The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

Two well-known drawbacks in fuzzy clustering are the requirement of assign in advance the number of clusters and random initialization of cluster centers.; the quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of FCM using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.

The study of the change in entropy during the formation of stars in collapsing molecular clouds is an important area of research in astrophysics. As the cloud decreases in size, the presence of gases leads to an increase in entropy. However, the extent of this change in entropy is influenced by the amount of space available for the gases. In this scientific investigation, I conduct a detailed analysis of entropy on a small scale within the contracting cloud, following the principles of the second law of thermodynamics. Initially, my focus is on a turbulent cloud composed of N particles with a mass of M, which collapses under the force of gravity. It becomes clear that in order for the collapse to occur, gravitational energy must overcome other pressure forces that oppose it. This process results in the rapid movement of particles within the cloud, ultimately leading to a change in entropy

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.

Generalisation from the local 4-dimensional spacetime form for a proper time interval provides an alternative basis for a unified theory contrasting with the more familiar approach of appending extra dimensions of space. In both cases the main goal is to derive a structure of matter that accounts for empirical observations from the properties of the additional components. Previous work has focussed upon the direct and significant connections that this new approach makes with the Standard Model of particle physics while also providing a link with dark matter models. In this paper we elaborate on how a further sector of generalised proper time, incorporating the key component of negative pressure, can account for the apparent dark energy fuelling the accelerating large-scale expansion of the universe. Through comparison with existing dark energy models we elucidate the elementary composition of this sector, its potential relation to an effective cosmological constant term, and the nature of possible interaction with the visible and dark matter sectors.

In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals. We begin with an overview of Husserlian phenomenology, focusing on aspects of inner time consciousness, namely, retention, primal impression, and protention. We then review active inference as a formal approach to modeling agent behavior, based on variational (approximate Bayesian) inference. Expanding upon Husserl’s model of time consciousness, we consider collective goal-directed behavior, emphasizing shared protentions among agents and their connection to the shared generative models of active inference. This integrated framework aims to formalize shared goals in terms of shared protentions, and to thereby shed light on the emergence of group intentionality. Building on this foundation, we incorporate mathematical tools from category theory; particularly, sheaf and topos theory, to furnish a mathematical image of individual and group interactions within a stochastic environment. Specifically, we employ morphisms between polynomial representations of individual agent models, allowing predictions not only of their own behaviors but also those of other agents and environmental responses. Sheaf and topos theory facilitate the construction of coherent agent worldviews and provides a way of representing consensus or shared understanding. We explore the emergence of shared protentions, bridging the phenomenology of temporal structure, multi-agent active inference systems, and category theory. Shared protentions are highlighted as pivotal for coordination and achieving common objectives. We conclude by acknowledging the intricacies stemming from stochastic systems and uncertainties in realizing shared goals.

This article is an early draft on a proposed alternative to the current Marxist mode of thought; one that seeks to reject the generally ill-conceived and dogmatic proposals formulated by Marx in favour of another predicated on the more unwavering emotional ideals of the philosophy that preceded it. It eliminates that dogmatic mode in favour of a wholly social society, one that is founded upon the Marxist superstructure and intends hence to capture that humanity and re-form particularly economic principles that are used to construct the utopia into what is instead an entirely socially idealised frame of living.

The present work investigates primarily the morphology evolution of the body-centered-cubic (BCC)/B2 phases in AlxNiCoFeCr high-entropy alloys (HEAs) with increasing Al content, which has been neglected so far. There exist two types of microscopic morphologies of BCC and B2 phases in this HEA series: one is the weave-like morphology induced by the spinodal decomposition, and the other is the microstructure of a spherical disordered BCC precipitation on the ordered B2 matrix that appears in HEAs with a much higher Al content. The shape of coherent precipitates is found to be closely related to the lattice misfit between BCC and B2 phases, which is sensitive to Al. The mechanical properties, including the compressive yielding strength and microhardness of the AlxNiCoFeCr HEAs, are also discussed in light of the concept of the valence electron concentration (VEC).

The real systems are often complex, nonlinear, and noisy in various areas including mathematics, natural science, and social science. We present the symplectic entropy (SymEn) measure as well as an analysis method based on SymEn to estimate the nonlinearity of the complex system by analyzing the given time series. The SymEn estimation is a kind of entropy based on symplectic principal component analysis (SPCA) which represent organized but unpredictable behaviors of systems. The key to SPCA is to preserve the global submanifold geometrical properties of the systems through symplectic transform in the phase space, which is a kind of the measure-preserving transforms. The capability of preserving the global geometrical characteristics makes the SymEn a test statistic to detect the nonlinear characteristics in several typical chaotic time series and the stochastic characteristic in the Gaussian white noise. The results are in agreement with findings in the approximate entropy (ApEn), the sample entropy (SampEn) and the fuzzy entropy (FuzzyEn). Moreover, the SymEn method is also used to analyze the nonlinearities of the real signals (including the EEG signals for ASD and healthy subjects, and the sound and vibration signals for the mechanical systems). The results indicate that the SymEn estimation can be taken as a measure for describing the nonlinear characteristics in the data collected from the natural complex systems.

In this study, the generality and prediction accuracy of a generalised series model for large eddy simulation of premixed and non-premixed turbulent combustion is explored. The model is based on Taylor series expansion of the chemical source term in scalar space and implemented into OpenFOAM. The mathematical model does not depend on the combustion regimes, and has the correct limiting behaviour. The numerical error sources are outlined and analysed. The model is first applied to a piloted methane/air non-premixed jet flame (Sandia Flame D). The statistical (time-averaged and RMS) results agree well with experimental measurements, particularly with regard to the mixture fraction, velocity, temperature, and concentrations of major species CH4, CO2, H2O, and O2. The concentrations of intermediates CO and H2 are over-predicted, due to the limitations of the reduced reaction mechanism employed. Then, a Bunsen piloted flame is simulated. Most of the statistical properties of both reactive species and progress variable are well reproduced. The only major discrepancy evident is in the temperature, which is attributed to the experimental uncertainties of temperature fields in the pilot stream. These findings have demonstrated the model`s generality for both premixed and non-premixed combustion simulation, as well as the accuracy of prediction of reactive species distribution.

High temperature Ni-superalloys are limited by reliance on critical elements and complex processing steps. High entropy alloys (HEAs) have demonstrated stable single/dual phase microstructures with strong ordering tendencies. A dual phase (FCC+BCC) Al0.5Co0.5CrFeNi1.5Ti0.25 alloy (developed using CALPHAD) was tested for room and high temperature compression behavior. The microstructure mainly comprises of coarse ordered FCC(L12) surrounding decomposed lamellae of ordered FCC(L12) and BCC(L21) phases, which coarsened upon annealing at high temperature (1100 °C) into a bi-continuous structure of disordered FCC+BCC(B2). Additionally, cold rollability of the cast alloy increased from <5% to ~40% after annealing, with a corresponding softening observed in room temperature compression mainly due to disordering of FCC and BCC phases. Peak flow stresses of 793.45MPa, 535.12MPa, and 324.40MPa were achieved at 800oC, 900oC, and 1000oC respectively for the high temperature annealed alloy.

This paper investigates five different GARCH models (GARCH, EGARCH, IGARCH, Component GARCH (CGARCH) and GJR-GARCH) along with six distributions (Normal, Student’s t, GED and their skewed forms), which are used to forecast the volatility for the Bulgarian Stock index SOFIX. We use a GARCH model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data covers the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at forecasting the volatility of SOFIX and which distribution is most appropriate. The results, based on BIC and AIC information criteria, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student t-distribution is preferred for forecasting. With the help of 5000 simulations, it is estimated that the chances of Index SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087.

Background: The modified Duke index derived from coronary computed tomography angiography (CCTA) was designed to predict cardiovascular outcomes based on the severity of coronary ste-nosis. However, it does not take into consideration the presence or severity of peri-coronary in-flammation. The peri-coronary fat attenuation index (FAI) is a novel imaging marker determined by CCTA which reflects the degree of inflammation in the coronary tree in patients with coronary artery disease. Purpose: To assess the association between the modified Duke index assessed by CCTA, cardiovascular risk factors and peri-coronary inflammation in the coronary arteries of pa-tients with coronary artery disease. Methods: One hundred seventy-two patients who underwent CCTA for typical angina were assigned into two groups based on the modified Duke index: group 1 – patients with low index ≤ 3 (n=107) and group 2 – patients with high index > 3 (n=65). Demo-graphic, clinical and CCTA data were collected for all patients, and FAI analysis of coronary in-flammation was performed. Results: Patients with increased values of the modified Duke index were significantly older compared to those with a low index (61.83 ± 9.89 vs. 64.78 ± 8.9; p = 0.002). No differences were found between the two groups in terms of gender distribution, hypertension, hypercholesterolemia or smoking history (all p > 0.5). The FAI score was significantly higher in patients from group 2, who presented a significantly higher score of inflammation compared to the patients in group 1, especially at the level of the right coronary artery (FAI score 20.85 ± 15.80 vs. 14.61 ± 16.66; p = 0.01 for the right coronary artery, 13.85 ± 8.04 vs. 10.91 ± 6.5; p = 0.01 for the circumflex artery, and 13.26 ±10.18 vs. 11.37 ± 8.84; p = 0.2 for the left anterior descending artery). CaRi-Heart® analysis identified a significantly higher risk of future events among patients with a high modified Duke index (34.84 % ± 25.86 % versus 16.87 % ± 15.80 %; p

Unification based upon the generalisation of proper time is proposed as a comprehensive framework to account for the fundamental structure of matter, in a manner contrasting with the more familiar approach based on extra dimensions of space. The elementary properties of matter to be incorporated include the Standard Model of particle physics together with a source for the dark sector and a coherent formalism for quantum gravity. We elaborate upon the manner in which all such material phenomena and empirical properties as distributed in an extended 4-dimensional spacetime can be encompassed within, and derived from, the continuous flow of time alone via a generalised arithmetic form for infinitesimal intervals of proper time. This approach will also be compared and contrasted with the basic structure of causal set theory as a means of demonstrating how it is possible to construct a full physical theory essentially from elements of time alone, as explicitly developed from the most elementary level. The conception of time as utilised and elucidated in this theory, with emphasis upon the causal continuum properties and as the basis for unification, will be clarified.

