Abstract: As a low-input crop, Miscanthus offers numerous advantages that, in addition to agricultural applications, permits its exploitation for energy, fuel, and material production. Depending on the Miscanthus genotype, season, and harvest time as well as plant component (leaf versus stem), correlations between structure and properties of the corresponding isolated lignins differ. Here, a comparative study is presented between lignins isolated from M. x giganteus, M. sinensis, M. robustus and M. nagara using a catalyst-free organosolv pulping process. The lignins from different plant constituents are also compared regarding their similarities and differences regarding monolignol ratio and important linkages. Results showed that the plant genotype has the weakest influence on monolignol content and interunit linkages. In contrast, structural differences are more significant among lignins of different harvest time and/or season. Analyses were performed using fast and simple methods such as nuclear magnetic resonance (NMR) spectroscopy. Data was assigned to four different linkages (A: b-O-4 linkage, B: phenylcoumaran, C: resinol, D: b-unsaturated ester). In conclusion, A content is particularly high in leaf-derived lignins at just under 70 % and significantly lower in stem and mixture lignins at around 60 % and almost 65 %. The second most common linkage pattern is D in all isolated lignins, the proportion of which is also strongly dependent on the crop portion. Both stem and mixture lignins, have a relatively high share of approximately 20 % or more (maximum is M. sinensis Sin2 with over 30 %). In the leaf-derived lignins, the proportions are significantly lower on average. Stem samples should be chosen if the highest possible lignin content is desired, specifically from the M. x giganteus genotype, which revealed lignin contents up to 27 %. Due to the better frost resistance and higher stem stability, M. nagara offers some advantages compared to M. x giganteus. Miscanthus crops are shown to be very attractive lignocellulose feedstock (LCF) for second generation biorefineries and lignin generation in Europe.

The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon’s energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three dimensional continuous version of the three discrete quantum numbers, that leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose’s entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency.

Modularity and organizational hierarchy are important concepts in understanding the structure and evolution of interactions in complex biological systems. In this work, we introduce and use a spectral characterization measure (Spectral Entropy) to quantify modularity in protein-to-protein interaction (PPI) networks in species across the tree of life. We evaluated the relation between the size of a PPI network and its (Spectral Entropy-based) modularity, and found a sigmoidal response between the two. We also found significant differences in the distribution of Spectral Entropy values among the three domains of life (Bacteria, Archaea, Eukaryotes). To explore further correlations with biological traits, we focused solely on bacterial PPI networks, which are the most numerous among the three domains and had associated trait metadata, and investigated how modularity impacts or is impacted by growth, aerobicity, selection and location on the tree of life. We found no relation between maximal growth rate and Spectral Entropy, but a strong dependence between G-C content (a proxy for selection) and Spectral Entropy. We also discovered that Spectral Entropy is negatively affected by phylogenetic placement (evolutionary distance from the last universal common ancestor). The general nature of the Spectral Entropy measure of hierarchical modularity in networks suggests that it will be useful in other settings where structural properties of real-world networks are being compared.

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.

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

To ensure consumers can purchase high-quality rice, accurate identification of rice varieties is particularly important. Methods: This article conducts research based on machine learning algorithms from the perspectives of image, spectrum, and spectrogram fusion. Six types of hyperspectral image data of rice were preprocessed using convolutional smoothing (SG) and multiple scatter correction (MSC). Texture information of the images was extracted using gray-level co-occurrence matrix. Spectra, texture, and spectrogram data were fused into a new matrix. Spectral, texture, and spectrogram fusion data were used as inputs for the model, and support vector machines (SVM), logistic regression (LR), and K-nearest neighbors (KNN) classification models were constructed and compared. Results: From the classification results, the spectrogram fusion classification performance was better than classification models using only spectra or texture. Conclusion: The research results showed that the accuracy of SVM and LR classification models exceeded 90%, and the LR model performed the best, effectively classifying rice varieties.

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 growing interest in benchtop NMR systems is visible in a vast number of applications in science and industry. Low-field nuclear magnetic resonance (LF-NMR) became an instant in technologies that productions are dependent on the reliable structure identification, grade and purity control, chemical process inspection or reaction monitoring. Beyond the benefits of being cost-, space-, maintenance- and user friendly, insufficient sensitivity and low signal resolution are the main drawbacks, due to which the low-field NMR (LF-NMR) in the fields of organic chemistry and synthesis remains limited to solely academic teaching purposes. Herein, we discuss the possibilities of LF-NMR for the needs of organic chemistry and synthesis on a set of compounds 1-4 achieved as the products of student’s laboratory course and organic derivatives 5-8 that are from our research interests. Chemical structure determination of all compounds 1-8 presented herein was performed using the benchtop-type NMR instrument operating at 60 MHz (Pulsar Oxford Ltd.). Structure of novel compounds 5-7 prepared under the aims of our research was characterized by combined 1H/19LF-NMR and compared with an appropriate high-field NMR data from Bruker Ascend Instrument (400 MHz). Finally, possibilities of the low-field NMR as an analytical tool for the research purposes in the fields of organic chemistry and synthesis are documented on a set of 1H and 2D 1H-1H COSY for azomethine 8.

