Energy Measurement and Verification (M&V) aims to make inferences about the savings achieved in energy projects, given the data and other information at hand. Traditionally, a frequentist approach has been used to quantify these savings and their associated uncertainties. We demonstrate that the Bayesian paradigm is an intuitive, coherent, and powerful alternative framework within which M&V can be done. Its advantages and limitations are discussed, and two examples from the industry-standard International Performance Measurement and Verification Protocol (IPMVP) are solved using the framework. Bayesian analysis is shown to describe the problem more thoroughly and yield richer information and uncertainty quantification than the standard methods while not sacrificing model simplicity. We also show that Bayesian methods can be more robust to outliers. Bayesian alternatives to standard M&V methods are listed, and examples from literature are cited.

Using the OCT platform, we can generate high-resolution data on retinal nerve fiber layer (RNFL) thickness in a given eye at a large number of angular-points defined on a circular coordinate system. However, insightful characteristics of OCT RNFL data such as its circularity and granularity generally remain unutilized in its common downstream statistical analyses. We present a new circular statistical framework that defines an Angular Decay function and thereby provides a directional representation of an eye in terms of its focused RNFL loss. By applying to a clinical cohort of Asian Indian eyes, the generated circular data was modeled with a finite mixture of von Mises distributions, which led to unsupervised identification in different age-groups of 2 recurrent clusters of glaucomatous eyes with distinct directional signatures of RNFL decay. New indices of global and local RNFL loss were computed for comparing the structural differences between these glaucoma clusters across the age-groups.

We propose a new statistical analysis of the Acoustic Emissions (AE) produced in a series of triaxial deformation experiments leading to fractures and failure of two different rocks, namely, Darley Dale Sandstone (DDS) and AG Granite (AG). By means of q-statistical formalism, we are able to characterize the pre-failure processes in both types of rocks. In particular, we study AE inter-event time and AE inter-event distance distributions. Both of them can be reproduced with q-exponential curves, showing universal features which are observed here for the first time and could be important in order to understand more in detail rock fractures dynamics.

The energy matrix worldwide has been going through difficulties in its discussions - such as irregular exploration, inefficient public policies, and arbitrariness concerning diplomatic and political definitions of those involved in this market. This work's general objective consists in analyzing associations and statistical inferences of the largest world oil producers, assimilating the contributions and singularities of this market from 1993 to 2020. Based on the Organization of the Petroleum Exporting Countries (OPEC), it was possible to identify the possible inferences and contributions of the ten largest oil producers in the world in more than two decades using statistical analysis through correlation, regression, and statistical analysis of variables. According to the research and the literature on the area, the oil market proposes support to its discussions, mainly in its productive approaches. It is possible to identify this market as a solid link to geopolitical actions, distributing the possibilities through economic bias and socio-cultural and historical factors on a global level.

This article is devoted to methods of processing random processes. Of particular relevance is the task of processing broadband non-stationary random processes. The processing of random processes is usually related to the assessment of their probabilistic characteristics. Very often, a non-stationary broadband random process is represented by a single implementation in a priori uncertainty about the type of distribution function. Such random processes occur in information and measuring communication systems in which information is transmitted at a real time pace (for example, radio telemetry systems of spacecraft). The use of methods of traditional mathematical statistics, for example, maximum likelihood methods to determine probability characteristics, in this case is not possible. The article discusses a method of processing non-stationary broadband random processes based on the use of non-parametric methods of decision theory. An algorithm for dividing the observation interval into stationary intervals using non-parametric Kendall statistics is considered, as well as methods for estimating probabilistic characteristics on the stationary interval using ordinal statistics. The article presents the results of statistical modeling using the Mathcad program.

In descriptive statistics, U -statistics arise naturally in producing minimum-variance unbiased estimators. In 1984, Serfling considered the distribution formed by evaluating the kernel of the U -statistics and proposed generalized L-statistics which includes Hodges-Lehamnn estimator and Bickel-Lehmann spread as special cases. However, the structures of the kernel distributions remain unclear. In 1954, Hodges and Lehmann demonstrated that if X and Y are independently sampled from the same unimodal distribution, X − Y will exhibit symmetrical unimodality with its peak centered at zero. Building upon this foundational work, the current study delves into the structure of the kernel distribution. It is shown that the kth central moment kernel distributions (k > 2) derived from a unimodal distribution exhibit location invariance and is also nearly unimodal with the mode and median close to zero. This article provides an approach to study the general structure of kernel distributions.

Background and Objective: Obtaining reliable and up-to-date information on mortality causes is essential for planning and implementation of effective preventive interventions. We present here an analysis of the leading causes of death in the US in 2022. Material and Methods: We conducted an electronic search of the US Centers for Control and Prevention (CDC) Web-based Injury Statistics Query and Reporting System (WISQARS) to obtain information on the leading causes of death in the US for the most recent searchable year (2022), stratified by age and sex. Results: Overall, heart disease was the leading cause of death (26.2% of all deaths), followed by malignant neoplasms (22.7%), unintentional injuries (8.5%) and coronavirus disease 2019 (COVID-19; 6.9%). Although heart disease and malignant neoplasms remained the leading causes of death in both sexes, unintentional injuries were the third cause for men (10.5%), while strokes were the third cause in women (7.5%). COVID-19 remained the fourth most common cause of death in both sexes (7.1% in men and 6.8% in women). The ten most common causes of death showed an increasing mortality tendency in parallel with the aging of population, with similar trends for both sexes. The only exception was unintentional injury, which was the most common cause of death in both sexes between the ages of 15 and 44 years, then reached a plateau, for increasing again in people aged 65 years or older. Conclusions: Greater efforts should be put into prevention and education, as heart disease, cancer and even unintentional injuries are preventable diseases.

This article aimed to evaluate, using statistical tools, the generation and composition of urban solid waste (MSW) in the city of Belém, Pará, from nine urban collection sectors in the municipality, and the average nominal income of the population. Approximately 900kg of urban solid waste were col-lected from the municipality in the period from 2021 to 2022. Statistical tests were carried out on hypotheses with 5% significance in comparative evaluations, and their respective average nominal incomes. The results indicated that the organic fraction corresponds to 55.57% of the waste generated in the municipality, 14.26% is inert waste (potentially contaminating) and 0.67% is miscellaneous waste. It was observed that the waste generated by families with high purchasing power tends to contain higher percentages of recyclables, while in families with lower purchasing power the highest percentages tend to be organic. Knowledge of the generation of MSW is fundamental for the choice and dimensioning of operations and processes involved in the management chain at the municipal level. The decentralization of services offered based on solid waste management would enable greater success in serving the population.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Mexico is a well-known seismically active country, which is primarily affected by several tectonic plate interactions along the southern Pacific coastline and by active structures in the Gulf of Baja California. In this paper we investigate this seismicity in the context of a non-extensive statistical approach based on Tsallis entropy. The analysis is performed using data from the corrected Mexican seismic catalogue provided by the National Seismic Service, spanning a period from January 2000 to October 2023. The Gutenberg-Richter law fitting to the earthquake sub-catalogues for all six regions studied indicates magnitudes of completeness between 3.30 and 3.76. All six regions display values of the entropic index in the range 1.52≲q≲1.61, which are lower than the previously estimated range 1.54≲q≲1.70 using catalogue data from 1988 to 2010. The cause of this discrepancy is certainly due to the use of modern recording devices, which are sensitive enough to detect a larger number of low-magnitude events compared to older instrumentation.

The novel COVID-19 disease is a contagious acute respiratory infectious disease whose causative agent has been demonstrated to be a new virus of the coronavirus family, SARS- CoV-2. Multiple studies have already reported that risk factors for severe disease include older age and the presence of at least one of several underlying health conditions. However, a recent physiopathological report and the French COVID-19 scientific council have postulated a protective effect of tobacco smoking. Thanks to a meta-analysis, we have been able to demonstrate the statistical significance in this regard of twelve series from China, France and in the US, reporting three different smoking status (current smoker,former smoker, with a smoking history) as well as disease severity (with respectively odds-ratio of 1.78 [1.08-3.10], 4.60 [3.13-7.17], 2.74 [0.63-5.89]). Subsequently and using a Bayesian approach we have established that past, and present smoking is associated with more severe COVID-19 outcomes. Finally, we refute claims linking general population smoking status (N=O(10^8) or O(10^9)) to much smaller disease course series (N=O(10^4)). The latter point in particular is presented to stimulate academic discussion, and must be further investigated by well-designed studies.

The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non extensive statistics have been formulated along the last several years, in particular a fractal structure in thermodynamics functions was recently proposed as a possible origin for non extensive statistics in physical systems. In the present work we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that evidenced the connections between those fluctuations and Tsallis statistics. Finally, the fractal scale invariance is discussed in terms of the Callan-Symanzik Equation.

This study explores the correlation between payment statistics and sector-wise gross value added (GVA) in the Indian economy from 2011 to January 2023, shedding light on the importance of payment and settlement systems. Through regression analysis, the impact of payment statistics on GVA across diverse sectors is assessed. The results indicate that, during the specified period, payment statistics do not exhibit a significant influence on sector-wise GVA. These findings emphasize the need for further investigation into alternative factors driving sector-wise GVA, while underscoring the pivotal role of payment and settlement systems in the Indian financial landscape.

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.

Recently, there appeared in this journal (Beh and Lombardo \textbf{2022}, {\it Symmetry}, 14, 1103) a paper that showed how to perform a correspondence analysis on a two-way contingency table where Bowker's statistic lies at the numerical heart of this analysis. Thus, we showed how this statistic can be used to visually identify departures from perfect symmetry. Interestingly, Bowker's statistic is a special case of the symmetry-version of the Cressie-Read family of divergence statistics. Therefore, this paper presents a new framework for visually assessing departures from perfect symmetry using a second-order Taylor series approximation of the Cressie-Read family of divergence statistics.

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.

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.