The self-assembly is an intriguing process of great importance in general soft matter and thus re-ceives an ever-growing scientific interest. Its most trivial example is the entropy-driven crystalli-zation of hard spheres. Past works have established the similarities and differences in the phase behavior of monomers and chains made of hard spheres. In the present work, inspired by the dif-ference in the melting points of the pure components, we study, through Monte Carlo simulations, the phase behavior of athermal mixtures composed of fully flexible polymers and individual monomers of uniform size. We analyze how the relative number fraction and the packing density affect crystallization and the established ordered morphologies. A synergetic effect is observed in the crystallization leading to synchronous crystallization of the two species. Structural analysis of the resulting ordered morphologies shows perfect mixing and thus no phase separation, which could split the system into polymer-rich and monomer-rich domains. Due to the constraints imposed by chain connectivity, the local environment of the individual spheres is systematically more spherical and more symmetric compared to the one of spheres belonging to chains. In general, increasing polymer content leads to reduction of the degree of crystallinity. According to the present findings, relative concentration is another determining factor to control the phase behavior of hard colloidal systems based on polymers.

：Non-Euclidean data, such as social networks, and citation relationships between documents, has node information and structural information. Graph Convolutional Network(GCN) can automatically learn node features and association information between nodes. The core ideology of the graph convolutional network is to aggregate node information by using edge information, thereby generating a new node feature. In the process of updating node features, there are two core influencing factors. One is the number of neighboring nodes of the central node, the other is the contribution of the neighboring nodes to the central node. Due to the previous GCN methods not simultaneously considering the numbers and different contributions of neighboring nodes to the central node, we design the Adaptive Attention Mechanism(AAM). To further enhance the representational capability of the model, we utilize Multi-Head Graph Convolution(MHGC). Finally, we adopt cross-entropy(CE) loss function to describe the difference between the predicted results of node categories and the ground truth (GT). Combined with backpropagation, this ultimately achieves accurate node classification. Based on AAM, MHGC and CE, we contrive the novel Graph Adaptive Attention Network (GAAN). Experiments show that the classification accuracy has achieved outstanding performances on Cora, Citeseer and Pubmed datasets.

Annually, the oak forests of the Zagros Mountain chains, in western Iran and northeastern Iraq, face recurring challenges posed by forest fires, particularly in the Kurdo-Zagrosian forests situated in western Iran and northeastern Iraq. Assessing fire susceptibility relies significantly on vegetation condition. Integrating in situ data, Remote Sensing (RS) data, alongside the integration of Geographical Information Systems (GIS), presents a cost-effective and precise approach to capturing environmental conditions before, during, and after fire events, minimizing the need for extensive fieldwork. This study refines and applies the Zagros Grass Index (ZGI), a local vegetation index tailored to discern between grass-covered surfaces from tree canopies in Zagros forests, identifying the grass masses as the most flammable fuel type. Utilizing Moderate Resolution Imaging Spectroradiometer (MODIS) Normalized Difference Vegetation Index (NDVI) product as input, from 2013 to 2022, the ZGI aims to mitigate the influence of tree canopies, isolating NDVI values solely attributable to grass cover. By incorporating phenological characteristics of forest trees and grass species, the ZGI outperforms NDVI in mapping grass-covered areas that are crucial for fire susceptibility assessment in the study region. Results demonstrate a strong overlap between ZGI-based maps and recorded fire occurrences, validating the efficacy of the index in fire susceptibility estimation.

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.

Abstract: The VSI represents a significant advancement in the assessment of gastrointestinal-specific anxiety among patients with Irritable Bowel Syndrome (IBS) and other Chronic Inflammatory Bowel Diseases (IBD). However, an Italian version of the instrument is not yet available for the reference population. This study utilized a national sample of 500 individuals, including healthy controls and patients with Ulcerative Colitis and Crohn's Disease, to test the validity and reliability of the Italian VSI. Using back-translation methodology to ensure translation fidelity, the research applied a questionnaire and the VSI through an online format to 500 participants. Data analysis revealed that the Italian VSI had excellent psychometric properties, demonstrating high internal consistency (Cronbach’s α = 0.95) and construct validity. The scale proved sensitive in detecting significant differences in visceral sensitivity among groups, highlighting its utility as a clinical and research assessment tool. Specifically, the Italian VSI exhibited a unidimensional factorial structure and maintained a strong correlation with other measures of anxiety and the severity of gastrointestinal symptoms, confirming its role in enhancing the understanding and management of IBS and IBD in Italy.

Managing a portfolio whose value closely tracks an index by trading only in a subset of the index constituents involves an NP-hard optimisation problem. In the prior literature, it has been suggested to solve this problem using sequential Monte Carlo (SMC, a.k.a. particle filter) methods. However, this literature does not take transaction costs into account, although transaction costs are the primary motivation for attempting to replicate the index by trading in a subset, rather than the full set of index constituents. This paper extends the SMC approach to index tracking to allow for proportional transaction costs and implements this extended method on empirical data for a variety stock indices. In addition to providing a more practically useful tracking strategy by allowing for transaction costs, we find that including a penalty for transaction costs in the optimisation objective can actually lead to better tracking performance.

Predicting the outcome of a future game between two National Basketball Association (NBA) teams poses a challenging problem of interest to statistical scientists as well as the general public. In this article, we formalize the problem of predicting the game results as a classification problem and apply the principle of maximum entropy to construct NBA maximum entropy (NBAME) model that fits to discrete statistics for NBA games, and then predict the outcomes of NBA playoffs by the NBAME model. The best NBAME model is able to correctly predict the winning team 74.4 percent of the time as compared to some other machine learning algorithms which is correct 69.3 percent of the time.

An analysis of the processes of plastic deformation and acoustic relaxation in a high-entropy alloy Al0.5CoCrCuFeNi was carried out. The following have been established: dominant dislocation defects; types of barriers that prevent the movement of dislocations; mechanisms of thermally activated movement of various elements of dislocation lines through barriers at room and low temperatures. Based on modern dislocation theory, quantitative estimates have been obtained for the most important characteristics of dislocations and their interaction with barriers.

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 and medical CT images. And the corresponding non-extensive parameter q can be evaluated by using self-adaptive Tsallis entropy algorithm. The results of this algorithm are compared with those of 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.

.Bacground: Sepsis remains a major health challenge worldwide, characterized by a dysre-gulated host response to infection, leading to high mortality and morbidity in intensive care units (ICUs). The Fibrosis 4 (FIB-4) index, originally developed to assess liver fibrosis in hepatitis C patients, has recently been explored for its potential prognostic value in sepsis patients. Method: This study retrospectively analyzed 309 sepsis patients admitted to the Internal Me-dicine and Anaesthesia ICUs between December 12, 2021, and December 15, 2023, to inves-tigate the relationship between FIB-4 levels, Acute Physiology and Chronic Health Evaluation (APACHE), and Sequential Organ Failure Assessment (SOFA) and clinical outcomes. Results: The study found that higher FIB-4 measurements were statistically significantly asso-ciated with increased 28-day mortality, with a cut-off value of 4.9 providing a sensitivity of 54.92% and specificity of 74.25%. Logistic regression analysis indicated that elevated Conclusion:FIB-4 levels were a significant predictor of early mortality, suggesting that the FIB-4 index could serve as a valuable prognostic tool in assessing the severity and prognosis of sepsis patients.

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches on it, we show that entropy has a universal stochastic definition which is not disorder. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept and promotes entropy as the mother of creativity and evolution. As social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether the maximum entropy, applied to the distribution of wealth quantified by annual income, can give an objective description. Using publicly available income data, we show that the income distribution is consistent with the principle of the maximum entropy. The increase of entropy is associated to increase of society’s wealth yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in development and increase of the entropy of income. Such findings are contrary to the theories of ecological economics and other theories which use the term entropy in a Malthusian perspective.

:. Background and Objectives: Pulmonary embolism, PE, incidence had been increasing in the last ten years. Computed thoracic pulmonary angiography, CTPA, had a major role in confirming PE di-agnosis.The main purpose of the study was to establish the prognostic value of a CTPA parameter: pulmonary artery obstruction index, PAOI, for PE risk assessment . A second objective of the re-search was to investigate the predictive accuracy of biomarkers (D-dimer, and cardiac Troponin T, c-TnT ), and PAOI, in 7-day mortality. The third objective of the study was the relationship between PAOI, and these biomarkers, in different etiologies of PE. Materials and Methods: The study com-prised 109 patients with PE, hospitalized, and treated between February 2021, and August 2022. They had different etiologies: deep vein thrombosis, DVT; persistent atrial fibrillation, AF; chronic obstructive pulmonary disease, COPD, exacerbation; Covid; and cancers. The investigations were the following: clinical examination; D-dimer testing, as a mandatory method for PE suspicion( values ≥ 500 µg/L were highly suggestive for PE); c-TnT , as a marker of myocardial injury(values ≥ 14 ng/L were abnormal); CTPA, with right ventricle dysfunction, RVD, signs, and PAOI. Treat-ments were according to PE risk: systemic thrombolysis (in high risk , and hemodynamic instability); low weight molecular heparins, LWMH, after systemic thrombolysis, or in high risk PE, with he-modynamic stability; direct oral anticoagulants, DOAC (in low, and intermediate risk). Results: The relationship PAOI- D-dimer, and PAOI- c-TnT, had very strong statistical correlation, for the entire sample, and for DVT, AF, COPD, Covid subgroups ( Rho = 0.815-0.982). PAOI had a high predic-tive accuracy for intermediate , and high risk together (area under curve, AUC=0.948), and high risk PE (AUC= 0.993). For 7-day mortality, D-dimer , and c-TnT had high predictive accura-cy(AUC=0.921, and 0.979). PAOI had statistical significance for 7-day mortality in Covid (p=0.045), and cancer (p=0.038) patients. Conclusions: PAOI was an important tool for PE risk as-sessment. D-dimer , and c-TnT were valuable predictors, for 7-day mortality in PE. PAOI, and D-dimer; PAOI, and c-TnT were strongly correlated, for the entire PE sample, and for DVT, AF, COPD, and Covid patients.