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.

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.

Relativistic shocks are one of the most plausible sites of the emission of strongly variable, polarized multi-wavelength emission from relativistic jet sources such as blazars, via diffusive shock acceleration (DSA) of relativistic particles. This paper summarizes recent results on a self-consistent coupling of diffusive shock acceleration and radiation transfer in blazar jets. We demonstrate that the observed spectral energy distributions (SEDs) of blazars strongly constrain the nature of hydromagnetic turbulence responsible for pitch-angle scattering by requiring a strongly energy-dependent pitch-angle mean free path. The prominent soft X-ray excess (``Big Blue Bump'') in the SED of the BL Lac object AO 0235+164 can be modelled as the signature of bulk Compton scattering of external radiation fields by the thermal electron population, which places additional constraints on the level of hydromagnetic turbulence. It has further been demonstrated that internal shocks propagating in a jet pervaded by a helical magnetic field naturally produce polarization-angle swings by 180$^o$, in tandem with multi-wavelength flaring activity, without requiring any helical motion paths or other asymmetric jet structures. The specific application of this model to 3C279 presents the first consistent, simultaneous modeling of snap-shot SEDs, multi-wavelength light curves and time-dependent polarization signatures of a blazar during a polarization-angle (PA) rotation. This model has recently been generalized to a lepto-hadronic model, in which the high-energy emission is dominated by proton synchrotron radiation. It is shown that in this case, the high-energy (X-ray and $\gamma$-ray) polarization signatures are expected to be significantly more stable (not showing PA rotations) than the low-energy (electron-synchrotron) signatures.

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.

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.

Weak signal spectral detection is a serious problem in many applications, especially the target possesses certain frequency band and under low signal-to-noise ratio (SNR). A kind of novel technique based on pre-whitening scale-transformation symmetric bistable parallel stochastic resonance (SR) is proposed to solve the problem. Firstly, the pre-whitening can ensure the even distribution of the receiving signal to fit the requirement of SR processing. Secondly, the scale- transformation can help to utilize the weak signal improvement property especially under low frequency band more effectively. Thirdly, the symmetric bistable parallel SR can try to reduce the variance of the clutter and additive noise fluently. Fourthly, by subtracting the steady state re-sponse of the selected symmetric bistable SR system from the parallel SR output, the weak signal spectral detection objective can be realized successfully. Simulation results based on the real sea clutter radar data guarantee the effectiveness and applicability of the proposed symmetric bistable PSR processing approach.

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.

The relentless advancement and integration of mechanization and intelligence within the coal mining industry, combined with the increasing depths of mining operations, necessitate significantly higher safety standards. This necessity arises due to the increasingly complex geological and coal seam conditions encountered as mining operations delve deeper into the earth. Traditionally, 3D seismic exploration technology has been fundamental in ensuring both operational efficiency and safety in the coal mining sector. However, despite its critical role, this technology still has limitations in detecting and characterizing small-scale geological structures which can pose substantial risks if not accurately identified and mitigated. To address these challenges, this paper introduces a sparsity-constrained adaptive hard thresholding algorithm designed to tackle the spectral inversion optimization problem with an norm constraint for the enhanced retrieval of reflection coefficients, thereby establishing a comprehensive workflow for enhancing seismic data resolution through compressed sensing spectral inversion. Real data validation has demonstrated that this method significantly enhances the resolution of seismic data while maintaining the amplitude integrity and fidelity of the original signals. This improvement allows for a more detailed and accurate characterization of small-scale geological features, which are critical in identifying and mitigating potential hazards within coal mining operations, thus offering robust support for the implementation of more effective safety protocols and disaster prevention strategies in coal mines.

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.

The efficacy of predicting geochemical parameters with a 2-chain workflow using spectral data as the initial input is evaluated. Spectral measurements spanning the approximate 400-25000nm spectral range are used to train a workflow consisting of a non-negative matrix function (NMF) step, for data reduction, and a random forest regression (RFR) to predict 8 geochemical parameters. Approximately 175000 spectra with their corresponding chemical analysis were available for training, testing and validation purposes. The samples and their spectral and chemical parameters represent 9399 drillcore. Of those, approximately 20000 spectra and their accompanying analysis were used for training and 5000 for model validation. The remaining pairwise data (150000 samples) were used for testing of the method. The data are distributed over 2 large spatial extents (980 km2 and 3025 km2 respectively) and allowed the proposed method to be tested against samples that are spatially distant from the initial training points. Global R2 scores and wt.% RMSE on the 150000 validation samples are Fe(0.95/3.01), SiO2(0.96/3.77), Al2O3(0.92/1.27), TiO(0.68/0.13), CaO(0.89/0.41), MgO(0.87/0.35), K2O(0.65/0.21) and LOI(0.90/1.14), given as Parameter(R2/RMSE), and demonstrate that the proposed method is capable of predicting the 8 parameters and is stable enough, in the environment tested, to extend beyond the training sets initial spatial location.