This study contended that learning statistics and its rudiments were perceived as complicated compared to some other courses offered at the university level. Further, this investigation contested the existence of statistics anxiety among postgraduate students in an in-site university setting. Relationships and differences were determined in this study utilizing the constructs of antecedents of statistics anxiety namely academic procrastination, perfectionism, and gender. The objectives were (1) to establish the relationship between academic procrastination and statistics anxiety; (2) to find out the relationship between perfectionism and statistics anxiety; and (3) to investigate the differences between gender and statistics anxiety. The data from randomly selected 136 postgrad students (Kampala International University, Uganda) referring to dispositional (procrastination and perfectionism) and environmental antecedents (gender) and statistics anxiety were scientifically elicited, processed and analyzed utilizing the quantitative- post positivist’s research paradigm model. The findings revealed a positive but insignificant relationship between academic procrastination and statistics anxiety; a significant adverse correlation between perfectionism and statistics anxiety; an insignificant positive correlation existed between gender and statistics anxiety, and differences in statistics anxiety between the female and male students existed. Notably from the results then, academic procrastination did not significantly affect the students’ statistics anxiety; the students with higher levels of perfectionism tended to have lower levels of statistics anxiety while the levels of statistics anxiety among the female students were slightly greater than that of the male students.

Groundwater is an important role of the environment in natural resources. The major sources of groundwater contamination in this study were open discharges of domestic sewage, inadequate sewerage system, open defecation, septic tanks, soak pits, contaminated water pools, unorganized solid waste dumping and use of fertilizers, pesticides for agriculture deteriorated the condition. In this present study revealed that the physical and chemical characteristics of ground water in different areas of Kannur district in Kerala have been determined different seasons with respect to its suitability for drinking and agricultural purposes. For this study the groundwater samples were collected during pre-monsoon and post-monsoon seasons from 70 wells representing the entire the study area. The groundwater samples were analyzed for Physico-chemical characteristics using standard techniques in laboratory and compared with standards. The samples were analyzed with reference to the WHO and BIS standards. The groundwater quality information of the entire study area have been prepared using statistical and GIS technique for all the parameters. This paper proved in GIS will be helpful for measuring, monitoring and managing the groundwater pollution in the study area and suggested to protect groundwater resources in the environment.

Drinking water quality is a major concern, especially in African countries. This manuscript aims to analyze the chemical composition of Lioua’s groundwater in order to determine the geological processes influencing the chemical elements' composition and origin. Therefore, chemometrics techniques such as multivariate statistical analysis (MSA) and time series methods (TSM) are used. Indeed, MSA includes a component analysis (PCA) and a cluster analysis (CA), while au-tocorrelation analysis (AA) supplemented by simple spectral density analysis (SDA) is used for TMS. PCA displays three main factors explaining a total variance (TV) of 85.01 %. Factors 1, 2, and 3 are 68.72%, 11.96%, and 8.89 % of TV, respectively. In the CA, three groups were controlled by TDS and EC. G1 reveals a close association between SO42−, K+, Ca2+, and TDS; G2 reveals a close association between Na+, Cl−, Mg2+, and EC; G3 shows the dissociation of bicarbonates HCO3− and NO3− from other chemical elements. AA shows a linear interrelationship of EC, Mg2+, Na+, K+, Cl−, and SO42−. However, NO3− and HCO3− indicate uncorrelated characteristics with other parameters. For SDA, the correlograms of Mg2+, Na+, K+, Cl−, and SO42− have a similar trend with EC. None-theless, pH, Ca2+, HCO3− and NO3− exhibit multiple peaks related to the presence of several dis-tinct cyclic mechanisms. The methods enabled the authors to conclude that the geochemical processes influencing the chemical composition are: (i) dissolution of evaporated mineral depos-its, (ii) water-rock interaction, and (iii) evaporation process. In addition, Groundwater exhibits two bipolar characteristics, one recorded with negative and positive charges on pH and Ca+ and another recorded only with negative charges on HCO3− and NO3−. On the other hand, SO42-, K+, Ca2+, and TDS are the major predominant elements in the groundwater’s chemical composition. The major participation of salts and chlorides is in the electrical conductivity of water. The dominance of the lithological factor in the overall mineralization of the Plio-Quaternary surface aquifer waters. The origins of HCO3− and NO3− are different. Indeed, carbonated for HCO3- has a carbonate origin, whereas NO3– has an anthropogenic origin. The salinity was affected by Mg2+, SO42-, Cl-, Na+, K+, and EC. Ca2+, HCO3− and NO3− are resulted from human activity fertilizers, the carbonate facies outcrops, and domestic sewage.

Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi Polygons; Delaunay Triangulations; Perpendicular Bisectors; Circumcenters; Convex Hulls; Minimal Spanning Trees; Ulam Trees; Pitteway Violations; Circularity; Clark-Evans spatial statistics; Variance to Mean Ratios; Gabriel Graphs; and, Minimal Spanning Trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s Law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation.

Generative Adversarial Networks (GANs) are powerful models for generative tasks but face significant challenges such as instability, mode collapse, and inefficient convergence. This paper introduces a theoretical framework leveraging Fermi-Dirac statistics, Ruppeiner geometry, phase transition dynamics, and graph theory to address these issues. The proposed theorems provide a robust mathematical foundation for enhancing GAN stability, diversity, and convergence. Experimental validation on the MNIST dataset demonstrates that the application of these theorems results in improved Inception Scores, reduced Fr´echet Inception Distances, and stable training dynamics, as indicated by Ruppeiner curvature analysis. The findings suggest that these theoretical insights offer a comprehensive solution to the persistent challenges in GAN training, paving the way for more reliable and effective generative models.

Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a class of estimators, consistent simultanously for both a semiparametric distribution and a distinct parametric distribution, is proposed. These efficient estimators are robust to both gross errors and departures from parametric assumptions, making them ideal for estimating the mean and central moments of common unimodal distributions. This article also illuminates the understanding of the common nature of probability distributions and the measures of them.

The objective of the analysis carried out in this paper is to quantify the impact of subsidies on the activity of two vegetable farms, of different sizes in terms of agricultural area under cultivation, 600 ha and 3000 ha, which can constitute a model at macroeconomic level, indicating the ways in which these farms can ensure their income. For the analysis carried out, indicators were taken into account concerning production, net profit and subsidies received over a period of three years for the agricultural crops grown on these farms, identifying their contribution and effects on profitability. Descriptive statistics, visual inspections and basic comparison methods were also used, thus determining the patterns of the impact of subsidies and their variation for each of the existing crops in the vegetable farms studied. The data on which the statistical models are based are extracted from the financial statements of the farms analysed, giving the possibility of a predictive extension of the evolution of income and, very importantly, of their profitability. The conclusions revealed, for the 600 ha vegetable farm, that this farm maintained its area constant during the analysis period, benefiting from annual subsidies, and that the practice of crop diversification (rape, barley, winter wheat, oats, soybean, maize, lucerne), appropriate rotation, conservation farming and crop irrigation on 85.34% of the area, ensured average yields/ha that exceeded those recorded at national and regional level, except for 2020. The economic performance of this farm is oscillating in the period 2018-2021, with the ability to consistently generate profit, but in 2020 it is close to break-even, a year in which subsidy income tipped the balance towards positive but modest financial results. For this farm, the statistical model carried out was inconclusive because the farm optimises its cropping plan every year, depending on agrometeorological predictions, subsidy levels and market trends, changing crops, thus not being able to estimate the extent to which each crop contributes to maintaining the financial balance of the farm. Thus, although subsidies have impacted the level of net income, the extent to which they have done so is unclear. For the 3000 ha farm, the findings revealed that this farm also has a roughly constant area in use over the analysis period and for which it receives subsidies. This farm practices crop diversification (rape, barley, winter wheat, sunflower, soybean, grain maize, late potatoes, sweet potato, carrot and flowers) and adequate crop rotation. The data highlight that subsidies played a significant and sometimes overwhelming role in determining the gross output of each crop to achieve a positive value of this indicator. Modern conservation farming technologies and crop irrigation on 74.14% of the area justify the average yields/ha achieved, which again exceeded those recorded at national, regional and county level, with the exception of 2020. Maize and soybean crops consistently contributed to the farm's income, with a high gross product and net income, despite changes in the average yield per hectare achieved each year. Good and rising economic performance for this farm during the period under review, which justifies the profitability of the business from an economic, financial and commercial point of view. Although there have been fluctuations in the value of yields realized on different crops, net revenues continued to be high and even up significantly in 2021. Thus, the study highlighted and identified trends and patterns in agriculture, patterns that can serve as a source of information for relevant policy decisions, playing a key role in guiding future research and allocating resources efficiently in the agricultural sector.

This document serves as supplemental information to Shapero et al. (2023), which is itself a comment on Nowell et al. (2022). Environmental Health Perspective’s publishing standards for article comments have strict word counts and do not allow the addition of new primary data analyses; therefore, this document provides an additional level of detail and supporting analyses that serve as an important backup to and expansion of Shapero et al. (2023) and that also respond to some comments within the author’s reply to our comments (Holmes and Nowell, 2023). Nowell et al. (2022) evaluated potential PM_2.5 community impacts from sugarcane harvesting. However, their analysis is flawed by erroneous assumptions and misapplied technical approaches, as discussed in Shapero et al. (2023) and as detailed in this supplemental information document. Additionally, the authors ended their analysis with 2018 data, but later data shows no marginal increase in PM_2.5 during sugarcane harvest following 2019 even using the authors’ approach (Holmes and Nowell, 2023). Therefore, the authors’ evaluations have no relevance to current conditions. Nonetheless, even their evaluation and conclusions regarding PM_2.5 concentrations purportedly attributable to sugarcane harvesting prior to 2019 are unsupported and technically unsound as detailed below.