Floods are a common natural disaster whose severity in terms of duration, water resource volume, peak and accumulated rainfall-based damage are likely to differ significantly for different geographical regions. In this paper, we first propose a novel hourly flood index (SWRI24−hr−S), derived from normalising the existing 24-hourly water resources index (WRI24−hr−S) in literature, to monitor flash flood risks on an hourly scale. The proposed SWRI24−hr−S is adopted to identify a flood situation and derive its characteristics, such as the duration (D), volume (V) and peak (Q). The comprehensive result analysis establishes the practical utility of SWRI24−hr−S in identifying flood situations at seven study sites in Fiji between 2014 and 2018 and deriving their characteristics (i.e., D, V, and Q). Secondly, this study develops a vine copula-probabilistic risk analysis system that models the joint distribution of flood characteristics (i.e., D, V, and Q) to extract their joint exceedance probability for the seven study sites in Fiji, enabling probabilistic flood risk assessment. The vine copula approach, particularly suited to Fiji’s study sites, introduces a novel probabilistic framework for flood risk assessment. The results show moderate differences in the spatial patterns of joint exceedance probability of flood characteristics in different combination scenarios generated by the proposed vine copula approach. In the worst-case scenario, the probability of any flood event occurring where the flood volume, peak and duration are likely to exceed the 95th-quantile value (representing an extreme flood event) is found to be less than 5% for all study sites. The proposed hourly flood index and the vine copula approach can be feasible and cost-effective tools for flood risk monitoring and assessment. The methodologies proposed in this study can be applied to other data-scarce regions where only rainfall data is available, offering crucial information for flood risk monitoring, assessment, and the development of effective mitigation strategies.

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The first and second moments of this jump-diffusion process are used to calculate the insurance premium based on mean-variance principle. The Laplace transform of the aggregated process is derived, and this leads to an application for pricing default-free bonds which could capture the impacts of both exogenous and endogenous shocks. Illustrative numerical examples and comparisons with other models are also provided.

An entropic origin of gravity is re-visited. Isothermal self-gravitating cloud seen as an ideal gas is analyzed. Gravitational attraction within the isothermal cloud in equilibrium is balanced by the pressure, which is of a pure entropic nature. The notion of the Jeans entropy of the cloud corresponding to the entropy of the self-gravitating cloud in mechanical and thermal equilibrium is introduced. Balance of the gravitational compression and the entropic repulsion yields the scaling relation hinting to the entropic origin of the gravitational force. The analysis of the Jeans instability enables elimination of the “holographic screen” or “holographic principle” necessary for grounding of the entropic origin of gravity.

Background: The Advanced Lung Cancer Inflammation Index (ALI) is a novel, comprehensive index that integrates inflammation and nutritional status, incorporating parameters such as albumin, body mass index (BMI), and the neutrophil-to-lymphocyte ratio (NLR). Unlike traditional inflammation biomarkers, this study aims to evaluate the prognosis of IPF patients by considering both inflammation and nutritional status. Method: A total of 102 patients with IPF were included in the study. Clinical data were obtained from the patients' medical records. NLR and ALI score were calculated based on data collected at the initiation of antifibrotic treatment using the following formula: Neut/Lym and albumin × BMI / NLR. Results: IPF subject subgroups in terms of ALI based on gender–age–physiology (GAP) stages (1,2,3), FVC (median split,

During planetary exploration mission operations, one of the key responsibilities of the instrument teams to determine data viability for subsequent analysis. During the 2019 CanMoon Lunar Sample Return Analogue Mission, the Lead Raman Specialist manually examined each spectra to provide quality assurance/validation. This non-trivial process requires years of experience to complete accurately. With the proven efficacy of Convolutional Neural Networks (CNNs) in classification tasks, and the increased use of automation and control loops on planetary space platforms for navigation and science targeting, an opportunity presents itself to approach this validation problem utilising CNNs. We present the Generalised Raman Validation Network (GRaVN), an neural network focused specifically on extracting the generalised structure of Raman spectra for quality assurance/validation. This work demonstrates the viability of utilising a CNN network in validation activities for Raman spectroscopy. Utilising only two hidden layers, a configuration was developed that provided good levels of accuracy on a manually curated dataset. This indicates that such a system could be useful as part of an autonomous control loop during planetary exploration activities.

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered and applied to numerical modeling results with the direct possibility to use in atmosphere monitoring especially in such strong events which follow magnetic storms. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on a vertical coordinate, that seriously complicates the problem solution. The relations connecting perturbations for acoustic and entropy modes are analytically established and led to the solvable diagnostic equations. These perturbation structures, found as the equation solutions specify acoustic and entropy modes in an arbitrary stratified gas under the condition of stability. These time-independent diagnostic relations link gas perturbation variables of the acoustic and the entropy modes. Hence, they provide the ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts uniquely at any instant within the all accessible heights range. As a prospective model, we consider the diagnostics at the height interval [120;180] km, where the equilibrium temperature of a gas depends linearly on the vertical coordinate. For such a heights range it is possible to proceed with analytical expressions for pressure and entropy perturbations of gas variables. Individual profiles of acoustic and entropy parts for some data, obtained by numerical experiment, are illustrated by the plots for the pure numerical data against ones obtained by the model. The total energy of a flow is determined for both approaches and its height profiles are compared.

Sentiment analysis plays a crucial role in understanding customer feedback, guiding product development, and informing business decisions. This paper introduces term sentiment entropy (TSE), a novel weighting method that leverages the distribution of sentiment labels associated with words to enhance text classification accuracy. TSE complements traditional TF-IDF techniques by capturing the nuances of sentiment variation across different contexts. Experiments across diverse public datasets demonstrate TSE's potential to improve sentiment analysis performance, especially in capturing subtle sentiment shifts and adapting to specific domains. While computational cost and label quality pose challenges, TSE offers a promising avenue for refining sentiment analysis and opening new research frontiers.

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.

In the paper the verification of forecasts of precipitation conditions measured by the standardized precipitation index SPI is presented. For the verification of categorical forecasts a contingency table was used. Standard verification measures were used for the SPI value forecast. The 30 day SPI moved every 10 days by 10 days was calculated in 2013-2015 from April to September on the basis of precipitation data from 35 meteorological stations in Poland. Predictions of the 30 day SPI were created in which precipitation was forecasted in the next 10 days (the SPI 10-day forecast) and 20 days (the SPI 20-day forecast). Both for the 10 and 20 days, the forecasts were skewed towards drier categories at the expense of wet categories. There was a good agreement between observed and 10-day forecast categories of precipitation. Less agreement is obtained for 20-day forecasts – these forecasts evidently “over-dry” the assessment of precipitation anomalies. The 10-day SPI value forecast accuracy is acceptable, whereas for the 20-day forecast is unsatisfactory. Both for the SPI categorical and the SPI value forecast, the 10-day SPI forecast is reliable and the 20-day forecast should be accepted with reservation and used with caution.

Recent analyses of cosmic microwave background surveys have revealed hints that there may be a non-trivial running of the running of the spectral index. If future experiments were to confirm these hints, it would prove a powerful discriminator of inflationary models, ruling out simple single field models. We discuss how isocurvature perturbations in multi-field models can be invoked to generate large runnings in a non-standard hierarchy, and find that a minimal model capable of practically realising this would be a two-field model with a non-canonical kinetic structure. We also consider alternative scenarios such as variable speed of light models and canonical quantum gravity effects and their implications for runnings of the spectral index.

How to build an optimal model where three terms “time, causality, and entropy” will be interrelated in a most correct way? This task has a semantic and physical aspect. We give in this article the solution that is based only on elementary perception. In physics, we experience time with our senses as the duration of material change running in space. This fact is the standpoint for our model where causality is only a principle, it is not a physical actuality and entropy runs only in space and not in time. Time is merely a duration of entropy increasing and is entering existence when measured by the observer.

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A—which is the area of the event horizon of the black hole-, a length L_P—which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function, with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local, statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations.

Climate change is challenging the agricultural sector worldwide. The pressure exerted by the altered thermal conditions drives the zonal shift for various cultivations. This study presents the multiyear analysis of the Growing Degree Days (GDD) index over the Northern Mediterranean Basin (NMB), focused on the high-value vine cultivation derived from the E-OBS dataset. To handle this extensive environmental dataset, R-language scripts and packages were applied, along with the capabilities of the GIS software. The investigated time period spans from 1969 to 2018, and the performed analysis indicates a broad shift/expansion in areas of GDD exceeding 2000 heat units. The extracted results specify the viticultural areas where the GDD index surpasses the suitable values for vine cultivation, owing to the increase of the thermal stress risk. In addition to mapping areas with GDD ≥ 2000, spatial calculations of the surface of areas meeting this criterion per country in the study area were made. In the northern parts of the NMB, the rise of the GDD index values indicates the establishment of vine plantations in the future.