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.

In this study, a novel method is proposed to estimate surface-spectral reflectance from camera responses that combines model-based and training-based approaches. An imaging system is modeled using the spectral sensitivity functions of an RGB camera, spectral power distributions of multiple light sources, unknown surface-spectral reflectance, additive noise, and a gain parameter. The estimation procedure comprises two main stages: (1) selecting the local optimal reflectance dataset from a reflectance database and (2) determining the best estimate by applying a neural network to the local optimal dataset only. In stage (1), the camera responses are predicted for the respective reflectances in the database, and the optimal candidates are selected in the order of lowest prediction error. In stage (2), most reflectance training data are obtained by a convex linear combination of local optimal data using weighting coefficients based on random numbers. A feed-forward neural network with one hidden layer is used to map the observation space onto the spectral reflectance space. In addition, the reflectance estimation is repeated by generating multiple sets of random numbers, and the median of a set of estimated reflectances is determined as the final estimate of the reflectance. Experimental results show that the estimation accuracies exceed those of other methods.

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.

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.

The study employed simulation-based measurement approaches to evaluate and compare the performance of conventional networks to IRS-enhanced systems in terms of upstream spectral efficiency. The study discovered that applying IRS greatly improves coverage, or transmitting potency, for 6G services.

As a renewable industrial crop, Miscanthus offers numerous advantages, namely high photosynthesis activity (as a C4 plant) and exceptional CO2 fixation rate. These properties make Miscanthus very attractive for industrial exploitation, such as lignin generation. Here, we present a systematic study analyzing the correlation of the lignin structure with Miscanthus genotype and plant portion (stem versus leaf). Specifically, the ratio of the three monolignols and corresponding building blocks as well as the linkages formed between the units have been studied. Depending on the Miscanthus genotype and plant component (leaf versus stem), correlations between chemical structure and properties of the lignins have been determined, i.e. correlations in molecular weight, polydispersity and decomposition temperature. Lignin isolation was performed using non-catalyzed organosolv pulping and the structure analysis includes NREL, FTIR, UV-Vis, HSQC-NMR, TGA, pyrolysis GC/MS. Structural differences were found for stem and leaf-derived lignins. Compared to beech wood lignins, Miscanthus lignins possess lower molecular weight and narrow polydispersities (< 1.5 Miscanthus vs. > 2.5 beech) corresponding to improved homogeneity. In addition to conventional univariate analysis of FTIR spectra, multivariate chemometrics revealed distinct differences for aromatic in-plane deformations of stem versus leaf-derived lignins. These results emphasize the potential of Miscanthus as low-input resource and Miscanthus-derived lignin as promising agricultural feedstock.

The optimal functionality and dependability of mechanical systems are important for the sustained productivity and operational reliability of industrial machinery which has direct impact on it’s longevity and profitability. Therefore, failure of a mechanical system or any of it component would be detrimental to production continuity and availability. Consequently,this study proposes a robust diagnostic framework for analyzing the blade conditions of shot blast industrial machinery. The framework involves analyzing the spectral characteristics of the vibration signals generated by Industrial Shot Blast. Additionally, a peak detection algorithms is introduced to identify and extract the unique features present in the peak magnitudes of each signal spectrum. A feature importance algorithm is then deployed as the feature selection tool, and these selected features are fed into 10 machine learning classifier, with Extreme gradient boosting (XGB) as the core classifier. Results show that the XGB classifier achieved the best accuracy of 98.05%, with a cost-efficient computational cost of 0.83 seconds. Other global assessment metrics were also implemented in the study to further validate the model.

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.

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.

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 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.

The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis.

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.

This study describes a novel method for grading pathological sections of gliomas. Our own integrated hyperspectral imaging system was employed to characterize 270 bands of cancerous tissue samples from microarray slides of gliomas. These samples were then classified according to the guidelines developed by the World Health Organization, which define the subtypes and grades of diffuse gliomas. We explored a hyperspectral feature extraction model called SMLME-Resnet using microscopic hyperspectral images of brain gliomas of different malignancy grades. The model combines the channel attention mechanism and multi-scale image features to automatically learn the pathological organization of gliomas and obtain hierarchical feature representations, effectively removing the interference of redundant information. It also completes multi-modal, multi-scale spatial and spectral feature extraction to improve the automatic classification of glioma subtypes. The proposed classification method demonstrated high average classification accuracy (>97.3\%) and Kappa coefficient (0.954), indicating its effectiveness in improving the automatic classification of hyperspectral gliomas. The method is readily applicable in a wide range of clinical settings, offering valuable assistance in alleviating the workload of clinical pathologists. Furthermore, the study contributes to the development of more personalized and refined treatment plans, as well as subsequent follow-up and adjustment of treatment, by providing physicians with insights into the underlying pathological organization of gliomas.

