This article analyzes 6 probability distributions from the Generalized Pareto family, with 3, 4 and 5 parameters, with main purpose to identify other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distributions use are presented like, the probability density functions, the complementary cumulative distribution functions, the quantile functions, the exact and approximate relations for estimating parameters, for both methods of parameters estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor river, to numerically present the analyzed distributions. The performance of this distributions is evaluated using relative mean error, relative absolute error and linear moments diagram.

Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing, and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented as well.

Introduction: Myasthenia gravis (MG), an immune disorder affecting nerve-muscle transmission, often necessitates tailored therapies to alleviative longitudinal symptom fluctuations. Here, we aimed to examine and compare the treatment cycle intervals and efficacy of efgartigimod in four patients. This case series mainly offers insights into personalized treatment cycle intervals and efficacy of efgartigimod for patients with MG in our facility in Japan. Methods: We retrospectively analyzed four patients with MG (2 patients with early-onset, 1 with late-onset, and 1 with seronegative MG, mainly managed with oral immunosuppressants as prior treatments) who completed four or more cycles of efgartigimod treatment from January 2022 to September 2023. We focused on changes in serum immunoglobulin (IgG) level, acetylcholine receptor antibody (AChR-Ab) titer, and quantitative MG (QMG) score. Results: Efgartigimod, administered at a median of 5.0 [IQR 5.0, 7.5] weeks between cycles, led to decreased serum IgG level in all patients and reduced AChR-Ab titers in seropositive patients. All patients showed sustained MG symptom improvement, with considerably reduced QMG scores before efgartigimod treatment. None of the patients required rescue medications or developed treatment-related adverse events. Conclusion: Customized efgartigimod administration intervals effectively enhanced clinical outcomes in patients with MG without notable symptom fluctuations, demonstrating the benefits of individualized treatment approaches and validating the safety of efgartigimod during the study period.

We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides deeper insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory.

The shear stress generated by wall turbulence is the main cause of wall friction resistance in turbulent flow through pipes. This paper investigates the impact of inserting rest periods (regions of constant Reynolds number) within the pulsating operating cycle of velocity on the fully turbulent flow at large time-averaged Reynolds numbers, using the Large Eddy Simulation (LES) method. The study aims to explore the effect of increasing rest periods within pulsations on drag resistance. The dimensionless shear stress and drag reduction rates during different time periods of rest were analyzed. Numerical simulation results indicate that the pulsating velocity operation mode does not necessarily lead to drag reduction; it may even result in increased resistance. Inserting rest periods within the pulsation cycle can achieve drag reduction effects, with the maximum drag reduction rate reaching 21.8\%. Comparisons with experimental data and Direct Numerical Simulation (DNS) from the literature validate the feasibility of using the LES method for pipe pulsating operation modes.

Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc…Using the PBN, many formulas, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi’s state function or Peliti’s standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman-Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential Applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT.

Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam's razor, machine learning, and password guessing.

The importance of conflict analysis and safety considerations during work zone intervals at signalized intersections cannot be overstated, as these periods pose unique challenges and safety risks for both motorists and pedestrians. Work zones introduce temporary changes to traffic patterns, lane configurations, and signal timings, which can disrupt the flow of traffic and increase the likelihood of conflicts between vehicles and pedestrians. By conducting comprehensive conflict analysis, it is possible to identify potential conflict points, such as merging areas, pedestrian crossings, and lane transitions, and implement targeted safety measures to mitigate risks. Additionally, considering safety considerations during work zone intervals is paramount to safeguarding the well-being of road users and minimizing the occurrence of conflicts or collisions. Measures such as enhanced signage, temporary traffic control devices, and increased enforcement efforts can help promote compliance with traffic regulations and ensure the safe passage of vehicles and pedestrians through work zones. This study investigates the dynamics of traffic behavior and safety implications within work zones at signalized intersections, aiming to address key challenges and enhance intersection management strategies. Through comprehensive analysis, varying frequencies of Vehicle-to-Vehicle (V2V) conflicts were observed across different movement directions, with significant occurrences identified in specific phases of the traffic signal cycle. Specifically, 69 V2V conflicts in phase #1, 181 in phase #2, 31 in phase #3, 207 in phase #4, 1 in phase #5, 274 in phase #6, 93 in phase #7, and 186 in phase #8 were recorded. Furthermore, the examination of Vehicle-to-Pedestrian (V2P) conflicts underscored the importance of prioritizing pedestrian safety, with notable occurrences observed in phases associated with pedestrian crossing movements. Meanwhile, despite the closure of left-turn movements, instances of red light running persisted, with 69 red light running events in phase #1, 181 in phase #2, 31 in phase #3, 207 in phase #4, 1 in phase #5, 274 in phase #6, 93 in phase #7, and 186 in phase #8.To mitigate these safety concerns during work zone intervals, proactive measures are essential. Strategies include improving communication through clear signage and advanced warning systems, enhancing enforcement efforts with red light cameras and increased police presence, and investing in infrastructure improvements such as temporary pedestrian facilities. Integration of real-time data from sensors, particularly LiDAR technology, offers significant advantages in detecting conflicts and red light runners during work zone intervals. LiDAR's precise, real-time data on vehicle and pedestrian movements, combined with its 360-degree coverage and high spatial resolution, facilitates accurate detection and tracking of potential conflict scenarios, contributing to enhanced intersection safety and traffic management efficiency. This study endeavored to conduct a traffic safety analysis during work zone intervals at a signalized intersection in Baltimore City, known for its high rate of traffic crashes, utilizing LiDAR sensor technology.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Drowsiness is a main factor for various costly defects, even fatal accidents in areas such as construction, transportation, industry and medicine, due to the lack of monitoring vigilance in the mentioned areas. The implementation of a drowsiness detection system can greatly help to reduce the defects and accident rates by alerting individuals when they enter a drowsy state. This research proposes an Electroencephalography (EEG) based approach for detecting drowsiness. EEG signals are passed through a preprocessing chain composed of artifact removal and segmentation to ensure accurate detection followed by different feature extraction methods to extract the different features related to drowsiness. This work explores the use of various machine learning algorithms such as Support Vector Machine (SVM) the K Nearest Neighbor (KNN) the Naive Bayes (NB) the Decision Tree (DT) and the Multilayer Perceptron (MLP) to analyze EEG signals sourced from the DROZY database, carefully labeled into two distinct states of alertness (awake, and drowsy). Segmentation into 10-second intervals ensures precise detection, while a relevant feature selection layer enhances accuracy and generalizability. The proposed approach achieves high accuracy rates of 99.84% and 96.4% for intra (subject by subject) and inter (cross-subject) modes, respectively. SVM emerges as the most effective model for drowsiness detection in the intra mode, while MLP demonstrates superior accuracy in the inter mode. This research offers a promising avenue for implementing proactive drowsiness detection systems to enhance occupational safety across various industries.

