The development of one technology can be portrayed by common methods like Gartner’s hype cycle or S-curve, however, there is no method to characterize the feature distributions of multiple technologies within a specific domain. This study proposes a big data-based method in terms of four proposed features, namely versatility, significance, commerciality, and disruptiveness, to characterize the technologies within a given domain. The features of technologies are quantitively portrayed using the representative keywords and volumes of returned search results from Google and Google Scholar in two-dimensional analytical spaces of technique and application. We demonstrate the applicability of this method using 452 technologies in the domain of intelligent robotics. The results of our assessment indicate that the versatility values are normally distributed, while the values of significance, commerciality, and disruptiveness follow power-law distributions, in which few technologies possess higher feature values. We also show that significant technologies are more likely to be commercialized or causing potential disruption, as such technologies have higher scores in these features. Further, we validly prove the robustness of our approach via comparing historical trends with literature and characterizing technologies in reduced analytical spaces. Our method can be widely applied in analyzing feature distributions of technologies in different domains, and it can potentially be exploited in decisions like investment, trade, and science policy.

Regulation of the diet in terms of the content of soluble and insoluble fibre is of great importance from the point of view of dietetics, microbiology of the gastrointestinal tract and immunology of the organism. Dietary fibre plays an important role in maintaining the balance between the con-tinuity of gut mucus production (intestinal mucosa), the stability of the intestinal microbiome composition, the regeneration of the intestinal epithelium and the immune status within the gut-associated lymphoid tissue (GALT) are played by pectin and their metabolic products in the form of pectin oligosaccharides. The main purpose of this review was to focus on pectin, their functions, their impact on the human's health and on some of the most promising prebiotics due to their solubility in the gastrointestinal tract in the form of pectin oligosaccharides. They have the properties of pectin, but have also additional features and postbiotics obtained in fermentation process can affect the intestinal microbiome and GALT-related immunity. They can be obtained from plant agro-wastes.

An exposition of entropy applications to highlight some potential entropic applications to artificial intelligence and knowledge transfer. Entropy is a basic idea in artificial intelligence that is applied to many different tasks, such as reinforcement learning, data compression, and decision-making. By quantifying uncertainty and information content, it helps artificial intelligence models provide predictions and decisions that are well-informed. Therefore, this paper shines on spotlighting the significance of entropy to attract the attention of artificial intelligence research community to entropy as a powerful tool to advance artificial intelligence.The significance of knowledge transfer (KT), particularly intergenerational knowledge transfer (IGT), in knowledge management is also covered in this paper. To quantify the complexity of knowledge distribution inside an organisation and assess the efficacy of knowledge transfer (KT) initiatives, the notion of knowledge entropy (KE) is presented. Additionally, the KT model—which is based on the conceptions of tacitness and information content—is introduced. It combines personalisation and codification methodologies. Future research directions are offered alongside a few difficult open problems.

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.

Predicting electricity prices is a very important issue in modern society, because the associated decision process under uncertainty requires accurate forecasts for the economic agents involved. In this paper, we apply the decision tree extension of Random Forests to the prediction of electricity prices in Spain, but with the novelty of modeling prices jointly with demand, with the purpose of achieving greater accuracy than with univariate response Random Forests, particularly in price prediction, as well as understanding the effect of the input variables (lagged values of price and demand, current production levels of available energy sources) on the joint of the two outputs. The results are very encouraging, providing significant increase in price prediction accuracy. Also, interesting methodological challenges appear as far as the appropriate choice of the relative weights of price and demand in the joint modeling is concerned and a new procedure to provide the importance variable ranking is proposed. The partykit (package of R software) library allowing for multivariate Random Forests has been used.

Postpartum haemorrhage (PPH) is a significant cause of maternal morbidity and mortality worldwide, particularly in low-resource settings. This study aimed to develop a predictive model for PPH using early risk factors and rank their importance in terms of predictive ability. The dataset was obtained from an observational case-control study in Northern Rwanda. Various statistical models and machine learning techniques were evaluated, including logistic regression, logistic re-gression with elastic-net regularisation, Random Forest, Extremely Randomized Trees, and gradient boosted trees with XGBoost. Random Forest emerged as the best predictive model for PPH across three different train-test data partitions. The important predictors identified in the study were haemoglobin level during labour and maternal age. However, there were differences in PPH risk factor importance in different data partitions, highlighting the need for further investigation. These findings contribute to understanding PPH risk factors, highlight the importance of considering different data partitions and implementing cross-validation in predictive modelling, and emphasise the value of identifying the appropriate prediction model for the application. Effective PPH pre-diction models are essential for improving maternal health outcomes on a global scale. This study provides valuable insights for healthcare providers to develop predictive models for PPH to identify high-risk women and implement targeted interventions

Entropy as a mathematical concept is the first of its own kind, and second to none. Barely one or two papers in literature have investigated fractal dimensions of very basic entropies, such as Shannon, Tsallis, and Rényi entropic expressions. This was a thoughtful inspiration to delve into a step forward towards a unified information- theoretic fractal theory. The storytelling of this current paper starts by introducing my third entropy formula, namely Ismail’s entropy, , as a novel generalization to Shannonian entropy with a visionary link to both long- and short-range interactions, (LRIs), (SRIs) respectively. Clearly, this would generate a fourfold unification with statistical mechanics as well as contemporary physics. Hence, this adds more credibility and weight for this study. The fractal dimension of , is identified in this paper. As an essential part of this work, it was influential to spotlight the importance of fractal geometry to space industry as well as education, which is crucial to develop our societies. Thus, some potential fractal applications to CubeSat Technologies and Education are highlighted. So, will the deep search for more ground-breaking research has come to an end. Certainly, not. This was another inspiration to propose new open problems to widen research gates to the scientific community for more research pathways. Consequently, the paper ends with closing remarks combined with some challenging open problems and the next phase of research.

Background: Endometriosis is a female chronic inflammatory disease in which endometrial tissue develops outside the uterine cavity. It is a complex pathology, that significantly contributes to morbidity in premenopausal women, leading to chronic pain, infertility, and subfertility negatively impacting the physical, and emotional well-being and overall quality of life. The public health burden of endometriosis remains elusive and challenging to determine, and this uncertainty can lead to inadequate healthcare services and treatments. Objective: To estimate the incidence and prevalence of endometriosis in Italy using the hospital discharge records database. Population-based retrospective study. Nationwide between 2011 and 2020. Methods: From the National Hospital Discharge Database were selected all admissions with a diagnosis of endometriosis (ICD-9-CM, codes 617.x), supported by the presence of a procedure code of laparoscopy or any other surgical procedure allowing direct visualisation of the lesions. Main outcomes measures Incidence and prevalence of endometriosis were estimated for the entire 2010-2020 period and by individual year, analysing the time trend and variability in different geographical areas of Italy. Results: A total of 134,667,646 women aged 15–50 years with one or more hospitalisations for endometriosis in all Italian hospitals. The incidence of endometriosis in Italy during this period was 0.839 per 1000 women (CI95% 0.834-0.844), exhibiting a statistically significant decreasing trend over the years. A discernible north-south gradient was observed, with higher rates documented in the northern regions. The prevalence rate stood at 14.0 per 1000 during the same period, and a similar north-south geographical gradient was identifiable in the prevalence rates as well. Conclusions: The utilization of national-level hospital data enables the generation of incidence and prevalence data for endometriosis without variations in methods and definitions, facilitating the evaluation of temporal trends and regional comparisons. Understanding and quantifying this phenomenon is essential for appropriate healthcare planning in various Italian regions.

The hard open problem of finding the lower bound for the Fokker Planck Kolmogorov’s time-dependent controller parameter probability density function is addressed for the first time in literature in this work. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to multi-interdisciplinary fields of human knowledge, and beyond. So, this by default adds more taste and credibility to this study. Concluding thoughts are included at the end of the work along with a difficult outstanding problem and the direction of future work.

This study aims to reveal the revolutionary Gamma Distribution Manifold (GDM) info-geometric analysis combined with potential Gamma distribution (GD) applications to advance Satellite Earth Observations (SEOs). An exposition of the GDM Fisher Information Matrix (FIM) was undertaken, together with the analytic investigation of the existence of FIM’s inverse. The derivation of GDM’s Geodesic Equations (GEs) is undertaken. The solution of the obtained Geodesic Equations is optimally complicated, and it provides more extensions to numerous open problems. Notably, the current paper provides a first-time unification between three multi-interdisciplinary fields, namely, information geometry theory, probability theory, and Satellite earth observations. Looking at the other side of the coin, the provided revolutionary approach in this current work reports the significant impact of info-geometric analysis on the probabilistic dynamics as well as the influential role of information geometry on satellite and space industry. This poses numerous open issues that initiates a new form of contemporary unification between these inter-disciplinaries to discover another visionary thinking out of traditional statistical frames. In other words, refraining ourselves from using classical statistical frames of thinking and delving into a new info-geometric vision of statistical distributions as well as examining real life applications of information geometry to advance satellite earth observations. The curtain is drawn on this paper by providing several challenging open problems in combination with a concluding remark and the next phase of research.