A Q-switched Nd:YAG laser was focused on Pb-Ti alloy samples in several Laser Induced Breakdown experiments in order to measure the Stark parameters of several spectral lines (58) of single ionized Titanium including the 3504.89 Å, and the 3510.83 Ålines (where we aported new experimental and theoretical values).Diagnostics of the laser induced plasmas (electron density and electron temperature) was performed using Balmer’s H alpha line (6562.7 Å).Temperatures were obtained by the Boltzmann Plot technique with spectral lines of Pb I (after correction for its evident self-absorption).Subsequently, calculations by the Griem approach of the Stark broadening parameters for several spectral lines were performed using the Gaunt factors proposed by Van Regemorter and those proposed by Douglas H. Sampson. In the latter cases the values obtained were very close to the experimental values. It allows us to assume that the calculations made for the spectral lines of Ti II, without experimental information, are more accurate using the Gaunt factors proposed by Sampson.

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.

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.

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).

Aerial image classification has become popular and has attracted extensive research efforts in recent decades. The main challenge lies in its very high spatial resolution but relatively insufficient spectral information. To this end, spatial-spectral feature extraction is a popular strategy for classification. However, parameter determination for that feature extraction is usually time-consuming and depends excessively on experience. In this paper, an automatic spatial feature extraction approach based on image raster and segmental vector data cross-analysis is proposed for the classification of very high spatial resolution (VHSR) aerial imagery. First, multi-resolution segmentation is used to generate strongly homogeneous image objects and extract corresponding vectors. Then, to automatically explore the region of a ground target, two rules, which are derived from Tobler’s First Law of Geography (TFL) and a topological relationship of vector data, are integrated to constrain the extension of a region around a central object. Third, the shape and size of the extended region are described. A final classification map is achieved through a supervised classifier using shape, size, and spectral features. Experiments on three real aerial images of VHSR (0.1 to 0.32 m) are done to evaluate effectiveness and robustness of the proposed approach. Comparisons to state-of-the-art methods demonstrate the superiority of the proposed method in VHSR image classification.

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.

Background: Depression presents with altered energy regulation and neural plasticity. Previous electroencephalography (EEG) studies showed that practice increases power in beta range (13-30 Hz) in healthy subjects but not in those with impaired plasticity. Here, we ascertain whether depression presents with alterations of spectral activity and connectivity before and after practice. Methods: We used publicly available resting state EEG (64 electrodes) of 122 subjects. Based on Beck Depression Inventory (BDI) score, they were assigned to either high BDI (hBDI, BDI&gt;13, N=46) or control (CTL, BDI&lt;7, N=75) group. We analyzed spectral activity, theta-beta and theta-gamma phase-amplitude coupling (PAC) of EEG recorded before and after a learning task. Results: At baseline, compared to CTL, hBDI group exhibited greater beta power over fronto-parietal regions and gamma over right parieto-occipital area. After practice, increases in all frequency ranges were observed only in CTL. Theta-beta and theta-gamma PAC were greater in hBDI before the task but not after the task. Conclusions: The lack of substantial post-task growth of beta power in depressed subjects likely represents power saturation due to greater baseline values. We speculate that inhibitory/excitatory imbalance, altered plasticity mechanisms, and energy dysregulation present in depression may contribute to this phenomenon.

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.

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.

In this study, seventeen faceted gem-quality chrysoberyls exhibiting an attractive canary yellow color were investigated by a series of gemological, spectral, and chemical methods. Microscopic observation reveals distinct growth lines and inclusions, including CO2 fluids, carbon, and mineral crystals such as calcite, quartz, sillimanite, and mica, identified by the Raman spectrum. The FTIR spectrum exhibits the 2405 and 2160 cm-1 feature peaks and a 3223 cm-1 peak in all samples, which can be accompanied by the 3112 cm-1 shoulder, 3301, and 3412 and 3432 cm-1 peaks. The UV-Vis spectrum shows a Fe-related peak at 440 nm, along with the 650–660 nm band and the absorption band in the blue zone of the visible light. The chemical results of EDXRF reveal a V-poor, Cr-poor, and Fe-rich feature. The spectral and chemical results could contribute to explaining the origin of the canary yellow color, which originates from the abundant amount of Fe with very little influence from Cr or V.

The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The phenomenon is investigated in the context of a nonrelativistic, spinless particle with mass m confined in a one-dimensional box, combining the spectral decomposition of the initially localized wave function (treated as a coherent superposition of energy eigenfunctions) with a dynamical analysis based on the hydrodynamic or Bohmian formulation of quantum mechanics. Actually, such a decomposition has been used to devise a simple and efficient analytical algorithm that simplifies the computation of velocity fields (flows) and trajectories. As it is shown, the development of space-time patters inside the cavity depends on three key elements: the shape of the initial wave function, the mass of the particle considered, and the relative extension of the initial state with respect to the total length spanned by the cavity. From the spectral decomposition it is possible to identify how each one of these elements contribute to the localized matter wave and its evolution; the Bohmian analysis, on the other hand, reveals aspects connected to the diffraction dynamics and the subsequent appearance of interference traits, particularly recurrences and full revivals of the initial state, which constitute the source of the characteristic symmetries displayed by these patterns. It is also found that, because of the presence of confining boundaries, even in cases of increasingly large box lengths, no Fraunhofer-like diffraction features can be observed, as happens when the same wave evolves in free space. Although the analysis here is applied to matter waves, its methodology and conclusions are also applicable to confined modes of electromagnetic radiation (e.g., light propagating through optical fibers).