The philosophy of testing statistical hypothesis is a natural consequence and functional extension of mathematical analysis of Probability. Along with the concept of recurrence when applied to random sequences and functions, it leads to the analysis of a priori and posterior which implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic, functional and dimensional considerations, which are found in the works of Laplace. Aspects of mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy, Information, and various functional dependencies are the main factors explained in the five properties that lead to implication of testing statistical hypothesis. Various interesting examples with modern scientific significance from genetics, astrophysics, and other areas give methodological access to answers of different problems and phenomena which are involved in the logic of testing statistical hypothesis.

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

It has been empirically observed that the upper tail of the firm size distribution follows either the Pareto distribution or the Zipf distribution, with both patterns being explained by Gibrat’s law (Gabaix, 1999). This article analyzed firm revenue data from China, spanning from 2005 to 2013, to examine the whole range of the firm size distribution. Our empirical analysis revealed that firm revenue data over these years is well fitted by a three-parameter generalized Pareto distribution, with the fitted parameters indicating a dichotomy: The size distribution of large-sized firms, namely the upper tail, is asymptotically characterized by a Pareto distribution or a Zipf distribution, whereas the size distribution of smaller and medium-sized firms is approximated by an exponential distribution. This finding suggests that Gibrat’s law should be extended to account for the emergence of a generalized Pareto distribution.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

Statistical modeling of lifetime data plays an essential role in a wide range of practical fields, such as health and engineering. There have been a lot of studies done to develop statistical models that can better describe health data than traditional models. For the first time, we pioneer a novel family of continuous probability distributions called the generalized odd beta prime generalized (GOBP-G) family of distributions. The cumulative distribution and probability density functions of the new family are presented. A new generalization of the Weibull distribution called "generalized odd beta prime-Weibull" (GOBPW) is proposed using the pioneered GOBP-G family. The mixture representations of the new distribution are defined and derived. Some formal statistical properties of the GOBPW distribution, such as the moments, moment generating function, incomplete moments, information generating function, entropies, stress-strength function, quantile function, and order statistics, are derived. The estimation of the parameters of the proposed distribution is evaluated using the maximum likelihood estimation approach. Different cancer disease data sets, such as the bladder, head and neck, acute bone, and blood cancers, are used to illustrate the applicability and usefulness of the new model and were compared using several statistical accuracy measures with that of well-established extended Weibull distributions, which are the beta modified Weibull distribution, Kumaraswamy modified Weibull distribution, gamma generalized modified Weibull distribution, gamma log-logistic Weibull distribution, and beta log-logistic Weibull distribution. The results show that the proposed model gives better results than the competitive models. This study could guide the relevant stakeholders in choosing a suitable statistical model for the health data instead of relying on traditional models to enhance decision-making.

A new generalized definition of Mersenne numbers is proposed of the form (a^n - (a-1)^n), called Global Generalized Mersenne numbers, or simply Generalized Mersenne numbers and noted GM_{a,n} where a is the base and n is the exponent, both being positive integers. The properties are investigated for prime exponents n and several theorems on Mersenne numbers regarding their congruence properties are generalized and demonstrated. In particular, it is found that, for any base a, Generalized Mersenne numbers are in general such that (GM_{a,n} - 1) are even and divisible by n, a and (a-1) for any odd prime exponent n and by (a(a-1)+1) for any prime exponent n > 5. The remaining factor is a function of triangular numbers of (a-1), specific to each prime exponent n. Four theorems on Mersenne numbers are generalized and four new theorems are demonstrated, allowing to show first, that (GM_{a,n} - 1) are divisible by 6, and more precisely GM_{a,n} are congruent to 1(mod 12) or 7(mod 12) depending on the congruence of the base a(mod 4); second, that (GM_{a,n} - 1) are divisible by 10 if n == 1(mod 4) and, if n == 3(mod 4), GM_{a,n} == 1(mod 10), or 7(mod 10) or 9(mod 10) depending on the congruence of the base a(mod 5); third, that all factors c_{i} of GM_{a,n} are of the form (2nf_{i}+1) with f_{i} natural integers such that c_{i} is prime itself or the product of primes of the form (2nj+1) with j natural integer; fourth, that for odd prime exponents n, all GM_{a,n} are periodically congruent to either +/-1\(mod 8) or +/-3(mod 8) depending on the congruence of the base a(mod 8); and fifth, that the factors of a composite GM_{a,n} is of the form (2nf_{i}+1) with f_{i} == u(mod 4) and u being either 0, 1, 2 or 3 depending on the congruence of the exponent n(mod 4) and on the congruence of the base a(mod 8). The potential use of Generalized Mersenne primes in cryptography is shortly addressed.

Despite the availability of COVID-19 vaccines, the global pandemic remains a significant health challenge. Timely detection of the virus is crucial for effective containment efforts, prompting the exploration of machine learning (ML) models for COVID-19 detection. highlights the ongoing significance of COVID-19 as a global health crisis despite the availability of vaccines. To address the need for timely virus detection, the study explores the efficacy of machine learning (ML) models, including DNN, Voting, Bagging, SVC_rbf, SVC_linear, SVC_polynomial, and SVC_sigmoid, in predicting COVID-19 infection probability. With a dataset comprising 4000 samples split into 3200 for training and 800 for testing, the analysis reveals that DNN and Voting models demonstrate the highest performance, achieving an impressive accuracy of 89%. These results underscore the potential of ML techniques, particularly DNN and ensemble methods like Voting, in facilitating early COVID-19 detection and contributing to effective pandemic management. The study emphasizes the importance of continued research to further refine and optimize ML-based COVID-19 detection systems.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

The rapid development of the Industrial Internet of Things (IIoT) has brought enormous opportunities to the industrial environment but has also posed significant challenges to network security, especially the physical layer security challenges,which is crucial for the reliable transmission of messages interconnected devices and sensors. Focus on the enhancing the physical layer security in the IIoT communication, this paper proposed a mechanism of Spatial Secrecy Outage Probability (SSOP) to ensure the secure transmission of data. The SSOP algorithm assumes that the location of legitimate device is known, while eavesdropper on the random distribution of device locations, forming the SSOP model related to device locations from the perspective of insecure regions (ISR) and secure regions (SR), and deduce the closed-form expression for its upper bound. Subsequently under the constraint of SSOP conditions, establish an optimization model with the objective of system throughput maximization based on Spatial Secrecy Outage Probability(SRM-SSOP). By optimizing the transmission rate of legitimate channels or controlling the transmission power, the maximization of system throughput can be achieved, thus reducing the consumption of communication resources. Through sophisticated modeling and simulation in the MATLAB, we verified the accuracy of the definition and derived upper bound of SSOP. The experimental results also show that SSOP algorithm gradually converges to a specific value as the number of antenna elements increases. In addition, we observed that when the receiver device is aligned with the normal direction of the transmit antenna array, the SSOP reaches a minimum value. These performance are crucial for understanding and optimizing the security performance of IIoT communication systems.