This paper provides a new discovery that adds to the contemporary theory of modelling of non-stationary queues, by capturing analytically the behavior of the root parameter, for the G1/M/1 PSFFA model of non-stationary Ek/M/1 queue. Additionally, it has been also revealed that the resulting root parameter reduces to the PSFFA model of non-stationary queue. Potential applications of PSFFA to Computer engineering are provided. Some challenging open problems are addressed combined with closing remarks and future research directions.

This paper investigates the search for an exact analytic solution to the state variable of the non-stationary queue. Currently, the only known solution to this problem is through simulation. However, this study proposes a constant ratio

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

In this data deposit, I describe a dataset that is the result of content mining 167,318 published articles for statistical test results. As a result of this content mining, 688,112 results from 50,845 articles were extracted. In order to provide a comprehensive set of data, the statistical results are supplemented with metadata from the article they originate from. The dataset is provided in a comma separated file (CSV) in long-format. For each of the 688,112 results, 20 variables are included, of which seven are article metadata and 13 pertain to the individual statistical results (e.g., reported and recalculated p-value). A five-pronged approach was taken to generate the dataset: (i) collect journal lists, (ii) spider journal pages for articles, (iii) download articles, (iv) add article metadata, and (v) mine articles for statistical results.

Let $(\{f_n\}_{n=1}^\infty, \{\tau_n\}_{n=1}^\infty)$ and $(\{g_n\}_{n=1}^\infty, \{\omega_n\}_{n=1}^\infty)$ be unbounded continuous p-Schauder frames ($0<p<1$) for a disc Banach space $\mathcal{X}$. Then for every $x \in ( \mathcal{D}(\theta_f) \cap\mathcal{D}(\theta_g))\setminus\{0\}$, we show that \begin{align}\label{UB} \|\theta_f x\|_0\|\theta_g x\|_0 \geq \frac{1}{\left(\displaystyle\sup_{n,m \in \mathbb{N} }|f_n(\omega_m)|\right)^p\left(\displaystyle\sup_{n, m \in \mathbb{N}}|g_m(\tau_n)|\right)^p}, \end{align} where \begin{align*} & \theta_f: \mathcal{D}(\theta_f) \ni x \mapsto \theta_fx \coloneqq \{f_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}), \quad \theta_g: \mathcal{D}(\theta_g) \ni x \mapsto \theta_gx \coloneqq \{g_n(x)\}_{n=1}^\infty\in \ell^p(\mathbb{N}). \end{align*} Inequality (1) is unexpectedly different from both bounded uncertainty principle \textit{[arXiv:2308.00312v1]} and unbounded uncertainty principle \textit{[arXiv:2312.00366v1]} for Banach spaces.

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these popular distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is the upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of a random discrete variable. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these legendary distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of the random discrete variable X. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

The Mann-Whitney effect is a measure for comparing survival distributions between two groups. The Mann-Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence assumption of two groups, the Mann-Whitney effect can be expressed as the traditional integral formula of survival functions. However, when the survival times in two groups are not independent each other, the traditional expression of the Mann-Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann-Witney effect with parametric survival models under dependence of two groups, which may arise in the potential outcome framework. In addition, we develop a Shiny web app that can implement the proposed method via simple commands (https://nkosuke.shinyapps.io/shiny_survival/). Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.

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.

In higher education, the cultivation of research competency is pivotal for students’ critical thinking development and their subsequent transition into the professional workforce. While statistics plays a fundamental role in supporting the completion of a research project, it is often perceived as challenging, particularly by students in majors outside mathematics or statistics. The connection between students’ statistical proficiency and their research competency remains unexplored despite its significance. To address this gap, we utilized the supervised machine learning approach to predict students’ research competency, as represented by their performance in a research methods class, with predictors of students’ proficiency in statistical topics. Predictors relating to students’ learning behavior in a statistics course such as assignment completion and academic dishonesty are also included as auxiliary variables. Results indicate that the three primary categories of statistical skills—namely, understanding of statistical concepts, proficiency in selecting appropriate statistical methods, and statistics interpretation skills— can be used to predict students’ research competency, as demonstrated by their final course scores and letter grades. This study advocates for strategic emphasis on the identified influential topics to enhance efficiency in developing students’ research competency. Findings could inform instructors in adopting a strategic approach to teaching the statistical component of research for enhanced efficiency.

When wildlife and motor vehicles collide, the result for the animals is often death (roadkill). A commercial roadkill Virtual Fence (VF) mitigation device (iPTE Traffic Solutions) was used in a field trial to test its effectiveness along a 4.9-km segment of road on Bruny Island, Tasmania. A total of 585 days of monitoring of roadkill by species was conducted, with six sections alternatively switched on or off, according to a variation of a Crossover and Multiple Before-After-Control-Impact (MBACI) experimental designs that divided monitoring into “off-on” then “on-off” blocks of periods with each “on” period followed by a 16 d “wash-out” period. For the six sections over the four periods that exclude wash-outs, the 24 aggregated values of daily counts of roadkill of Tasmanian pademelons (Thylogale billardierii), that gave a total count of 222, were modelled. Other species were killed in insufficient numbers for analysis to be informative. The statistical analysis exploited the MBACI design to estimate the VF effect using a log-odds ratio parameter (LORP) while accounting for local spatio-temporal effects. Both versions of the analysis, either averaging over the three spatial replicates (paired sections) or two temporal replicates (blocks) gave no statistically significant effect of the VF judged as a LORP estimate not sufficiently below zero. Corresponding percentage reduction estimates of 9% and 16% were derived from the LORP estimates and given parameter uncertainty estimates the power to detect as significant a LORP corresponding to a 50% reduction in rate were 0.5 and 0.6, respectively. This study confirms results from a similar field trial carried out in 2018 also in southern Tasmania and adds to the evidence that this VF is likely to give if anything only a minor reduction in roadkill for a commonly killed species for which researchers have the best chance of detecting any practically useful reduction.

Extraction techniques of important bioactive molecules from the major concern of Seafood byproducts are getting emphasis for better valorization. Employing green extraction technologies for efficient and quality production of these bioactive molecules is also strictly required. Hence, understanding the extraction process parameters to effectively design an applicable optimization strategy could make this real. In this review, statistical optimization strategies applied for the extraction process parameters of bioactive molecules from Seafood byproducts are focused. The type of experimental designs, and techniques applied to criticize and validate the effects of independent variables on the extraction output was addressed. Dominant parameters studied were enzyme/substrate ratio, pH, time, temperature and power of extraction instruments. The yield of bioactive compounds, chitin and chitosan, proteins and peptides, enzymes and carotenoids (Astaxanthins) were the most studied responses. Efficiency and/or economic and quality considerations and their selected optimization strategies that favour the production of potential bioactive molecules were also reviewed.

Ranked Set Sampling (RSS) is a useful technique for improving the estimator of population mean when the sampling units in a study can be easily ranked than the actual measurement. RSS performs better than simple random sampling (SRS) when the mean of units corresponding to each rank is used. The performance of RSS can be increased further by assigning weights to the ranked observations. In this paper, we propose weighted RSS procedures to estimate the population mean of positively skew distributions. It is shown that the gain in the relative precisions of the population mean for chosen distributions are uniformly higher than those based on RSS. The gains in relative precisions are substantially high. Further, the relative precisions of our estimator are slightly higher than the ones based on Neyman’s optimal allocation model for small sample sizes. Moreover, it is shown that, the performance of the proposed estimator increases as the skewness increases by using the example of lognormal family of distributions.

This work reports measurements of calcified gallstone elemental compositions using laser-induced optical emission spectroscopy. The experimental results support the importance of the magnesium concentration in gallstone growth. Granular stones reveal an increased magnesium concentration at the periphery of the granules, suggesting the inhibition of further growth. Non-granular gallstones reveal lower overall magnesium concentrations but with higher values near the center.

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

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.

This paper addresses the issues of how we can quantify structural information for nonparametric distributions and how we can detect its changes. Structural information refers to an index for a global understanding of a data distribution. When we consider the problem of clustering using a parametric model such as a Gaussian mixture model, the number of mixture components (clusters) can be thought of as structural information in the model. However, there does not exist any notion of structural information for nonparametric modeling of data. In this paper we introduce a novel notion of {\em kernel complexity} (KC) as structural information in the nonparametric setting. The key idea of KC is to combine the information bias inspired by the Gini index with the information quantity measured in terms of the normalized maximum likelihood (NML) code length. We empirically show that KC has a property similar to the number of clusters in a parametric model. We further propose a framework for structural change detection with KC in nonparametric distributions. With synthetic and real data sets we empirically demonstrate that our framework enables us to detect structural changes underlying the data and their early warning signals.