In this work, we propose simple and robust technique for the retrieval of underlying surface spectral albedo using spaceborne observations. It can be used to process both multispectral moderate resolution satellite data and also multi - zone high spatial resolution data. The technique can work automatically for different types of land surfaces without using huge databases accumulated in advance. The new cloud discrimination and retrieval of the water vapor content in atmosphere procedures are presented. The key point of the proposed atmospheric correction technique is the suggested single-wavelength method for determining the atmospheric aerosol optical thickness without reference to a specific type of underlying surface spectrum. The retrievals of spectral albedo for various land surfaces with developed technique, performed using computer simulation and experimental data, have demonstrated a high retrieval accuracy.

Bistatic radar experiments have been used to study surface characteristics of extra-terrestrial bodies in the Solar System, including the Moon, Venus, Mars, and Titan. This paper proposes a 3D model to characterize the scattered field of a Gaussian rough surface on an extra-terrestrial body for an orbital bistatic radar configuration. Specifically, this model will investigate how the variability of surface roughness impacts the spectral broadening of the received signal using physical optics approximations and ray tracing on a surface model using a facet approach with Gaussian properties. A linear relationship between spectral broadening of the signal and surface roughness was found. This relationship is in line with results obtained by commonly used analytical models for bistatic radar on planetary surfaces.

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.

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.

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For the Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0 and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for the Geronimus transformations.

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.

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.

As a fast and nondestructive spectroscopic analysis technique, Raman spectroscopy has been widely applied in chemistry. However, noise is usually unavoidable in Raman spectra. Hence, denoising is an important step before Raman spectral analysis. A novel spectral denoising method based on variational mode decomposition (VMD) was introduced to solve the above problem. The spectrum is decomposed into a series of modes (uk) by VMD. Then, the high frequency noise modes are removed and the remaining modes are reconstructed to obtain the denoised spectrum. The proposed method was verified by two artificial noised signals and two actual Raman spectra. As comparison, empirical mode decomposition (EMD), Savitzky-Golay (SG) smoothing and discrete wavelet transformation (DWT) are also investigated. At the same time, signal-to-noise ratio (SNR) was introduced as evaluation indicators to verify the performance of the proposed method. The results show that compared with EMD, VMD can significantly improve mode mixing and endpoint effect. Some information of the small sharp peak is lost after VMD denoising. However, VMD lost fewer information than that of EMD, SG smoothing and DWT. Moreover, the Raman spectrum by VMD denoising is more excellent than that of EMD, SG smoothing and DWT in terms of visualization and SNR. Therefore, VMD provides superior denoising capabilities for Raman spectra.

Despite great technical capabilities, the theory of non-contact temperature measurement is usually not fully applicable to the use of measuring instruments in practice. While black body calibrations are in practice well established and easy to accomplish, this calibration protocol is never fully applicable to measurements of real objects under real conditions. Currently, the best approximation to real world radiation thermometry is grey body radiation thermometry, which is supported by most measuring instruments to date. Nevertheless, the metrological requirements necessitate traceability, therefore real body radiation thermometry is required for temperature measurements of real bodies. This article documents the current state of temperature calculation algorithms for radiation-thermometers and the creation of a traceable model for radiation thermometry of real bodies that uses a digital twin model of the system of measurement to compensate for the loss of data, caused by spectral integration, which occurs when thermal radiation is absorbed on the active surface of the sensor. To solve this problem, a hybrid model with variable scalar inputs is proposed, in which the scalar input parameters are calculated to correspond to the system of measurement. The method for calculating the effective parameters is proposed and verified with the theoretical model of non-contact thermometry. The sum of effective instrumental parameters is presented for different temperatures to show that the rule of radiation thermometry of grey bodies, according to which the sum of instrumental emissivity and instrumental reflectivity equals to 1, does not hold in radiation thermometry for real bodies. Using the derived models of radiation thermometry, the uncertainty of radiation thermometry due to the uncertainty of spectral emissivity is analysed by simulated measurements along the temperature ranges of various radiation thermometers, enabling traceable non-contact temperature measurements with known measurement uncertainty under any known conditions.

Stark widths for 23 transitions in Al IV have been calculated employing modified semiempirical method. The results are obtained for an electron density of 10^17 cm−3 and temperatures from 10,000 K up to 160,000 K. The results obtained in this investigation are used for the examination of the influence of Stark broadening in Al IV stellar spectra, as well as to check Stark width regular behavior and similarites within Al IV spectrum.