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

Bootstrapping is a flexible, powerful and well-established statistical approach to quantify the uncertainty of virtually any point estimate. While multiple versions of bootstrap confidence intervals are already available in Stata, dbs implements the double (iterated) bootstrap. Instead of relying on parametric assumptions such as the non-parametric resampling bootstrap confidence interval does, it is more flexible and derives critical values directly from that data. To do so, multiple methods are available (analytic approach, double resampling, jackknife estimation). In a comparative simulation study it is empirically demonstrated that the strengths of the double bootstrap are particularly evident for small samples (n < 100) when heteroscedasticity is present. While all other approaches result in undercoverage, only the double bootstrap reaches the target coverage level and hence avoids incorrect statistical conclusions. The computational burden is not even necessarily larger than for other bootstrap approaches.

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

This paper discusses about the quantum energy levels of muonic hydrogen considering only Coulomb interaction. The computational analysis in this paper will help the reader get a good understanding of how different a muonic hydrogen is from its electronic counterparts. Energy eigenvalues are calculated by numerical method and the probability density distribution of muon around the nucleus is plotted for different quantum states using special functions. The code is written in python. A comparative study of emission spectra between the muonic hydrogen and hydrogen has also been discussed.

For the set of probability measures ${\sf I}(X)$, where $X$ is a compact Hausdorff space, we propose a new way to introduce the topology by using open subsets of the space $X$. Then, among other things, we give a new proof that for a compact Hausdorff space $X$ the space ${\sf I}(X)$ is also a compact Hausdorff space. For a Tychonoff space $X$, we consider the topological space ${\sf I_{\tau}}(X)$ of $\tau$-smooth idempotent probability measures on $X$,and show that the space ${\sf I_{\tau}}(X)$ is \v{C}ech-complete if and only if the given space $X$ is \v{C}ech-complete.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

Many papers in recent years have been devoted to estimating the per pixel proportions of three broad classes of materials (e.g. photosynthetic vegetation, non-photosynthetic vegetation and bare soil) using data from multispectral sensors. Many of these papers use estimation methods based on the linear mixture model. Very few of these papers assess the accuracy of their estimators. I show how to produce confidence intervals (CIs) and joint confidence regions (JCRs) for the proportions associated with various linear mixture models. There are two main models, both of which assume that the coefficients in the model are non-negative. The first model assumes that the coefficients sum to 1. The second does not, but uses rescaling of the estimated coefficients to produce estimated proportions. Three variants of these two models are also analysed. JCRs are shown to be particularly informative, because they are typically better at localising the information than CIs are. The methodology is illustrated using examples from Landsat Thematic Mapper data at 1169 locations across Australia, each of which has associated field observations. There is also discussion about the extent to which the methodology can be extended to hyperspectral data.

In recent years, with the rapid development of technology, artificial intelligence(AI) security issues represented by adversarial sample attack have aroused widespread concern in society. Adversarial samples are often generated by surrogate models and then transfer to attack the target model, and most AI models in real-world scenarios belong to black boxes, thus transferability becomes a key factor to measure the quality of adversarial samples. The traditional method relies on the decision boundary of the classifier and takes the boundary crossing as the only judgment metric without considering the probability distribution of the sample itself, which results in an irregular way of adding perturbations to the adversarial sample, an unclear path of generation, and a lack of transferability and interpretability. In the probabilistic generative model, after learning the probability distribution of the samples, a random term can be added to the sampling to gradually transform the noise into a new independent and identically distributed sample. Inspired by this idea, we believe that by removing the random term, the adversarial sample generation process can be regarded as static sampling of the probabilistic generative model, which guides the adversarial samples out of the original probability distribution and into the target probability distribution, and helps to improve transferability and interpretability. Therefore, we propose a Score Matching-Based Attack(SMBA) method to perform the adversarial sample attacks by manipulating the probability distribution of the samples, which can show good transferability in the face of different datasets and models, and give reasonable explanations from the perspective of mathematical theory and feature space. In conclusion, our research establishes a bridge between probabilistic generative models and adversarial samples, provides a new entry angle for the study of adversarial samples, and brings new thinking to AI security.

In this work, an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically is introduced. The goal is to optimally partition the sensor characteristic, i.e. to select the vertices of the approximating polyline (approximant) along with their positions on, the sensor characteristics so that the distance (i.e. the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative non-linear optimization problems are solved, whose essential difference is in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by numerical minimization of the L^1--metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by minimizing numerically the L^2-metric (area-, or energy-based separation measure) for the same set of optimization variables –the locations, and the number of polyline vertices.

In this paper, we investigate some elementary properties of two kinds modified Szasz type basis functions, depending on non-negative parameters. We study some shape preserving properties of these operators concerning monotonicity, convexity, starlikeness, semi-additivity and smoothness.

(1) Background: Breast cancer is the second leading cause of cancer death among women. The accurate prediction of survival intervals will help physicians make informed decisions on treatment strategies or the use of palliative care for patients; (2) Methods: The gene expression is predictive and correlates to patient prognosis. To establish a reliable prediction tool, we collected the RNA-seq data of breast cancer patients, a total of 1187 RNA-seq data (median age 58 years), in FPKM format from the TCGA database. Among them, 144 RNA-seq data with date of death information was selected to establish the SaBrcada-AD dataset. We first normalized the SaBrcada-AD dataset to transcripts per million (TPM) to build survival prediction model SaBrcada. After normalization and dimension raising, the differential gene expression data were used for testing eight different deep learning architectures. Among them, GoogLeNet performed the best. Considering the effect of age on prognosis, we examined all ages between the lower and upper quartiles of patient age for a stratified random sampling test; (3) Results: Stratifying by age based on a cut-off of 61 years of age improved the accuracy of SaBrcada compared to previous findings, resulting in an accuracy of 0.798. We also built a free website tool to provide 5 kinds of predicted survival period information for clinician reference; (4) Conclusions: We established a breast cancer survival analysis prediction model, SaBrcada, and a website tool with the same name. Through this highly reliable survival analysis model and website tool, information on survival intervals will be provided for clinicians as part of precision medicine.

Terrestrial LiDAR becomes more and more popular to estimate leaf and plant area density. Voxel-based approaches account for this vegetation heterogeneity and significant work has been done in this recent research field, but no general theoretical analysis is available. Although estimators have been proposed and several causes of biases have been identified, their consistency and efficiency have not been evaluated. Also, confidence intervals are almost never provided. In the present paper, we solve the transmittance equation and use the Maximum Likelihood Estimation (MLE), to derive unbiased estimators and confidence intervals for the attenuation coefficient, which is proportional to leaf area density. The new estimators and confidence intervals are defined at voxel scale, and account for the number of beams crossing the voxel, the inequality of path lengths in voxel, the size of vegetation elements, as well as for the variability of element positions between vegetation samples. They are completed by numerous numerical simulations for the evaluation of estimator consistency and efficiency, as well as the assessment of the coverage probabilities of confidence intervals. • Although commonly used when the beam number is low, the usual estimators are strongly biased and the 95% confidence intervals can be ≈±100% of the estimate. • Our unbiased estimators are consistent in a wider range of validity than the usual ones, especially for the unbiased MLE, which is consistent when the beam number is as low as 5. The unbiased MLE is efficient, meaning it reaches the lowest residual errors that can be expected (for an unbiased estimator). Also the unbiased MLE does not require any bias correction when path lengths are unequal. • When elements are small (or voxel is large), 103 beams entering the voxel leads to some confidence intervals ≈±10%, but when elements are larger (or voxel smaller), it can remain wider than ±50%, even for a large beam number. This is explained by the variability of element positions between vegetation samples. Such a result shows that a significant part of residual error can be explained by random effects. • Confidence intervals are much smaller (±5 to 10%) when LAD estimates are averaged over several small voxels, typically within a horizontal layer or in the crown of individual plants. In this context, our unbiased estimators show a reduction of 50% of the radius of confidence intervals, in comparison to usual estimators. Our study provides some new ready-to-use estimators and confidence intervals for attenuation coefficients, which are consistent and efficient within a fairly large range of parameter values. The consistency is achieved for a low beam number, which is promising for application to airborne LiDAR data. They entail to raise the level of understanding and confidence on LAD estimation. Among other applications, their usage should help determine the most suitable voxel size, for given vegetation types and scanning density, whereas existing guidelines are highly variable among studies, probably because of differences in vegetation, scanning design and estimators.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

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.

