, dependency, and household structure significant at two‐tailed test. The study's impact can be found in influencing the decision of policymakers and stakeholders in framing the mitigation strategies and policy documents. [ABSTRACT FROM AUTHOR]

In today's highly competitive business environment, firms strive to maximize profitability by minimizing or eliminating disruptions and failures to maintain a competitive edge. This study focuses on evaluating risks in a hydraulic pump factory as a means to achieve sustainable growth. To accomplish this, a team of experts was formed to identify potential errors, utilizing a combination of risk priority number criteria weighted by Fuzzy Shannon's entropy and a fusion of multi‐criteria decision‐making and failure mode and effects analysis for evaluating and ranking failures. Moreover, the study emphasizes the importance of considering the interaction among risk assessment indicators, the inclusion of cost of failure, and modeling under fuzzy uncertainty circumstances, as they have a notable impact on the final ranking of failures to be processed for risk mitigation action planning. This research brings a new dimension to enhance the overall effectiveness of risk assessment by aggregation, as evidenced by a novel use of data classification in machine learning and correlation in statistics. The findings indicate that the aggregated ranking data series is best matched and most influenced by the weighted aggregated sum product assessment method, with the highest rate of recall and precision accomplished. [ABSTRACT FROM AUTHOR]

In this paper, a generalized bivariate Kummer-beta distribution is proposed. The name derives from the fact that its particular cases include univariate Kummer-beta distributions. This distribution generalizes a number of existing bivariate beta distributions, including Nadarajah's bivariate distributions, Libby and Novick's bivariate beta distribution and a central bivariate Kummer-beta distribution. Various properties associated with this newly introduced distribution are derived. The derived properties include product moments, marginal densities, marginal moments, conditional densities, conditional moments, Rényi entropy and Shannon entropy. Motivated by possible applications in economics, genetics, hydrology, meteorology, nuclear physics, and reliability, we also derive distributions of the product and the ratio of the components following the proposed distribution. Parameter estimation by maximum likelihood method is discussed by deriving expressions for score functions. Inference based on maximum likelihood estimation supposes that the maximum likelihood estimators have zero bias and zero mean squared errors. A simulation study is performed to check this for finite samples. [ABSTRACT FROM AUTHOR]

The bound state solutions of the Schrödinger equation (SE) under a deformed hyperbolic potential are used in this paper to investigate the correlation between the information content, such as Shannon entropies and Fisher information, and the variance of a quantum system in both momentum and position spaces. The variance was obtained from the expectation moments in conjugated spaces and used to get the uncertainty products, Fisher information products and Shannon entropic sums for different potential parameters. These information measures were observed to vary with the potential parameters and obey their lowest bound inequalities. An increase in the Fisher information leads to a lower uncertainty and less information while decreases in the Fisher information result in higher uncertainties. We proposed a relationship between the Shannon entropies, Fisher information and the variance where an increase in the Fisher information leads to a lower Shannon entropy or a lower spread of the probability distribution and vice versa. The numerical results obtained with the proposed relations agree with the most utilized method in the literature. This current work simplifies the calculation of the Shannon entropies notably for complex potential functions. [ABSTRACT FROM AUTHOR]

Multi-period portfolio optimization (MPO) is one of the most important problems to be solved to help investors select optimal portfolios for investment plans. The portfolios are influenced by the risk factors in the market and it is important to select optimal portfolios that can maximize the returns with minimum risk values. Other than the risk factor, there are several other influential factors that reduce the optimality of the portfolios. Therefore, by considering all possible constraints, this study proposes a multi-constraint MPO model that selects the optimal portfolio based on the asset returns. To solve the multi-constrained problem, a novel quantum-inspired whale optimization algorithm (QWOA) is introduced in this paper. The proposed algorithm enhances the traditional optimization model to work in a multi-constrained scenario. Here, quantum entanglement is adapted to reduce the slow convergence issue of whale optimization. Apart from considering only the risk factors, this paper also considers certain higher-order moments (HOM), such as skewness, kurtosis, transaction cost, diversification, boundary and budget constraints. These factors affect the portfolios as the market is dynamic, and timely changes are always seen. Thus, optimizing the mentioned factors aids in attaining an optimal portfolio. Empirical evaluations are performed, and the results suggested that the proposed model provided beneficial outcomes as compared with other algorithms like whale optimization algorithm (WOA), gray wolf optimization (GWO), fruitfly optimization algorithm (FOA), particle swarm optimization (PSO) and fruitfly algorithm (FA). The overall net return rate of the proposed model is always above 0.85% for different values of upper bounds, and the obtained Sharpe ratio, Sortino ratio, STARR ratio, information ratio, Shannon entropy, and downside deviation values of the proposed algorithm are 5.016254, 0.89327, − 0.01987, 0.103826, 3.04452 and 0.2854. Hence, the proposed approach is highly effective for optimizing the constrained MPO. [ABSTRACT FROM AUTHOR]

In this study, we examined how the nonlinearity  α  of the Langevin equation influences the behavior of extremes in a generated time series. The extremes, defined according to run theory, result in two types of series, run lengths and surplus magnitudes, whose complex structure was investigated using the visibility graph (VG) method. For both types of series, the information measures of the Shannon entropy measure and Fisher Information Measure were utilized for illustrating the influence of the nonlinearity  α  on the distribution of the degree, which is the main topological parameter describing the graph constructed by the VG method. The main finding of our study was that the Shannon entropy of the degree of the run lengths and the surplus magnitudes of the extremes is mostly influenced by the nonlinearity, which decreases with with an increase in  α. This result suggests that the run lengths and surplus magnitudes of extremes are characterized by a sort of order that increases with increases in nonlinearity. [ABSTRACT FROM AUTHOR]