Purpose: The purpose of this study is to apply the Composite Radiographic Index modified (CRIm) in CBCT scans of patients with Medication related osteonecrosis of the jaws (MRONJ) in order to detect its validity, and corelate the radiologic findings with the clinical staging of the disease. Methods: This study included 43 patients with MRONJ diagnosis and CBCT scans performed in the School of Dentistry and approved by the Research Ethics Committee. Clinical staging for every patient (0-3) was provided according to AAOMS 2022 guidelines. In cases of patients with both jaws affected, each jaw was evaluated independently resulting to 52 CBCT scans. The 52 CBCT scans were assessed under standardized viewing conditions by 2 observers who evaluated independently the following 8 radiologic features: lytic changes, sclerosis, periosteal reaction, sequestration, non-healing extraction sockets and other findings (sinus implication, inferior alveolar canal involvement, jaw fracture). The CRIm index was constructed to assess the extent of osseous changes. The radiologic features were scored as absent (0), localized/single (1), extensive/multiple (2), yielding a theoretical range of 0–12. For statistical analysis Fisher’s exact test and Spearman’s correlation coefficient were performed. Results: A statistically significant association of clinical stage with lytic changes, sequestration and inferior alveolar canal involvement was found. Also, a statistically significant correlation of clinical stage with CRIm index classification was obtained. Conclusions: The CRIm index tends to increase as the clinical stages of MRONJ advance, suggesting a correlation between the clinical stage of MRONJ and the CRIm index.

Aim: To investigate inflammation indices and erythropoietin (EPO) levels for their potential role in distinguishing polycythemia vera (PV) from secondary polycythemia (SP), and to compare different parameter combinations in terms of diagnostic accuracy. Methods: This retrospective cohort was created from patients assessed for polycythemia from January 2020 to December 2023. PV diagnosis was made according to the 2016 WHO criteria (n=145). Those who did not fulfill the criteria were defined as having SP (n=84). Results: NLR, PLR and SII were significantly higher in the PV group (p

People have always hoped to be able to fill an entire plane with ``single unit cells'' without periodicity. This wish was realized after the mathematician discovered a 13-sided ``single unit cell'' named `einstein'. These non-periodic tessellations generally exhibit anisotropic properties, making them superior in terms of mechanical performance compared to periodic structures. From the perspective of information entropy, the reason behind the improved mechanical properties of these structures is the higher entropy associated with non-periodic configurations. To quantify the disorder of non-periodic structures, we propose an entropy expression for the `einstein' metamaterial. To demonstrate the mechanical properties of these high-entropy structures, we fabricate specimens using 3D printing and conducte mechanical experiments. For comparative analysis, we also use ABAQUS to perform finite element analysis of the problem. The research results reveal that the mechanical properties of high-entropy structures created by the non-periodic stacking of cells are significantly improved compared to those of low-entropy structures created by periodic stacking. The conclusions drawn from the study of individual issues are generalizable and may be of assistance in future material and structural design.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

This research aimed to investigate the relationship between climate policy uncertainty (CPU), clean energy (ENERGY), carbon emission allowance prices (CARBON), and Bitcoin returns (BTC) for the period from August 2012 to August 2022. The empirical analysis strategies utilized in this study included the Fourier Bootstrap ARDL long-term coefficient estimator, Fourier Granger Causality, and Fourier Toda Yamamoto Causality methods. Following the confirmation of cointegration among the variables, we observed a positive relationship between BTC and CARBON, a positive relationship between BTC and CPU, and a negative relationship between BTC and ENERGY. In terms of causal associations, we identified one-way causality running from CARBON to BTC, BTC to CPU, and BTC to the ENERGY variable. The study underscores the potential benefits and revenue opportunities for investors seeking diversified investment strategies in light of climate change concerns. Furthermore, it suggests actionable strategies for policymakers, such as implementing carbon taxes and educational campaigns, to foster a transition towards clean energy sources within the cryptocurrency mining sector and thereby mitigate environmental impacts.

In this work, satellite data from the Clouds and Earth’s Radiant Energy System (CERES) and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments is analyzed to determine how the global absorbed sunlight and global entropy generation rate have changed during the time period from 2002 to 2023. The data is used to test hypotheses derived from the Maximum Power Principle (MPP) and Maximum Entropy Production Principle (MEP) about the evolution of earth’s surface and atmosphere. The results indicate that the amount of absorbed sunlight has increased over the last 20 years but rising surface temperatures have caused the entropy generation rate to remain approximately constant despite that decrease in albedo. The results are simpler to explain using the MPP but do not completely rule out the MEP. Given the acceptance of the MPP or MEP, some extensions and nuances are discussed.

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.

The existing segmentation-based scene text detection methods mostly need complicated post-processing, and the post-processing operation is separated from the training process, which greatly reduces the detection performance. The previous method, DBNet successfully simplified post-processing and integrated the post-processing into a segmentation network. However, the training process of the model took a long time for 1200 epochs and the sensitivity to texts of various scales was lacking, leading to some text instances being missed. Considering the above two problems, we design the text detection Network with Binarization of Hyperbolic Tangent(HTBNet). First of all, we propose Binarization of Hyperbolic Tangent (HTB), optimized along with which, the segmentation network can expedite the initial convergent speed by reducing the amount of epochs from 1200 to 600. Because features of different channels in the same scale feature map focus on the information of different regions in the image, to better represent the important features of all objects in the image, we devise the Multi-Scale Channel Attention(MSCA). Meanwhile considering that multi-scale objects in the image cannot be simultaneously detected, we propose a novel module named Fused Module with Channel and Spatial(FMCS), which can fuse the multi-scale feature maps from channel and spatial dimension. Finally we adopt cross entropy as the loss function, which measures the difference between predicted values and ground truths. The experimental results show that HTBNet compared with lightweight models has achieved competitive performance and speed on Total-Text(F-measure:86.0%, FPS:30) and MSRA-TD500 (F-measure:87.5%, FPS:30).

Background: Obesity remains a widely debated issue, often criticized for the limitations in its identification and classification. This study aims to compare two distinct systems for classifying obesity: Body Mass Index (BMI) and body fat percentage (BFP) as assessed by bioelectrical impedance analysis (BIA). By examining these measures, the study seeks to clarify how different metrics of body composition influence the identification of obesity-related risk factors. Methods: The study enrolled 1255 adults, comprising 471 males and 784 females, with a mean age of 36 ± 11.90 years. Participants exhibited varying degrees of weight status, including optimal weight, overweight, and obesity. Body composition analysis was conducted using the TANITA Body Composition Analyzer BC-418 MA III device (T5896, Tokyo, Japan), evaluating the following parameters: current weight, basal metabolic rate (BMR), adipose tissue (%), muscle mass (%), and hydration status (%). Results: Age and psychological factors like cravings, fatigue, stress, and compulsive eating were significant predictors of obesity in the BMI model but not in the BFP model. Additionally, having a family history of diabetes was protective in the BMI model (OR: 0.33) but increased risk in the BFP model (OR: 1.66). The BMI model demonstrates exceptional predictive ability (AUC=0.998). In contrast, the BFP model, while still performing well, exhibits a lower AUC (0.975), indicating slightly reduced discriminative power compared to the BMI model. Conclusions:BMI classification demonstrates superior predictive accuracy, specificity, and sensitivity. This suggests that BMI remains a more reliable measure for identifying obesity-related risk factors compared to the BFP model.

COPD is currently the fourth leading cause of death in the world. Globally, due to continued exposure to COPD risk factors and an aging population, the burden of COPD is expected to increase in the coming decades. The BODE (body mass index, airflow obstruction, dyspnea, and exercise capacity) index is a practical and multidimensional predictor for prognosis of COPD, and better than FEV1.We used the database of Kaohsiung Chang Gung Memorial Hospital medical center, Taiwan to analyze the correlation between BODE index, healthcare resource utilization, and Charlson comorbidity index (CCI). This retrospective study to collect COPD patients with complete BODE index data who had undergone a 6-minute walk examination in our hospital from January 2015 to December 2016. The medical cost and comorbidities database were analyzed from January 1, 2015, to August 31, 2017. Of 396 patients, 382 (96.5%) were male, with an average age of 71.3 ± 8.4 years. There was a significant association between the BODE index and the CCI of COPD patients (p < 0.001). Healthcare resource utilization was positively correlated with the BODE index during the 32 months of retrospective clinical outcomes: positively correlated with the number of hospitalizations (p<0.001), hospitalization days (p<0.001), hospitalization expenses (p=0.005), and total medical expenses (p=0.024), respectively. Our findings provide the crucial information for clinician to predict medical burden and comorbidities in patients with COPD by using BODE index.

Floods are among the most serious natural disasters worldwide; they cause enormous crop losses every year and threaten world food security. There are many studies focused on flood impact assessments for administrative districts but fewer on postdisaster impact assessments for specific crops. Therefore, this study used remote sensing data, including the normalized difference vegetation index (NDVI), elevation data, slope data, and rainfall data, combined with crop growing season data to construct a crop flood damage assessment index (CFAI). First, an analytic hierarchy process (AHP) was used to assign weights to the impact factors; then, the weighted composite score method was used to calculate the CFAI; and finally, the impact was classified as slight, moderate, or severe based on the magnitude of the CFAI . This method was used for the Missouri River floods of 2019 in the U.S. Due to the lack of measured data, the disaster vegetation damage index (DVDI) was used to validate the results. The combined approach achieved a high degree of consistency in spatial distribution. The CFAI can respond well to the degree of crop impact after flooding, providing new ideas and reference standards for agriculture-related departments.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences, notably lifetime, medical, and financial sciences. The Heavy tailed Nadarajah Haghighi model is introduced by compounding the heavy tailed family and Nadarajah Haghighi distribution in this paper. The so obtained model has three parameters accounting for the scale and shape of the distribution. The proposed distribution's fundamental characteristics such as probability density, cumulative distribution, hazard rate, and survival functions are provided, and several key statistical properties are established, and several entropy information measures are proposed. The estimation of model parameter is performed via the ML procedure. Further, different simulation experiments are conducted to demonstrate the performance of proposed estimator’s using some measure, like the average estimate, the average bias, and associated mean square error. Finally, we are applied our proposed model to analyze three different real datasets. In our illustration, we are compared the practicality of the recommended model with several well-known competing models.