Background: Anxiety disorders can be both an independent risk factor of many somatic conditions and the cause of complications of various organic disorders leading to poor prognosis. Objectives: The purpose of this study is to compare the heart rate variability (HRV) recorded both during the day and at night in patients with anxiety disorders and healthy individuals. Methods: The study was conducted on fifty consecutive outpatients with anxiety disorders who participated in intensive group psychotherapy. The diagnosis was made according to DSM-IV-TR criteria using the PSE-10 questionnaire. Out of 50 patients under study, 17 were diagnosed with panic disorder (PD) and 21 with generalized anxiety disorder (GAD). The control group consisted of 40 healthy people. The resulting three groups were compared in terms of circadian HRV using the Oxford Medilog Suprima Holter System. Results: The HRV analysis showed the nocturnal falls in the time and frequency parameters related to parasympathetic activity (rMSSD, pNN50, HF). The most unfavourable alterations were observed in the PD group, which comprised the disappearance of day vs. night amplitude of the majority of HRV parameters. Hence, the PD group was particularly susceptible to the arrhythmic events. It was noticeable that nocturnal vagotonia in the PD group was significantly lower as compared with the GAD and control group. Conclusions: The innovative aspect of the present study was to find a distinct profile of HRV with regard to the types of anxiety disorders because of the existing considerable differences between the nature of PD and GAD.

Based on recent contributions regarding the treatment of unsteady hydraulic conditions into the state-of-the-art of scour literature, the theoretically derived probability distribution of bridge scour is introduced. The model is derived assuming a rectangular hydrograph shape with a given duration, and random flood peak following a Gumbel distribution. A model extension for a more complex flood event is also presented, assuming a synthetic exponential hydrograph shape. The mathematical formulation can be extended to any flood-peak probability distribution. The aim of the manuscript is to move forward the current approaches adopted for the bridge design coupling hydrological, hydraulic, and erosional models in a mathematical closed form.

Philippines as an archipelago and tropical country, which is situated near the Pacific ocean, faces uncertain rainfall intensities. This makes environmental, agricultural and economic systems affected by precipitation difficult to manage. Time series analysis of Philippine rainfall pattern has been previously done, but there is no study investigating its probability distribution. Modeling the Philippine rainfall using probability distributions is essential, especially in managing risks and designing insurance products. Here, daily and cumulative rainfall data (January 1961 - August 2016) from 28 PAGASA weather stations are fitted to probability distributions. Moreover, the fitted distributions are examined for invariance under subsets of the rainfall data set. We observe that the Gamma distribution is a suitable fit for the daily up to the ten-day cumulative rainfall data. Our results can be used in agriculture, especially in forecasting claims in weather index-based insurance.

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

Background: There are anecdotal reports on reversible QTc prolongation during therapeutic hypothermia (TH) for moderate to severe neonatal encephalopathy after asphyxia. As the QTc interval is a relevant biomarker to assess safety during medication development, a structured search and review on published neonatal QTc values to generate reference values is warranted to facilate medication development in this specific population. Methods: A structured search and literature assessment (PubMed, Embase, Google Scholar) with ‘Newborn/Infant, QT and hypothermia’ was conducted (October 2021). Retrieved individual values were converted to QTc (Bazett) over postnatal age (day 1-7). Results: We retrieved 94 QTc intervals [during TH (n=50, until day 3) or subsequent normothermia (n=44, day 4-7)] in 33 neonates from 6 publications. The median (range) of QTc intervals during TH was 508 (430-678), and 410 (317-540) ms afterwards (difference 98 ms, or +28 ms/°C decrease). Four additional cohorts (without individual QTc intervals) confirmed the pattern and magnitude of the effect of body temperature on the QTc interval. Conclusions: We added a relevant non-maturational covariate (TH, °C dependent) and generated reference values for the QTc interval in this specific neonatal subpopulation. This knowledge on QTc during TH should be considered and integrated in neonatal medication development.

This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context the numerical test is illustrated by two examples where we find meaningful numerical results.

This article explores the enduring mysteries of consciousness and the afterlife, two enigmatic topics that have fascinated humanity for ages. Despite extensive scientific efforts, the existence of an afterlife remains unproven, and understanding consciousness remains a significant challenge. The research introduces new hypotheses through simple experiments with empirical evidence and theoretical foundations. It delves into the complexities of consciousness, its relationship with the brain, and the need for interdisciplinary approaches. Boldly contemplating the probability of a continuous consciousness after death, the study argues that existing evidence strongly supports this idea. In other words, if we do not accept the hypothesis of an afterlife, we may not be able to discuss the experimental results in the context of any alternative theories. Beyond theoretical implications, it envisions practical outcomes, suggesting that insights into these mysteries could enhance human well-being and contribute to a more harmonious world. This article sheds light on age-old questions about consciousness and the afterlife. Through fresh methodologies, it seeks to provide new perspectives that could reshape our understanding of existence and inspire intellectuals to positive individual and societal advancements including psychological well-being and intelligence.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Healthcare leaders are faced with many financial challenges in the contemporary environment, leading to many bankruptcies in recent years. What is not well understood are the specific conditions that lead to organizational economic failure. Ideally, hospital leaders could examine the literature for guidance to predict bankruptcy before it occurs. However, existing regression methods have proven inadequate, especially when the finance variables follow a nonnormal frequency pattern. Furthermore, the regression approach encounters difficulties due to multicollinearity and nonnormality issues. Therefore, an alternate stochastic approach for predicting the probability of hospital bankruptcy is warranted. This new method includes computing and interpreting the correlations between the hospital’s revenue and expenses for bivariate lognormal data, calculating the risk of bankruptcy due to the mismatch between revenues and expenses, determining the likelihood of a hospital’s expense exceeding the state’s median expense level, and evaluating a hospital’s financial memory level. Ultimately in our research, we demonstrate a novel approach to anticipate hospital bankruptcy, which can be particularly useful for health policy analysts and hospital leaders in making informed financial decisions and proactively managing risks to ensure the sustainability and stability of their institutions.