Background: Archaea and Bacteria are distinct domains of life that are adapted to a variety of ecological niches. Several genome-based methods have been developed for their accurate classification, yet many aspects of the specific genomic features that determine these differences are not fully understood. In this study, we used publicly available whole-genome sequences from bacteria ( N = 2546 ) and archaea ( N = 109 ). From these, a set of genomic features (nucleotide frequencies and proportions, coding sequences (CDS), non-coding, ribosomal and transfer RNA genes (ncRNA, rRNA, tRNA), Chargaff's, topological entropy and Shannon's entropy scores) was extracted and used as input data to develop machine learning models for the classification of archaea and bacteria. Results: The classification accuracy ranged from 0.993 (Random Forest) to 0.998 (Neural Networks). Over the four models, only 11 examples were misclassified, especially those belonging to the minority class (Archaea). From variable importance, tRNA topological and Shannon's entropy, nucleotide frequencies in tRNA, rRNA and ncRNA, CDS, tRNA and rRNA Chargaff's scores have emerged as the top discriminating factors. In particular, tRNA entropy (both topological and Shannon's) was the most important genomic feature for classification, pointing at the complex interactions between the genetic code, tRNAs and the translational machinery. Conclusions: tRNA, rRNA and ncRNA genes emerged as the key genomic elements that underpin the classification of archaea and bacteria. In particular, higher nucleotide diversity was found in tRNA from bacteria compared to archaea. The analysis of the few classification errors reflects the complex phylogenetic relationships between bacteria, archaea and eukaryotes. [ABSTRACT FROM AUTHOR]

In this study, we analyze the changes over time in the complexity and structure of words used in article titles and the connections between articles in citation networks, focusing on the topic of artificial intelligence (AI) up to 2020. By measuring unpredictability in word usage and changes in the connections between articles, we gain insights into shifts in research focus and diversity of themes. Our investigation reveals correspondence between fluctuations in word complexity and changes in the structure of citation networks, highlighting links between thematic evolution and network dynamics. This approach not only enhances our understanding of scientific progress but also may help in anticipating emerging fields and fostering innovation, providing a quantitative lens for studying scientific domains beyond AI. [ABSTRACT FROM AUTHOR]

Effective identification of key nodes in social networks plays an important role in the control and guidance of public opinion. Aiming at the problem of social network public opinion dissemination, a control method based on key node identification is proposed. Firstly, a key node identification method based on dual index Shannon entropy is designed. Considering the importance of nodes in the global network and local network topology, the intermediate number and struc- tural hole constraint coefficient index are used as the information function to construct the node distribution probability, and then the node information entropy is calculated to identify the key nodes in the public opinion dissemination according to the size of the information entropy. Secondly, the effectiveness of the key node identification method is verified through simulation experiments, and the role of the identified key nodes in the public opinion communication is analyzed based on the SIR model. Finally, the control strategy is given. The experimental results show that this method can effectively identify the"bridge"node in the network except the network center node. In the public opinion propagation simulation, the speed and range of public opinion propagation are significantly reduced after adding the control bridge node, and the public opinion control effect is optimal when the number of key nodes is within the range of 2%-3%, and the marginal utility beyond this range is significantly reduced. [ABSTRACT FROM AUTHOR]

The information entropy budget and the rate of information transfer between variables is studied in the context of a nonlinear reduced‐order atmospheric model. The key ingredients of the dynamics are present in this model; namely, the baroclinic instability, the instability related to the presence of an orography, the dissipation related to the surface friction, and the large‐scale meridional imbalance of energy. For the parameters chosen, the solutions of this system display a chaotic dynamics reminiscent of the large‐scale atmospheric dynamics in the extratropics. The detailed information entropy budget analysis of this system reveals that the linear rotation terms play a minor role in the generation of uncertainties compared with the orography and the surface friction. Additionally, the dominant contribution comes from the nonlinear advection terms, and their decomposition in synergetic (covariability) and single (impact of each single variable on the target one) components reveals that for some variables the covariability dominates the information transfer. The estimation of the rate of information transfer based on time series is also discussed, and an extension of the Liang's approach to nonlinear observables is proposed. [ABSTRACT FROM AUTHOR]

In this work, we investigate different timescales of chaotic dynamics in a multi-parametric 4D symplectic map. We compute the Lyapunov time and a macroscopic timescale, the instability time, for a wide range of values of the system's parameters and many different ensembles of initial conditions in resonant domains. The instability time is obtained by plain numerical simulations and by its estimates from the diffusion time, which we derive in three different ways: through a normal and an anomalous diffusion law and by the Shannon entropy, whose formulation is briefly revisited. A discussion about which of the four approaches provide reliable values of the timescale for a macroscopic instability is addressed. The relationship between the Lyapunov time and the instability time is revisited and studied for this particular system where in some cases, an exponential or polynomial law has been observed. The main conclusion of the present research is that only when the dynamical system behaves as a nearly ergodic one such relationship arises and the Lyapunov and instability times are global timescales, independent of the position in phase space. When stability regions prevent the free diffusion, no correlations between both timescales are observed, they are local and depend on both the position in phase space and the perturbation strength. In any case, the instability time largely exceeds the Lyapunov time. Thus, when the system is far from nearly ergodic, the timescale for predictable dynamics is given by the instability time, being the Lyapunov time its lower bound. [ABSTRACT FROM AUTHOR]

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 nonparametric 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. [ABSTRACT FROM AUTHOR]