Pragmatic trials aim to assess intervention efficacy in usual patient care settings, contrasting with explanatory trials conducted under controlled conditions. In aging research, pragmatic trials are important designs for obtaining real-world evidence in elderly populations, which are often underrepresented in trials. In this review, we discuss statistical considerations from a frequentist approach for the design and analysis of pragmatic trials. When choosing the dependent variable, it is essential to use an outcome that is highly relevant to usual medical care while also providing sufficient statistical power. Besides traditionally used binary outcomes, ordinal outcomes can provide pragmatic answers with gains in statistical power. Cluster randomization requires careful consideration of sample size calculation and analysis methods, especially regarding missing data and outcome variables. Mixed effects models and generalized estimating equations (GEEs) are recommended for analysis to account for center effects, with tools available for sample size estimation. Multi-arm studies pose challenges in sample size calculation, requiring adjustment for design effects and consideration of multiple comparison correction methods. Secondary analyses are common but require caution due to the risk of reduced statistical power and false-discovery rates. Safety data collection methods should balance pragmatism and data quality. Overall, understanding statistical considerations is crucial for designing rigorous pragmatic trials that evaluate interventions in elderly populations under real-world conditions. In conclusion, this review focuses on various statistical topics of interest to those designing a pragmatic clinical trial, with consideration of aspects of relevance in the aging research field.

High dimensional statistical analysis for the yield of large-scale circuits is quite difficult due to expensive simulations, especially for the memory circuits with high sigma requirement (e.g., SRAM). In this paper, we developed an efficient sparse additive model to substitute simulations. To fit high sigma region accurately, the modeling center is moved to near failure boundary searched by scaling the shape of sampling function. To solve the model efficiently, the process variables are grouped by standard cells so that the model can be solved by our developed blockwise greedy algorithm. The experiments on the 28nm memory circuits validate that our method achieves high accuracy and efficiency compared with other state-of-art works.

The paper presents theoretical notions with practical applications for establishing of one dental bur lifetime (durability and reliability based on the active part wear considering a series of statistical indicators. For the justification application of theoretical notions in practice, a conical-cylindrical dental bur was studied experimentally, to obtain a series of data in the work process, necessary for statistical calculation. The parameter taken into consideration in this paper is mass lost through the dental bur active part wear, tested. This is useful for the dental bur lifetime establishment and its extension or even optimization in operation. The loss of mass of the dental bur active part is analyzed in the work process by the results and experimental data obtained and validated by a numerical calculation statistical-mathematical. The numerical calculation approximates very well the mass lost through the wear at different rotation speeds and operation times, with those experimentally determined ones, based on which it was established lifetime. The results showed that the dental bur works with high yield in the first 20 hours of work, , after which it should be replaced with a new one.

Four decades of snooker rankings are analyzed in terms of prize money distributions. In particular, it is investigated how much these rankings are dominated by the top players, and also by players from the UK. The main conclusions are: (1) with an increasing amount of available prize money, the rankings are less dominated by the top players, and (2) players from the UK have historically earned a significantly larger share of the available prize money than could be reasonably expected based on the actual percentage of UK players.

Congestion pricing has received lots of attention in the scientific discussion. Congestion pricing means that the operator increases prices at the time of congestion and the traffic demand is expected to decrease. In a certain sense, shadow prices are an optimal way of congestion pricing: users are charged shadow prices, i.e., the expectations of future losses because of blocked connections. The shadow prices can be calculated exactly from Howard’s equation, but this method is difficult. The paper presents simple approximations to the solution of Howard’s equation and a way to derive more exact approximations. If users do not react by lowering their demand, they will receive higher bills to pay. Many users do not react to increased prices but would want to know how the congestion pricing mechanism affects the bills. The distribution of the price of a connection follows from knowing the shadow prices and the probability of a congestion state. There is another interesting distribution. The network produces profit to the operator, or equivalently, blocked connections produce a cost to the operator. The average cost rate can be calculated from Howard’s equation, but the costs have some distribution. The distribution gives the risk that the actual costs exceed the average costs, and the operator should include this risk to the prices. The main result of this paper shows how to calculate the distribution of the costs in the future for congestion pricing by shadow prices and for congestion pricing with a more simple pricing scheme that produces the same average costs.

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure, alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the actual estimation of the noise power. A complete Bayesian study over the model parameters and the scale parameter can be also performed. Numerical experiments show the benefits of the proposed approach.

The Dual-Frequency Precipitation Radar (DPR) on the Core GPM satellite provides spaceborne 3-dimensional observations of the precipitation field and surface rainfall rate with quasi global coverage. The present study evaluates the behavior of liquid precipitation intensity, radar reflectivity factor (ZKu and ZKa) and Drop Size Distribution (DSD) parameters (weighted mean diameter Dm and intercept parameter Nw) of the GPM DPR derived products version 07 from 2014 to 2023. Observations from seven Parsivel disdrometers located in different topographic zones in the Western Mediterranean are taken as ground reference. Four matching techniques between satellite estimates and ground level observations were tested, and best results were found for the so-called optimal comparison approach. Overall, GPM DPR products capture well the variability of the observed DSD at different rainfall intensities. However, overestimation of the mean Dm and underestimation of the mean Nw are observed, being much more sensitive to errors in drop diameters larger than 1.5 mm. Moreover, lowest errors were found for radar reflectivity factor and Dm, and highest for Nw and rainfall rate. In addition, the GPM DPR convective and stratiform classification was tested and it was found a substantial overestimation of stratiform cases compared to disdrometer observations.

Genetic similarity determines the extent to which two genotypes share common genetic material. It can be measured in various ways, such as comparing DNA sequences, proteins, or other genetic markers. The significance of genetic similarity is multifaceted and encompasses various fields, including evolutionary biology, medicine, forensic science, animal and plant breeding, and anthropology. Genetic similarity is an important concept with wide application across different scientific disciplines. In the presented study, six measures for calculating genetic similarity were compared: Euclidean, Jaccard, Kulczyński, Sokal and Michener, Nei, and Rogers. The research material included 21 rapeseed genotypes (ten interspecific Brassicaceae hybrids of F2 generation, and 11 of their parental forms) and 146 alleles, obtained using 21 ISSR molecular markers. The results indicate that the research material was divided into two identical groups using any of the proposed methods, despite differences in the values of genetic similarity coefficients. Two of the presented measures of genetic similarity (Sokal and Michener, and Euclidean) were the same.

Statistics modules are included in most university degrees, independent of the degree area. They have an important role in preparing students for the real world. The overall goal of this paper is to identify the common statistical issues students face during the transition from secondary education to tertiary education. Drawing upon data from the University College Dublin (UCD) Math Support Center (MSC) and Universidad Rey Juan Carlos (URJC), our approach aims to optimize learning experiences while advancing sustainability objectives. In this paper, we conducted a categorization of statistical concepts taught in university (based on URJC). Using this categorization, UCD MSC tutor comments were categorized and validated, and subsequently descriptive analyses and text mining were used on the UCD MSC comments to achieve a deeper understanding of the statistical issues. Building on this study, we plan to develop a suite of evidence-based sustainable educational applications and games to support undergraduate students internationally in first-and second-year statistical modules. Our findings on students’ main statistical issues contribute to the cultivation of lasting statistical literacy among students. This research advances the sustainability agenda within statistical education.

Efficient textual data distributions (TDD) alignment and generation are open research problems in textual analytics and NLP. It is presently difficult to parsimoniously and methodologically confirm that two or more natural language datasets belong to similar distributions, and to identify the extent to which textual data possess alignment. This study focuses on addressing a segment of the broader problem described above by applying multiple supervised and unsupervised machine learning (ML) methods to explore the behavior of TDD by (i) topical alignment, and (ii) by sentiment alignment. Furthermore we use multiple text generation methods including fine-tuned GPT-2, to generate text by topic and by sentiment. Finally we develop a unique process driven variation of Kullback-Leibler divergence (KLD) application to TDD, named KL Textual Distributions Contrasts (KL-TDC) to identify the alignment of machine generated textual corpora with naturally occurring textual corpora. This study thus identifies a unique approach for generating and validating TDD by topic and sentiment, which can be used to help address sparse data problems and other research, practice and classroom situations in need of artificially generated topic or sentiment aligned textual data.

Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider binomially distributed variables in the example of medication testing with fixed placebo efficacy, asking how many experiments are needed in order to achieve a significance of 95 %. In the next step, we take the probability distribution of the placebo efficacy into account, which to the best of our knowledge has not been done so far. Depending on the specifics, we show that in order to obtain identical significance, it may be necessary to perform twice as many experiments than in a setting where the placebo distribution is neglected. We proceed by considering more general probability distributions and close with comments on some erroneous assumptions on probability distributions which lead, for instance, to a trivial explanation of the fat tail.