In public health literature the risk of death or disease associated with a dietary, environmental of behavioral factor is most commonly denoted by odds ratio (OR), hazard ratio (HR) or risk ratio (RR). The ratio indices have several desirable statistical properties. However, the most important question is whether there are some evolved innate norms of perception of risk that people use and what they are. We conducted a simple one question survey of 98 individuals with different age, sex, educational and professional backgrounds. The respondents were asked to judge the relative perceived risk of four different hypothetical habits for which data on the percentage of people affected by the disease with and without the habit was given. They were asked to rank the risks for the four habits. Results showed that the habits that had the highest difference between probability of acquiring the disease were ranked high on risk perception. The probability ratios did not affect risk perception significantly. Further age, sex, profession or formal training in statistics did not affect the response significantly. Even individuals that were formally trained to use OR and HR as risk indicators, preferred using probability differences over ratios for judging their own risk in the perceived context. This preliminary inquiry into intuitive statistical perception suggests that designing statistical indices based on people’s innate perception may be a better strategy than trying to train people to understand the indices designed by expert statisticians.

Identifying the SARS-CoV-2 virus has been a unique challenge for the scientific community. In this paper, we discuss a practical solution to help guide clinicians with interpretation of the probability that a positive, or negative, COVID-19 test result indicates an infected person, based on their clinical estimate of pre-test probability of infection.The authors conducted a small survey on LinkedIn to confirm that hypothesis that that the clinical pre-test probability of COVID-19 increases relative to local prevalence of disease plus patient age, known contact, and severity of symptoms. We examined results of PPA (Positive Percent Agreement, sensitivity) and NPA (Negative Percent Agreement, specificity) from 73 individual laboratory experiments for molecular tests for SARS-CoV-2 as reported to the FIND database ¹, and for selected methods in FDA EUA submissions^2,3. Authors calculated likelihood ratios to convert pre-test to post-test probability of disease and designed an online calculator to create graphics and text to report results. Despite best efforts, false positive and false negative Covid-19 test results are unavoidable^4,5. A positive or negative test result from one laboratory has a different probability for the presence of disease than the same result from another laboratory. Likelihood ratios and confidence intervals can convert the physician or other healthcare professional’s clinical estimate of pre-test probability to post-test probability of disease. Ranges of probabilities differ depending on proven method PPA and NPA in each laboratory. We recommend that laboratories verify PPA and NPA and utilize a the “Clinician’s Probability Calculator” to verify acceptable test performance and create reports to help guide clinicians with estimation of post-test probability of COVID-19.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

Mutations in KRT1 (keratin 1) or KRT10 (keratin 10) underlie a spectrum of diseases known as keratinopathic ichthyoses. Epidermolytic ichthyosis (EI) is caused by heterozygous missense mutations in the genes KRT1 or KRT10, mutations in the gene KRT2 (keratin 2) lead to superficial epidermolytic ichthyosis, and congenital reticular ichthyosiform erythroderma is caused by frameshift mutations in the genes KRT10 or KRT1, which lead to the phenomenon of revertant mosaicism. Epidermolytic ichthyosis is also present in a mosaic pattern known as epidermolytic (acantholytic) nevus, isolated or diffuse. In the latter case, gonadic involvement is possible, leading to a rare pedigree in which a parent with diffuse epidermolytic nevus (linear EI) gives birth to a child affected by EI. We present here an update on the phenotypic presentations of keratinopathic ichthyoses and their molecular mechanisms.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

In this paper, we introduce the generalized Tetranacci quaternions and present some properties of these quaternions.

This paper investigates generalized Bayesian (GB) inference in the context of a one-parameter Pareto distribution. The study focuses on the derivation of generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the Pareto distribution using type II censored data. In addition, the study investigates a one-sample prediction approach to examine generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP). To evaluate the performance of these estimation and prediction methods, Monte Carlo simulations were performed comparing GBE with GEBE and GBP with GEBP for different parameter values and learning rate parameters (LRP).

In the paper, we suggest a method for calculating optimal time intervals in the queue analysis. The suggested method processes partitioning of the time interval and utilizes the epsilon-entropy and epsilon-capacity of the partition for finding an optimal partition. Optimality of the partition is specified based on its epsilon-information. The suggested method is illustrated by defining the intervals for histograms of differently distributed samples and demonstrated its effectiveness in comparison with the existing methods.

Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modelling, a flexible family of two-parameter distribution functions associated with the exponential distribution is proposed here. Mathematical and statistical properties of the novel distribution are examined, including quantiles, mode, moments, hazard rate function, and its characterization. The parameter estimation procedure using the maximum likelihood method was carried out, and applications to environmental and engineering data were also considered. To this end, various statistical tests are used, along with some other information criterion indicators to determine how well the model fits the data. The proposed model is found to be the most efficient plan in most cases for the datasets considered.

One of creators of quantum mechanics P. Jordan in his work on quantum biology claimed that life's missing laws were the rules of chance and probability of the quantum world. The article presents author’s results of studying frequencies (or probabilities) of nucleotides on so-called epi-chains of long DNA sequences of various eukaryotic and prokaryotic genomes. DNA epi-chains are algorithmically constructed subsequencies of DNA nucleotide sequences. According to the algorithm of construction of any epi-chain of the order n, the epi-chain is such nucleotide subsequence, in which the numerations of adjacent nucleotides differ by natural number n (n = 1, 2, 3, 4,…). Correspondingly each epi-chain of order n ≥ 2 contains n times less nucleotides than the original DNA sequence. The presented results unexpectedly discover that in long single-stranded and double-stranded DNA of any tested genome its DNA epi-chains of different orders n (values n are not too large) have practically identical frequencies (or probabilities) of each kind of nucleotides. These data allow considering DNA as a regular rich set of epi-chains, which can play a certain role in genetic and epigenetic phenomena as the author belives. Appropriate rules of nucleotide frequencies on epi-chains of long DNA sequences are formulated for further their tests on a wider set of genomes. These results testify on existence of long-range coherence in long DNA and remind the Fröhlich's theory of long-range coherence in biological systems. The phenomenological data are discussed from different standpoints: the DNA double helices and helical antennas with circular polarizations of electromagnetic waves; relations with the Fröhlich's theory; numerical analysis of DNA epi-chains under binary representations of nucleotides. Results are useful for developing quantum and algebraic biology.

We give two examples of the appearance of heavy-tailed distributions in applications to social sciences. Among these distributions are the laws of Pareto, Lotka, and some new ones. The examples are illustrated by constructing suitable toy models.

This article presents six probability distributions from the Gamma family with three parameters, for the flood frequency analysis in hydrology. The choice of the Gamma family of statistical dis-tributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the im-provement of the estimation of maximum flows and including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected pa-rameters was researched, being an element of novelty. The linear moments method is better than MOM because it avoids the choice of skewness depending on the origin of the flows, practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed, using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented like, quantile functions, the exact and ap-proximate relations for estimating parameters and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river, to verify the proposed methodology. The per-formance of this distributions is evaluated using Kiling-Gupta and Nash-Sutcliff coefficients.