In the past two decades, research in the field of chaotic synchronization has attracted extensive attention from scholars, and at the same time, more synchronization methods, such as chaotic master–slave synchronization, projection synchronization, sliding film synchronization, fractional-order synchronization and so on, have been proposed and applied to chaotic secure communication. In this paper, based on radial basis function neural network theory and the particle swarm optimisation algorithm, the RBFNN-PSO synchronisation method is proposed for the Sprott B chaotic system with external noise. The RBFNN controller is constructed, and its parameters are used as the particle swarm particle optimisation parameters, and the optimal values of the controller parameters are obtained by the PSO training method, which overcomes the influence of external noise and achieves the synchronisation of the master–slave system. Then, it is shown by numerical simulation and analysis that the scheme has a good performance against external noise. Because the Sprott B system has multiple chaotic attractors with richer dynamics, the synchronization system based on Sprott B chaos is applied to the image encryption system. In particular, the Zigzag disambiguation method for top corner rotation and RGB channel selection is proposed, and the master–slave chaotic system synchronisation sequences are diffused to the disambiguated data streams, respectively. Therefore, the encryption and decryption of image transmission are implemented and the numerical simulation results are given, the random distribution characteristics of encrypted images are analysed using histogram and Shannon entropy methods, and the final results achieve the expected results. [ABSTRACT FROM AUTHOR]

Higher-order relationships are a central concept in the science of complex systems. A popular method of attempting to estimate the higher-order relationships of synergy and redundancy from data is through the O-information. It is an information–theoretic measure composed of Shannon entropy terms that quantifies the balance between redundancy and synergy in a system. However, bias is not yet taken into account in the estimation of the O-information of discrete variables. In this paper, we explain where this bias comes from and explore it for fully synergistic, fully redundant, and fully independent simulated systems of n = 3 variables. Specifically, we explore how the sample size and number of bins affect the bias in the O-information estimation. The main finding is that the O-information of independent systems is severely biased towards synergy if the sample size is smaller than the number of jointly possible observations. This could mean that triplets identified as highly synergistic may in fact be close to independent. A bias approximation based on the Miller–Maddow method is derived for the O-information. We find that for systems of n = 3 variables the bias approximation can partially correct for the bias. However, simulations of fully independent systems are still required as null models to provide a benchmark of the bias of the O-information. [ABSTRACT FROM AUTHOR]

The processes involved in encoding and decoding signals in the human brain are a continually studied topic, as neuronal information flow involves complex nonlinear dynamics. This study examines awake human intracranial electroencephalography (iEEG) data from normal brain regions to explore how biological sex influences these dynamics. The iEEG data were analyzed using permutation entropy and statistical complexity in the time domain and power spectrum calculations in the frequency domain. The Bandt and Pompe method was used to assess time series causality by associating probability distributions based on ordinal patterns with the signals. Due to the invasive nature of data acquisition, the study encountered limitations such as small sample sizes and potential sources of error. Nevertheless, the high spatial resolution of iEEG allows detailed analysis and comparison of specific brain regions. The results reveal differences between sexes in brain regions, observed through power spectrum, entropy, and complexity analyses. Significant differences were found in the left supramarginal gyrus, posterior cingulate, supplementary motor cortex, middle temporal gyrus, and right superior temporal gyrus. This study emphasizes the importance of considering sex as a biological variable in brain dynamics research, which is essential for improving the diagnosis and treatment of neurological and psychiatric disorders. [ABSTRACT FROM AUTHOR]

Entropy measures are fundamental tool in information theory and various areas of sciences. We establish various lower bounds to the cumulative residual entropy and cumulative entropy based on Gini's mean difference. Applying new results on upper bounds in Balakrishnan, Buono, and Longobardi (2022), we obtain sharper upper bounds for the cumulative residual entropy and cumulative entropy. New generalized cumulative residual entropy and cumulative entropy are also proposed. [ABSTRACT FROM AUTHOR]

This study aims to investigate the impact of spatio-temporal dynamics of urban sprawl on habitats in Istanbul, using the CORINE 1990 and 2018 land cover datasets. In this context, by means of geographic information system (GIS) tools and techniques, land cover maps are created for land cover change analysis and visualization, the Shannon's entropy method is performed for measuring urban growth and sprawl, and the landscape metrics method is applied for assessing habitat loss and fragmentation. Results indicate that the rate of urban sprawl in the area increased by 0.1230 as per the Shannon's entropy index over the 28-year period. Similarly, the Shannon Diversity Index and the Shannon Evenness Index rose from 1.74 to 1.85 and from 0.68 to 0.70, respectively, indicating an increase in urbanization within the area. Moreover, an analysis of patch numbers reveals that habitat fragmentation increased in shrub and/or herbaceous vegetation associations (72.55%), heterogeneous agricultural areas (45.11%), arable lands (42.5%), forests (36.13%) and pastures (15.05%), due to urbanization. Habitat fragmentation has had a detrimental effect on the local biodiversity. While 15 flora species were identified as vulnerable, 13 as endangered and 9 as critically endangered, 19 fauna species were identified as vulnerable and 5 as endangered. This study highlights that the natural habitats and biodiversity of Istanbul will suffer further decline due to urbanization unless sustainable urban planning and management policies are put into practice. It is essential to have controlled urban development to preserve the ecosystem's carrying capacity, and urbanization decisions must consider this requirement. [ABSTRACT FROM AUTHOR]