This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided.

This review article explores the innovative application of software sensors for monitoring and controlling biosystems, emphasizing their advantage in managing the complexities of various biological processes. Biosystems—from cellular interactions to ecological dynamics—are characterized by intrinsic nonlinearity, temporal variability, and uncertainty, posing significant challenges for traditional monitoring approaches. A critical challenge highlighted is that what is typically measurable may not align with what needs to be monitored. Software sensors bridge this gap by combining hardware sensor data with advanced computational modelling techniques to indirectly infer hard-to-measure target variables, such as stress level, animal and human health indicators, and chemical soil properties. The article outlines advancements in sensor technologies and their integration into model-based monitoring and control systems, leveraging the capabilities of Internet of Things (IoT) devices, wearables, remote sensing, and smart sensors. It provides an overview of common methodologies for designing software sensors, focusing on the modelling process. The discussion contrasts hypothetico-deductive (mechanistic) models with inductive (data-driven) models, illustrating the trade-offs between model accuracy and interpretability. Specific case studies are presented, showcasing software sensor applications such as the use of Kalman filter in greenhouse control, remote detection of soil organic matter, and sound recognition algorithms for early detection of respiratory infections in animals. Key challenges in designing software sensors, including the complexity of biological systems, inherent temporal and individual variabilities, and the trade-offs between model simplicity and predictive performance, are also discussed. This article positions software sensor as remarkable tool for advancing biosystem management, driving forward the potential for sustainable practices in various sectors such as agriculture, healthcare, and environmental monitoring.

This paper presents the preservation property of the average intensity order and the preservation property of the monotonic average intensity classes under distorted distributions. Several sufficient conditions are given to get the preservation properties. It is shown that the imposed conditions are achievable as we examine in some examples. The preservation of the average intensity order and the preservation of the decreasing average intensity class under the structure of a parallel system with independent and identically distributed components' lifetime are made. A lower bound for the average intensity function of a random lifetime with an increasing failure rate in average distribution is derived. The results are applied to some semiparametric models as a particular standard family of distorted distribution.

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.

Spatially resolved, line-of-sight measurements of aluminum monoxide emission spectra in laser ablation plasma are used with Abel inversion techniques to extract radial plasma temperatures. Contour mapping of the radially deconvolved signal intensity shows a ring of AlO formation near the plasma boundary with the ambient atmosphere. Simulations of the molecular spectra were coupled with the line profile fitting routines. Temperature results are presented with simultaneous inferences from lateral, asymmetric radial, and symmetric radial AlO spectral intensity profiles. This analysis indicates that we measured shockwave phenomena in the radial profiles, including a temperature drop behind the blast wave created during plasma initiation.

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.

Human milk (HM) feedings are associated with reduced risks of neurodevelopmental and neurocognitive delays and systemic inflammatory diseases in infants born prematurely and/or at a low birth weight. Utilizing a neonatal piglet model, HM feedings were compared to bovine milk-derived infant formula (IF)-feedings with the aim of understanding the underlying mechanisms involved in reducing these risks. Six male piglets at postnatal-day (PD)2 were randomized into two feeding groups: HM-fed (n = 3) or IF-fed (n = 3) for 28 days. At 3- and 4-weeks-old, piglet memory and learning performance were assessed using novel object recognition (NOR). At PD30 piglets were euthanized, and whole brains were excised, weighed, and preserved for further analyses, and brain microglial morphology, and systemic inflammatory cytokines were quantified. During NOR, HM-fed piglets had significantly more non-novel revisits at both 3- and 4-weeks-old compared to IF-fed piglets. Microglia of HM-fed piglets had longer processes, more branch points, more endpoints, and a larger territorial volume compared to IF-fed piglets at PD30. In a neonatal piglet model, HM-feedings may improve cognition and reduce brain inflammatory response compared to IF-feedings.

In this work, the nearest neighbor distances and Voronoi cell features of the Cu-Ag deposits were analyzed and fitted with Lognormal, Weibull, and Gamma distributions. The nearest neighbor distance distributions of the samples were compared with those of complete spatially random points, showing spatial inhomogenity due to the nucleation exclusion effect. The radial distribution function was calculated, showing both influences from the grain size and the nucleation exclusion effect. Voronoi cells were generated based on the shape of the grains. The size, occupancy, and coordination of the Voronoi cells were examined and fitted. The results show that despite the Cu-Ag deposits seem to be governed by instantaneous nucleation mode, the spatial distribution of the nuclei is more impacted by the nucleation exclusion effect than the Cu-only samples. This behavior is also justified by the grain size distribution generated with Voronoi cell size and occupancy distributions.

This work seeks to approach the comparative analysis of the distribution of POFs (polymeric optical fibers) arranged in a random and sorted manner in the manufacture of translucent concretes. The following characteristics were analyzed: compressive strength, flexural tensile strength, capillary water absorption and light transmittance. Portland cement, water, fine aggregate (sand), silica fume, polycarboxylate ether-based superplasticizer and polymeric optical fiber were used in the production of the composites. Except the fiber content, the mixture of all other inputs was kept as a fixed parameter. Groups with the following levels of POFs were produced: 0%, 2%, 3.5% and 5%. The POF content is the sum of the areas of the fiber sections in the composite with the total area of the translucent surface. The results showed that for the analysis of mechanical behavior (flexural tensile and compressive strength) and durability (capillary water absorption), composites with random and sorted fibers within the 2% POF presented to belong to statistically distinct groups. For the other fiber contents, there was no pattern of behavior, that is, it cannot be said that there is a difference within 3.5% or 5% POF between sorted and random fibers in relation to the mechanical and durability characteristics analyzed. As for the light transmittance, it was attributed that the statistical difference between the fiber arrangements only within the 5% POF content can be a consequence of their accumulation in certain points of the material, thus influencing this characteristic measured by a light meter.

In statistics and probability theory, one of the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent and identically distributed random variables is one of the interesting topics for authors. This paper presents the probability density functions for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Pranav, Rani, and Ram Awadh. In order to determine all aforementioned distributions, the problem-solving methods are applied which is based on the change-of-variables technique.

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions from a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de-Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for estimating the family parameters. We investigate the properties of one special model called a new Kumaraswamy-Weibull (NKwW) distribution. Parameter estimation is dealt and maximum likelihood estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of this distribution. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull, exponentiated-Weibull and Weibull distributions when applied to these data sets. The bivariate extension of the family is proposed and the estimation of parameters is given. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

We derive an ab initio equilibrium statistical mechanics of the gas-liquid-solid contact angle on planar periodic, monodisperse, textured surfaces subject to electrowetting. To that end, we extend an earlier theory that predicts how advance or recession of the contact line amount to distinct first-order phase transitions of the filling state in the ensemble of nearby surface cavities. Upon calculating the individual capacitance of a cavity subject to the influence of its near neighbors, we show how hysteresis, which is manifested by different advancing and receding contact angles, is affected by electrowetting. The analysis reveals nine distinct regimes characterizing contact angle behavior, three of which arise only when a voltage is applied to the conductive liquid drop. As the square voltage is progressively increased, the theory elucidates how the drop occasionally undergoes regime transitions triggering jumps in the contact angle, possibly changing its hysteresis, or saturating it at a value weakly dependent on further voltage growth. To illustrate these phenomena and validate the theory, we confront its predictions with four data sets. A benefit of the theory is to forsake trial-and-error when designing textured surfaces with specific contact angle behavior.

In this paper the problem of sampling from uniform probability distributions is approached by means of space-filling curves (SFCs), a topological concept that has found a number of important applications in recent years. Departing from the theoretical fact that they are surjective but not necessarilly injective, the investigation focused upon the structure of the distributions obtained when their domain is swept in a uniform and discrete manner, and the corresponding values used to build histograms, that are approximations of their true PDFs. This work concentrates on the real interval [0,1], and the Sierpinski space-filling curve was chosen because of its favorable computational properties. In order to validate the results, the Kullback-Leibler distance is used when comparing the obtained distributions in several levels of granularity with other already established sampling methods. In truth, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. In this fashion, sequences resulting from this sort of process are not truly random.