SStatistical characteristics of the wind speed in Samaria region of Israel have been analyzed by processing 11 years of wind data provided by the Israeli Meteorological Service, recorded at 10 m height above the ground. The cumulative mean wind speed at measurement height was shown to be 4.53 m/s with standard deviation of 2.32 m/s. Prevailing wind direction is shown to be char-acterized by cumulative mean azimuth of 226° with standard deviation of 79.76°. The results were extrapolated to 70-meter height in order to estimate wind characteristics at hub height of a me-dium-scale wind turbine. Moreover, Weibull distribution parameters were calculated annually, monthly and seasonally, demonstrating a good match with histogram-based statistical repre-sentations. Shape parameter of the Weibull distribution was shown to reside within a narrow range of 1.93 to 2.15, allowing us to assume a Rayleigh distribution, thus simplifying wind tur-bines energy yield calculations. The novelty of the current paper is related to gathering wind statistics for a certain area (Samaria) we are not aware of any published statistics regarding wind velocity and direction in this area. The data may be interesting for potential regional wind energy development in which the obtained Weibull distribution can be used in calculations of expected power generation of particular turbines with known power dependence on velocity. We also point out that the fact that realistic wind velocity statistics is well described by an analytic formula (Weibull distribution) is not trivial, and in fact the fit may have been poor.

Reference evapotranspiration (ETo) is a key agrometeorological index for rational irrigation management. The standard method for ETo estimation, proposed by FAO, is based on a complicated Penman-Monteith equation, requires great number of meteorological inputs thus making it difficult for practical use by farmers. To the moment, there are many alternative simplified approaches for ETo estimation, most of them are directed to cutting the number of required meteorological inputs for calculation. Among them, special attention should be paid to various temperature-based methods of ETo assessment. One of the temperature-based models for ETo computation was realized in free mobile app ETo Calculator (Ukraine). The app gives Ukrainian farmers an opportunity to assess ETo values on daily or monthly scale using mean air temperature as the only input. The goal of the study was to test the app accuracy comparing to FAO-based calculations in five key regions of Ukraine, each of which representing a particular climatic zone of the country. It was established that the app provides relatively good accuracy of ETo estimation even in raw (not adjusted to windspeed and relative air humidity) run; the results of statistical comparison with the FAO-calculated values are: R2 within 0.82-0.87, RMSE within 0.74-0.81 mm, MAE within 0.60-0.70, MAPE within 18.07-25.50% depending on the region. ETo Calculator (Ukraine) is a good alternative for complicated Penman-Monteith method and could be recommended for Ukrainian farmers to be used for irrigation management.

Within the spectrum of a natural image, the amplitude of modulation decreases with spatial frequency. The speed of such an amplitude decrease, or the amplitude spectrum slope, of an image affects the perceived aesthetic value. Additionally, a human observer would consider a symmetric image more appealing than they do an asymmetric one. We investigated how these two factors jointly affect aesthetic preferences by manipulating both the amplitude spectrum slope and the symmetric level of images to assess their effects on aesthetic preference on a 6-point Likert scale. Our results showed that the preference ratings increased with the symmetry level but had an inverted U-shape relation to amplitude spectrum slope. In addition, a strong interaction existed between symmetry level and amplitude spectrum slope on preference rating, in that symmetry can amplify the amplitude spectrum slope’s effects. Such effects can be described by a quadratic function of the spectrum slope. That is, preference is an inverted U-shape function of spectrum slope whose intercept is determined by the number of symmetry axis. In addition, the interaction between the two factors is manifested as the modulation depth of the quadratic function.

A popular approach to learning about admixture from population genetic data is by computing the allele-sharing summary statistics known as f-statistics. Compared to some methods in population genetics, f-statistics are relatively simple, but interpreting them can still be complicated at times. In addition, f-statistics can be used to build admixture graphs (multi-population trees allowing for admixture events), which provide more explicit and thorough modeling capabilities but are correspondingly more complex to work with. Here, I discuss some of these issues to provide users of these tools with a basic guide for protocols and procedures. My focus is on the kinds of conclusions that can or cannot be drawn from the results of f₄-statistics and admixture graphs, illustrated with real-world examples involving human populations.

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.

This study aims to identify modern bureaucratic government phenomenon expressed in W.H. Auden’s poem “The Unknown Citizen” (UC). This phenomenon will be revealed through the use of figures of speech, symbols and imagery in the poem. This poem is chosen as the object of the study since phenomenon happened in the poem represents people’s life and government practice in the modern era. Government, in the poem, seems to be very dominant. Its bureaucratic apparatus is powerful. Through its sophisticated technology, the bureau of statistics is able to detect the citizen’s identity. But, ironically, it could have not identified UC’s name as he lived in the world. He, then, was honored by the state by being erected the marble monument. The poem is analyzed by applying phenomenological criticism. The analysis finds that the representation of modern government is expressed through symbols emphasized by dramatic irony and supported by the use of internal sensation imagery. UC is the allegory of the average person with his bravery he sacrifices for the country. The state ought to give him an honor. In this poem Auden, actually, wants to write a parody for establishing monuments in some countries to honor the struggles of their soldiers who died in the World War I. Those monuments are really tombs since the function of a monument is a state’s thanksgiving for their sacrifice.

Based on the total scholarly article output of Norway, we investigated the coverage and degree of openness according to three bibliographic services 1) Google Scholar, 2) oaDOI by Impact Story and 3) 1findr by 1science. According to Google Scholar, we find that more than 70% of all Norwegian articles are openly available. However, degrees are profoundly lower according to oaDOI and 1findr, respectively 31% and 52%. Varying degrees are mainly caused by different interpretations of openness, with oaDOI being most restrictive. Furthermore, open shares vary considerably by discipline, with the Medcine and Health sciences at the upper and the Humanities at the lower end. We also determined the citation frequencies using Cited-by values as of Google Scholar, applying year and subject normalization. We find a significant citation advantage for open articles. However, this is not the case for all types of openness. In fact, the category Open Access journals was by far lowest cited, indicating that young journals with a declared open access policy still lack recognition.

With the continual global increase of PV power systems and the inherent weather-induced volatility of their power output, understanding the underlying variability of solar radiation in both space and time is important for the planning and reliable operation of future power grids. This paper concisely reviews recent advances in the characterization of irradiance variability with an emphasis on small spatial and temporal scales (respectively less than about 10\,km and 1\,min), for which comprehensive data sets are time consuming and expensive to collect, and although needed have not been available until recently. Special attention is given to studies dealing with the quantification of variability using such unique data, the analysis and modeling of spatial smoothing, and the evaluation of temporal averaging.

Statistical modeling lies at the heart of product design and development throughout numerous engineering disciplines, especially since processing large amounts of data has become increasingly ubiquitous. While mathematical statistics provide elegant guidance pertaining to the question of whether or not some particular underlying modeling assumptions are justified and appropriate, when pursuing a more comprehensive assessment of product design and development other considerations often increase in significance. Therefore, we will examine and analyze the tedious interactions and implications of statistical modeling choices and product liability exposure. To the best of our knowledge, this paper is the first to draw attention to and explore some often overlooked or oversimplified dangers and pitfalls that enter the equation when product design heavily relies on statistical modeling. In particular, through a diligent analysis of both statistical and legal aspects we will explore how statistically optimal procedures may yield far from optimal outcomes in terms of product liability when applied to actual real life problems and why suboptimal nonparametric or robust approaches may constitute better alternatives.

Background: COVID-19 pandemic has pulled us all a few steps back, were we never shake hands or hug each other when we meet our friends and family after a gap, but instead we greet them by saying Namaste and joining our hands together. As we all know, COVID-19 spreads through air and the only way to shield ourselves is by maintaining a safe distance from one another. Methodology: In order to conduct a meta-analysis on the number of COVID-19 cases in Kerala and India, the data was retrieved from various sites hosted by the government bodies. The data for analysis was collected from May 2020 to July 2020. The average number of days required to reach every 5000 fresh cases were also calculated using this data. COVID-19 has affected all the economy holistically regardless of financial, behavioral, or societal aspects. Conclusion: Lifting of the lockdown in a step by step process keeping in mind the necessities for the nation was a thoughtful act, but the people who mistook this opportunity and did not remain in quarantine after coming from abroad was recognized as the reasons behind the sudden and uncontrolled rise in the number of COVID-19 cases in Kerala, India. The government authorities had no other option but to lift the restrictions to reduce the economic burdens that had already affected the daily wage worker and farmers prompting them to give up their lives.

Data leakage by statistical officers represents a significant statistical crime under the Indonesian Statistics Law. However, despite the legal provisions, there has been a notable absence of enforcement actions against such breaches, raising questions about the effectiveness and applicability of the current legal framework for addressing statistical crimes related to data leakage. This study identifies a research gap in the enforcement and operationalization of existing laws, emphasizing the lack of empirical data on how these legal provisions are applied in practice. Utilizing an empirical research methodology, this study analyzes data and real-world instances of statistical data leakage. The findings reveal that unethical behavior among statistical officers, inadequate data security measures, and the threat of social engineering significantly contribute to the potential for data breaches. The study's strength lies in its focus on providing a comprehensive understanding of these issues and proposing actionable solutions. This research not only fills the existing gap by offering empirical insights but also advances practical recommendations for enhancing data protection and legal enforcement mechanisms within Indonesia’s statistical framework.

Precipitation patterns are critical for understanding the hydrological and climatological dynamics of any region. Sicily, the largest island of the Mediterranean sea, with its diverse topography and climatic conditions, serves as an ideal case study for analyzing precipitation data to gain insights into regional water resources, agricultural productivity, and climate change impacts. This paper employs advanced statistical physics methods, particularly Tsallis q-statistics, to analyze sub-hourly precipitation data from 2002 to 2023, provided by the Sicilian Agrometeorological Informative System (SIAS). We investigate several critical variables related to rainfall events, including duration, depth, maximum record, and inter-event time. The study spans two decades (2002-2012 and 2013-2023), analyzing the distributions of relevant variables. Additionally, we examine the simple returns of these variables to identify significant temporal changes, fitting these returns with q-Gaussian distributions. Our findings reveal the scale-invariant nature of precipitation events, the presence of long-range interactions and memory effects, characteristic of complex environmental processes.