Most cities in the world suffer from excessive population and unplanned urban growth. The objective of the present study was to investigate the spatiotemporal changes of built-up areas and their growth in the proposed Greater Silchar City (GSC) (Assam, India). The obtained LANDSAT satellite data from 1991 to 2021 for the GSC have divided into non-built-up and built-up land use categories, and recode tools in Erdas Imagine 2014 software have been used to improve the accuracy of the output. The study area has been classified into 8 spatial directions and 11 concentric circles with radial distances of 1 km and resulted from intersected areas consisting of 60 gradient zones. The study used Shannon entropy model for detailed urban sprawl study of every nook and corner. FRAGSTATS v4.2 tools have been used to analyse landscape metrics in respective spatial directions. The built-up area growth of the city was 15.18 km2 during the mentioned period. The landscape metrics and LU/LC results show the maximum built-up growth has taken place in South to South-West direction (3243.87 ha) and the area within a 2–3-km radius (221.85 ha) of the central business district, which is the periphery of the existing Silchar municipal limits. The entropy values indicated that the GSC has compacted infill growth form in the core area, while the dispersed urban sprawl trends followed with increasing distance from the city centre. Moreover, the research findings will provide a conceptual model for assessing urban growth trends for other cities as well. [ABSTRACT FROM AUTHOR]

In response to the increasing demand for an intelligent system to avoid abnormal events, many models for detecting and locating anomalous behaviors in surveillance videos have been proposed. Nevertheless, significant flaws of inadequate discriminating ability are present in the majority of these models. A novel newton form and monotonic function based deep bidirectional long short-term memory (NFMF-DBiLSTM) human anomaly recognition system was discussed in this paper to tackle those issues. Initially, videos are transformed into frames; after that, the duplicate frames are removed, and by utilizing the shannon entropy centered contrast limited adaptive histogram equalization (SE-CLAHE) algorithm, the contrast has been elevated. By using the probabilistic matrix factorization kernel density estimation (PMF-KDE) technique, the background is subtracted after estimating only the motion of the object. After this, the silhouette function is performed utilizing the dirac depth silhouette function (DDSF). In addition, clustering is done by sorting and average-based K-means (SA-KM). The features are extracted from the suspected human and are then chosen by utilizing Poisson Eurasian oystercatcher optimization (PEOO). For classifying normal or anomaly, the selected features are subjected directly into the NFMF-DBiLSTM. When contrasted with the prevailing methodologies, the proposed model is found to be more efficient. [ABSTRACT FROM AUTHOR]

Industry 4.0 represents a shift from centralized to decentralized production, involving cyber-physical systems. This transformation aims to reduce costs and waste by implementing timely preventive measures. This study proposes an optimized model for production processes in cellular manufacturing systems of Industry 4.0. For this purpose, a combination of failure mode and effects analysis (FMEA) method, prospect theory (PT), and Shannon entropy is used. The critical failure modes are identified through comparison with reference points. Shannon entropy is used to determine the importance of each risk factor in the FMEA method. By calculating the utility value through the prospect method, critical failure modes are prioritized. Thus, FM7 and FM14 are assigned the first and second priority, respectively. To validate the proposed method, its efficiency is evaluated in an auto parts manufacturing plant. The proposed framework helps managers to improve the effectiveness of the risk analysis and control factors and impact of failure modes. On the other hand, it makes to increase safety and reliability levels in production systems. [ABSTRACT FROM AUTHOR]

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate 'estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data. [ABSTRACT FROM AUTHOR]

Patterned polarizers are prepared using liquid crystals (LC) doped with a black dichroic dye and in combination with a linear polarizer. The pattern is achieved with a nanostructured LC alignment surface, that is generated using a two-photon polymerization direct laser write (2PP-DLW). This technique creates a pattern of high-resolution grooves in the photoresist at any arbitrary angle. The angle governs the LC orientation at any substrate surface point, determining the transmitted light linear polarization angle. This paper presents the first use of a 2PP-DLW cured positive tone photoresist for dichroic dye-doped LC alignment. Two complementary photoresists have been employed: conventional negative tone SU-8 photoresist and, in this context novel, positive tone S1805 photoresist. The alignment quality of the polarizers has been assessed by analyzing the transmission using an additional polarizer. For SU-8, the resulting grayscale pattern and a contrast ratio (CR) of 14 has measured. The uniformity of the alignment has been measured to be 65% using normalized Shannon entropy (H). For S1805, a CR of 37 was measured, and a uniformity of 63% was obtained. 2PP-DLW allows for shaping complex patterns in submicron dimensions and for the fabrication of arbitrarily patterned polarizers and other LC devices. [ABSTRACT FROM AUTHOR]

Background: Noncommunicable diseases (NCDs) predominantly affect adults, but pathophysiological changes begin decades earlier, as a continuum, with initial events apparent in adolescence. Hence, early identification and intervention are crucial for the prevention and management of NCDs. We investigated the complex network of socioeconomic, behavioral, and metabolic factors associated with the presence of NCD in Brazilian adolescents. Methods: We conducted a cross-sectional study nested within the São Luís segment of the Ribeirão Preto, Pelotas, and São Luís (RPS) cohort's consortium, focusing on 18–19-year-olds (n = 2515). Data were collected prospectively, from which we constructed a complex network with NCD-related factors/indicators as nodes and their co-occurrences as edges. General and sex-based models analyzed: socioeconomic status, behavioral (smoking, alcohol, and other drugs use, unhealthy diet, poor sleep, physical inactivity), and metabolic factors (overweight/obesity, elevated blood pressure, poor lipid profile). We also looked for NCDs in adolescence like asthma, abnormal spirometry, depression, suicide risk, and poor oral health. The network was characterized by degree, betweenness, eigenvector, local transitivity, Shannon entropy, and cluster coefficient. Results: The adolescents had an average age of 18.3 years, 52.3% were female and 47.7% male. 99.8% of them have a diet rich in free sugars, 15% are overweight/obese and 72.3% had an elevated TyG index. High free sugar emerged as the central hub, followed by high TyG index (an early marker of insulin resistance) and low socioeconomic class. In males, low fiber intake and a high triglycerides/HDL ratio highlighted cardiometabolic concerns; in females, sedentary behavior and poor sleep marked metabolic and psychological challenges, along with caries in both sexes. Conclusions: Our findings provide insights into central health challenges during adolescence, such as high free sugars, insulin resistance, and low socioeconomic indicators, suggesting that interventions targeted at these central hubs could have a significant impact on their NCD network. [ABSTRACT FROM AUTHOR]