The present study analyses the influence of scratches and fatigue on the mechanical characteristics of aluminium alloys commonly used in the aviation industry: 2024-T4, 6061-T4, 6061-T4 uncoated, 6061-T6 uncoated, 7075-T0, and 7076-T6. 120 specimens were used for the study. Out of these, 60 samples were scratched, and the other 60 samples were also scratched under the same circumstances and then subjected to low-cycle fatigue (LCF) before undergoing the tensile test. Based on the statistical examination of the measured data, mathematical prediction models have been established. Compared to their unscratched counterparts, the results indicate a significant decrease in the mechanical properties of both scratched and scratched-fatigued sample sets. The LCF pre-treatment contributes to the negative impacts of scratches, resulting in a reduced value for the ultimate tensile strength and elongation at break. The results conclude that surface integrity plays an essential role in preserving aircraft components' structural strength.

Hands-on gardening is linked with healthy eating behaviors, increased outdoor activities, and overall well-being. Although these positive associations are widely established for adults and school-agers, little evidence can be found on how such relationships may extend to early childhood, especially in the preschool years (3-5 years). One recent study conducted in North Carolina (NC) showed that participating in hands-on gardening significantly increased preschoolers’ accurate identification of fruits and vegetables (FV) and FV consumption compared to children who did not participate in hands-on gardening, but no association was found between participation in hands-on gardening and children’s liking (eating preferences) of FV. FV identification and liking during the early years may lead to lifelong healthy eating behaviors and preferences, making hands-on gardening a critical health intervention in early childhood environments, especially in childcare centers where a majority of the 13 million children in the United States between the ages of 0 and 5 spend most of their waking hours. This research aimed to investigate how hands-on gardening in childcare centers may impact preschoolers’ (3-5 years old) FV knowledge (identification) and liking in a semi-arid climate zone with a high concentration of Hispanic families by conducting experimental research with eight childcare centers and one hundred forty-nine children (n=149) in Lubbock County located in West Texas. Findings showed changes in average liking scores are generally positive in the experiment group of children who participated in hands-on gardening (compared to the control non-gardening group), implying improved liking. The findings indicate that the benefits of hands-on gardening in childcare centers for enhancing healthy eating preferences are evident even in a semi-arid climate zone, where high temperatures and limited rainfall present significant gardening challenges. This research underscores the importance of integrating hands-on gardening into childcare programs, highlighting its potential as an effective obesity prevention strategy not only within the U.S. but also in other regions with similar environmental constraints.

Labelling techniques such as electron paramagnetic resonance spectroscopy and single-molecule fluorescence resonance energy transfer, allow access to distances in the range of tens of angstroms, corresponding to the size of proteins and small to medium-sized protein complexes. Such measurements do not require long-range ordering and are therefore applicable to systems with partial disorder. Data from spin-label-based measurements can be processed into distance distributions that provide information about the extent of such disorder. Using such information in modelling presents several challenges, including a small number of restraints, the influence of the label itself on the measured distance and distribution width, and balancing the fitting quality of the long-range restraints with the fitting quality of other restraint subsets. Starting with general considerations about integrative and hybrid structural modelling, this review provides an overview of recent approaches to these problems and identifies where further progress is needed.

In this paper, we introduce the notions of nearly Sasakian and nearly Kähler statistical structures with a non-trivial example. The conditions for a real hypersurface in a nearly Kähler statistical manifold to admit a nearly Sasakian statistical structure are given. We also study Invariant and anti-invariant statistical submanifolds of nearly Sasakian statistical manifolds. At the end, some conditions under which such a submanifold of a nearly Sasakian statistical manifold is itself a nearly Sasakian statistical manifold are given.

In this paper, we derive the distribution of eigenvalues for a 2×2 random confusion matrix stemming from a machine learning (ML) evaluation problem. Additionally, we present the distributions of both the matrix’s trace and the difference between the two traces of random confusion matrices. We also illustrate the application of these derived distributions in calculating the superiority probability of four baseline ML models.

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.

Increasingly measured data in the context of smart cities can be used to develop new and innovative business models to increase efficiency and the value of life. A time-series classification algorithm can support to automatize many different processes such as forecasting services. In order to ensure data security and privacy, Federated Learning trains a global model collaboratively on multiple clients. Having different data-distributions and data-quantities across participating clients, neural networks suffer from slow convergence and overfitting. Based on different data-distributions, data-quantities and number of clients, we develop and evaluate different data-clustering strategies to update global model weights in comparison to the state of the art. We use public time-series data, generate various synthetic datasets and train a Relational-Regularized Autoencoder for classification purposes. Our results show an improvement of model performance concerning generalization.

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

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.

Crash prediction of the sharp horizontal curve segment (SHCS) of a freeway is an important tool in analyzing safety of SHCSs and in building a crash prediction model (CPM). The design and crash report data of 88 SHCSs from different institutions were surveyed and three negative binomial (NB) regression models and three generalized negative binomial (GNB) regression models were built to prove that the interactive influence of explanatory variables plays an important role in fitting goodness. The study demonstrates the effective use of the GNB model in analyzing the interactive influence of explanatory variables and in predicting freeway basic segments. Traffic volume, highway horizontal radius, and curve length have been formulated as explanatory variables. Subsequently, we performed statistical analysis to determine the model parameters and conducted sensitivity analysis. Among the six models, the result of model 6, which considered interactive influence, is much better than those of the other models by fitting rules. We also compared the actual results from crashes of 88 SHCSs with those predicted by models 1, 3, and 6. Results demonstrate that model 6 is much more reasonable than models 1 and 3.

Lessons learned and risk-based outcomes from modernising the Australian Standard for post-mortem inspection and disposition judgement of beef, sheep, goat and pig carcases are described. Initial Risk Profiles identified priorities for quantitative assessments. The main difficulty encountered was the paucity of quantified performance of current inspection. Resolving this involved acquiring gross abnormality data representing regional production/proportional abattoir volumes, the range of gross abnormalities appearing nationally, proportional occurrence at carcase sites, and seasonality to enable comparisons. Evidence and discussion are provided for associated challenges experienced including preventing contamination, use of food chain information to support amendment, inspection as a part of industry Quality Assurance and opportunities to improve inspector training. Criteria considered by the Competent Authority for determination of equivalence of alternative post-mortem inspection techniques included comparisons of public health risk, non-detection rates for gross abnormalities, and microbial contamination resulting from inspection activities, as appropriate. Most gross abnormalities detected arose from animal health and welfare conditions affecting wholesomeness and did not present as food safety hazards. Non-detection rates between current and alternative inspection (observation) were negligible. A Quantitative Risk Assessment for Cysticercus bovis was conducted. Carcases with multiple gross abnormalities predominantly reflected historic infections (prior septicaemia) where trimming achieved wholesomeness unless cachexic.

Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood-Dirac quasi probability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts.

It has been known for nearly over 150 years that fatigue life data exhibits a considerable amount of variability. Furthermore, statistically modeling fatigue life adequately is challenging. Different empirical approaches have been used, each of which has merit; however, none is appropriate universally. Even when a sufficiently robust database exists, the scatter in the fatigue lives may be extremely large and difficult to characterize. The complications in empirical modeling are exacerbated for long life estimation when experimental observations are rare. The purpose of this work is to review traditional and more modern empirically based methodologies for estimating the cumulative distribution functions for fatigue life, given an applied load. To assess the applicability of the methods confidence bounds will be estimated. The analyses will be performed on an historic set of data for annealed aluminum wire tested in reverse torsion fatigue. These data are available in publications. It is recommended that a time dependent distribution function that is an based on principles of reliability that can be generalized for a variety of modeling applications should be considered for fatigue life estimation.

Currently, natural philosophy (Physics) lacks the most fundamental model and a complete set of self-consistent explanations. This article attempts to address several issues to fill in the gaps. Starting from the most basic philosophical paradoxes, I deduce a physical model (the natural philosophical outlook) to describe the laws governing the operation of the universe. Based on this model, a mathematical model is established to describe the generalized diffusion behavior of a moving particle swarm, and its simple verification is carried out. In this article, the gravitational force and relativistic effects are interpreted for the first time as a statistical effect of randomly moving particles. Thus, the gravitational force and special relativistic effects are integrated into a single equation (achieved by selecting an initial wave function with a specific norm when solving it), and the cause of stable particle formation is also revealed. The derived equation and the method of acquiring the initial wave function are fully self-consistent with the hypotheses stated in the physical model, thereby also proving the reliability of the physical model to some extent. Some of these ideas may have potential value as a basis for understanding the essence of quantum mechanics, relativity and superstring theory, as well as for gaining a further understanding of nature and the manufacture of quantum computers.

Economics has long sought to bridge the principles of microeconomics into the realm of macroeconomics. This paper presents a formal attempt to do so by using a maximum entropy based approach derived from statistical mechanics coupled with subjective game theory and elements from political philosophy. This approach is then applied to income distributions and to the Cobb-Douglas production function, to create a framework for future applications, and to illustrate where past work had made implicit assumptions regarding the system. The paper then explores the consequences of the approach, illustrating self-contradictions in the political philosophy of distributive justice, formally deriving an equation of state for the transactions on the Bitcoin network, and deriving from this the ideal gas law and polytropic process for an economy proving that expansionary monetary policy is not stimulative.