Plant leaf area index (LAI) is a key characteristic affecting field canopy microclimate. In addition to traditional professional measuring instruments, smartphone camera sensors have been used to measure plant LAI. However, when smartphone methods were used to measure conifer forest LAI, very different performances were obtained depending on whether the smartphone was held at the zenith angle or at a 57.5° angle. To validate further the potential of smartphone sensors for measuring conifer LAI and to find the limits of this method, this paper reports the results of a comparison of two smartphone methods with an LAI-2000 instrument. It is shown that both methods can be used to reveal the conifer leaf-growing trajectory. However, the method with the phone oriented vertically upwards always produced better consistency in magnitude with LAI-2000. The bias of the LAI between the smartphone method and the LAI-2000 instrument was explained with regard to four aspects that can affect LAI: gap fraction, leaf projection ratio, sensor field of view (FOV), and viewing zenith angle (VZA). It was concluded that large FOV and large VZA cause the 57.5° method to overestimate the gap fraction and hence underestimate conifer LAI, especially when tree height is greater than 2.0 m. For the vertically upward method, the bias caused by the overestimated gap fraction is compensated for by an underestimated leaf projection ratio.

To enhance the applicability of dual-phase high-entropy alloys (HEAs) like Fe32Cr33Ni29Al3Ti3, fabricated via selective laser melting (SLM), a focus on improving their mechanical properties is essential. As part of this effort, heat treatment was explored. This study compares the microstructure and mechanical properties of the as-printed sample with those cooled in water after undergoing heat treatment at temperatures ranging from 1000 to 1200 ℃ for 1 hour. Both pre- and post-treatment samples reveal a dual-phase microstructure comprising FCC and BCC phases. Although heat treatment led to a reduction in tensile and yield strength, it significantly increased ductility compared to the as-printed sample. This strength-ductility trade-off is related to changes in grain sizes with ultrafine grains enhancing strength and micron grains optimizing ductility, also the influence of the content of FCC/BCC phases and dislocation density. In particular, the sample heat-treated at 1000 °C for 1 hour and then water-cooled exhibited a better combination of strength and ductility, a yield strength of 790 MPa, and an elongation of 13%. This research offers innovative perspectives on crafting dual-phase HEA of Fe32Cr33Ni29Al3Ti3, allowing for tailorable microstructure and mechanical properties through a synergistic approach involving SLM and heat treatment.

In order to solve the problem of feature extraction of underwater acoustic signals in complex ocean environment, a new method for feature extraction from ship radiated noise is presented based on empirical mode decomposition theory and permutation entropy. It analyzes the separability for permutation entropies of the intrinsic mode functions of three types of ship radiated noise signals, and discusses the permutation entropy of the intrinsic mode function with the highest energy. In this study, ship radiated noise signals measured from three types of ships are decomposed into a set of intrinsic mode functions with empirical mode decomposition method. Then, the permutation entropies of all intrinsic mode functions are calculated with appropriate parameters. The permutation entropies are obviously different in the intrinsic mode functions with the highest energy, thus, the permutation entropy of the intrinsic mode function with the highest energy is regarded as a new characteristic parameter to extract the feature of ship radiated noise. After that, the characteristic parameters, namely, the energy difference between high and low frequency, permutation entropy, and multi-scale permutation entropy, are compared with the permutation entropy of the intrinsic mode function with the highest energy. It is discovered that the four characteristic parameters are at the same level for similar ships, however, there are differences in the parameters for different types of ships. The results demonstrate that the permutation entropy of the intrinsic mode function with the highest energy is better in separability as the characteristic parameter than the other three parameters by comparing their fluctuation ranges and the average values of the four characteristic parameters. Hence, the feature of ship radiated noise can be extracted efficiently with the method.

Surface water distribution extracted from remote sensing data has been used in water resource assessment, coastal management, and environmental change studies. Traditional manual methods for extracting water bodies cannot satisfy the requirements for mass processing of remote sensing data; therefore, accurate automated extraction of such water bodies has remained a challenge. The histogram bimodal method (HBM) is a frequently used objective tool for threshold selection in image segmentation. The threshold is determined by seeking twin peaks, and the valley values between them; however, automatically calculating the threshold is difficult because complex surfaces and image noise which lead to not perfect twin peaks (single or multiple peaks). We developed an operational automated water extraction method, the modified histogram bimodal method (MHBM). The MHBM defines the threshold range of water extraction through mass static data; therefore, it does not require the identification of twin histogram peaks. It then seeks the minimum values in the threshold range to achieve automated threshold. We calibrated the MHBM for many lakes in China using Landsat 8 Operational Land Imager (OLI) images, for which the relative error (RE) and squared correlation coefficient (R2) for threshold accuracy were found to be 2.1% and 0.96, respectively. The RE and root-mean-square error (RMSE) for the area accuracy of MHBM were 0.59% and 7.4 km2. The results show that the MHBM could easily be applied to mass time-series remote sensing data to calculate water thresholds within water index images and successfully extract the spatial distribution of large water bodies automatically.

Properties of time domain parameters of the vibration signal have been extensively studied for the fault diagnosis of rolling element bearings (REB). Parameters like kurtosis and Envelope Harmonic-to-Noise Ratio are most widely applied in this field and some important progress has been made. However, since only one-sided information is contained in these parameters respectively, problems still exist in practice when the signals collected are of complicated structure and/or contaminated by strong background noises. A new parameter, named Shock pulse index (SPI), is proposed in this paper. It integrates the mutual advantage of both parameters above and can help effectively identify fault related impulse components under the interference of strong background noises, unrelated harmonic components and random impulses. The SPI optimizes the parameters of Maximum Correlated Kurtosis Deconvolution (MCKD), which is used to filter the signals under consideration. Finally, the interested transient information contained in the filtered signal can be highlighted through demodulation with Teager Energy Operator (TEO). Fault related impulse components can therefore be extracted accurately. Simulations and experiment analyses verify the effectiveness and correctness of the SPI.

Abstract: Doppler renal resistive index (RRI) has been used for several decades as a potential indi-cator for renal disease and progression. In recent years, RRI has emerged as a useful prognostic indicator for a range of co-morbidities in patients who are acutely unwell and as a potential marker for sub-clinical acute kidney injury (AKI) and post procedural AKI risk. Despite this, the clinical and theoretical determinants of RRI are poorly understood and remain contentious. Method: A narrative review of studies exploring the theoretical, experimental, and clinical evidence for factors affecting RRI. No date restrictions were set. Findings: Both experimental and clinical data confirm that RRI is markedly affected by a range of systemic and renal determinants and is influenced closely by the underlying risk factors and sys-temic vascular changes that lead to progressive renal damage. Discussion: This paper provides an overview of the key haemodynamic determinants of renal re-sistive index and aims to clarify their relative importance. With reference to a simplified theoretical model, evidence from experimental and clinical studies is reviewed. Pathophysiological factors and patient characteristics that influence RRI are explored to provide a better understanding of why RRI values change in the presence of common or complex pathologies. Conclusion: By gaining a better understanding of the complex systemic and renal factors that influ-ence RRI, ultrasound users will be better prepared to understand and interpret changes in RRI across a range of patient presentations.

The fetal splenic artery pulsatility index (PI) is a parameter that reflects fetal well-being and has been used as a predictor of adverse pregnancy outcomes. The aim of this study was to investigate the predictive value of splenic artery PI in GDM class A1 cases for NICU admission. In this prospective case controlled study, only sixty single pregnancy cases diagnosed with gestational diabetes mellitus class A1 were evaluated. Fetal splenic artery Doppler parameters Peak systolic velocity (PSV), Pulsatility index (PI), Resistivity index (RI) and End diastolic velocity (EDV) were measured in all cases. The rate of re-quirement of need of neanoatal intensive care unit was noted. In cases with need fetal intensive care, fetal splenic PI index was found to be statistically significantly lower than in healthy cases without it (0.94 ± 0.29 vs. 1.70 ± 0.53, respectively, p

Droughts have negative impacts on agricultural productivity and economic growth. Effective monitoring and accurate forecasting of drought occurrences and trends are crucial for minimizing drought losses and mitigating their spatial and temporal effects. In this study, trend dynamics in monthly total rainfall time series measured at Cape Town International Airport were analyzed using Mann-Kendall (MK) test, Modified Mann-Kendall (MMK) and innovative trend analysis (ITA) were examined. Additionally, we utilized hybrid prediction method that combined the model with the complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique, the autoregressive integrated moving average (ARIMA) model, the long short-term memory (LSTM) network (i.e. CEEMDAN-ARIMA-LSTM) to forecast SPI values of 6-, 9-, and 12-months using rainfall data between 1995 and 2020 from Cape Town International Airport meteorological rainfall stations. The results demonstrate the following essential points: (1) The trend analysis results of the total monthly rainfall values indicate a significant decreasing trend with the negative z-score (MK= -3.7541 and MMK= - 4.0773). ITA also indicated a significant downwards trend of rainfall in the study area. (2) As the forecasting horizon increases, the prediction accuracy of the models and CEEMDAN-combined models gradually improves, reaching their optimum performance at the 12-month horizon. (3) CEEMDAN efficiently stabilizes time-series data, resulting in greater prediction accuracy in the hybrid model compared to individual models at all timescales. (4) The RMSE and R2 values for the hybrid CEEMDAN-ARIMA-LSTM model at a 12-month forecasting horizon are 0.042 and 0.995, demonstrating the applicability of this hybrid approach for drought forecasting.