This paper presents a novel CNN-based architecture, referred to as Q-Net, to learn local feature descriptors that are useful for matching image patches from two different spectral bands. Given correctly matched and non-matching cross-spectral image pairs, a quadruplet network is trained to map input image patches to a common Euclidean space, regardless of the input spectral band. Our approach is inspired by the recent success of triplet networks in the visible spectrum, but adapted for cross-spectral scenarios, where for each matching pair there are always two possible non-matching patches; one for each spectrum. Experimental evaluations on a public cross-spectral VIS-NIR dataset shows that the proposed approach improves the state-of-the-art. Moreover, the proposed technique can also be used in mono-spectral settings, obtaining a similar performance to triplet network descriptors, but requiring less training data.

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.

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.

Spectral image analysis has the potential to replace traditional approaches for assessing plant responses to different types of stress including herbicide, through non-destructive and high-throughput screening (HTS). Therefore, this study was conducted to develop a rapid bioassay method using a multi-well plate and spectral image analysis for diagnosis of herbicide activity and mode of action. Crabgrass (Digitaria ciliaris) as a model weed was cultivated in multi-well plates and subsequently treated with 6 herbicides with different modes of action when they reached the 1-leaf stage, using only a quarter of the recommended dose. To detect plant response to herbicides, plant spectral images were acquired after herbicide treatment using RGB, infrared (IR) thermal, and chlorophyll fluorescence (CF) sensors and analyzed for diagnosing herbicide efficacy and mode of action. Principal Component Analysis (PCA) using all spectral data successfully distinguished herbicides and clustered depending on their modes of action. The performed experiments have shown that the multi-well plate assay combined with spectral image analysis can be successfully applied for herbicide bioassay. In addition, the use of spectral image sensors, especially in CF image, would facilitate HTS by enabling rapid observation of herbicide response, as early as 3 hours after herbicide treatment.

Selecting drought-tolerant and more water-efficient wheat genotypes is a research priority, spe-cifically in regions with irregular rainfall or areas where climate change is expected to result in reduced water availability. The objective of this work was to use high-throughput measurements with morphophysiological traits to characterize wheat genotypes in relation to water stress. Field experiments were conducted from May to September 2018 and 2019, using a sprinkler bar irriga-tion system to control water availability to eighteen wheat genotypes: BRS 254; BRS 264; CPAC 01019; CPAC 01047; CPAC 07258; CPAC 08318; CPAC 9110; BRS 394 (irrigated biotypes) and Aliança; BR 18_Terena; BRS 404; MGS Brilhante; PF 020037; PF 020062; PF 120337; PF 100368; PF 080492; TBIO Sintonia (rainfed biotypes). The water regimes varied from 22 to 100% of the crop evapotranspiration replacement. Water stress negatively affected gas exchange, vegetation indices and grain yield. High throughput variables TCARI, NDVI, OSAVI, SAVI, PRI, NDRE and GNDVI had higher correlation with yield and morphophysiological measurements. The drought re-sistance index indicated that genotypes Aliança BRS 254, BRS 404, CPAC 01019, PF 020062, and PF 080492 were more drought tolerant.

It is strongly desirable to accurately detect the clouds in hyperspectral images onboard before compression. However, conventional onboard cloud detection methods are not appropriate to all situation such as shadowed cloud or darken snow covered surfaces which are not identified properly in the NDSI test. In this paper, we propose a new spectral–spatial classification strategy to enhance the orbiting cloud screen performances obtained on hyperspectral images by integrating threshold exponential spectral angle map (TESAM), adaptive Markov random field (aMRF) and dynamic stochastic resonance (DSR). TESAM is performed to classify the cloud pixels coarsely based on spectral information. Then aMRF is performed to do optimal process by using spatial information, which improved the classification performance significantly. Some misclassification points still exist after aMRF processing because of the noisy data in the onboard environment. DSR is used to eliminate misclassification points in binary labeling image after aMRF. Taking level 0.5 data from hyperion as dataset, the average overall accuracy of the proposed algorithm is 96.28% after test. The method can provide cloud mask for the on-going EO-1 images and related satellites with the same spectral settings without manual intervention. The experiment indicate that the proposed method reveals better performance than the classical onboard cloud detection or current state-of-the-art hyperspectral classification methods.

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.

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 negative 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 gravity have 5-states within small distance. 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 galaxy rotation curve problem), and that 3) The gravitational acceleration toward the center changes at long distances compared to the classical theory of gravity. We show that it is an extension of Newton's 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.

Hyperspectral anomaly detection is to recognize anomalies from complex scene in an unsupervised way. Currently, many spectral-spatial detection methods have been proposed with a cascaded manner. However, they often neglect complementary characteristics between spectral and spatial dimensions, which easily leads to yield high false alarm rate. To alleviate this issue, a spectral-spatial information fusion (SSIF) method is designed for hyperspectral anomaly detection. First, an isolation forest is exploited to obtain spectral anomaly map, in which the object-level feature is constructed with entropy rate segmentation algorithm. Then, a local spatial saliency detection scheme is proposed to produce spatial anomaly result. Finally, the spectral and spatial anomaly scores are integrated together followed by a domain transform recursive filtering to generate the final detection result. Experiments on five hyperspectral datasets prove that the proposed SSIF produces superior detection result over other state-of-the-art detection techniques.