Quantum physics through the lenses of Bayesian statistics consider probabilities to be degree of believes or knowledge and subjective. A Bayesian derivation of the probability density function in phase space is presented. The entropy proposed by Geiger and Kedem \cite{GeiKed2022a,GeiKed2022b} in phase space is expanded to define quantitatively interference and entanglement. Comparisons between each of these two quantities and the entropy are made. A brief presentation of entanglement in phase space to the spin degree of freedom and to mixed states completes the work.

The enzymatic activities of bacterial isolates have been widely studied, but a spatial distribution of this activity is rarely focused. New antibiotic-producing microorganisms can be discovered in a more efficient manner if spatial statistical techniques are applied to the distribution of the activity of bacterial isolates in different terrains. This study is focused to generate a series of maps illustrating the spatial distribution of different soil parameters and the inhibition against relative-safe pathogens (like Escherichia coli, Staphylococcus aureus, Klebsiella pneumoniae, Salmonella, Pseudomonas fluorencens and Enterobacter cloacae) in an urban park in València (Spain). This spatial data has demonstrated a higher proportion of isolates was specifically allocated. This routine of data presentation is valuable for understanding bacterial population dynamics at a local level.

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.

The purpose of this study is to estimate the mean transitioning probabilities from a Healthy state to malaria positive uncomplicated state or to malaria positive severe state. It also classifies the various transitioning probabilities of moving through the various states based on some baseline characteristics. Malaria test results for 2019 over a 12-month period were collected from the University of Ghana school clinic. An H-U model for the study was developed and the transition rates from the cross-sectional data are indicated. With two states Healthy (H) and Uncomplicated (U) forming a state space, there were four possible transitions. The results show that the probability of transitioning from a Healthy state to a malaria positive state is 0.03% while the probability that an individual will remain at Healthy state (H) after the test is 99.73%. It was found that if an individual is already positive and has taken medication the probability that its second test came out negative is 6.45% while the chances that it will remain positive but uncomplicated is 93.55%. The study also showed that in the long run, about 95.98% of persons who visited the student clinic with malaria symptoms recorded negative tests for malaria parasite while about 4% recorded positive for malaria. In terms of disaggregation by gender, it was realized that the number of reported negative test results were higher for females (97.08%) than for males (96.13%). However, the infection rate is higher for males (3.87%) than females (2.92%). It is recommended that in as much as the University of Ghana has two health centers (a clinic and hospital), there should be a centralized system to track students’ health so research done would not be biased.

The interaction between single or a fixed number of photons with a single absorber is of fundamental interest in quantum technology. The harnessing of light matter interactions at the single particle limit has several potential applications ranging from quantum communication and quantum metrology to quantum imaging. In this letter, a setup for heralded two-photon absorption at the single absorber level is proposed. The setup is based on a heralded two-photon source utilizing spontaneous parametric down-conversion, entanglement swapping and sum frequency generation for joint detection. The feasibility of the scheme is discussed by reviewing recent achievements in utilizing entangled and correlated photons for two-photon absorption as well as single photon absorption experiments at the limit of single absorbers in the context of applications in imaging (here mainly microscopy) and spectroscopy.

In this paper we present experimental results concerning Acoustic Emission (AE) recorded during cyclic compression tests on two different kinds of brittle building materials, namely concrete and basalt. The AE inter-event times were investigated through a non-extensive statistical mechanics analysis which shows that their decumulative probability distributions follow q-exponential laws. The entropic index q and the relaxation parameter q  1=Tq, obtained by fitting the experimental data, exhibit systematic changes during the various stages of the failure process, namely (q; Tq) linearly align. The Tq = 0 point corresponds to the macroscopic breakdown of the material. The slope, including its sign, of the linear alignment appears to depend on the chemical and mechanical properties of the sample. These results provide an insight on the warning signs of the incipient failure of building materials and could therefore be used in monitoring the health of existing structures such as buildings and bridges.

We present a methodology to enable users to interact with statistical information owned by an institution and stored in a cloud infrastructure. Mainly based on R, this approach was developed following the open-data philosophy. Also, since we use R, the implementation is mainly based on open-source software. R gives several advantages from the point of view of data management and acquisition, as it becomes a common framework that can be used to structure the processes involved in any statistical operation. This simplifies the access to the data and enable to use all the power of R in the cloud information. This methodology was applied successfully to develop a tool to manage the data of the Centre d’Estudis d’Opinió, but it can be applied to other institutions to enable open access to its data. The infrastructure also was deployed to a cloud infrastructure, to assure the scalability and a 24/7 access.

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

Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of q-Statistics. Fast forward to Constantino Tsallis’ illustrious 80th birthday celebration in 2023, where Deniz Eroglu and Ugur Tirnakli delved into Constantino’s collaborative network, injecting renewed vitality into the project. With hearts brimming with appreciation for Tsallis’ enduring inspiration, Eroglu, Boghosian, Borges and Tirnakli proudly present this meticulously crafted manuscript as a token of their gratitude.

In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or κ-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable only in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the κ → 0 limit.

The study of energy sources has been an awareness of the modern world due to constraints on the current energy worldwide supply chain. The complexity of the theme as well as the consciousness of finite sources also the need of saving energy has become a priority. Although many papers have moved in this direction there is no record of papers studying the variables in a house heating system, which represents the highest energy consumption in many cold countries. This paper explores the energy-saving theme by studying the main variables present in houses’ heating systems in the winter season in cold countries like Canada, Russia, Norway, Iceland, Finland, etc. By using a novel combination of numerical thermal simulation by COMSOLTM and statistical analysis by MiniTabTM , it was possible to design an efficient thermal distribution in a house with the variables of the system by determining their significance and interaction qualitatively.

The very first case of corona-virus illness was recorded on 30 January 2020, in India and the number of infected cases, including the death toll, continues to rise. In this paper, we present short-term forecasts of COVID-19 for 28 Indian states and five union territories using real-time data from 30 January to 20May 2020. Applying Holt’s second-order exponential smoothing method and autoregressive integrated moving average (ARIMA) model, we generated 10-day ahead forecasts of the likely number of infected cases and deaths in India until 29 May2020. Our results show that the number of cumulative cases in India will rise to169109 [PI 95% (14426, 19455)], concurrently the number of deaths may increase to 4863 [PI 95% (4221, 5551)] by 29 May 2020.Further, we have marked the states (e.g. Delhi, Uttar Pradesh, Rajasthan, Madhya Pradesh, Maharashtra, Gujarat, and Tamil Nadu) where outburst is expected by considering the cases above three standard deviations. Under the worst-case scenario, Maharashtra is likely to be the most affected state with around 62628 [PI 95% (52840, 73555)] cumulative cases by 29 May 2020. However, Kerala and Karnataka are likely to remain in the lesser affected region. The presented results mark the states where lockdown by 1 June2020, can be loosened.

Limnologists often adhere to a discretized view of waterbodies—they classify them, divide them into zones, promote discrete management targets, and use research tools, experimental designs, and statistical analyses focused on discretization. This approach to limnology has profoundly benefited the way we understand, manage, and communicate about waterbodies. But the research questions and the research tools in limnology are changing rapidly with consequences for the relevance of our current discretization schemes. Here, I examine how and why we discretize and argue that selectively rethinking the extent to which we must discretize gives us an exceptional chance to advance limnology in new ways.

In a previous paper\cite{simplified}, a variation of the Collision-time Statistics method was applied to identify the relevant perturbers for line broadening under the action of a constant magnetic field. As discussed, that version was simplified and inadequate for low magnetic field and/or large perturber mass (ions). The purpose of the present work is to augment the previous work, so that such cases, corresponding to the Larmor radius exceeding the maximum impact parameter, can be handed efficiently. The results may also be used to construct analytic, i.e. impact/unified models under the usual assumptions in these models.

The interest in random fiber lasers (RFLs), first demonstrated one decade ago, is still growing and their basic characteristics have been studied by several authors. RFLs are open systems that present instabilities in the intensity fluctuations due to the energy exchange among their non-orthogonal quasi-modes. In this work, we present a review of the recent investigations on the output characteristics of a continuous-wave erbium-doped RFL, with emphasis on the statistical behavior of the emitted intensity fluctuations. A progression from the Gaussian to Lévy and back to the Gaussian statistical regime was observed by increasing the excitation laser power from below to above the RFL threshold. By analyzing the RFL output intensity fluctuations, the probability density function of emission intensities was determined, and its correspondence with the experimental results was identified, enabling a clear demonstration of the analogy between the RFL phenomenon and the spin-glass phase transition. A replica-symmetry-breaking phase above the RFL threshold was characterized and the glassy behavior of the emitted light was established. We also discuss perspectives for future investigations on RFL systems.

Single particle tracking is a powerful technique to investigate the motion of molecules or particles. Here we review methods for analyzing the reconstructed trajectories, step needed for deciphering the underlying mechanisms driving the motion. First, we review the traditional analysis based on the mean square displacement (MSD), highlighting sometimes-neglected factors potentially affecting results accuracy. We then report methods that exploit distributions of parameters other than displacements, e.g. angles, velocities, and times and probabilities of reaching a target, discussing how they are more sensitive in characterizing heterogeneities and transient behaviors masked in MSD analysis. Hidden Markov Models are also used for this purpose, and these allow identifying different states, their populations and the switching kinetics. Finally, we discuss a rapidly expanding field: trajectory analysis based on machine learning. Various approaches, from random forest to deep learning, are used to classify trajectory motions, which can be identified by motion models or by model-free sets of trajectory features, either previously defined or automatically identified by the algorithms. We also review free software available for some of the analysis methods. We emphasize that approaches based on combined different methods, including classical statistics and machine learning, may be the way to obtain the most informative and accurate results.

A new family of inequality indices based on the deviation between the expected maximum and the expected minimum of random samples, called the nth Gini index is presented. These indices generalize the Gini index. At the same time, this family of indices and the S-Gini index are generalised by proposing the uv−Gini index, which turns out to be a convex combination of the S-Gini index and the Lorenz family of inequality measures. This family of Gini indices provides a methodology for achieving perfect equality in a given distribution of incomes. This is achieved through a series of successive and equal increases in the incomes of each individual.