Strongly convex functions as a subclass of convex functions, still equipped with stronger properties, are employed through several generalizations and improvements of the Jensen inequality and the Jensen–Mercer inequality. This paper additionally provides applications of obtained main results in the form of new estimates for so-called strong f-divergences: the concept of the Csiszár f-divergence for strongly convex functions f, together with particular cases (Kullback–Leibler divergence, χ 2 -divergence, Hellinger divergence, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence.) Furthermore, new estimates for the Shannon entropy are obtained, and new Chebyshev-type inequalities are derived. [ABSTRACT FROM AUTHOR]

The epidemic and outbreaks of influenza B Victoria lineage (Bv) during 2019–2022 led to an analysis of genetic, epitopes, charged amino acids and Bv outbreaks. Based on the National Influenza Surveillance Network (NISN), the Bv 72 strains isolated during 2019–2022 were selected by spatio-temporal sampling, then were sequenced. Using the Compare Means, Correlate and Cluster, the outbreak data were analyzed, including the single nucleotide variant (SNV), amino acid (AA), epitope, evolutionary rate (ER), Shannon entropy value (SV), charged amino acid and outbreak. With the emergence of COVID-19, the non-pharmaceutical interventions (NPIs) made Less distant transmission and only Bv outbreak. The 2021–2022 strains in the HA genes were located in the same subset, but were distinct from the 2019–2020 strains (P < 0.001). The codon G → A transition in nucleotide was in the highest ratio but the transversion of C → A and T → A made the most significant contribution to the outbreaks, while the increase in amino acid mutations characterized by polar, acidic and basic signatures played a key role in the Bv epidemic in 2021–2022. Both ER and SV were positively correlated in HA genes (R = 0.690) and NA genes (R = 0.711), respectively, however, the number of mutations in the HA genes was 1.59 times higher than that of the NA gene (2.15/1.36) from the beginning of 2020 to 2022. The positively selective sites 174, 199, 214 and 563 in HA genes and the sites 73 and 384 in NA genes were evolutionarily selected in the 2021–2022 influenza outbreaks. Overall, the prevalent factors related to 2021–2022 influenza outbreaks included epidemic timing, Tv, Ts, Tv/Ts, P137 (B → P), P148 (B → P), P199 (P → A), P212 (P → A), P214 (H → P) and P563 (B → P). The preference of amino acid mutations for charge/pH could influence the epidemic/outbreak trends of infectious diseases. Here was a good model of the evolution of infectious disease pathogens. This study, on account of further exploration of virology, genetics, bioinformatics and outbreak information, might facilitate further understanding of their deep interaction mechanisms in the spread of infectious diseases. [ABSTRACT FROM AUTHOR]

The general connectivity indices (including the general Randić index, the general sum-connectivity index, the general ABC index and the general ABS index) are an important degree-based topological index in chemical informatics. In this paper, the general connectivity entropies of a graph are defined as the Shannon's entropy based on the information functional that associates the general connectivity indices. We compute the general connectivity entropies for certain interconnection networks like butterfly networks, Benes networks, and mesh derived networks, which can be helpful to understand their underlying topologies and structural complexity. [ABSTRACT FROM AUTHOR]

Climatic change over the globe due to global warming affects the characteristics of climate variables that have critical implications on large fraction of population that depends on agriculture for livelihood like Pakistan. Consequently, this study examined how high horizontal grid resolution CMIP6 models simulate the observed precipitation variability during 1981–2014 and further explored the future changes during 2017–2050 under high emission scenario SSP5‐8.5 over Pakistan region. The performances of 12 (CMIP6) High Resolution Model Inter‐comparison Project version 1.0 (hereafter; HighResMIP) GCMs and their ensemble means in reproducing the observed climate were calculated at each station in the study domain and formed the basis for deriving HighResMIP ranking. Further, the study employed Shannon's Entropy and a modified version of Criteria Importance through Inter‐Criteria Correlation (D‐CRITIC) method to build an ensemble mean from the best performing models. Evaluation of HighResMIP GCMs performance revealed that most models showed mixed signals in the region, with fewer models such as HadGEM3‐GC31‐HH, HadGEM3‐GC31‐HM and HadGEM3‐GC31‐MM showing good agreement with the observed precipitation. Overall, HighResMIP multi‐model ensemble outperforms precipitation distribution over individual models. D‐CRITIC based ensemble mean implies higher increase in precipitation than entropy approach. Future changes depict an increase in mean annual in the northern region relative to the historical period. A pronounced increase of about 16%–18% in precipitation was noted in HadGEM3‐GC31‐HH and HiRAM‐SIT‐HR. Conversely, FGOAL‐f3‐H project noteworthy reduction (21%) in precipitation in the near future (2017–2050). The projected seasonal precipitation shows upsurge pattern of 5%–28% in pre‐monsoon season, whereas the reduction in monsoon precipitation is projected to be 29%–40%. The findings of this study can help in building future climate resilience and developing strategic policies in Pakistan. [ABSTRACT FROM AUTHOR]