Spectral unmixing represents both an application per se and a pre-processing step for several applications involving data acquired by imaging spectrometers. However, there is still a lack of publicly available reference data sets suitable for the validation and comparison of different spectral unmixing methods. In this paper we introduce the DLR HyperSpectral Unmixing (DLR HySU) benchmark dataset, acquired over German Aerospace Center (DLR) premises in Oberpfaffenhofen. The dataset includes airborne hyperspectral and RGB imagery of targets of different materials and sizes, complemented by simultaneous ground-based reflectance measurements. The DLR HySU benchmark allows a separate assessment of all spectral unmixing main steps: dimensionality estimation, endmember extraction (with and without pure pixe assumption), and abundance estimation. Results obtained with traditional algorithms for each of these steps are reported. To the best of our knowledge, this is the first time that real imaging spectrometer data with accurately measured targets are made available for hyperspectral unmixing experiments. The DLR HySU benchmark dataset is openly available online and the community is welcome to use it for spectral unmixing and other applications.

In this study, we investigate spectral structure of conformable Sturm-Liouville problems and with this end, we obtain representation of solutions under different initial conditions and asymptotic formulas for eigenfunctions, eigenvalues, norming constants and normalized eigenfunctions. Consequently, we prove the existence of infinitely many eigenvalues. Also, we compare the solutions with graphics with different orders, different eigenvalues, different potentials and so, we observe the behaviors of eigenfunctions. We give an application to the α-orthogonality of eigenfunctions and reality of eigenvalues for conformable Sturm-Liouville problems defined by [15] in the last section.

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.

In the fast-evolving landscape of web services, success relies on optimizing efficiency, reliability, and user satisfaction. Decision-making in real-world applications demands a blend of quantitative (numerical values of quality of Service factors) and qualitative data of experts’ ratings of the quality of service factors. This paper proposes an optimization technique that integrates Hesitant and Intuitionistic Fuzzy Linguistic Terms with TOPSIS, leveraging Entropy Objective weights. There is limited research on Hesitant Intuitionistic Fuzzy Linguistic terms and the need to model fuzziness, haste and intuition in data precisely from experts rating. Thus, this article introduces an Entropy-based model tailored for web service optimization. Using the WS-DREAM dataset, quantitative data was extracted and objective weights were determined through the Entropy algorithm and qualitative evaluations from five experts, employing Hesitant Intuitionistic Fuzzy Linguistic Terms, were integrated. The process involved computing criteria weights and experts' assessment of Quality of Service factors for four services (S1, S2, S3, and S4) to form the Fuzzy Decision Matrix using modified Online output software. Applying the proposed technique to a web service optimization problem validated its effectiveness. The results indicated optimal selection of S1 as the best web service, supported by Coefficient Index values (0.785). This study introduces a novel approach, Entrop – Hesitationistic - Fuzz-TOPSIS, for web service optimization, integrating quantitative and qualitative data through an Entropy-based model. The effectiveness of the proposed technique, validated through application on the WS-DREAM dataset, underscores its potential in addressing real-world decision-making challenges. The optimal selection of S1 as the best web service suggests practical utility. The study encourages further exploration of this technique's applicability to diverse Multiple Criteria Decision Making (MCDM) problems, opening avenues for future research and application.

With the deepening of the diversification and openness of financial system, financial vulnerability, as an endogenous attribute of financial system, becomes an important measurement of financial security. Based on network analysis, we introduce network curvature indicator improved by Copula entropy as an innovative metric of financial vulnerability. Compared with previous network curvature analysis method, CE-based curvature proposed in this paper can measure market vulnerability and systematic risk with significant advantages.

The thermocontextual interpretation (TCI) establishes a system’s exergy, entropic energy, and thermal entropy as thermocontextual properties of state, defined with respect to its positive temperature surroundings. This work extends previous applications of the TCI to irreversible and statistical transitions. The TCI defines statistical entropy as a transactional process of derandomization and transition to a negative-entropy state. Statistical measurements of a confined quantum particle’s position are detailed in terms of reversible processes of instantiation and actualization. The TCI then formalizes the MaxEnt as a fundamental physical principle. We apply MaxEnt and statistical entropy measurements to the double-slit experiment. Particles passing through parallel slits record a wave interference pattern, but a “which-slit” detector eliminates wave interference. Richard Feynman called the double-slit experiment the only mystery, at the heart of quantum mechanics. The TCI offers a simple explanation. The which-slit detector breaks the system’s symmetry, enabling particles to pass through one slit or the other, and MaxEnt selects the asymmetrical transition, which has no wave interference and a higher statistical entropy.

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined and complexity measures based on this entropy as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena like the El Nino/La Nina Southern Oscillation.