Type 2 diabetes mellitus (T2DM) is a global health concern driven by factors such as obesity, sedentary behavior, and poor diet. This study uses data from the 2017-18 Bangladesh Demographic and Health Survey (BDHS) to analyze regional and individual predictors of diabetes and predi-abetes. Employing a Bayesian multinomial mixed-effects model, we account for regional varia-bility and individual factors like age, gender, BMI, residence, wealth, education, employment, and hypertension. Our results indicate significant regional differences and associations between de-mographic and health-related factors with diabetes risk. Younger individuals and those with higher BMI are more likely to be diabetic, while hypertension significantly increases diabetes risk. We applied machine learning (ML) models, including logistic regression, decision trees, k-nearest neighbor, linear discriminant analysis, and random forest, to classify diabetic status using these predictors, assessing their accuracy through 10-fold cross-validation. Logistic regression and linear discriminant analysis demonstrated robust performance across various response distributions. Simulation studies further examined the impact of different response distributions on model performance, revealing significant differences in classification accuracies. This approach of esti-mating parameters with a Bayesian model, applying ML for prediction, and conducting simulation studies to explore various scenarios highlights the importance of integrating these methodologies for effective diabetes prediction, providing insights for public health strategies to mitigate T2DM's impact.

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.

This paper examines patterns and drivers of energy choices for cooking and lighting in South Africa using the Statistics South African (StatSA, 2022) Census data at district municipality (districts) levels. Employing spatial and regression analysis, the findings show that electricity is the main source of energy for cooking across South Africa. However, there is a large swathe of the country covering districts, such as Vhembe and Mopani in Limpopo, eastern Mpumalanga, KwaZulu-Natal, and northern Eastern Cape provinces, where wood is the predominantly used energy type for cooking. There is almost uniform use of gas for cooking across the country. Electricity is the main energy source for lighting in South Africa. It is followed by candles, likely explained by loadshedding, and surprisingly solar energy a distant third. In terms of drivers, dwelling types play statistically significant role in what energy type to use for cooking and lighting, albeit differently. In terms of lighting, formal dwelling is positively related to the choice of electricity and informal dwelling is related to the choice of electricity (negatively) and candles (positively) for lighting. The level of higher education, household size, and the dependency ratio have varied statistically significant roles in the choice of either energy type for cooking or lighting by formal, informal, and traditional dwellers. Relevant policy prescriptions that are needed to engender the country towards sustainable energy use, diversification of energy types from electricity to other renewable energy sources, such as solar, and reduction in over-dependency on the biomass energy sources, such as paraffin and wood, especially in rural and poor districts, are proposed.

The calibration of length is related to the national economy and people's livelihood. The traditional calibration of length value was sent the uncalibrated instrument to the laboratory and the intrinsic error of the tested instrument was obtained in the laboratory. However, calibrating the instrument in the site produced additional error. In this article, a remote calibration method of length measurement based on optical fiber information transmission following with a proof of principle system was studied to reduce the additional error. The 1.0-level displacement guide rail was calibrated according to this method. The results showed that the relative error of guide rail displacement under different lengths was within 0.6%. The expanded uncertainties of 10 μm, 100 μm and 1 mm were analyzed respectively. The calibration results meet the actual standards of the guide rail. This optical method is a good candidate for remote calibration.

In an era characterized by rapid technological advancements, economic fluctuations, and global competition, adaptability and resilience have become critical success factors for businesses navigating uncertainty and complexity. This article explores the role of enterprise agility in today’s business landscape at Latam branch of Tata Consultancy Services (TCS), where organizations face complex and diverse operations. We aim to examine how companies can become more agile in the face of emerging challenges and seize opportunities swiftly to drive growth and deliver value. Since 2014, the division has embarked on an agile transformation journey to drive growth, deliver value, foster innovation, and build resilience in an increasingly dynamic environment. We scrutinize an approach to measuring and enhancing enterprise agility, employing statistical analysis and continuous improvement methodologies to tackle real-world challenges while offering valuable insights and recommendations for organizations aiming to implement similar systems. The results of an agile transformation in a certain company’s Latam branch serve as a compelling case study, demonstrating how the implementation of targeted measures and continuous improvement can significantly bolster enterprise agility. Methodologically, our work applies a novel sequence of parametric statistical tests which, to the best of our knowledge, have not been used in the industry to validate the results of business agility metrics. In future work, we aim to create a new workflow considering non-parametric tests to address data with other statistical distributions. We conclude our work by proposing a sequence of steps for organizations to implement business agility metrics.

Directed acyclic graphs (DAGs) are nonparametric causal path diagrams that have substantial utility as principled representations of disease and healthcare pathways, and of the underlying ‘data generating mechanisms’ these pathways involve. As such, DAGs provide a valuable bridge between: the aetiological knowledge, operational insight and professional experience on which clinical training and practice depend; and the more abstract epistemological and analytical considerations required to extract robust statistical insight from health and healthcare data. DAGs are nonetheless vulnerable to imperfect biomedical paradigms, partial clinical knowledge and limited empirical data. DAGs drawn under such circumstances offer limited scope for statistical insight free from cognitive, analytical or inferential bias if: they misrepresent the data generating mechanisms involved; or ignore the important role that omitted variables (whether measured, unmeasured or unacknowledged) might play therein. To address these weaknesses and broaden the appeal and application of DAGs, this chapter provides ten simple steps that educators can use to improve the analytical competence and statistical confidence of the healthcare students, qualified practitioners and experienced researchers they support. These steps use temporal logic to draw DAGs so as to: reduce reliance on uncertain knowledge, incomplete information, flawed assumptions or guesswork; and avoid, mitigate or acknowledge the errors and biases that each of these incur. The chapter comprises an accessible, non-technical overview of the perspective and thoughtfulness required to generate temporally coherent DAGs as objective representations of the probabilistic causal paths involved in context-specific data generating mechanisms. It encourages a focus on those variables operating as potential sources of analytical or inferential bias when estimating the plausible, probabilistic causal relationship between two pre-specified variables; and specifically addresses the challenges posed by: omitted; time-variant; non-asynchronous; and temporally obscure variables. The chapter includes a worked example based on a published clinical study to demonstrate how each of the steps required to generate temporally-informed DAGs can be applied to: critically appraise the analytical decisions made during applied healthcare research; and inform the decisions required when designing, undertaking and analysing primary and secondary, prospective and retrospective research. The appendices include a summary of ten recommendations for improving the reporting and interrogability of DAGs and DAG-informed analyses.

The origins of directed acyclic graphs (DAGs) date back to the emergence of ‘graph theory’ in the early 1700s (Biggs et al. 1986). DAGs are conceptual or literal, diagrammatic representations of causal paths between variables which are constructed – as their name suggests – on the basis of two over-riding principles: first, that all causal paths are ‘directed’ (i.e. for each pair of variables, only one can represent the cause, while the other must be its consequence); and second, that no direct cyclical paths, or indirect cyclical pathways (comprising sequences of consecutive paths) are allowed, such that no consequence can be considered its own direct or indirect cause (hence ‘acyclic’; Law et al., 2012). As such DAGs reflect the knowledge, presumptions, assumptions and/or speculation of the analyst(s) concerned regarding the causal relationships between each of the variables included therein. Current convention dictates that variables are represented as nodes/vertices, and that any causal paths between variables are represented as directed arcs/edges/lines, often in the form of arrows (see Figure 1). Although each arc indicates the presence and direction of a known/presumed/assumed/speculative causal relationship between the two variables concerned, drawing an arc does not require the sign, magnitude, precision or shape of the relationship to be known or declared (Tennant et al., 2021). In this respect, DAGs provide a simple, uncomplicated, accessible and entirely nonparametric approach for postulating causal relationships amongst any variables of interest even when these are uncertain, unknown or entirely speculative (Ellison, 2020). Nonetheless, as a result of the parametric constraints imposed by the presence/absence of possible arcs within any given DAG, these also reflect and support a number of more sophisticated statistical applications which make it possible to use DAGs to inform the design of multivariable statistical models that reflect the causal structure(s) involved – albeit without the need to know or understand the mathematical technicalities on which these are based (Lewis and Kuerbis, 2016). These features make DAGs attractive cognitive, educational and analytical tools for strengthening the epistemological, theoretical and empirical basis of causal inference, and there has been a recent proliferation in the use of DAGs across a range of applied scientific disciplines (e.g. Knight and Winship, 2013), and an associated upsurge in analytical methods training (e.g. Elwert, 2011; Gilthorpe, 2017; Hernán 2018; Roy, 2021; Hünermund, 2021). This Chapter reflects on a decade of delivering medical statistics training to undergraduate medical students at the University of Leeds between 2012-2021 in which the third year research, evaluation and special studies module (‘RESS3’) has used DAGs to support the development of applied statistical skills relevant to the extended student-selected research and evaluation projects (ESREP) students undertake in their fourth and final years (Ellison, 2021; Ellison et al., 2014a,b). Based on successive iterations of the structure and content of the RESS3 module, together with notes made during formal and informal planning and review meetings with module leads, lecturers, tutors and students, we draw on the claims and criticisms made of DAGs in the epidemiological literature to identify a number of explicit strengths (and associated, often implicit. weaknesses) that are central to their use in prediction and causal inference modelling. While using DAGs requires (and benefits from) a clear understanding of their non-parametric nature and parametric implications, the weaknesses of DAGs seem likely to reflect both: the challenges inherent in the modelling of data generating processes when these are imperfectly understood; and troublesome cognitive and heuristic tendencies common to all analytical tools – in which the tool facilitates the task in hand by reducing the necessity (and benefits of) exploring uncertainties and identifying assumptions. These, more epistemological considerations appear particularly challenging for medical undergraduates to grasp (Ellison, 2021), but also appear poorly understood by many established analysts and clinical epidemiologists (Ellison, 2020).

Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the gamma-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights.