The article considers the available methods of image recognition of continuous wavelet spectra of noisy signals with linear and nonlinear frequency modulations using convolutional neural networks. A procedure is proposed for preparing spectral images for their processing in a neural network, ensuring a sufficient probability of recognizing a given type of signal out of twenty possible ones. The methodology for solving the problem finds an image preparation algorithm that provides image augmentation by changing continuous wavelets, which ensures the identification of signals under conditions of limited resonance frequency and bandwidth. The algorithm changes the frequency of the continuous spectrum by processing the phase grating signal with different continuous wavelets after adding non-stationary noise. Signals with linear and nonlinear modulation prepared in this way, as well as signal spectra of other regular forms, are used as input data of the convolutional neural network. The procedure of dividing images of wavelet spectra into classes is performed by checking the homogeneity of the class based on the Shannon entropy value. The minimum entropy value indicates the homogeneity of the subset and the absence of "impurities" from images of other classes. The developed model of a neural network with augmentation by continuous wavelet spectra under the conditions of a limited data set has an accuracy of up to 97.95%. [ABSTRACT FROM AUTHOR]

Gini entropy is a simplification of Shannon entropy. Due to the convenience of calculation, Gini entropy is often used in engineering calculations. Recently, the extropy proposed by Lad et al. has been widely studied. As a special kind of entropy, extropy provides a new perspective to measure uncertainty. This article proposes Gini eXtropy and maximum Gini eXtropy. Gini eXtropy and Gini entropy have a multiple relationship, the former is always smaller than the latter. In addition, the relationship between Gini extropy and other entropies is also studied. When the probability is uniformly distributed, Gini eXtropy reaches the maximum value, and the limit of the maximum value is 1. The convergence speed of the maximum Gini eXtropy is slower than the maximum Gini entropy and the maximum extropy. [ABSTRACT FROM AUTHOR]

This research assesses Herat City's urban ecological degradation in 2000, 2013, and 2021 using Landsat and MODIS data. A Mean Remote Sensing Ecological Index (MRESI) is developed by integrating Known Granulation Entropy (KGE) and COmprehensive Distance-Based RAnking (COBRA) algorithms. Five ecological elements are considered: humidity, greenness, heat, dryness, and AOD. MRESI declined from 0.4544 to 0.4100, indicating deteriorating urban ecological quality. Spatial degradation increased from six to nine districts. MRSEI identified as the most representative indicator, effectively reflecting the urban ecological quality of Herat city. This approach offers an effective and economical method for managing urban development and spatial control. [ABSTRACT FROM AUTHOR]

Tsallis entropy has been widely used in image thresholding because of its non-extensive properties. The non-extensive parameter q contained in this entropy plays an important role in various adaptive algorithms and has been successfully applied in bi-level image thresholding. In this paper, the relationships between parameter q and pixels' long-range correlations have been further studied within multi-threshold image segmentation. It is found that the pixels' correlations are remarkable and stable for images generated by a known physical principle, such as infrared images, medical CT images, and color satellite remote sensing images. The corresponding non-extensive parameter q can be evaluated by using the self-adaptive Tsallis entropy algorithm. The results of this algorithm are compared with those of the Shannon entropy algorithm and the original Tsallis entropy algorithm in terms of quantitative image quality evaluation metrics PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity). Furthermore, we observed that for image series with the same background, the q values determined by the adaptive algorithm are consistently kept in a narrow range. Therefore, similar or identical scenes during imaging would produce similar strength of long-range correlations, which provides potential applications for unsupervised image processing. [ABSTRACT FROM AUTHOR]

Brushed DC motors and generators (DCMs) are extensively used in various industrial applications, including the automotive industry, where they are critical for electric vehicles (EVs) due to their high torque, power, and efficiency. Despite their advantages, DCMs are prone to premature failure due to sparking between brushes and commutators, which can lead to significant economic losses. This study proposes two approaches for determining the temporal and frequency evolution of Shannon entropy in armature current and stray flux signals. One approach indirectly achieves this through prior analysis using the Short-Time Fourier Transform (STFT), while the other applies the Stockwell Transform (S-Transform) directly. Experimental results show that increased sparking activity generates significant low-frequency harmonics, which are more pronounced compared to mid and high-frequency ranges, leading to a substantial rise in system entropy. This finding enables the introduction of fault-severity indicators or Key Performance Indicators (KPIs) that relate the current condition of commutation quality to a baseline established under healthy conditions. The proposed technique can be used as a predictive maintenance tool to detect and assess sparking phenomena in DCMs, providing early warnings of component failure and performance degradation, thereby enhancing the reliability and availability of these machines. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to assess the efficiency of climate change competitiveness via a case study on EU regions by using the data envelopment analysis (DEA) model and Shannon entropy. First, on the same premise as similar composite indicators, we develop a DEA model to assess the relative performance of the regions in climate change competitiveness. Then, we extend our calculations with a DEA-like model and Shannon entropy to derive global estimates of a new competitiveness index by using common weights. Results show that the proposed DEA-Entropy model enables the construction of a regional climate change competitiveness index among all regions via a set of common weights. The proposed model's common weight structure demonstrates more discriminative power compared to the weights obtained through pure DEA or DEA-like methods. In order to validate the proposed DEA-Entropy model, it was applied to 120 EU regions. The results are meaningful for the regions to improve their competitiveness. [ABSTRACT FROM AUTHOR]