The knowledge of the optical properties of biological tissues in a wide spectral range is highly important for the development of noninvasive diagnostic or treatment procedures. The absorption coefficient is one of those properties, from which various information about tissue components can be retrieved. Using transmittance and reflectance spectral measurements acquired from ex vivo rabbit brain cortex samples, allowed to calculate its optical properties in the ultraviolet to the near infrared spectral range. Melanin and lipofuscin, the two pigments that are related to the ageing of tissues and cells were identified in the cortex absorption. By subtracting the absorption of these pigments from the absorption of the brain cortex, it was possible to evaluate the true ratios for the DNA/RNA and hemoglobin bands in the cortex – 12.33 fold (at 260 nm), 12.02 fold (at 411 nm) and 4.47 fold (at 555 nm). Due to the fact that the accumulation of melanin and lipofuscin increases with the ageing of the brain tissues and are related to the degeneration of neurons and their death, further studies should be performed to evaluate the evolution of pigment accumulation in the brain to prevent the development of Alzheimer, Parkinson and stroke pathologies in the brain.

Non-destructive, accurate, and timely approach for crop yield prediction at field scale is vital for precision agriculture. This study aimed to investigate the appropriate wavelengths and their combinations to explore the new SIs derived from UAV hyperspectral images in predicting yield during the growing season of spring maize. The best wavelengths and new SIs, including the difference spectral index, ratio spectral index, and normalized difference spectral index forms, were obtained by the contour maps constructed by the coefficient of determination (R2) from the linear regression models between the yield and all possible SIs screening out from the 450-950 nm wavelengths. The results showed that the most sensitive wavelengths were 640-714 nm at WJQ, 450-650 nm and 750-950 nm at SKS, and 450-700 nm and 750-950 nm at FJJ. The new SIs established here were different across the three experimental fields, and their performance on maize yield prediction were generally better than that of the published SIs. In addition, the new SIs presented different response to various N fertilization levels. This study demonstrated the potential of exploring new spectral characteristics from remote sensing technology for predicting field-scale crop yield in spring maize cropping systems before harvest.

Data on Stark broadening parameters, spectral line widths and shifts, for 15 multiplets of N VI, which spectral lines are broadened by collisions with electrons, protons, alpha particles (He III) and B III, B IV, B V and B VI ions, are presented. They have been calculated, using the semiclassical perturbation theory, for temperatures from 50,000 K to 2,000,000 K, and perturber densities from 1016 cm−3 up to 1024 cm−3. These data are particularly of interest for the analysis and modelling of atmospheres of hot and dense stars, as e.g. white dwarfs, and for investigation of their spectra, but also for analyis ad modelling of laser driven plasma in proton-boron fusion research.

Spectral calibration consists of the calibration of wavelengths and the measurement of the instrument's spectral response function (SRF). Unlike conventional slits, the absorbed aerosol sensors (AAS) are used as a slit homogenizer, in which the spectral response function (SRF) is not a conventional Gaussian curve. To be more precise, the SRF is the convolution of the slit function of the spectrometer, the line spread function of the optical system, and the detector response function. The SRF of the slit homogenizer is a flat-topped multi-Gaussian function. Considering the convenience of fitting, a super-Gaussian function, which looks like a similar distribution to the flat-topped multi-Gaussian function, is used to fit the measured data in a spectral calibration. According to the results, the SRF’s shapes, due to the Earth port, resemble a Gaussian curve with a flatted top could be concluded, which contains an FWHM of 1.78–1.82 nm for the AAS. The results show that the correlation coefficients are about 0.99, which proves that the fitting function could better characterize the SRF of the instrument.

We propose a method for the estimation of the spectral response of a photodetector, using only the variation of the temperature of a black body source without the need of an expensive monochromator or a circular filter. The proposed method is suitable especially for infrared detectors in which the cut – off wavelength and the responsivity vs. wavelength is not exactly known. The method provides a rough estimation of the curve S(l) solving a Fredholm integral equation of the first kind. The precision of this technique depends on the number of temperatures at which the detector output is measured. Some example is given in order to better explain the proposed technique.

Multi-task Gaussian processes (MTGPs) are a powerful approach for modeling structured dependencies among multiple tasks. Researchers on MTGPs have contributed to enhance this approach in various ways. Current MTGP methods, however, cannot model nonlinear task correlations in a general way. In this paper we address this problem. We focus on spectral mixture (SM) based kernels and propose an enhancement of this type of kernels, called multi-task generalized convolution spectral mixture (MT-GCSM) kernel. The MT-GCSM kernel can model nonlinear task correlations and mixtures dependency, including time and phase delay, not only between different tasks but also within a task at the spectral mixture level. Each task in MT-GCSM has its own generalized convolution spectral mixture kernel (GCSM) with a different number of convolution structures and all spectral mixtures from different tasks are dependent. Furthermore, the proposed kernel uses inner and outer full cross convolution between base spectral mixtures, so that the base spectral mixtures in the tasks are not necessarily aligned. Extensive experiments on synthetic and real-life datasets illustrate the difference between MT-GCSM and other kernels as well as the practical effectiveness of MT-GCSM.