NS-3 is one of the most used Network Simulators because it includes different modules, applications and protocols to simulate a wide range of network. Since new proposals usually involve a large number of simulations, a procedure to automatize the simulation process and extract statistics is very useful. "Statistical Framework" (SF) is an important module of NS-3 because it fulfills this need. SF allows us to collect simulation data and obtain statistical reports for NS-3. In this report, we present a detailed description of statistical framework module and two useful examples of its configuration.

We propose two methods for obtaining estimations on the minimum distance and covering radius of orthogonal arrays. Both methods are based on knowledge about the (feasible) sets of distance distributions of orthogonal arrays with given length, cardinality, factors and strength. New bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of orthogonal arrays with parameters in doable ranges.

We show that the van der Waals gas does not exhibit just the celebrated liquid-gas 1 transition but also a quantum-classical one. We study the issue with reference to the LMC statistical 2 complexity and in relation to the order-disorder contrast.

Nowadays, speed up development and use of digital devices such as smartphones have put people at risk of internet crimes. The evidence of present crimes in a computer file can be easily unreachable by changing the prefix of a file or other algorithms. In more complex cases, either file divided into different parts or the parts of a file that has information about the file type are deleted, where the file fragment recognition issue is discussed. The known files are divided into different fragments, and different classification algorithms to solve the problems of file fragment recognition. A confusion matrix measures the accuracy of type recognition. In the present study, first, the file is divided into different fragments. Then, the file fragment features, which are obtained from Binary Frequency Distribution (BFD), are reduced by 2 feature reduction algorithms; Sequential Forward Selection algorithm (SFS) as well as Sequential Floating Forward Selection algorithm (SFFS) to delete sparse features that result in increased accuracy and speed. Finally, the reduced features are given to 3 classifier algorithms, Multilayer Perceptron (MLP), Support Vector Machines (SVM), and K-Nearest Neighbor (KNN) for classification and comparison of the results. In this paper, we proposed the algorithm of file type recognition that can recognize 6 types of useful files ( pdf, txt, jpg, doc, html, exe), which may distinguish a type of file fragments with higher accuracy than the similar works done.

The present paper investigates flaw strength distributions established using various flexural tests on batches of SiC bar test specimens: 4-point bending as well as 3-point bending with different span lengths. Flaw strength is given by the elemental stress operating on the critical flaw at fracture of a test specimen. Fracture inducing flaws and their locations are identified by fractography. A single population of pores was found to dominate fracture. The construction of diagrams of p-quantile vs elemental strengths was aimed at assessing the Gaussian nature of flaw strengths. Then, empirical cumulative distributions of strengths were constructed using the normal distribution function. Weibull cumulative probability distributions were derived from the mean and the standard deviation using the first moment equation. Agreement was obtained between both Weibull and normal flaw strengths distributions. The cumulative distributions for the different bending tests were predicted satisfactorily from the flaw strength density function using the elemental strength model. Flaw strength distributions that include potential weaker flaws encountered in larger test pieces are extrapolated using the p-quantile diagrams. Implications are discussed about the pertinence of an intrinsically representative flaw strength distribution, about failure predictions, about size effects, and about the significance of flaw spatial distributions.

In this paper, a novel strategy is adopted in a degradation model to affect the implied lifetime distribution. The multiplicative degradation model is utilized as a postulate in the model. It will be established that the implied lifetime distribution forms a classical mixture model. In this mixture model, time-to-failure is lying with some probabilities between two first passage times of the degradation process to reach two specified levels. Stochastic comparisons in the model under a change in the probabilities are studied. Several examples are provided to highlight the applicability of the results in the cases when typical degradation models are candidate.

Understanding swash zone dynamics is of crucial importance for coastal management as the swash motion, consisting of the uprush of the wave on the beach face and the subsequent downrush, is responsible for driving changes the beach morphology trough sediment exchanges between the sub-aerial and sub-aqueous beach. Improved understanding of the probabilistic characteristics of these motions has the potential to allow coastal engineers to develop improved sediment transport models which, in turn, can be further developed into coastal management tools. In this paper, novel descriptors of swash motions are obtained by combining field data and statistical modelling. Our results indicate that the probability distribution function (PDF) of shoreline height (p(ζ)) and trough-to-peak swash heights (p(ρ)) measured at a high energy, sandy beach were both inherently multimodal. Based on the observed multimodality of these PDFs, Gaussian Mixtures are shown to be the best method to statistically model them. Further, our results show that both offshore and surf zone dynamics are responsible for driving swash zone dynamics, which indicates unsaturated swash. The novel methods and results developed in this paper, both data collection and analysis, could aid coastal managers to develop improved swash zone models in the future.

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

Major depressive disorder (MDD) is a prevalent mental health condition with substantial social and economic consequences. This study focuses on the interplay between genetic and environmen-tal factors in MDD, with particular emphasis on epigenetic mechanisms such as stochastic epige-netic mutations (SEMs), epigenetic age acceleration, and epigenetic drift. We conducted a meta-analysis of DNA methylation patterns across six datasets (n=1125 MDD cases, 398 controls in whole blood; n=95 MDD cases, 96 controls in brain tissues) from the Gene Expression Omnibus. The analysis did not reveal significant global methylation differences between MDD cases and controls. However, a brain-specific probe (cg25801113) near the SHF gene consistently exhibited hypomethylation, suggesting its potential relevance to MDD. SEMs were assessed, revealing a dis-tinct burden at the gene level in MDD cases, though no significant findings emerged for epigenetic age acceleration, indicating it may not play a central role in MDD. The study also identified rare epivariations in specific genes unique to MDD cases. In blood tissue, 51 genes were associated with these unique epivariations, while 1 gene was highlighted in the brain tissue. These results un-derscore the importance of exploring rare epivariations in understanding the molecular mecha-nisms underlying MDD and offer potential targets for further investigation.

Soil nitrogen (N) is a common limiting factor where soil N cycling is a key component of agro-ecosystems. Soil N transformation processes are largely mediated by microbes and understanding bacteria involvement in soil N cycling in agricultural systems has both agronomic and environmental importance. This 2-yr field scale study examined the abundances and spatial distributions of total bacterial community (16s RNA), bacterial involved in nitrification (amoA), and de-nitrification (narG, nirK, and nosZ) and soil physicochemical properties of winter wheat (Triticum aestivum L.) – soybean (Glycene max L.) double cropping with 2-3 weeks of spring grazing (WGS) and without grazing (WS) and of tall fescue (Festuca arundinacea (L.) Schreb.) pasture (TF) managed to near natural conditions with similar grazing. The TF had a significantly higher abundance of 16S rRNA, amoA, narG, nirK, and nosZ genes than the WS and WGS, which had similar levels between themselves. Soil organic matter (OM) and soil pH had a stronger effect on the N-cycling bacteria gene abundance. All bacterial gene concentrations and soil pH showed non-random distribution patterns with 141-186 m range autocorrelation. These results indicate that biological N transformation processes are more important in natural agricultural systems and the abundance of N-cycling bacteria can be manipulated by field scale management strategies.

Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for his claim is insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is adequate framework for elaboration of the measurement problem. It considers signals to be stochastic processes, whether they correspond to variables or distribution densities. Signal processing like that utilizes statistical properties to perform its tasks, which is the definition of statistical signal processing. A hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has generalized to an open system by the use of duality in frame theory.

We discuss what we believe could be an improvement in future discussions of the ever-changing brain. We do so by distinguishing different types of brain variability and outlining methods suitable to analyse them. We argue that, when studying brain and behaviour data, classical methods such as regression analysis and more advanced approaches both aim to decompose the total variance into sensible variance components. In parallel, we argue that a distinction needs to be made between innate and acquired brain variability. For varying high-dimensional brain data, we present methods useful to extract their low-dimensional representations. Finally, to trace potential causes and predict plausible consequences of brain variability, we discuss how to combine statistical principles and neurobiological insights to make associative, explanatory, predictive, and causal enquires; but cautions are needed to raise association- or prediction-based neurobiological findings to causal claims.

Far too often, one meets patients who went for years or even decades from doctor to doctor, without getting a valid diagnosis. This brings pain to millions of patients and their families, not to speak of the enormous costs. Often patients cannot tell precisely enough which factors (or combinations thereof) trigger their problems. If conventional methods fail, we propose the use of statistics and algebra to give doctors much more useful inputs from patients. We use statistical regression for independent triggering factors for medical problems, and “balanced incomplete block designs” for non-independent factors. These methods can supply doctors with much more valuable inputs, and can also detect combinations of multiple factors by incredibly few tests. In order to show that these methods do work, we briefly describe a case in which these methods helped to solve a 60 year old problem in a patient, and give some more examples where these methods might be very useful. As a conclusion, while regression is used in clinical medicine, it seems to be widely unknown in diagnosing. Statistics and algebra can save the health systems much money, and the patients also a lot of pain.