Estimating the parameters of statistical distributions generally involves solving a system of nonlinear equations or a nonlinear equation, being a technical difficulty in their usual application in hydrology. This article presents improved approximations and, in some cases, new approximations for the estimation with the method of ordinary moments and the method of linear moments, which are useful for the direct calculation of the parameters, because the errors in the approximate estimation are similar to the use of iterative numerical methods. Thirteen statistical distributions of two and three parameters frequently used in hydrology are presented, for which parameter estimation was laborious. Thus, the approximate estimation of the parameters by the two methods is simple but also precise and easily applicable by hydrology researchers. The approximate forms characterized by very small errors are the result of the research conducted within the Faculty of Hydrotechnics to update the romanian normative standards in the hydrotechnical field.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

Immunological aging type definition requires establishing reference intervals from the distribution of immunosenescence biomarkers conditional on age. For 1,605 individuals (18–97 years), we determined the comprehensive IMMmune Age indeX IMMAX from flow cytometry-based blood cell sub-populations, and identified age-specific centiles by fitting generalized additive models for location, scale and shape. The centiles were uncorrelated with age, and facilitated the categorization of individuals as immunologically slow or fast aging types. Using its 50th percentile as reference, we rescaled IMMAX to equivalent years-of-life (EYOL), and computed the immunological age gap as difference between EYOL and chronological age. Applied to preliminary baseline and follow-up measurements from 53 participants of the Dortmund Vital Study (Clinical-Trials.gov Identifier: NCT05155397), the averaged changes in IMMAX and EYOL conformed to the 5-year follow-up period, whereas no significant changes occurred concerning IMMAX centiles and age gap. This suggested that the participants immunologically adapted to aging, and kept their relative positions within the cohort. Sex was non-significant. Methodical comparisons indicated that future confirmatory analyses with the completed follow-up examinations could rely on percentile curves estimated by simple linear quantile regression, while the selection of the immunosenescence biomarker will greatly influence the outcome, with IMMAX representing the preferable choice.

Background: Interventions with the performance of sessions with sprints in different intensity manipulations, can be a great alternative to improve physical performance. Objective: To verify the influence of different break times between sprints on the performance of amateur futsal athletes Methods: 10 individuals, men, amateur futsal athletes (Age: 21.5 ± 1.6; Weight: 72.4 ± 6.88; Height: 1.72 ± 0.05; BMI: 24.3 ± 1.2; Fat%: 13.7 ± 3.3, VO2peak: 49.1 ± 10.5) participated in the study. For the intervention, individuals were randomly selected to perform sessions with sprints (10 sets 20 meters) with different pause times, being 15 (S15), 30 (S30) and 60 (S60) seconds. For performance analysis, the speed (km / h) applied to each sprint was used, monitored by a device with a photocell (CEFISE Biotecnologia Esportiva®, Nova Odessa, São Paulo) and the statistical treatment of all data was through the software Statistica 7.0 (Statsoft ™, Tulsa, OK, USA) using a significance level of p≤0.05. Results: There was an interaction between speed and interval time (p = 0.000). For condition S15, a greater reduction in performance was observed (p≤0.05), while for S30 and S60, no significant reduction in performance was observed (p> 0.05). The data for the area under the curve showed a significant difference (p = 0.000), where the interval of 60 seconds (S60) was longer compared to the values of 30 (S30) (p = 0.000) and 15 seconds (S15) (p = 0.000). However, there were no significant differences between the 30 and 15 second data (p = 0.248). Conclusion: Shorter time (15 seconds) of interval between repeated sprints can significantly affect performance when compared to longer breaks (30 and 60 seconds). But, all the conditions tested here, can be positive for the improvement of the performance, mainly in sports that demand fast and efficient motor actions, as for example, futsal.

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails less than 50%. Theoretical models for a static case and for five dynamic cases, without and with rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds, it is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.

This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold $M$. The geometry of family of probability densities on $M$ are inherited from probability densities on Euclidean spaces $\left\{U_\alpha \right\}$ via bundle morphisms, induced by an orientation-preserving diffeomorphisms $\rho_\alpha:U_\alpha \rightarrow M$. Current literature inherits densities on $M$ from tangent spaces via Riemannian exponential map $\exp: T_x M \rightarrow M$; densities on $M$ are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on $U_\alpha$ can be inherited to family of densities on $M$. Furthermore, we provide explicit expressions for parametrized probability densities on $\rho_\alpha(U_\alpha) \subset M$. Finally, using the component densities on $\rho_\alpha(U_\alpha)$, we construct parametrized mixture densities on totally bounded subsets of $M$. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.

We show the tensor properties of joint probabilities on a Riemannian parametric manifold. Initially we develop a binary data matrix for parameter measurements of a large number of particles confining in a closed system in order to retrieve the joint probability densities of related parameters. By introducing a new generalized inner product as a multilinear operation on dual basis of parametric space, we extract the set of joint probabilities and prove them to meet contravariant tensor properties in a general Riemannian parametric space. We show these contravariant tensors reduce to classical ordinary partial derivatives definition in ordinary Euclidean parametric space. Finally we prove by a theorem that symmetrized iterative contravariant derivative of cumulative probability function on Riemannian manifold gives the set of joint probabilities in those manifold. We bring some examples for compatibility with physical tensors.

Generalized Bayesian (GB) is a Bayesian approach based on the learning rate parameter (LRP) () as a fraction of the power of the likelihood function. In this paper, we consider the GB method to perform inference studies for a class of exponential distributions. Generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the considered distributions were obtained based on the censored type II samples. In addition, generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP) were considered using a one-sample prediction scheme. Monte Carlo simulations were performed to compare the performance of the GBE and GEBE estimation results and the GBP and GEBP prediction results for different values of the LRP.

Let an odd integer \(\mathcal{X}\) be expressed as $\left\{\sum\limits_{M > m} b_M 2^M\right\} + 2^m - 1,$ where $b_M \in \{0, 1\}$ and $2^m - 1$ is referred to as the Governor. In Collatz-type functions, a high index Governor is eventually reduced to $2^1 - 1$. For the $3\mathcal{Z} + 1$ sequence, the Governor occurring in the Trivial cycle is $2^1 - 1$, while for the $5\mathcal{Z} + 1$ sequence, the Trivial Governors are $2^2 - 1$ and $2^1 - 1$. Therefore, in these specific sequences, the Collatz function reduces the Governor $2^m - 1$ to the Trivial Governor $2^{\mathcal{T}} - 1$. Once this Trivial Governor is reached, it can evolve to a higher index Governor through interactions with other terms. This feature allows $\mathcal{X}$ to reappear in a Collatz-type sequence, since $2^m - 1 = 2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1).$ Thus, if $\mathcal{X}$ reappears, at least one odd ancestor of $\left\{\sum\limits_{M > m} b_M 2^M\right\} + 2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1)$ must have the Governor $2^m - 1$. Ancestor mapping shows that all odd ancestors of $\mathcal{X}$ have the Trivial Governor for the respective Collatz sequence. This implies that odd integers that repeat in the $3\mathcal{Z} + 1$ sequence have the Governor $2^1 - 1$, while those forming a repeating cycle in the $5\mathcal{Z} + 1$ sequence have either $2^2 - 1$ or $2^1 - 1$ as the Governor. Successor mapping for the $3\mathcal{Z} + 1$ sequence further indicates that there are no auxiliary cycles, as the Trivial Governor is always transformed into a different index Governor. Similarly, successor mapping for the $5\mathcal{Z} + 1$ sequence reveals that the smallest odd integers forming an auxiliary cycle are smaller than $2^5$. Finally, attempts to identify integers that diverge for the $3\mathcal{Z} + 1$ sequence suggest that no such integers exist.