Objective: To analyse the association between maternal risk factors such as age, body mass index (BMI) and cigarette smoking, with perinatal outcomes. Materials and Methods: This a retrospective analysis from prospectively collected data performed at Hospital Universitario de Torrejón (Madrid, Spain), between September 2017 and December 2019. All pregnant women with singleton pregnancies and non-malformed live fetuses attending their routine ultrasound examination at 11+0 to 13+6 weeks' gestation were invited to participate. Association between preeclampsia, preterm birth, gestational diabetes mellitus (GDM), small for gestational age (SGA) or fetal growth restricted (FGR) neonates and type of delivery according to maternal age, BMI, and cigarrete smoking was studied. Logistic mixed models were used to analyze the data. Results: 1921 patients were included in the analysis. Women of 40 years old had a significantly higher risk of having GDM (Odds Ratio (OR) 1.61, 95% Confidence Interval (CI) 1.08 to 2.36), and SGA neonates (OR 1.54, 95% CI 1.00 to 2.37). Women with a BMI &lt;18 had an increased rate of birth SGA and FGR neonates (OR 3.28, 95% CI 1.51 to 7.05, and OR 3.73, 95% CI 1.54 to 8.37, respectively), whereas women with a BMI ≥35 had a higher risk of GDM (OR 3.10, 95% CI 1.95 to 4.89). Smoking increased the risk of having SGA and FGR neonates (OR 1.83, 95% CI 1.36 to 2.46, and OR 1.91, 95% CI 1.29 to 2.78). Conclusions: Advanced maternal age, low or high BMI, and smoking status are significant risk factors for pregnancy complications. Both clinicians and society should concentrate their efforts on addressing these factors to enhance reproductive health.

The prevailing interpretations of physics are based on deeply entrenched assumptions, rooted in classical mechanics. Logical implications include: the denial of entropy as a fundamental physical property, and the inability to explain irreversible change, random quantum measurements, or nonlocality without untestable and implausible metaphysical implications. We propose a conceptual model that is based on empirically justifiable assumptions and consistent with observations. The WYSIWYG Conceptual Model (WCM) assumes no hidden properties: “What You can See Is What You Get.” The WCM contextually defines a system’s state with respect to its actual ambient background, and it extends existing models of physical reality by defining entropy and exergy as objective contextual properties of state. The WCM establishes the irreversible dissipation of exergy and the Second law of thermodynamics as a fundamental law of physics, it recognizes physical randomness, and it provides a physical explanation for nonlocality, consistent with Special Relativity, without hidden variables, superdeterminism, or “spooky action.”

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still correspond to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea current at the time that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be done in a reversible process rather than the work that was actually done. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step-change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appro-priately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work done in-ternally and externally.

The role of energy and entropy in decomposition of turbulent velocity flow-fields is to be shown in the paper. The decomposition methods based on energy concept are taken into account, namely the Proper Orthogonal Decomposition (POD) and its extension Bi-Orthogonal Decomposition (BOD). Entropy motivated view on the decomposed modes could offer new possibilities in the modes physical interpretation and in Reduced Order Modelling (ROM) strategy efficiency evaluation.

We examined a series of real-world, pictorial photographs with varying characteristics, along with their modification by noise addition and unsharp masking. As response metrics we used three different versions of the aesthetic measure originally proposed by Birkhoff. The first aesthetic measure, which has been used in other studies, and which we used in our previous work as well, showed a preference for the least complex of the images. It provided no justification for noise addition, but did reveal enhancement on unsharp masking. Optimum level of unsharp masking varied with the image, but was predictable from the individual image’s GIF compressibility. We expect this result to be useful for guiding the processing of pictorial photographic imagery. The second aesthetic measure, that of informational aesthetics based on entropy alone failed to provide useful discrimination among the images or the conditions of their modification. A third measure, derived from the concepts of entropy maximization, as well as the hypothesized preference of observers for “simpler”, i.e., more compressible, images, yielded qualitatively the same results as the more traditional version of the measure. Differences among the photographs and the conditions of their modification were more clearly defined with this metric, however.

During the last years some new variants of Permutation entropy have been introduced and applied to EEG analysis, among them a conditional variant and variants using some additional metric information or being based on entropies different from the Shannon entropy. In some situations it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.

{Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighbouring values in a time series. This makes it possible to describe the signal as efficiently as prior proposed parameters such as permutation entropy (PE) or modified permutation entropy (mPE), but (1) reduces the size of the sample that is necessary to estimate the parameter value, and (2) enables the use of the Kullback-Leibler divergence to estimate the "distance" between the time series data and random signals.

Experimental recordings of the collective activity of interacting spiking neurons exhibit random behavior and memory effects, thus the stochastic process modeling the spiking activity is expected to show some degree of time irreversibility. We use the thermodynamic formalism to build a framework, in the context of spike train statistics, to quantify the degree of irreversibility of any parametric maximum entropy measure under arbitrary constraints, and provide an explicit formula for the information entropy production of the inferred Markov maximum entropy process. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

(1) Background: Parents of children with autism spectrum disorders often experience psychological distress, which can affect the quality of childcare they provide. It is crucial to screen for psychiatric symptoms among these parents. The Core Symptom Index (CSI) is a widely used tool for assessing general symptoms such as depression, anxiety, and somatic symptoms, with demonstrated validity and reliability across various populations. However, there is limited research on the validity and reliability of the CSI in the general Chinese population. This study aimed to investigate the psychometric properties of the Chinese version of the CSI among parents of children with autism spectrum disorders using Confirmatory Factor Analysis (CFA). (2) Methods: A total of 794 Chinese parents raising children with autism participated in this study. All completed the CSI, along with the social inhibition subscale of the Interpersonal Problems Inventory and the Couple Satisfaction Index. Factorial validity was assessed using CFA to determine how well the bifactor three-factor model fits the data. Various structural models were compared using model fit indices. Convergent and discriminant validity were examined by exploring correlations with the social inhibition subscale and the Couple Satisfaction Index. Invariance testing of the CSI was conducted across multiple groups based on gender, age, and education using CFA. The reliability of the CSI was evaluated using McDonald’s omega coefficients. (3) Results: The bifactor model emerged as the best-fitting model for the data, suggesting that the total score of the CSI adequately represents overall psychiatric symptoms. The CSI exhibited significant correlations with the social inhibition subscale (r = 0.41, p &lt; 0.01) and smaller correlation coefficients with the Couple Satisfaction Index (r = -0.16, p &lt; 0.05), indicating both convergent and discriminant validity. Invariant tests supported scalar invariance levels based on gender and age but only partial invariance for education. The Chinese version of the CSI demonstrated high consistency, with McDonald's omega coefficients ranging between 0.86 and 0.95. (4) Conclusions: The bifactor model of the Chinese version of the CSI is validated, making it a suitable tool for measuring depression, anxiety, and somatization symptoms among parents of children with autism spectrum disorders. Further research on other Chinese populations is encouraged.

Droughts are a common occurrence in various climates and are primarily caused by a prolonged decrease in rainfall. Several factors contribute to droughts, including temperature, wind speed, relative humidity, rainfall timing, amount, and intensity during the growing season. The objective of this study is to establish a new index, named soil moisture and evapotranspiration revealed drought index (SERDI), for displaying dry and wet conditions based on combining both soil moisture and evapotranspiration (Penman-Monteith) to improve drought early warning and its severity globally. For validation of the SERDI with other indices such as LST, VHI, NDVI, and NDWI, different ways used such as R-square, RMSE, MAPE, and P-value to estimate the accuracy, variability of data, the forecast conditions, and how the significance of data. The results showed that the low RMSE and high r² were found between SERDI with LST and VHI. In contrast, the low R- square and high RMSE were between SERDI with NDVI and NDWI in most of the semi-arid areas. Furthermore, most of the semi-arid areas from Iran, Iraq, Syria, Jordan, and Israel experienced moderate and severe dry conditions, except some parts of these regions had normal conditions in Iran and Syria. The SERDI analysis revealed a strong correlation between (LST) and a moderate correlation with (VHI) across all study areas. However, the relationship between other indices, like (NDWI) and (NDVI), varied depending on the regions. To conclude, SERDI can be used globally for detecting drought based on soil moisture and evapotranspiration.

Random variations in microelectronic circuit structures represent the source of entropy for physical unclonable functions (PUFs). In this paper, we investigate delay variations that occur through the routing network and switch matrices of a field programmable gate array (FPGA). The delay variations are isolated from other components of the programmable logic, e.g., Look-up tables (LUTs), flip-flops (FFs), etc. using a feature of Xilinx FPGAs called dynamic partial reconfiguration (DPR). A set of partial designs are created that fix the placement of a time-to-digital converter (TDC) and supporting infrastructure to enable the path delays through the target interconnect and switch matrices to be extracted by subtracting out common-mode delay components. Delay variations are analyzed in the different levels of routing resources available within FPGAs, i.e., local routing and across chip routing. Data is collected from a set of Xilinx Zynq 7010 devices, and a statistical analysis of within-die variations in delay through a set of the randomly-generated and hand-crafted interconnects is presented.

This study introduces a method for quantitatively assessing the complexity and predictability of fish behavior in closed systems through the application of information entropy, offering a novel lens to understand how fish adapt to environmental changes. Utilizing simulations rooted in a random walk model for fish movement, we delve into entropy fluctuations under varying environmental conditions, including responses to feeding and external stimuli. Our findings underscore the utility of information entropy in capturing the intricacies of fish behavior, particularly highlighting the synchrony in collective actions and adaptations to environmental shifts. This research not only broadens our comprehension of fish behavior but also paves the way for its application in fields like aquaculture and resource management. Through our analysis, we discovered that smaller grid sizes in simulations capture detailed local fluctuations, while larger grids elucidate general trends, pinpointing a 2.5m grid as optimal for our study. Moreover, changes in swimming speeds and behavioral adaptations during feeding were quantitatively analyzed, with results illustrating significant behavior modifications. Additionally, employing a Gaussian Mixture Model helped to clarify the nuanced changes in fish behavior in response to altered light conditions, demonstrating the layered complexity of fish responses to environmental stimuli. This investigation confirms the efficacy of information entropy as a robust metric for evaluating fish shoal behavior, offering a fresh methodology for ecological and environmental studies, with promising implications for sustainable management practices.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

Topological indices are invariant numerical fields of a graph that give facts about the structure of graphs and are found to be very helpful in predicting the physical properties of aluminophosphates. The characteristics of the aluminophosphates are similar to those of zeolites. Two examples of current applications are natural gas dehydration and humidity sensor. New frameworks are being synthesised by researchers in chemistry and materials science. There are many layers and holes in these substances. In this study, Vertex version of distance-based topological indices, the entropy of topological indices and their numerical analysis are explained.