Background Bacterial RNA polymerase (RNAP) is a promising target for antimicrobial chemotherapy due to its indispensable role in bacterial growth and survival. Among its components, only the rpoB gene encoding the β-subunit is known for its association with rifampicin resistance. We recently identified a variant of the RNAP α-subunit (RpoA) in Pseudomonas aeruginosa, conferring heightened bacterial susceptibility to antimicrobials. This susceptibility was attributed to the specific down-regulation of the MexEF-OprN efflux pump. Objectives We asked how to distinguish antimicrobial-susceptible variant strains from clinical isolates. Methods In this study, we identified various P. aeruginosa RpoA variants from clinical sources. Using the sequence alignment of different bacterial RpoA species, we computed the positional conservation of substitutions in RpoA variants using Shannon Entropy. Results Our findings revealed that selective RpoA variant strains exhibited distinct profiles of antimicrobial susceptibility. Notably, RpoA variant strains, containing single-substitutions in the C-terminal domain (α-CTD) but not the N-terminal domain (α-NTD), showed attenuated MexEF-OprN expression and increased susceptibility to MexEF-OprN-specific antibiotics. Furthermore, we observed a close correlation between the susceptibility of these α-CTD RpoA variant strains to antibiotics and the conservation degrees of positional substitutions. Conclusions Our findings demonstrate the prevalence of antimicrobial-susceptible RpoA variant strains among P. aeruginosa clinical isolates. The identified positional conservation pattern in our study facilitates the rapid classification of RpoA variant strains with distinct drug resistances. Given the high conservation of RNAP across bacterial species, our findings open a new therapeutic perspective for precisely and efficiently combating pathogenic RpoA variant strains with specific antimicrobials. [ABSTRACT FROM AUTHOR]

In system reliability, coherent systems play a central role since without them any system is considered flawed. A system is coherent if all the components are relevant to that system i.e. functioning of every component has an effect in the functioning of the system and the structure of the system is monotone. Monotone structure means that improving any component will not deteriorate the system. A mixed system is a stochastic mixture of coherent systems and any coherent system is a special case of a mixed system. In reliability engineering, one major problem is to compare various coherent and mixed systems so that the better system can be used to increase the overall reliability. Another important problem is to measure the complexity of systems. A highly complex system will naturally have a higher running and maintenance cost associated with it and it is desirable for a reliability engineer to have an understanding regarding the complexity of systems beforehand. In this paper, we address these two problems from an information theoretic approach. Extropy is a measure of information which is the dual of the famous Shannon entropy measure. Recently, a new measure related to extropy, called cumulative residual extropy (CREx), was introduced in the literature by Jahanshahi et al. (Probab Eng Inf Sci 1–21, 2019). This measure is based on the survival function of the underlying random variable and it has some advantages over extropy measure. In this work, we analyze the CREx measure for coherent and mixed systems and develop some comparison results among systems. We also obtain some bounds of CREx of coherent and mixed systems consisting of independent and identically distributed (iid) and dependent and identically distributed (d.i.d.) components. We propose a new divergence measure to calculate the complexity of systems having iid components. Also, we introduced a new discrimination measure to compare various coherent and mixed systems when pairwise comparisons by usual stochastic order is not possible. Finally, we discuss analysis of the CREx measure of coherent systems having heterogeneous components. We also provide applications involving redundancy allocation. Various numerical examples are considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

We establish a novel family of Kumaraswamy-X probability distributions in the present investigation. We discussed the KumaraswamyExponential univariate probability distribution. The new distribution with three parameters possesses density function with unimodal and reverse J-shape and hazard rate function of bathtub shaped. We study various statistical properties for it and derive the expressions for its density function, distribution function, survival and hazard rate function, Probability weighted Moments, lth moment, moment generating function, quantile function and Shannon entropy. For the derived distribution order statistics is also discussed. The parameters are estimated using the maximum likelihood estimation approach, and the performance of the estimators was evaluated using a Monte Carlo simulation. Through extensive Monte Carlo simulations and comparative analyses, we assess the performance of the Kumaraswamy-X distribution against other common probability distributions used in engineering contexts. When we apply it to real datasets, it offers a more suitable fit than other existing distributions. We explore the characteristics and potential applications of the Kumaraswamy-X distribution in the context of engineering problems through a comprehensive simulation-based investigation. [ABSTRACT FROM AUTHOR]

The common goal for investors is to minimise the risk and maximise the returns on their investments. This is often achieved through diversification, where investors spread their investments across various assets. This study aims to use the MAD-entropy model to minimise the absolute deviation, maximise the mean return, and maximise the Shannon entropy of the portfolio. The MAD model is used because it is a linear programming model, allowing it to resolve large-scale problems and nonnormally distributed data. Entropy is added to the MAD model because it can better diversify the weight of assets in the portfolios. The analysed portfolios consist of cryptocurrencies, stablecoins, and selected world indices such as the SP500 and FTSE obtained from Yahoo Finance. The models found that stablecoins pegged to the US dollar, followed by stablecoins pegged to gold, are better diversifiers for traditional cryptocurrencies and stocks. These results are probably due to their low volatility compared to the other assets. Findings from this study may assist investors since the MAD-Entropy model outperforms the MAD model by providing more significant portfolio mean returns with minimal risk. Therefore, crypto investors can design a well-diversified portfolio using MAD entropy to reduce unsystematic risk. Further research integrating mad entropy with machine learning techniques may improve accuracy and risk management. [ABSTRACT FROM AUTHOR]

The pacing of a marathon is arguably the most challenging aspect for runners, particularly in avoiding a sudden decline in speed, or what is colloquially termed a "wall", occurring at approximately the 30 km mark. To gain further insight into the potential for optimizing self-paced marathon performance through the coding of comprehensive physiological data, this study investigates the complex physiological responses and pacing strategies during a marathon, with a focus on the application of Shannon entropy and principal component analysis (PCA) to quantify the variability and unpredictability of key cardiorespiratory measures. Nine recreational marathon runners were monitored throughout the marathon race, with continuous measurements of oxygen uptake ( V ˙ O2), carbon dioxide output ( V ˙ CO2), tidal volume (Vt), heart rate, respiratory frequency (Rf), and running speed. The PCA revealed that the entropy variance of V ˙ O2, V ˙ CO2, and Vt were captured along the F1 axis, while cadence and heart rate variances were primarily captured along the F2 axis. Notably, when distance and physiological responses were projected simultaneously on the PCA correlation circle, the first 26 km of the race were positioned on the same side of the F1 axis as the metabolic responses, whereas the final kilometers were distributed on the opposite side, indicating a shift in physiological state as fatigue set in. The separation of heart rate and cadence entropy variances from the metabolic parameters suggests that these responses are independent of distance, contrasting with the linear increase in heart rate and decrease in cadence typically observed. Additionally, Agglomerative Hierarchical Clustering further categorized runners' physiological responses, revealing distinct clusters of entropy profiles. The analysis identified two to four classes of responses, representing different phases of the marathon for individual runners, with some clusters clearly distinguishing the beginning, middle, and end of the race. This variability emphasizes the personalized nature of physiological responses and pacing strategies, reinforcing the need for individualized approaches. These findings offer practical applications for optimizing pacing strategies, suggesting that real-time monitoring of entropy could enhance marathon performance by providing insights into a runner's physiological state and helping to prevent the onset of hitting the wall. [ABSTRACT FROM AUTHOR]

Machine learning (ML) and artificial intelligence (AI) have emerged as the most advanced technologies today for solving issues as well as assessing and forecasting occurrences. The use of AI and ML in various organizations seeks to capitalize on the benefits of vast amounts of data based on scientific approaches, notably machine learning, which may identify patterns of decision-making and minimize the need for human intervention. The purpose of this research work is to develop a suitable neural network model, which is a component of AI and ML, to assess and forecast crack propagation in a bearing with a seeded crack. The bearing was continually run for many hours, and data were retrieved at time intervals that might be utilized to forecast crack growth. The variables root mean square (RMS), crest factor, signal-to-noise ratio (SNR), skewness, kurtosis, and Shannon entropy were collected from the continuously running bearing and utilized as input parameters, with the total crack area and crack width regarded as output parameters. Finally, utilizing several methodologies of the Neural Network tool in MATLAB, a realistic ANN model was trained to predict the crack area and crack width. It was observed that the ANN model performed admirably in predicting data with a better degree of accuracy. Through analysis, it was observed that the SNR was the most relevant parameter in anticipating data in bearing crack propagation, with an accuracy rate of 99.2% when evaluated as a single parameter, whereas in multiple parameter analysis, a combination of kurtosis and Shannon entropy gave a 99.39% accuracy rate. [ABSTRACT FROM AUTHOR]

The paper considers the existing methods of image recognition of continuous wavelet spectra of noisy signals with linear and nonlinear frequency modulation using convolutional neural networks. A procedure for preparing spectral images for processing in a neural network is proposed, which ensures a sufficient probability of recognizing a given type of signal out of twenty possible ones. The methodology for solving the problem consists of finding an image preparation algorithm that provides image augmentation by the method of changing continuous wavelets, which ensures the identification of signals under conditions of limited resonance frequency and bandwidth. The algorithm involves changing the frequency of the continuous spectrum by processing the phase grating signal with different continuous wavelets after the additive addition of non-stationary noise. Signals with linear and nonlinear modulation prepared in this way, as well as signal spectra of other regular forms, are used as input data of the convolutional neural network. The procedure of dividing wavelet spectrum images into classes is performed by checking the homogeneity of the class based on the Shannon entropy value. The minimum entropy value indicates the homogeneity of the subset and the absence of “impurities” from images of other classes. The developed model of a neural network with augmentation by continuous wavelet spectra in the conditions of a limited data set has an accuracy of up to 97.95%. [ABSTRACT FROM AUTHOR]

Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis entropy, CRTE, and an alternative measure of CRTE of order η. Applications of these results are given for order statistics and record values with uniform, exponential, and power marginals distributions. In addition, the empirical cumulative Tsallis entropy is suggested as a method to calculate the new information measure. Finally, a real-world data set has been analyzed for illustrative purposes, and the performance is quite satisfactory [ABSTRACT FROM AUTHOR]

Cortical neurons integrate upstream signals and random electrical noise to gate signaling outcomes, leading to statistically random patterns of activity. Yet classically, the neuron is modeled as a binary computational unit, encoding Shannon entropy. Here, the neuronal membrane potential is modeled as a function of inherently probabilistic ion behavior. In this new model, each neuron computes the probability of transitioning from an off-state to an on-state, thereby encoding von Neumann entropy. Component pure states are integrated into a physical quantity of information, and the derivative of this high-dimensional probability distribution yields eigenvalues across the multi-scale quantum system. In accordance with the Hellman–Feynman theorem, the resolution of the system state is paired with a spontaneous shift in charge distribution, so this defined system state instantly becomes the past as a new probability distribution emerges. This mechanistic model produces testable predictions regarding the wavelength of free energy released upon information compression and the temporal relationship of these events to physiological outcomes. Overall, this model demonstrates how cortical neurons might achieve non-deterministic signaling outcomes through a computational process of noisy coincidence detection. [ABSTRACT FROM AUTHOR]