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle (MGRP). Within this framework new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: {\bf(i)} We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and the tensor to scalar ratio $r$. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. {\bf(ii)} The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. {\bf(iii)} For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a {\it new non-diagonal} coherent state representation complementary to the known Sudarshan diagonal one. {\bf(iv)} Mean value generators of $Mp(2)$ are related to the adiabatic invariant and topological charge of the spacetime (matrix element of the transition $-\infty < t < \infty$). {\bf(v)} The basic {\it even} and {\it odd} $n$-sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (in particular continuum for $n \rightarrow \infty$), they do not require any extrinsic generation process as the standard Schrodinger cat states, and are {\it entangled}. {\bf(vi)} The gravity or cosmological domains in one side and another of the Planck scale are {\it entangled}. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity reqion and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. {\bf(vii)} The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.

Background: Periodontitis is a disease that leads to serious functional and aesthetic dysfunctions resulting in impairment of life quality; it exists in different forms and its etiology is related with multiple component causes. Angiogenesis, together with inflammatory infiltrate, are two key processes in the evolution of inflammatory processes involving gingival tissues. The aim of this study was to evaluate their alterations in relation to some important periodontal diseases-associated factors (i.e. smoke, sex, age, plaque, pus, probing pocket depth) in patients with diagnosis of Generalized Aggressive Periodontitis (GAP). Methods: Eighteen subjects with GAP were enrolled for this study. Percentage of inflammatory cells and vascular area were measured and evaluated in relation with each periodontal diseases-associated factor. Results: The results showed a significant decrease of the percentage of vascular area in association with almost all the periodontal diseases-related factors (smoke, age, PPD, plaque) and not significant differences in the percentage of inflammatory cells. Conclusions: Data suggest that, even if these factors are often commonly related to worsening of periodontal status, they did not affect inflammatory and vascular pattern, as we can assume. For the future, additional studies, aimed to evaluated each singular factor in a wider sample size, should be planned.

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.

In this study, we propose the Signal Integration Reconstruction Peak Detection (SIRPD) algorithm for reliable Cardiac Beat Interval (CBI) measurement using functional Near-Infrared Spectroscopy (fNIRS) signals. This algorithm enhances reliability by identifying a regular waveform in cerebral blood flow associated with heartbeats. The SIRPD algorithm assesses the Signal Quality Index (SQI) per channel, discards signals from unavailable channels, and interpolates oxygenated and total hemoglobin concentration signals, thereby boosting resolution and integrating the signal into a single channel. The integrated and smoothed signal is transformed to identify the most significant periodic waveform, from which the CBI is extracted. Validated with data from 20 healthy subjects who simultaneously recorded fNIRS and ECG signals, our findings confirm the equivalence of the CBI derived from ECG and calculated through the SIRPD algorithm from fNIRS (R^2 = .98, RMSE = .011, ICC = .991). We also extracted heart rate variability (HRV) features, confirming no significant difference in all features between ECG and fNIRS devices. Uniquely, this study regards the fNIRS heart signal not as an artifact source but as a valuable bio signal. The proposed method, which allows for the detection of cardiac beat intervals from cerebral blood flow oscillations, suggests the potential clinical applicability of fNIRS as an auxiliary indicator for various cardiovascular factors.

Most petrochemical plants still maintain a Proportional-Integral-Differential controller(PID) system, which is a feedback control system. However, gradually, the PID system is being extended and introduced to the Advanced Process Controller (APC) system, which is an integrated control system of feedforward and feedback that predicts external influences in advance. In the process of conducting on-site plant tests and calculating APC model parameter for the application of APC systems, a problem arises that Model Parameter are implemented differently depending on the proficiency of APC engineers. To minimize this problem, a technique for estimating APC model parameter without a plant test is required. In order to estimate the APC model parameter, it is necessary to train on dynamic interval data. In this paper, we use statistical techniques such as PELT, Linear Kernel, and Radial Basis Function Kernel of Change Point Detection (CPD) to extract dynamic data with minimum Mean Absolute Error (MAE) from time series data of a real petrochemical plant. Then, the hyper parameter is fixed and the APC model parameter is estimated by learning the dynamic section data. By applying the estimated APC model parameter to the APC Model Tool and measuring the fitting rate, it was confirmed that it is possible to estimate the APC model parameter with excellent control performance without plant test.

Whole blood viscosity, a hemorheological factor, is currently used for diagnosis, as it is correlated with various vascular diseases that are difficult to diagnose early with a general blood test. It was determined that it was necessary to set reference intervals for further studies and utilization of whole blood viscosity in cats, a representative companion animal, and this study was conducted. 50 healthy cats were recruited for the study and whole blood viscosity, complete blood count, and serum chemistry tests were performed. The reference intervals of whole blood viscosity were 15.169 to 43.684 cP at a shear rate of 1 s-1 reflecting diastole, and 3.524 to 5.544 cP at a shear rate of 300 s-1 reflecting systole. Red blood cells, hematocrit, hemoglobin, white blood cells, and neutrophils in the complete blood count, and total protein, albumin, globulin, and cholesterol in the serum chemistry were significantly correlated with whole blood viscosity. The results of this study set reference intervals of whole blood viscosity for healthy cats in a wide shear rate range that has not yet been fully established and investigated its correlation with other blood indicators.

In this work, we derive the spectral efficiency, secrecy outage probability, and bit error rate of a communication system assisted by a large intelligent surface (LIS). We consider a single-antenna user and an array of antennas at the transmitter side and the possibility of a direct link between transmitter and receiver. Additionally, there is a single-antenna eavesdropper with a direct link to the transmitter, which is modeled as a Nakagami-m distributed fading coefficient. The channels from transmitter to the LIS and from the LIS to the user may or may not have the line-of-sight (LoS) and are modeled by the Nakagami- m distribution. Moreover, we assume that the LIS elements perform non-ideal phase cancellation leading to a residual phase error that assumes a Von Mises distribution. We show that the resulting channel can be accurately approximated by a Gamma distribution whose parameters are analytically estimated using the moments of the equivalent signal-to-noise ratio. We also provide an upper bound for the error probability for M-QAM modulations. With the derived formulas, we analyze the effect of the strength of the LoS link by varying the Nakagami parameter, m.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

In this paper, we present a rigorous proof demonstrating the stabilization of percolation probability in supercritical regimes for percolation models. We analyze a sequence of expanding compact balls in ℝ