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

Multivariate statistical approaches (MSA), such as principal components analysis and multidimensional scaling, seek to uncover meaningful patterns within datasets by considering multiple response variables in a concerted fashion. Although these techniques are readily used by ecologists to visualize and explain differences between study sites, they could theoretically be employed to differentiate organisms within an experimental framework while simultaneously identifying response variables that drive documented experimental differences. Therefore, MSA were used herein to attempt to understand the response of the common, Indo-Pacific reef coral Seriatopora hystrix to temperature changes using data from laboratory-based temperature challenge studies performed in Southern Taiwan. Gene expression and physiological data partitioned experimental specimens by time of sampling, treatment temperature, and site of origin upon employing MSA, signifying that S. hystrix and its dinoflagellate endosymbionts display physiological and molecular signatures that are characteristic of sampling time, site of colony origin, and/or temperature regime. These findings promote the utility of MSA for documenting biologically meaningful shifts in the physiological and/or sub-cellular response of marine invertebrates exposed to environmental change.

In the realm of construction industry, the management of claims constitutes a pervasive and multifaceted issue, with potential repercussions extending to project delays, cost overruns, work suspensions, and, in extreme cases, project termination. This challenge is a significant and unavoidable hurdle due to the unique features of construction projects, which are complex, involve many stakeholders and come with inherent risks. To address this complex issue, it becomes imperative to undertake a comprehensive appraisal of the claims management procedures employed within the industry, culminating in the presentation of findings within a risk-based framework. The overarching objective of this endeavour is threefold: firstly, to discern the pivotal attributes that affect each category of construction claims; secondly, to establish a coherent decision-making paradigm for the effective administration of such claims; and finally, to provide data that can be harnessed to either address concerns related to claims or enhance the effectiveness of the claims administration process. Keeping this in mind, this study serves to evaluate the factors associated with claim management gathered from a wide overview of literature, encompassing a range of construction projects, varying in terms of types, sizes/capacities and contractual arrangements. Hence, it advanced a refined method within the domain of fuzzy group decision-making, denoted as the Modified Fuzzy Group Decision-Making Approach (FGDMA) in addition to extensive statistical analysis using SPSS.V.25 software. They were applied to assess, analyze and prioritize claim about 108 claim management factors based on the responses obtained from the comprehensive questionnaire survey involving 104 industry professionals. This multi-faceted approach, which combines the insights from previous publications, along with the collective experience of the surveyed professionals with the analytical capabilities of the FGDMA- Statically Factor Analysis, reinforces the robustness and practical applicability of proposed methodology within the context of construction claims management.

Smoking has been established as a major risk factor for developing oral squamous cell carcinoma (OSCC), but less attention has been paid to the effects of smokeless tobacco products. Our objective is to identify potential biomarkers to distinguish the biological effects of combustible tobacco products from those of non-combustible using oral cell lines. Normal human gingival epithelial cells (HGEC), non-metastatic (101A) and metastatic (101B) OSCC cell lines were exposed to different tobacco product preparations (TPPs) including cigarette smoke total particulate matter (TPM), whole-smoke conditioned media (WS-CM), smokeless tobacco extract in complete artificial saliva (STE), or nicotine (NIC) alone. We performed microarray-based gene expression profiling and found 3456 probe sets from 101A, 1432 probe sets from 101B, and 2717 probe sets from HGEC to be differentially expressed. Gene Set Enrichment Analysis (GSEA) revealed xenobiotic metabolism and steroid biosynthesis were the top two pathways that were upregulated by combustible but not by non-combustible TPPs. Notably, aldo-keto reductase genes, AKR1C1 and AKR1C2, were the core genes in the top enriched pathways and were statistically upregulated more than 8 fold by combustible TPPs. Our qRT-PCR results statistically support AKR1C1 as a potential biomarker for differentiating the biological effects of combustible from non-combustible tobacco products.

At the plasma membrane, transmembrane receptors are at the interface between cells and their environment. They allow sensing and transduction of chemical and mechanical extracellular signals. The spatial distribution of receptors and the specific recruitment of receptor subunits to the cell membrane is crucial for the regulation of signaling and cell behavior. However, it is challenging to define what regulates such spatial patterns for receptor localization, as cell shapes are extremely diverse when cells are maintained in standard culture conditions. Bone morphogenic protein receptors (BMPRs) are serine-threonine kinases, which build heteromeric complexes of BMPRI and II. These are especially interesting targets for receptor distribution studies, since the signaling pathways triggered by BMPR-complexes depends on their dimerization mode. They might exist as pre-formed complexes, or assemble upon binding of BMP, triggering cell signaling which leads to differentiation or migration. In this work we analyzed BMPR receptor distributions in single cells grown on micropatterns, which allows not only to control cell shape, but also the distribution of intracellular organelles and protein assemblies. We developed a script called ComRed (Center Of Mass Receptor Distribution), which uses center of mass calculations to analyze the shift and spread of receptor distributions according to the different cell shapes. ComRed was tested by simulating changes in experimental data, showing that shift and spread of distributions can be reliably detected. Our ComRed-based analysis of BMPR-complexes indicates that receptor distribution depends on cell polarization. The absence of a coordinated internalization after addition of BMP suggests that a rapid and continual recycling of BMPRs occurs. Receptor complexes formation and localization in cells induced by BMP might yield insights into the local regulation of different signaling pathways.

Background: Bayesian Network (BN) modeling is a prominent methodology in computational systems biology. However, the incommensurability of datasets fre- quently encountered in life science domains gives rise to contextual dependence and numerical irregularities in the behavior of model selection criteria (such as MDL, Minimum Description Length) used in BN reconstruction. This renders model features, first and foremost dependency strengths, incomparable and diffi- cult to interpret. In this study, we derive and evaluate a model selection principle that addresses these problems. Results: The objective of the study is attained by (i) approaching model eval- uation as a classification problem, (ii) estimating the effect that sampling error has on the satisfiability of conditional independence criterion, as reflected by Mutual Information, and (iii) utilizing this error estimate to penalize uncertainty with the novel Minimum Uncertainty (MU) model selection principle. We vali- date our findings numerically and demonstrate the performance advantages of the MU criterion. Finally, we illustrate the advantages of the new model evaluation framework on real data examples. Conclusions: The new BN model selection principle successfully overcomes per- formance irregularities observed with MDL, offers a superior average convergence rate in BN reconstruction, and improves the interpretability and universality of resulting BNs, thus enabling direct inter-BN comparisons and evaluations.

We derive the thermal noise spectrum of the Fourier transform of the electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the complex frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting electrons. We analyze separately the longitudinal and transverse case with their peculiarities. The Nyquist formula for vanishing frequency and wave vector, as well as its modification for non-vanishing frequencies and wave vectors follow immediately. Furthermore we discuss also the noise of the photon occupation numbers. It is important to stress that no additional assumptions at all were used in this straightforward proof.

The structure of turbulent flow over non-flat surfaces is a topic of major interest in practical applications in both engineering and geophysical settings. A lot of work has been done in the fully rough regime at high Reynolds numbers where the effect on the outer layer turbulence structure and the resulting friction drag is well documented. It turns out that surface topology plays a significant role on the flow drag especially in the transitional roughness regime and therefore, hard to characterize. Survey of literature shows that roughness function depends on the interaction of roughness height, flow Reynolds number and topology shape. In addition, if the surface topology contains large enough scales then it can impact the outer layer dynamics and in turn modulate the total frictional force. Therefore, it is important to understand the mechanisms underlying drag increase from systematically varied surface undulations in order to better interpret quantifications based on mean statistics such as roughness function. In this study, we explore the mechanisms that modulate the turbulence structure over a two-dimensional (2D) sinusoidal wavy surface with a fixed amplitude, but varying slope. To accomplish this, we model the turbulent flow between two infinitely wide 2D wavy plates at a friction Reynolds number, $Re_{\tau}=180$. We pursue two different but related flavors of analysis. The first one adopts a roughness characterization flavor of such wavy surfaces. The second one focuses on understanding the non-equilibrium near surface turbulence structure and their impact on roughness characterization. Analysis of the different statistical quantifications show strong dependence on wave slope for the roughness function indicating drag increase due to enhanced turbulent stresses resulting from increased production of vertical velocity variance from the surface undulations.

A highly dirt resistant paint for building facades without chemicals harmful to nature and environment, is developed which resolves the unattractive disfigurement of building walls caused by dirt. The experimentation is scientifically and statistically planned with the aid of computer programming. It consists of a sequence of phases which include the selection of appropriate raw materials, adopting of Basic Language computer programming to generate a target population of paint formulations. The average PVC percentage is computed using theory and found to be 54.98% for the target population of 543143 paint formulations hence verifies the literature results. Experimentation and statistical analysis are performed to compare the classical conventional agitator with latest lab equipment like Nano mill and it is concluded that Nano mill performs better on the average than conventional agitator in preparation of paint formulations. Hence the sample of paint formulations is prepared on Nano mill and tested in laboratory using advanced available technology for the analysis and comparison of paint properties to determine the best paint formulation. The results are analyzed using Analysis Of Variance Technique (ANOVA) and it is concluded that the paint formulation named “O3” has the highest dirt resistance on the average. The final selected formula O3 is compared with three other competitor paints in market under natural environment for a period of almost one year. A regression model is also constructed to study the effect of environmental factors like time, temperature and humidity on dirt resistance of paints. It is found that O3 formulation is the best environment friendly which performs equally well with one competitor paint and has higher dirt resistance than two other competitor paint formulations containing harmful chemicals. The regression model of dirt resistance on variables including time, temperature and humidity shows that these factors are significantly affecting the dirt resistance of a given paint at 5% level of significance. 95.34% variation in the dirt resistance of a given paint is due to and explained by the given factors. The regression model is useful to predict the average dirt resistance of a given paint with a certain level of confidence. The project exemplifies the work of an applied research from conceptualization to successful commercialization for the paint industry.

This paper presents the results of an experimental investigation about target detecting with passive sonar in Persian Gulf. Detecting propagated sounds in the water is one of the basic challenges of the researchers in sonar field. This challenge will be complex in shallow water (like Persian Gulf) and noise less vessels. Generally, in passive sonar the targets are detected by sonar equation (with constant threshold) which increase the detection error in shallow water. Purpose of this study is proposed a new method for detecting targets in passive sonars using adaptive threshold. In this method, target signal (sound) is processed in time and frequency domain. For classifying, Bayesian classification is used and prior distribution is estimated by Maximum Likelihood algorithm. Finally, target was detected by combining the detection points in both domains using LMS adaptive filter. Results of this paper has showed that proposed method has improved true detection rate about 27% compare other the best detection method.

The objective of this paper was to verify the applicability of statistical learning (SL) compared to human reasoning with respect to the Universal Thermal Climate Index (UTCI), a complex tool for the assessment of outdoor thermal stress. UTCI is an equivalent temperature index based on the 48-dimensional output of an advanced model of human thermoregulation formed by 12 variables at four consecutive 30-minute intervals, which were calculated for 105642 thermal conditions from extreme cold to extreme heat. Comparing the performance of SL algorithms to the results accomplished by an international endeavor involving more than 40 experts from 23 countries, we found that random forests and k-nearest neighbors closely predicted UTCI values, but that clustering applied after dimension reduction algorithms (principal component analysis and t-distributed stochastic neighbor embedding) were inadequate for risk assessment in relation to the UTCI stress categories. This indicates a potential supportive role for SL, as it will not (yet) fully replace the bio-meteorological expert knowledge.

Recent studies have shown correlations between the microbiota's composition and various health conditions. Machine learning (ML) techniques are essential for analyzing complex biological data, particularly in microbiome research. ML methods help analyze large datasets to uncover microbiota patterns and understand how these patterns affect human health. This study introduces a novel approach combining statistical physics with the Monte Carlo (MC) methods to characterize bacterial species in the human microbiota. We assess the significance of bacterial species in different age groups by using notions of statistical distances to evaluate species prevalence and abundance across age groups and employing MC simulations based on statistical mechanics principles. Our findings show that the microbiota composition experiences a significant transition from early childhood to adulthood. Species such as Bifidobacterium breve and Veillonella parvula decrease with age, while others like Agathobaculum butyriciproducens and Eubacterium rectale increase. Additionally, low-prevalence species may hold significant importance in characterizing age groups. Finally, we propose an overall species ranking by integrating the methods proposed here in a multicriteria classification strategy. Our research provides a comprehensive tool for microbiota analysis using statistical notions, ML techniques, and MC simulations.

This study delves into the dynamics of 'Variations' and 'Claims' within construction projects, specifically under the FIDIC-Red Book 1999 (FIDIC 1999) framework. It aims to identify, categorize, and devise mitigation strategies for key types of Variations and Claims, aligning with the FIDIC Conditions of Contract. The research, drawing on inputs from construction industry professionals including Contract Administrators and Project Managers, focuses on the MENA re-gion. This choice is driven by the region's extensive adoption of FIDIC standards and its rapidly growing construction sector. Data collection encompassed a questionnaire distributed to 80 industry experts, predominantly through interviews, focusing on countries like Saudi Arabia, UAE, Kuwait, and Egypt. These locations were chosen to reflect diverse construction practices and the involvement of international firms. Utilizing SPSS-V.25 for statistical analysis, the study uncovers the most prevalent and impactful causes of Variations and Claims, highlighting the critical need for managerial intervention. A key feature of this study is the integration of Scientometric Analysis for a quantitative review of current literature, providing a comprehensive academic context. A significant addition to the methodology is the implementation of a k-means clustering analysis. This advanced statistical technique further classifies the data into distinct clusters, each representing unique combinations of 'Frequency' and 'Impact' of Variations and Claims. The k-means analysis elucidates intricate patterns and potential solutions, offering profound insights into effectively managing these issues. These analytical advancements are crucial in identifying significant and manageable responses to reduce the frequency and impact of Variations and Claims in construction projects.

$\beta$-decay is one of the key factors to understand the $r$-process and evolution of massive stars. The Gamow-Teller (GT) transitions drive the $\beta$-decay process. We employ the proton-neutron quasiparticle random phase approximation (pn-QRPA) model to calculate terrestrial and stellar $\beta$-decay rates for 50 top-ranked nuclei possessing astrophysical significance according to a recent survey \cite{Nab21}. The model parameters of the pn-QRPA model effect the predicated results of $\beta$-decay. The current study investigates the effect of nucleon-nucleon pairing gaps on charge-changing transitions and the associated $\beta$ decay rates. Three different values of pairing gaps, namely TF, 3TF and 5TF, were used in our investigation. It was concluded that both GT strength distributions and half-lives are sensitive to pairing gap values. The 3TF pairing gap scheme, in our chosen nuclear model, resulted in best prediction with around 80$\%$ of the calculated half-lives within a factor 10 of the measured ones. The 3TF pairing scheme also led to calculation of biggest $\beta$-decay rates in stellar matter.

COVID-19 outbreak started in the Chinese city of Wuhan and spread around the globe in months due to its high contagious level. Hence, this disease posed a great challenge to researchers and mathematicians. Numerous mathematical models have been suggested to visualize the spreading speed and trends of this pandemic. In this paper, a comparison of a widely established and accepted method, the Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model with a newly-proposed fractional-order SEIQRDP is studied. Densely populated Countries of Asia (Pakistan, India, and Bangladesh) have been chosen as data sets and both algorithms have been applied to their data. The same comparison technique has also been used on the data of two polar countries, New Zealand and Russia, that validated our findings. Error comparison of both algorithms has been recorded in a tabulated form which shows multi-fold erroneous trends over WHO data of selected countries.

The development of Imaging Atmospheric Cherenkov Telescopes (IACTs) unveiled the sky in the teraelectronvolt regime, initiating the so-called “TeV revolution” at the beginning of the new millennium. This revolution was also facilitated by the implementation and adaptation of statistical tools for analyzing the shower images collected by these telescopes and inferring the properties of the astrophysical sources that produce such events. The image reconstruction techniques, the background discrimination and the signal-detection analyses are just a few of the pioneering studies applied in the last decades in the analysis of IACTs data. This (succinct) review has the intent of summarizing the most common statistical tools that are used for analyzing data collected with IACTs, focusing on their application in the full analysis chain, giving references to the past literature for a deepened examination.

When participants in a statistical learning paradigm are asked to learn from two incompatible or competing inputs, they often fail to learn from one or both inputs. This study presents the results of two experiments that were both completed by one group of typically developing four-year-old children. One experiment targeted word-medial consonant patterns (phonotactics), whereas the other targeted strong-weak and weak-strong stress patterns (prosody). The order of the experiments was critical for learning outcomes in the phonotactics experiment: When children learned phonotactics first, their production accuracy increased following exposure to a high frequency input. When children learned phonotactics second, however, their production accuracy dropped when they were exposed to the high frequency input. Results from the prosody experiment were inconclusive, with limited evidence of any learning effect. Overall, the results suggest that children may conflate learning experiences, and patterns learned from an initial experimental input compete with patterns in a subsequent experiment. When considering natural language acquisition, the results suggest that an isolated episode of learning may lead to generalizations that are incompatible with later input, and possibly, with larger patterns in the language.