Attempts to find and quantify the supposed low entropy of organisms and its preservation are revised. Absolute entropy of the mixed components of non-living biomass (around -1.6 x 103 J K-1 L-1) is the reference to which other entropy decreases would be ascribed to life. Compartmentation of metabolites and departure from the equilibrium of metabolic reactions account for 1 and 40-50 J K-1 L-1, respectively, decreases of entropy and, though small, are distinctive features of living tissues. DNA and proteins do not supply significant decreases of thermodynamic entropy, but their low informational entropy is relevant for life and its evolution. No other living feature contributes significantly to the low entropy associated to life. The photosynthetic conversion of radiant energy to biomass energy accounts for the most of entropy (2.8 x 105 J K-1 carbon kg-1) produced by living beings. The comparative very low entropy produced in other processes (around 4.8 x102 J K-1 L-1 day-1 in human body) must be rapidly exported outside as heat to preserve the low entropy decreases due to compartmentation and non-equilibrium metabolism. Enzymes and genes are described whose control minimize the rate of production of entropy and could explain selective pressures in biological evolution and the rapid proliferation of cancer cells.

Entropy is usually understood as the quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are definitely obscure. This leads to numerous misinterpretations of entropy. We propose to see the disorder as an absence of symmetry and to identify “ordering” with symmetrizing of a physical system; in other words, introducing the elements of symmetry into initially disordered physical system. We demonstrate with the binary system of elementary magnets that introducing elements of symmetry necessarily diminishes its entropy. This is true for 1D and 2D systems of elementary magnets. Imposing symmetry does not influence the Landauer Principle valid for the addressed systems. Imposing the symmetry restrictions onto the system built of particles contained within the chamber divided by the permeable partition also diminishes its entropy.

Multifunctional landscapes are complex systems that integrate biophysical, cultural-historical and socio-economic components into unique territorial structures and regional ensembles. Facing increasing pressures generated by urbanization, climate change and overexploitation of natural resources, assessing the sustainability of these landscapes has become an urgent priority. The present research is based on the development and parametrization of a new tool for evaluating the sustainability of multifunctional landscapes that aims to measure the level of biocultural resilience of a landscape, integrating biological, cultural and socio-economic indicators in a single analytical framework. This index, called the biocultural resilience index (BRI), provides a holistic perspective on the dynamics of landscapes, allowing the identification of vulnerability areas and the development of conservation and sustainable management strategies. The evaluation of the of multifunctional landscapes sustainability requires a comprehensive approach that has to integrate both biological aspects, such as biodiversity and ecosystem health, as well as identity and cultural aspects, such as cultural value and the relationship of the local communities with the environment. In this context, this study highlights the fact that the development of appropriate tools and methods for assessing and monitoring the sustainability of multifunctional landscapes becomes essential for their sustainable management and for protecting the benefits they offer to society. Our findings show that the biocultural resilience index (BRI) can be used in a variety of contexts and fields, including spatial planning, biodiversity conservation, sustainable rural development and ecotourism. In the meanwhile, this index offers a robust and flexible analytical framework, adaptable to the needs and particularities of different regions and communities.

The numerical simulation of entropy generation at mixed natural free and forced convection flow in a square lid-driven cavity filled with an eletrically conducting binary fluids saturated porous media in the presence of a magnetic field is performed in this investigation. Both the top and bottom horizontal walls of the cavity are kept at constant and different temperatures while the left and right vertical walls are adiabatic and insulated. The magnetic field is applied in normal direction to the cavity. The Darcy model, including Brinkman term relative to viscous effects and Forchheimer term due to inertial forces, is used for the momentum equations, and the SIMPLER algorithm, based on the control volume finite-element method approach is used to solve the pressure –velocity coupling. The flow pattern and the heat transfer characteristics inside the cavity are presented in the form of isotherms, streamlines and isentropic lines and average Nusselt number trend. The entropy generation rate is determined for various values of Darcy number (10^-3 ≤ Da ≤ 1) and for a range of Hartmann number (0 ≤ Ha ≤ 10²). This study is limited to Pr = 7 which corresponds to water. It is observed that entropy generation is very affected by the variations of dimensionless control parameters considered.

Quantum physics is intrinsically probabilistic. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such state. The degrees of freedom of a quantum state are position and spin, and upon their specification Born's rule in phase space defines randomness. We focus on the spin degree of freedom and elucidate the spin entropy. Then, we present some of its properties and show how entanglement increases spin entropy. Some speculative predictions on the decay of the $Z^0,W^{+,-}$ gauge bosons conclude the paper.

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.

Unquestionably the rapidly changing climate and, therefore, alterations in the associated bioclimate, constitute an alarming reality with implications in daily practice and natural capital management. In this research the present and projected bioclimate evolution over the phytogeographical regions of Greece is displayed. For this purpose, ultrahigh-resolution computation results on the spatial distribution of the Emberger index’s Q2 classes of bioclimatic characterisation are analysed and illustrated for the first time. The assessments are performed over the reference period (1970–2000) and two future time frames (2021–2040; 2041–2060) under the RCP4.5 and RCP8.5 emission scenarios. By 2060 and under the extreme RCP8.5, intense xerothermic trends are demonstrated owing to the resulting significant spatial evolution mainly of the Arid-Hot, Semi-Arid-Very Hot, Semi-Arid-Hot and Semi-Arid-Temperate Q2 classes, respectively, over the phytogeographical regions of Kiklades (up to 29% occupation), Kriti and Karpathos (up to 30%), West Aegean Islands (up to 26%), North East (up to 56%)–North Central (up to 31%). The RCP8.5 long-term period exhibits the strongest impacts over approximately the right half of the Greek territory the bioclimate of which appears as more dry-thermal in the future.

This paper initiates the study of the mathematical aspects of the ad-hoc Lanzhou index. If G is a graph with the vertex set {x1,⋯,xn}, then the ad-hoc Lanzhou index of G is defined by Lz¯(G)=∑i=1ndi(n−1−di)2, where di represents the degree of the vertex xi. Several identities for the ad-hoc Lanzhou index, involving some existing topological indices are established. The problems of finding graphs with the extremum values of the ad-hoc Lanzhou index from the following sets of graphs are also attacked: (i) set of all connected ξ-cyclic graphs of a fixed order, (ii) set of all connected molecular ξ-cyclic graphs of a fixed order, (iii) set of all graphs of a fixed order, (iv) set of all connected molecular graphs of a fixed order.

Strong yet ductile alloys have long been desired for industrial applications to enhance structural reliability. This work produced two (CoCrNi)93.5Al3Ti3C0.5 medium-entropy alloys with exceptional strength-ductility combinations, via short/medium (3 min/30 min)-time annealing after hot-rolling. Three types of intergranular precipitates including MC, M23C6 carbides, and L12 phase were detected in both the samples. Noticeably, the high density of intragranular L12 precipitates were only founded in the medium-time annealed sample but not in another one. Upon inspection of deformed substructure, it was revealed that the plane slip is the dominant deformation mechanism of both the alloys. This is related to the lower stacking fault energy, higher lattice friction induced by C solute, and slip plane softening caused by intragranular dense L12 precipitates. Additionally, we noted that the stacking fault and twinning act as the mediated mechanisms in deformation of the short-time annealed alloy, while only the former in the medium-time annealed one. It is attributed to the higher energy stacking faults and the increased critical twinning stress caused by intragranular dense L12 precipitates that inhibited the twinning tendency. Our present findings provide not only a guidance for optimizing the mechanical properties of high/medium-entropy alloys, but also a fundamental understanding of deformation mechanisms.

The model of an oscillating universe proposed by A. Friedmann in 1922 dominated cosmology for a long time. R. Tolman put forward a thermodynamic argument against the cyclic cosmological model, believing that entropy should accumulate from cycle to cycle. J. Bekenstein and S. Hawking discovered a tremendous amount of entropy associated with black holes. This discovery led to the conclusion that the majority of the Universe's entropy is contained in black holes. N. Poplawski considers a Universe that oscillates within a black hole. This paper analyzes the relationship between the entropy of black holes and the oscillating Universe inside a large black hole. It is demonstrated that the entropy of a black hole can only be defined for an external observer. For an observer inside the black hole, its entropy is zero. This opens up the possibility of constructing a cyclic cosmology in which entropy and the size of the visible part of the Universe change strictly periodically. This does not violate the second law of thermodynamics because the continuous accumulation of entropy from cycle to cycle pertains to the surface of the big black hole, which is invisible to the internal observer.

Proteins in biological systems function at the interface of single molecule and bulk chemistry and thus provide novel insights into the basic physical chemistry of scaling and emergent phenomena. For example, a binary mechanical model based on the chemistry of muscle contraction unifies molecular mechanics and thermodynamics and provides an explicit solution to the Gibbs paradox. Using the same model system, here I show that chemical activities of molecular states have no effect on chemical kinetics or energetics. Specifically, while the concentration or number of molecules in a molecular state is widely thought to contribute to reaction free energies, here I show that it is not the physical presence of molecules that pushes a reaction forward but the number of microstates, , accessible in a chemical state that pulls a reaction toward equilibrium with an entropic force down an entropic funnel. With the derivation of an entropic contribution to chemical kinetics, I develop a novel chemical kinetic formulation that fully describes the chemical thermodynamics of both equilibrium and non-equilibrium reactions in terms of an a priori system reaction energy landscape.

Living cells are complex systems that may be characterized by fluids crowded by hundreds of different elements in particular by a high density of polymers; they are an excellent and challenging laboratory to study exotic emerging physical phenomena where entropic forces emerge from organization processes of many-body interactions. The competition between microscopic and entropic forces may generate complex behaviors like phase transitions that living cells may use to accomplish their functions. In the era of the big data, when biological information abounds but general principles and precise understanding of the microscopic interactions scarce, the entropy methods may offer significant information. In this work we develop a model where the thermodynamic equilibrium results from the competition between an effective electrostatic shortrange interaction and the entropic forces emerging in a fluid crowded by different size polymers. The target audience for this article are interdisciplinary researchers in complex systems, particularly in thermodynamics and biophysics modeling.