We prove that the probability of “A OR B”, where A and B are events or hypotheses that are recursively dependent (OR is the logico-probabilistic operator) is given by a "Hyperbolic Sum Rule” (HSR) relation isomorphic to the hyperbolic-tangent double-angle formula, and that this HSR is Maximum Entropy (MaxEnt). The possibility of recursive probabilities is excluded by the “Conventional Sum Rule” (CSR) which we also prove MaxEnt (within its narrower domain of applicability). The concatenation property of the HSR is exploited to enable analytical, consistent and scalable calculations for multiple recursive hypotheses: such calculations are not conveniently available for the CSR, and are also intrinsic to current artificial intelligence and machine learning architectures presently considered intractable to analytical study and methodological validation. We also show that it is as reasonable to state that “probability is physical” (it is not merely a mathematical construct) as it is to state that “information is physical” (now recognised as a truism of communications network engineering). We relate this treatment to the physics of Quantitative Geometrical Thermodynamics which is defined in complex hyperbolic (Minkowski) spacetime, and show how the HSR is isomorphic to other physical quantities including certain components important for digital signal processing.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator.The notion of entangled probability distribution is reviewed. Evolution equations describing the time-dependence of probability distributions identified with quantum system states are discussed.The connection with the Schrödinger equation and the von Neumann equation is clarified.

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

In this article we explore the limiting behavior of the universal prior distribution obtained when applied over multiple meta-level hierarchy of programs and output data of a computational automata model. We were motivated to alleviate the effect of Solomonoff's assumption that all computable functions or hypotheses of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case, the set of all possible program strings of a fixed-length converges to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in digital physics and the constructor theory of life.

Although the vegetation of the Cerrado biome is prone to fire, plant species composition can be altered according to its severity and frequency. Furthermore, many Cerrado plant species are resistant and can adapt to frequent fires. Little is known about how plant species of Cerrado environments respond to fire and the extent to which fire is beneficial for their conservation. The present study analyzed the responses of plant species of areas of campo sujo to fire and changes in floristics and vegetation structure at different post-fire intervals. Areas with frequent fires had a greater diversity of species, while the area with 10 years without burning had lower diversity and greater DBH. The distribution of species differed among the four the studied areas. We conclude that fire was beneficial for species diversity in the studied areas of Cerrado since it was able to promote the insertion and removal of species during intervals between fires.

Behavior analysis is a widely used non-invasive tool in the practical production routine, as the animal acts as a biosensor capable of reflecting its degree of adaptation and discomfort to some environmental challenge. Predominantly, conventional statistics use occurrence data for behavioral evaluation and well-being estimation, disregarding the temporal sequence of events. The Generalized Sequential Pattern (GSP) algorithm is a data mining method that identifies recurrent sequences that exceed a user-specified support threshold, whose potential has not yet been investigated for broiler chickens in enriched environments. Enrichment aims to increase environmental complexity with promising effects on animal welfare, stimulating priority behaviors and potentially reducing the deleterious effects of heat stress. The objective was to validate the application of the GSP algorithm to identify temporal correlations between heat stress and the behavior of broiler chickens in enriched environments through proof of concept. Video image collection was carried out automatically for 48 continuous hours, analyzing a continuous period of seven hours, from 12:00 PM to 6:00 PM, during two consecutive days of tests for chickens housed in enriched and non-enriched environments under comfort and stress temperatures. Chickens at comfort temperature showed high motivation to perform the behaviors of Preening (P), Foraging (F), Lying down (Ld), Eating (E), and Walking (W) whose sequences &lt;{Ld,P}&gt;; &lt;{Ld,F}&gt;; &lt;{P,F,P}&gt;; &lt;{Ld,P,F}&gt; and &lt;{E,W,F}&gt; were the only ones observed in both treatments. All other sequential patterns (comfort and stress) were distinct, suggesting that environmental enrichment alters the behavioral pattern of broiler chickens. Heat stress drastically reduced the sequential patterns found at the 20% threshold level in the tested environments. The behavior of lying laterally "Ll" is a strong indicator of heat stress in broilers and was only frequent in the non-enriched environment, which may suggest that environmental enrichment provides the animal with better opportunities to adapt to stress-inducing challenges, such as heat.

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of Modern Physics, Astrophysics, and Cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the General Relativity and quantum field theories, as well as all of that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D Universe’s expansion and its following acceleration.

We study the generalized χ and η cross helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). χ and η, the additional label translation symmetry group, have been used to generalize the cross helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behaviour in non-ideal MHD, we derive the time derivative of both helicities using the non-ideal MHD equations taking viscosity, finite resistivity and heat conduction into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that χ and η cross helicities are not strict constant of motion in the non-ideal MHD and show the rate of dissipation which is compared to the dissipation of other topological constants of motion.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Low pasture biomass production and fodder scarcity are among the major challenges affecting productivity of dairy cattle farms in Sri Lanka. As a potential solution to this, two Napier hybrid cultivars CO-5 and Sampoorna were recently introduced and a field experiment was conducted to evaluate their growth, dry matter production and nutritional composition during May to September 2020. Plant measurements and samples were collected at five harvest intervals (4, 6, 8, 10 and 12 weeks after planting), with the plant samples subjected to biomass and nutritional assessments. The number of tillers and leaf length differed (P=0.01) between the two cultivars at 4 weeks harvesting interval (HI) whilst number of leaves differed at 12 HI respectively. Dry matter yield increased (P=0.16) almost linearly whilst crude protein declined exponentially with CO-5 greater than Sampoorna (P=0.057; 9.3% vs 8.7%), with increasing harvesting intervals respectively. In-vitro Organic Matter Digestibility and In-vitro Metabolizable Energy contents were similar across weeks 4, 6 and 8 but then decreased. This study demonstrates that higher dry matter yields (12.54 t/ha) can be obtained by harvesting both cultivars at 12 HI, but from a nutritional perspective harvesting at 6 HI during Yala season of the year would be optimum for farmers.

Let $n \geq 2$ be a fixed integer and $\mathcal{A}$ be a $C^*$-algebra. A permuting $ n $-linear map $ \mathcal{G} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ is known to be symmetric generalized $n$-derivation if there exists a symmetric $n$-derivation $ \mathfrak{D} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ such that $ \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i} x_{i}^{\prime}, \ldots, x_{n}\right)= \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i}, \ldots, x_{n}\right) x_{i}^{\prime}+x_{i} \mathfrak{D} (x_{1}, x_{2},\ldots, x_{i}^{\prime}, \ldots, x_{n})$ holds for all $x_{i}, x_{i}^{\prime} \in \mathcal{A} $. In this paper, we investigate the structure of $C^*$-algebras involving generalized linear $n$-derivations. Moreover, we describe the forms of traces of linear $n$-derivations satisfying certain functional identity.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

Let {ξ1, ξ2. . . .} be a sequence of independent possibly differently distributed random variables defined on a probability space (Ω, F, P) with distribution functions {F_ξ1., F_ξ2 , . . .}. Let η be a counting random variable independent of sequence {ξ1, ξ2. . . .}. In this paper, we find conditions under which distribution function of randomly stopped sum Sη = ξ1 + ξ2 + . . . + ξη belongs to the class of generalized subexponential distributions.