Gait abnormalities are one of the distinguishing symptoms of patients with Parkinson's disease (PD) that contribute to fall risk. Our study compares the gait parameters of people with PD when they walk through a predefined course without assistance, with a conventional walker, and with a motorized walker under different speed cues. Six PD subjects were recruited at the New York Institute of Technology College of Osteopathic Medicine to participate in this study. Spatial posture and gait data of the test subjects were collected via a VICON motion capture system. We developed a framework to process and extract gait features and applied statistical analysis on these features to examine the significance of the findings. The results showed that motorized walkers with haptic cues significantly improved gait symmetry of PD subjects. Specifically, the asymmetry index of the gait cycle time was reduced from 6.7% when walking without assistance to 0.56% and below when using a walker. Furthermore, the double support time of a gait cycle was reduced by 4.88% compared to walking without assistance.

Developing countries like Pakistan is among those where lack of adoption to science and technology advancement is a major constraint for Satellite Remote Sensing use in crops and land use land cover digital information generation. Exponential rise in country population, increased food demand, limiting natural resources coupled with migration of rural community to urban areas had further led to skewed official statistics. This study is an attempt to demonstrate the possible use of freely available satellite data like Landsat8 under complex cropping system of Okara district of Punjab, Pakistan. An Integrated approach has been developed for the satellite data based crops and land use/cover spatial area estimation. The resultant quality was found above 96% with Kappa statistics of 0.95. Land utilization statistics provided detail information about cropping patterns as well as land use land cover status. Rice was recorded as most dominating crop in term of cultivation area of around 0.165 million ha followed by autumn maize 0.074 million ha, Fallow crop fields 0.067 million ha and Sorghum 0.047 million ha. Other minor crops observed were potato, fodder and cotton being cultivated on less than 0.010 million ha. Population settlements were observed over an area of around 0.081 million ha of land.

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.

Since 1990s, Petri nets have been used in systems biology for quantitative modeling. Despite the increasing number of models developed during this period, doubts remain about their biological relevance. Although biological systems predominantly exhibit intracellular or cellular structures, the models rely largely on deterministic predictions, failing to capture the inherent randomness and uncertainties of such systems. The question arises whether these models accurately describe the dynamic behavior of biological systems. This paper introduces a methodology for selecting the appropriate modeling paradigms in systems biology. Initially, we construct a Petri net model and perform deterministic, stochastic, and fuzzy stochastic simulations. Then we perform various statistical tests to measure the discrepancies between the simulation results. Based on scale-density analysis, we determine the modeling approach that best approximates the biological system. Finally, we compare the results of the statistical tests and the scale-density analysis to identify the optimal modeling approach. We applied the proposed methodology to the synthesis of spinal motor neuron protein from the spinal motor neuron-2 gene. Analysis revealed significant discrepancies between the simulation results of different modeling paradigms. Due to the sparse nature of the underlying drug-disease network, we conclude that the fuzzy stochastic paradigm provides the most biologically relevant results. We predict drug combinations that could lead to an up to 149-fold increase in spinal motor neuron protein levels, indicating a promising treatment for the disease. This methodology has potential for application to other gene-drug-disease networks and broader biological systems.

This paper explores the feasibility of applying Bayesian statistical methods to study the distortion patterns induced by carburizing heat treatment. By establishing posterior and predictive distribution models for torsion bar dimensions, we aim to accurately understand and predict the expansion behavior, thus enhancing control over carburizing-induced dimensional changes. Bayesian methods allow for the integration of prior knowledge and real-time data, providing a more comprehensive understanding of the distortion phenomena. This approach not only improves the precision of dimensional predictions but also contributes to optimizing the overall manufacturing process, ensuring that the torsion bars meet the rigorous standards required for high-performance applications in demanding industrial environments.

The BL Lacertae (BL Lac) object OJ 287 underwent an intense X-ray activity phase, exhibiting its brightest recorded X-ray flare in 2016-2017, characterized by much softer X-ray spectra and, concurrently, its first-ever recorded very-high-energy (VHE) emission (100--560 GeV), reported by the VERITAS observatory. Broadband spectral energy distribution reveals a new jet emission component similar to high-synchrotron-peaked BL Lac objects, thereby implying the soft X-ray spectrum for the synchrotron emission. Using the advantage of simultaneous X-ray and VHE spectral information, as well as the source being a low-synchrotron-peaked BL Lac object, we systematically explored the extragalactic background light (EBL) spectrum by demanding that the VHE spectrum cannot be harder than the X-ray spectrum. We used three different phenomenological forms of the EBL spectral shape (power-law, parabola, and polynomial) motivated by current constraints on the EBL with the Bayesian Monte Carlo approach to infer the credible EBL range. Our study favors an almost flat power-law spectral shape and is consistent with previous studies. The other spectral forms capable of capturing curvature though result in a better statistics value; the improvement is statistically insignificant given the additional parameters.

The Katerini-Kolindros aquifer system (KKas) is a critical freshwater resource, essential for the local and regional economy. To understand contamination sources, groundwater flow paths, and assess the aquifer's health, an extensive dataset of 751 samples from 113 wells collected between 2010 and 2020 was analyzed using multivariate statistical analysis (MVSA) and hydrogeochemical diagrams. The prevailing water types identified were Ca-HCO₃ and Mg-HCO₃, with mixed water types resulting from various factors affecting groundwater quality. The chemistry of groundwater in the KKas is shown to be affected by ion exchange processes and to a lesser extent by reverse ion exchange processes. No indications of sea-water intrusion have been identified in the water wells monitored. On the other hand, nitrate contamination has been detected in specific water wells spatially associated with urban-type land uses and activities. It is considered that nitrate contamination originates primarily from septic tanks and urban sewage networks or secondarily from fertilization of football pitches, cemeteries or urban waste management practices.

The Topographic Ruggedness Index (TRI) is one of the essential measurement in topographic analysis, as well as in explaining biodiversity and geo-diversity. This study demonstrate how to utilize Geographic Information Systems (GIS) to generate TRI for Nyanga District using Digital Elevation Model (DEM). Though the TRI strongly depends on a local scale slope derived from an average adjacent neighbor slope algorithm, and selection of different lag distances in the computation of spatial variability, the measurement demonstrated that areas of higher altitude have higher ruggedness index. The TRI model was generated by computing focal statistics to determine focal sum of DEM and of DEM ². The final TRI was computed using Math Algebra (Raster Calculator) to generate layers of different ruggedness suitable for topographic and biodiversity analysis. The algorithm presented could also be used for smaller areas with high quality data and corrected DEMs. Despite widespread adoption, ruggedness metrics require thorough testing using both artificial landscapes and real world applications.

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.

Information is physically measurable as a selection from a set of possibilities, the domain of information. This defines the term "information". The domain of the information must be known together reproducibly beforehand. As a practical consequence, digital information exchange can be made globally efficient, interoperable and searchable to a large extent by online definition of application-optimized domains of information. There are even more far-reaching consequences for physics. The purpose of this article is to present prerequisites and possibilities for a physical approach that is consistent with the precise definition of information. This concerns not only the discretization of the sets of possible experimental results, but also the order of their definition along time. The access to or comparison with the domain of information is the more frequent, the earlier it was defined. The geometrical appearance of our space is apparently a delayed statistical consequence of a very frequent connection with the common primary domain of information.

Evidence-based data for endometriosis management are limited. Experiments are excluded without adequate animal models. Data are limited to symptomatic women and occasional observations. Hormonal medical therapy cannot be blinded if recognised by the patient. Randomised controlled trials are not realistic for surgery since a variable disease with low numbers. Each diagnosis and treatment is an experiment with an outcome and experience is Bayesian updating from the past. If the experience of many is similar, this has more value than an opinion. The combined experience of a group of endometriosis surgeons was used to discuss problems in the management of endometriosis. Considering endometriosis as several genetically/epigenetically different diseases is important for medical therapy. Imaging cannot exclude endometriosis and diagnostic accuracy is limited for superficial lesions, deep lesions, and cystic corpora lutea. Surgery should not be avoided for emotional reasons. Shifting infertility treatment to IVF without considering fertility surgery is questionable. The concept of complete excision should be reconsidered. Surgeons should introduce quality control and teaching should move to explain why it is done. The perception of information has a personal bias. These are the major problems in the management of endometriosis identified by the combined experience of endometriosis surgeons.

The advancement in network security threats led to the development of new Intrusion Detection Systems(IDS) that rely on deep learning algorithms known as deep IDS. Along with other systems based on deep learning, deep IDS suffer from adversarial examples: malicious inputs aiming to change the prediction of a machine learning/deep learning model. Protecting deep learning against adversarial examples remains an open challenge. In this paper, we propose “NIDS-Defend” a framework to enhance the robustness of Network IDS against adversarial attacks. Our framework is composed of two layers: a statistical test and a classifier that together detect adversarial examples in real-time. The detection process consists of two steps: (1) flagging flows that contain adversarial examples with a statistical test, and (2) extracting individual adversarial examples in the previously flagged flows with a classifier. Our approach is evaluated on binary IDS with the NSL-KDD dataset. To generate adversarial examples, the crafting methods used are (1) Boundary attack and (2) HopSkipJumpAttack. We investigate the vulnerabilities of a Network IDS against adversarial examples, then apply our defense. The statistical test can confidently distinguish adversarial flows with more than 95% accuracy, and the classifier detects individual adversarial examples with more than 80% accuracy. We also show that our framework detects adversarial examples crafted by an adversary aware of the defense and confirm the effectiveness of our solution against adversarial attacks.

Nighttime lights (NTL) are a popular type of data for evaluating economic performance of regions and economic impacts of various shocks and interventions. Several validation studies use traditional statistics on economic activity like national or regional Gross Domestic Product (GDP) as a benchmark to evaluate the usefulness of NTL data. Many of these studies rely on dated and imprecise Defence Meteorological Satellite Program (DMSP) data and use aggregated units such as nation-states or the first sub-national level. Yet applied researchers who draw support from validation studies to justify their use of NTL data as a proxy for economic activity increasingly focus on smaller and lower level spatial units. This study uses a 2001-19 time-series of GDP for over 3100 US counties as a benchmark to examine the usefulness of the recently released version 2 VIIRS nighttime lights (V.2 VNL) products as proxies for local economic activity. Contrasts are made between cross-sectional predictions for GDP differences between areas and time-series predictions of GDP changes within areas. Disaggregated GDP data for various industries are used to examine what types of economic activity are best proxied by NTL data and comparisons are also made with the predictive performance of earlier NTL data products.

Many scientific and technological problems are studied with the help of computer codes that simulate the phenomena of interest rather than via traditional laboratory experiments. Such models play an important role in neuroscience where they are used to mimic brain function from the sub-cellular to the macroscopic level. Exploration with computer models carries with it a number of statistical challenges: where to sample the input space for the simulator, how to make sense of the data that is generated, how to estimate unknown parameters in the model, how to validate a model. The simulator setting also has some unique problems and possibilities. This review paper describes statistical research on these issues and how that work might be applied to neural simulations.

In recent years, UAV-enabled wireless energy transfer (WET) has attracted significant attention for its ability to provide efficient and stable power for ground devices by flexibly navigating 3-dimensional (3-D) space and utilizing the favorable line-of-sight (LoS) channels. Meanwhile, energy beamforming utilizing multiple antennas has been touted as a key technology to substantially enhance the radio frequency (RF)-based WET efficiency by focusing energy beams towards devices in desirable directions. However, energy beamforming design for UAV-enabled WET systems has not been studied, despite its tremendous utility. In this paper, we propose a joint design of the UAV’s altitude and channel statistics based energy beamforming to minimize the overall charging time required for all energy havesting devices (EHDs) to meet their energy demands, while alleviating the additional resources and cost for channel estimation. Unlike previous works that considered only the LoS dominant channel without small-scale fading, we adopt a more general air-to-ground (A2G) Rician fading channel, where the LoS probability as well as the Rician factor depends on the UAV’s altitude. To tackle the highly non-convex and non-linear problem, we first examine a single EHD scenario in order to draw insights by deriving an optimal energy beamformihng in a closed-form, and then devise the efficient methods to jointly design the altitude and energy beamforming for a multiple EHDs scenario. Our numerical results exhibit that the proposed joint design considerably reduce the overall charging time, while benefiting from significantly lowering the computational complexity compared the conventional methods.

Smallsats are becoming the predominant electro-optical Earth observation (EO) imaging platforms. While atmospheric correction of smallsat data enhances its utility, an established pathway to do so may constrain accuracy and utility. The alternative, Closed-form Method for Atmospheric Correction (CMAC), developed for smallsat application provides surface reflectance derived solely from scene statistics. In a prior paper, CMAC closely agreed with Land Surface Reflectance Code (LaSRC) software for correction of the four VNIR bands of Landsat-8/9 images for conditions of low to moderate atmospheric effect over quasi-invariant warehouse-industrial targets. Those results were accepted as surrogate surface reflectance to support analysis of CMAC and LaSRC reliability for surface reflectance retrieval in two contrasting environments: shortgrass prairie and barren desert. Reliability was defined and tested through a null hypothesis: the same top-of-atmosphere reflectance under the same atmospheric condition will provide the same estimate of surface reflectance. Evaluated against the prior surrogate surface reflectance, the results found decreasing error with increasing wavelength for both methods. From 58 comparisons across the four bands, LaSRC average absolute error ranged from 0.59% (NIR) to 50.30% (blue). CMAC error was well constrained from 0.01% (NIR) to 0.98% (blue) sustaining the null hypothesis for reliability.

Femtoscopy is a unique tool to investigate the space-time geometry of the matter created in ultra-relativistic collisions. If the probability density distribution of hadron emission is parametrized, then the dependence of its parameters on particle momentum, collision energy, and collision geometry can be given. In recent years, several measurements came to light that indicated the adequacy of assuming a Lévy-stable shape for the mentioned distribution. In parallel, several new phenomenological developments appeared, aiding the interpretation of the experimental results, or providing tools for the measurements. In this paper we review and discuss some of these advances, phenomenological and experimental.

We show succinctly a natural origin of the beautiful Gamma function in light of the WJ distribution, linking to quite distinct fields.

Outliers can influence regression model parameters and change the direction of the estimated effect, over-estimating or under-estimating the strength of the association between a response variable and an exposure of interest. Identifying visit-level outliers from longitudinal data with continuous time-dependent covariates is important especially when the distribution of such variable is highly skewed at follow-up visits. The primary objective was to identify potential outliers at follow-up visits using interquartile range (IQR) statistic, motivated by a large TEDDY dietary longitudinal and time-to-event data with a continuous time varying vitamin B12 intake as the exposure of interest and time to developing Islet Autoimmunity (IA) as the response variable. The IQR method was also applied to simulated data. To assess the impact of IQR-method detected outliers, data was analyzed using Cox-proportional hazard model with robust sandwich estimator. Partial residual diagnostic plots were used to detect highly influential outliers. Results showed how some of the detected outliers had large influence on the Cox regression model and changed both the direction of hazard ratios and the strength of association with the risk of developing IA. In conclusion, the IQR method is useful in identifying potential outliers at visit-level which can be further investigated.

With data for SARS-CoV-2 and with many countries entering the second wave of contagion required the improvement of the forecasting model, structuring its model to forecast the peak of the first and second contagion wave in Brazil. The Model Estimation for SARS-CoV-2 Peak Contagion (MESPC) was structured, capable of estimating the peak of contagion for SARS-CoV-2 in the first and second waves, as the main objective of this work. Using the MESPC model, it was possible to estimate, with a certain reliability degree, the peak of contagion for the first and second waves in Brazil, with one day difference from the real to the forecast. It is possible to use MESPC to forecast the peak of contagion for several regions, provided that the necessary structure and calibration are respected.

The fossil record is notorious for being incomplete and distorted, frequently conditioning the type of knowledge that can be extracted from it. In many cases, this often leads to issues when performing complex statistical analyses, such as classification tasks, predictive modelling, and variance analyses, such as those used in Geometric Morphometrics. Here different Generative Adversarial Network architectures are experimented with, testing the effects of sample size and domain dimensionality on model performance. For model evaluation, robust statistical methods were used. Each of the algorithms were observed to produce realistic data. Generative Adversarial Networks using different loss functions produced multidimensional synthetic data significantly equivalent to the original training data. Conditional Generative Adversarial Networks were not as successful. The methods proposed are likely to reduce the impact of sample size and bias on a number of statistical learning applications. While Generative Adversarial Networks are not the solution to all sample-size related issues, combined with other pre-processing steps these limitations may be overcome. This presents a valuable means of augmenting geometric morphometric datasets for greater predictive visualization.

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the3literature of non-equilibrium statistical mechanics. This article provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the5mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics

In California, an average of 41,900 patients are diagnosed annually with Staphylococcus bacterial infection; out of these, 24,090 patients have methicillin-resistant Staphylococcus aureus (MRSA) infection and 17,810 patients have methicillin-sensitive Staphylococcus aureus (MSSA) infection. The aim of this paper is to find out whether there is a significant difference in strain dominancy and in what direction. The paper gathered and analyzed data for period of five years of infection rate due to Staphylococcus aureus. This study indicates that a significant difference in dominancy exists, the MRSA infection rate (an average of five years period) is 1.35 times higher than the MSSA infection rate (P-value < 0.05, CI: 95%), but the gap between the two infection rates is decreasing. The infection rate of both MRSA and MSSA is in a path of decline.

There are no studies that quantitatively compare life histories among scorpion species. Statistical procedures applied to 94 scorpion species indicate that those with larger bodies do not necessarily have larger litters or longer life cycles, opposite to some theoretical predictions.

Data obtained by Direct Numerical Simulations (DNS) of pressure-driven turbulent channel flow are studied in the range 180 ≤ Reτ≤ 10,000. Reynolds number effects on the Mean Velocity Profile (MVP) and second order statistics are analyzed with a view of finding logarithmic behavior in the overlap region or even further from the wall, well in the boundary layer’s outer region. Values of Kármán constant for the MVPs and the Townsend-Perry constants for the streamwise and spanwise fluctuation variances are determined for the Reynolds numbers considered. A data-driven model of the MVP, proposed and validated for zero pressure gradient flow over a flat plate, is employed for pressure-driven channel flow by appropriately adjusting Coles’ strength of the wake function parameter, Π. There is excellent agreement between the analytic model predictions of MVP and the DNS-computed MVP as well as of the Reynolds shear stress profile. The skin friction coefficient Cf is calculated analytically. The agreement between the analytical model predictions and the DNS-based computed discrete values of Cf is excellent.

Staudinger taught us that macromolecules were made up of the covalently bonded monomer repeat units chaining up as polymer chains. The chemical nature of the monomer directed the type of covalent bonds conferring most of the specific properties of the polymer. The more the number of repeat units the longer the chains and the more the possibility for the chains to assume a variety of shapes, from an extended elongated one to a more compact coiled one. Also, the chemical process that resulted in the synthesis of macromolecules produced many chains, often not with the same shape or size. The properties of the polymers improved when the chains became longer but it was more difficult to process them: their viscosity increased with molecular weight; viscosity was no longer an intensive property like it was for small liquids. The main question raised in polymer physics remains: how do these long chains interact and move as a group when submitted to shear deformation at high temperature when they are viscous liquids? This question is debated in a field of polymer physics called RHEOLOGY, whose purpose is to understand the viscoelastic aspects of polymer melts deformation. The current consensus is that we need to distinguish two cases: the deformation of “un-entangled chains” for macromolecules with molecular weight, M, smaller than Me, “the entanglement molecular weight”, and the deformation of “entangled” chains for M > Me. Several eminent scientists have extensively studied these 2 cases over the last 70 years. Paul J. Flory, in 1974, and Pierre-Gilles de Gennes, in 1991, have been awarded the Nobel Price in Chemistry and Physics, respectively, for their significant theoretical contribution to understand these challenging problems. For both of these authors the properties of polymers derive from the statistical characteristics of the macromolecule itself, the designated statistical system that defines the thermodynamic state of the polymer. Me, the molecular weight between entanglements, is defined from the rubber elasticity theory and is known to be equal to Mc/2 where Mc is the molecular weight for the entanglements when viscosity measurements are made. The current paradigm is that the viscoelasticity of un-entangled melts ( M < Mc) is well described by the Rouse model and that the entanglement issues raised by the impact of the increase of the length of the macromolecules on the melt viscoelasticity, when M > Mc, are well understood by the reptation model introduced by de Gennes and co-workers. Both models can be classified in the category of “chain dynamics statistics”. In this paper we examine in details the failures and the current challenges facing the current paradigm of polymer rheology: the Rouse model for M < Mc, the reptation model for M > Mc, the time-temperature superposition principle, the strain induced time dependence of viscosity, shear-refinement and sustained-orientation. The basic failure of the current paradigm and its inherent inability to fully describe the experimental reality is documented in this paper. In the discussion and conclusion of the paper we suggest that a different solution to explain the viscoelasticity of polymer chains and of their “entanglement” is needed. This requires a change of paradigm to describe the dynamics of the interactions within the chains and across the chains. A brief description of our currently proposed open dissipative statistical approach, “the Grain-Field Statistics”, is presented.

This paper proposes an optimal trading algorithm based on a novel application of the conventional Control Engineering (CE). We consider a fundamental CE concept, namely, the feedback control and apply it to the Algorithmic Trading (AT). The concrete feedback control strategy is designed in a form of the celebrated Proportional-Integral-Derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realisation of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above makes it possible the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in the financial engineering, namely, the "stock market energy" concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python based prototype software. We finally apply the corresponding prototype software to a dataset from the Binance BTC / USDT stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT.

We present a general process for the halting problem, valid regardless of the time and space computational complexity of the decision problem. It can be interpreted as the maximization of entropy for the utility function of a given Shannon-Kolmogorov-Bernoulli process. Applications to non-polynomials problems are given. The new interpretation of information rate proposed in this work is a method that models the solution space boundaries of any decision problem (and non polynomial problems in general) as a communication channel by means of Information Theory. We described a sort method that order objects using the intrinsic information content distribution for the elements of a constrained solution space - modeled as messages transmitted through any communication systems. The limits of the search space are defined by the Kolmogorov-Chaitin complexity of the sequences encoded as Shannon-Bernoulli strings. We conclude with a discussion about the implications for general decision problems in Turing machines.

Social and spatial characteristics of a population often interact to influence health outcomes, suggesting a need to jointly analyze both to offer useful insights in community health. However, researchers have used either social or spatial analyses to examine community-based health issues and inform intervention programs. We propose a combined socio-spatial analytic approach to develop a social network with spatial weights and a spatial statistic with social weights, and apply them to an ongoing study of mental and physical well-being of rural Latino immigrants in North Florida, USA. We demonstrate how this approach can be used to calculate measures, such as social network centrality, support contact dyads, and spatial kernel density based on a health survey data. Findings reveal that the integrated approach accurately reflected interactions between social and spatial elements, and identified community members (who) and locations (where) that should be prioritized for community-based health interventions.

In recent years, online social media information has been subject of study in several data science fields due to its impact on users as a communication and expression channel. Data~gathered from online platforms such as Twitter has the potential to facilitate research over social phenomena based on sentiment analysis, which usually employs Natural Language Processing and Machine Learning techniques to interpret sentimental tendencies related to users opinions and make predictions about real events. Cyber attacks are not isolated from opinion subjectivity on online social networks. Various security attacks are performed by hacker activists motivated by reactions from polemic social events. In this paper, a methodology for tracking social data that can trigger cyber attacks is developed. Our main contribution lies in the monthly prediction of tweets with content related to security attacks and the incidents detected based on ℓ1 regularization.

The expansion of Open World Video Games (OWVGs) has seen the emergence of multiple new fictional worlds. This type of video game is characterized by total immersion in a world built for the players entertainment. What videogames developers want when players enter an OWVG is that they could feel like if they were open a door to an entirely new world and leave the real world behind. These virtual worlds manifest as a complement, an alternative, or the successor to the physical universe, and in some way continue the philosophical tradition of possible worlds begun by Leibniz. Accustomed to ‘surviving’ in hostile environments, millions of people continued to improve their skills in the midst of the COVID-19 pandemic while locked in their homes. Once the pandemic seems to start to be left behind, the paper analyzes the virtual worlds created by the video games and the relations between the pandemic and these fictional worlds.

Channel estimation is an important module to enhance the performance of orthogonal frequency division multiplexing (OFDM) systems. However, the presence of a large amount of noise in multipath fading time-varying channels significantly affects the channel estimation accuracy and thus the recovery quality of the received signals. Therefore, this paper proposes a double-threshold (DT) channel estimation method based on adaptive frame statistics (AFS). The method first adaptively determines the number of statistical frames based on the temporal correlation of the received signals, and preliminarily detects the channel structure by analyzing the distribution characteristics of multipath sampling points and noise sampling points during adjacent frames. Subsequently, a multi-frame averaging technique is used to expand the distinction between multipath and noise sampling points. Finally, the DT is designed to better recover the channel based on the preliminary detection results. Simulation results show that the proposed adaptive frame statistics-double-threshold (AFS-DT) channel estimation method is effective and has better performance compared with many existing channel estimation methods.

We developed a novel approach in the field of spatiotemporal modelling, based on the spatialisation of time: the Timescape algorithm. It is especially aimed at sparsely distributed datasets in ecological research, whose spatial and temporal variability is strongly entangled. The algorithm is based on the definition of a spatiotemporal distance that incorporates a causality constraint and that is capable of accommodating the seasonal behaviour of the modelled variable as well. The actual modelling is conducted exploiting any established spatial interpolation technique, substituting the ordinary spatial distance with our Timescape distance, thus sorting, from the same input set of observations, those causally related to each estimated value at a given site and time. The notion of causality is expressed topologically and it has to be tuned for each particular case. The Timescape algorithm originates from the field of stable isotopes spatial modelling (isoscapes), but in principle it can be used to model any real scalar random field distribution.

The main goal of the paper is to compare the effects of the wave spectrum, computed using the Discrete Interaction Approximation (DIA) and the Webb–Resio–Tracy (WRT) methods, on statistical wave properties such as skewness and kurtosis. The statistical properties are obtained by integrating the three-dimensional free-surface Euler equations with a high-order spectral method combined with a phenomenological filter to account for the energy dissipation due to breaking waves. In addition, we investigate the minimum spatial domain size required to obtain meaningful statistical wave properties. The numerical simulations are performed over a physical domain of size 4.13 km × 4.13 km. The results indicate that statistical properties must be computed over an area of at least 4 km2. The results also suggest that selecting a more computationally expensive WRT method does not affect the statistical values to a great extent. The most noticeable effect is due to the energy dissipation filter that is applied. It is concluded that selecting the WRT or the DIA algorithm for computing the wave spectrum needed for the numerical simulations does not lead to major differences in the statistical wave properties. However, more accurate energy dissipation mechanisms due to wave breaking are needed.

The novel coronavirus pneumonia (COVID-19) is a contagious acute respiratory infectious disease whose causative agent has been demonstrated to be a novel virus of the coronavirus family, SARSCoV-2. A recent pre-print study has showed a heme attack on the 1-beta chain of hemoglobin by COVID19. Beta-thalassemia results of a default in the hemoglobin beta- chain synthesis. 1,5% global population are heterozygotes for this disease. In this study, by a multiple linear regression, we have analyzed the evolution of COVID-19 infection in three Italian regions (Puglia, Sardinia, Sicilia) with different beta-thalassemic prevalences, in order to search a link. The results have showed that betathalassemic heterozygote population prevalence is correlated to immunity against COVID-19, by a regression. This paper is only for academic discussion, the hypotheses and conclusions needs to be confirmed by further research .

To gain insight into the differences between onshore and offshore atmospheric turbulence, 2 pressure fluctuations were measured for offshore wind under different environmental conditions. 3 A durable piezo-electric sensor was used to sample turbulent pressure data at 50 kHz. Offshore 4 measurements were performed at 100 m height on Germany’s FINO3 offshore platform in the 5 German Bight together with additional meteorological data provided by Deutscher Wetterdienst 6 (DWD). The statistical evaluation revealed that the stability state in the atmospheric boundary has a 7 large impact on turbulent fluctuations. Therefore, we used higher statistical properties (described 8 by so-called shape factors) to the stability state. Data was classified to be either within the unstable, 9 neutral or stable stratification. We found that in case of stable stratification, the shape factor is 10 mostly close to zero, indicating that a thermally stable environment produces closer-to Gaussian 11 distributions. Non-Gaussian distributions were found in unstable and neutral boundary layer states 12 and an occurrence probability was estimated. Possible impact on laminar-turbulent transition on the 13 blade is discussed with application of so-called laminar aerofoils on wind turbine blades. Use of a 14 cut-off frequency to separate load and aerodynamic turbulence is proposed.

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

This paper intoduces a non-standard research technique to clarify how complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using fractal dynamical models with and without stochastic forces. This method for conducting research involves tracing the his- torical evolution of understaning an empirical medical process faciltated by the fractal calculus perspective. Herein we trace the analysis of the time series for heart rate varability (HRV) developed for diagnosing the cardiovascular health of a patient. This is done herein by introducing four (one empirical which en- tails three theoretical fractal models) distinct but related fractal models each one introduced to solve a particular problem arising from a fundamental defect in the previous model but in generalizing a model at one stage to resolve the problem associated with the defect another is invariably introduced by the re- placement model. It is through the utilization of the fractional calculus that the necessity for rethinking how to systematically incorporate additonal layers of complexity are revealed ultimately resulting in a 'complete' description of its empirical dynamics in fractal terms.