In geotechnical engineering applications, it is very important to obtain the undrained shear strength of remolded soils accurately and reliably. This study aims to obtain a trustworthy solution to determine the undrained shear strength of remolded clay mixtures using Atterberg limit test results in various states of consistency. An experimental study was carried out involving a wide range of clay mixtures of varying plasticity and geological origin. In the analyses, the variation of the remolded undrained shear strength depending on the cone penetration depth, water content, flow index, liquidity index and log liquidity index were investigated. In the study, the highest undrained shear strength of 100% Na-montmorillonite (NaM) was obtained at 171.89 kPa at 56.60% water content, while the lowest undrained shear strength was obtained for 100% Sepiolite (S), 9.28 kPa at 31.65% water content. The results of this study revealed that the shear strength is significantly affected by soil conditions, rather than dominant clay mineral. Besides, it was observed that the undrained shear strength at the plastic limit was approximately 30-35 times greater than that at liquid limit. The equations of liquid limit-flow index and plasticity index- flow index were proposed. It was concluded that the interdependence between undrained shear strength, liquidity index, log liquidity index, and flow index is not unique due to the different physical and chemical properties of clays.

The aim of this report is to evaluate the segmental rib index (RI) from T1-T12 spinal level in mild and moderate idiopathic scoliosis (IS) curves of thoracic, thoracolumbar and lumbar type by gender. The relationship of segmental RI to the frontal plane radiological deformity presented as the Cobb angle and to the posterior truncal surface deformity presented as the scoliometric readings of Angle of Trunk Rotation (ATR) in these patients is also assessed. Any statistical significant rela-tionship of these parameters would be very important for biomechanical relations of the rib cage (RC) deformity presented as the rib hump deformity (RHD) and the deformity in the spine and it would thus provide valuable information about scoliogeny. The segmental rib index (RI) is presented in 83 boys and girls with mild and moderate IS. The measurements include the scoliometric readings for truncal asymmetry (TA), the Cobb angle assessment and the segmental RI from T1-T12. The statistical package SPSS 23 was used for statistical analysis. The TA is documented and the Cobb angle is presented by gender and curve type. The segmental RI of thoracic, thoracolumbar and lumbar curves are presented for the first time. The correlations of the segmental RI to surface deformity presented as the rib hump deformity (RHD) in all IS patients and particularly in thoracic curves, to Cobb angle by gender and age and the comparison of the segmental RI index of asymmetric but not scoliotic children to the scoliotic peers by curve (in thoracic, thoracolumbar, lumbar curves) in boys and girls are presented. The findings emphasize the significant protagonistic role of the thoracic asymmetry in relation to the spinal deformity mainly in girls for the thoracic and in boys for the thoracolumbar curves. The cut-off point of age of the examined scoliotics is 14 years, that is when the RI shows stronger correlation with the spinal deformity, namely when the thoracic deformity is decisively effective to the developing thoracic spinal deformity, in terms of Cobb angle. In summary, the results of this study provide aetiological implications for IS, as far as the role of thorax is con-cerned.

The Metropolitan Economic Freedom Index (MEFI) ranks cities based on their support of free market enterprise. In its current state, MEFI purports to measure three constructs (government spending, taxation, and labor market freedom) with three equally weighted variables for each one, assuming perfect substitutability of variables. This study investigates the statistical consistency of MEFI through Confirmatory Factor Analysis. Multiple models investigate current variable selection by providing a potentially better indicator of labor market freedom, aggregation assumptions by removing the requirements for fixed and equal weights, and statistical consistency by evaluating the fit between the data and models. Results indicate that the current MEFI model is not statistically consistent with the data, that weighting of variables should not be equal, that variable selection should be investigated, and that constructs should be re-imagined. The models investigated provide an initial starting point for redefining MEFI.

In this paper, we introduce generalized entropy, the acceleration of its entropy and its the partial entropy. We assume that generalized entropy can be expressed as a second-order polynomial by applying the idea of logistics function to its entropy. In other words, we assume that the acceleration of generalized entropy is a constant. Besides, we show that the inverse of the partial entropy can express Newton's classical gravity, which is an inverse square law. By applying these concepts, we attempt to explain that 1) Gravity is constant within small distances with some conditions, It is possible that there exists 6-states within the distance R is small. Furthermore, within small distance, we show the possibility that the gravitational potential and the Coulomb potential can be treated in the same way. that 2) The rotation speed of a galaxy does not depend on its radius if the radius is within the size level of the universe. (the galactic rotation curve problem), and that 3) The gravitational acceleration toward the center changes at long distances compared to the classical theory of gravity. Furthermore, we show that the possibility of the existence of some constants which controls gravity and the speed of galaxies, and that gravity may relate on entropy.

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations to date that have been fully carried out are discussed in two main situations: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh-Jeans radiation, and second where only these radiation fields exist within a cavity. The emphasis here will be on the first more difficult situation where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in clasical statistical mechanics involving probabilistic notions of phase space occupation, the calculations to date for both particles and fields or for fields alone, follow the caloric entropy method where the notions of heat flow, adiabatic surfaces, and isothermal conditions, are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have been successfully utilized.

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed––are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented––and demonstrated on grease degradation, battery charging and discharging, metal fatigue and pump flow––can be used for design, analysis, and support of diagnostic monitoring and optimization.

Hund's rule of maximum multiplicity is a powerful empirical tool for determining the electron population of electronic shells. It was recently discovered that it is also the rule of minimum Shannon entropy. This study extends these findings to the Aufbau rule and discusses them from the perspective of emergent dimensionality, providing a monotonically increasing entropy function. We observed that some elements that violate the Aufbau rule have the same entropies in the actual and Aufbau electron configurations. On the other hand, lower entropies of all actual elements' configurations are associated with higher or equal numbers of unpaired electrons in these configurations compared to the Aufbau configurations. The only exception to this rule is palladium.

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.

Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.

In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].

Double-spiral galaxies are common in the Universe. It is known that the logarithmic double spiral is a Maximum Entropy geometry and represents spiral galaxies well. It is also known that the virial mass of such a galaxy can be approximately determined from the entropy of its central supermassive black hole. But over time the black hole must accrete mass, and therefore the overall galactic entropy must increase. From the associated entropic Euler-Lagrange equation (forming the basis of the Principle of Least Exertion, and also enabling the application of Nöther’s theorem) we show that the galactic entropy production is a conserved quantity, and we derive an appropriate expression for the relativistic entropic Hamiltonian of an idealised spiral galaxy. We generalise Onsager’s celebrated expression for entropy production and demonstrate that galactic entropy production has two parts, one many orders of magnitude larger than the other, and where the smaller is comparable to the Hawking radiation of the central supermassive black hole. We conclude that galaxies cannot be isolated, since even idealised spiral galaxies have non-zero entropy production.

Generalised Modules for Membrane Antigens (GMMA) are outer membrane vesicles derived from Gram-negative bacteria that can be used to design affordable subunit vaccines. GMMA are highly immunogenic and capable to induce an optimal antigen-specific humoral immune response both in animals and humans. Despite their potent immunogenicity, GMMA are usually formulated with aluminum salts (Alum) to reduce their potential systemic reactogenicity. GMMA, in fact, contain agonists of Toll-Like Receptor 4 (TLR4) and TLR2 that possess pro-inflammatory activity. The adsorption of GMMA onto Alum is believed to reduce their systemic exposure. However, it has been found that GMMA formulated without Alum did not induce concerning signs of systemic reactogenicity in the rabbit model. Here we asked whether GMMA promote local reactogenicity. We immunized mice intramuscularly with GMMA alone or formulated with Alum and we analyzed the injection site during 7 days after treatment. We found that GMMA alone promoted only mild inflammation within the muscle, whereas Alum induced severe muscle inflammation, as expected. Thus, in the mouse model, GMMA demonstrated to possess mild reactogenic potential locally, while Alum is confirmed a major driver of local reactogenicity. Our results further support the idea to investigate the reactogenicity of GMMA formulated without Alum in clinical studies.

Droughts have a substantial effect on water resources, agriculture, and ecosystems on a worldwide scale. In the Mekong Delta of Vietnam, droughts exacerbated by climate change are significantly endangering the region's agricultural sustainability and output. Conventional forecasting techniques frequently do not capture the intricate dynamics of meteorological phenomena associated to drought effectively, prompting the exploration of more advanced methodologies. This work utilises artificial intelligence, par-ticularly machine learning methods like Gradient Boosting and Extreme Gradient Boosting (XGBoost), to enhance drought pre-diction in the Mekong Delta. The study utilises data from 11 meteorological stations spanning from 1990 to 2022 to create and evaluate Machine Learning models based on several climatic factors. We utilise Gradient Boosting and XGBoost algorithms to estimate the Standardised Precipitation-Evapotranspiration Index (SPEI) and evaluate their effectiveness in comparison to con-ventional forecasting techniques. The results show that Machine Learning, particularly XGBoost, surpasses traditional approaches in predicting SPEI accuracy at various time scales. XGBoost demonstrates skill in understanding the complex relationships between climatic factors, with R² values falling between 0.90 and 0.94 for 1-month forecasts. The progress highlights the potential of Machine Learning in improving drought management and adaptation tactics, proposing the incorporation of Machine Learning forecasting models into decision-making processes to enhance drought resistance in susceptible areas.

The notion of the informational measure of symmetry is introduced according to: HsymG=-i=1kPGilnPGi, where PGi is the probability of appearance of the symmetry operation Gi within the given 2D pattern. HsymG is interpreted as an averaged uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as HsymD3=1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. Informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. Informational measure of symmetry does not correlate neither with the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns.