In this study, an attempt was made to investigate the Kenya case of multivariate causality of carbon dioxide emissions by employing a time series data spanning from 1961-2011 using the ARDL method of cointegration analysis. The long-run elasticities show that, a 1% increase in financial development increases carbon dioxide emissions by 0.28%, a 1% increase in GDP per capita increases carbon dioxide emissions by 1.32% and a 1% increase in urbanization decreases carbon dioxide emissions by 1.14%. There was a unidirectional causality running from financial development, food production index, GDP per capita, industrialization and urbanization to carbon dioxide emissions. The innovation accounting shows that 20% of future shocks in carbon dioxide emissions are due to fluctuations in financial development, 9% of future shocks in financial development are due to fluctuations urbanization and 22% of future shocks in food production index are due to fluctuations in carbon dioxide emissions.

In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations are discussed. It is also shown that if the stochastic volatility matrices are diagonal, which is the case if the univariate time series are estimated separately instead of being jointly estimated, then the empirical copula process behaves as if the innovations were observed; a remarkable property. As a by-product, one also obtains the asymptotic behavior of rank-based measures of dependence applied to residuals of these time series models.

A semi–numerical approach proposed many years ago for describing gravitational collapse in the post–quasi–static approximation , , , , is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi–homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post–quasi–static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids and therefore we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g. luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.

In order to deal with imprecision, ambiguity, and uncertainty in data analysis, Pawlak introduced rough set theory in 1982. This paper aims to expand the scope of basic set theory developed by presenting the notions of δP-upper and δP-lower approximations, that are based on the notion of δP-open sets, we additionally examine a few of their fundamental characteristics.

Given a fuzzy normed space $ \left( X,N \right) $‎, ‎we will introduce the notion of fuzzy near best approximation within a relative distance $ \rho \geq 0 $‎. ‎Some basic properties are characterized and also many examples for illustration are presented‎.

Social media platforms have been entirely an undeniable part of the lifestyle for the past decade. Analyzing the information being shared is a crucial step to understanding human behavior. Social media analysis aims to guarantee a better experience for the user and risen user satisfaction. However, first, it is necessary to know how and from which aspects to compare users. In this paper, an intelligent system has been proposed to measure the similarity of Twitter profiles. For this, firstly, the timeline of each profile has been extracted using the official TwitterAPI. Then, all information is given to the proposed system. Next, in parallel, three aspects of a profile are derived. Behavioral ratios are time-series-related information showing the consistency and habits of the user. Dynamic time warping has been utilized for the comparison of the behavioral ratios of two profiles. Next, the audience network is extracted for each user, and for estimating the similarity of two sets, Jaccard similarity is used. Finally, for the Content similarity measurement, the tweets are preprocessed respecting the feature extraction method; TF-IDF and DistilBERT for feature extraction are employed and then compared using the cosine similarity method. Results have shown that TF-IDF has slightly better performance; therefore, the more straightforward solution is selected for the model. Similarity level of different profiles. As in the case study, a Random Forest classification model was trained on almost 20000 users revealed a 97.24% accuracy. This comparison enables us to find duplicate profiles with nearly the same behavior and content.

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.

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operations are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operation are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

Boltzmann codes are essential tools for studying cosmology. Most of the codes are based on a seminal work by Ma and Bertschinger. We found that the formalism employed in those codes has at least three possible problems which need to be understood. i) The equation of motion for baryons are gauge incompatible, ii) they break the Bianchi identity, and iii) it is not clear from the equations of motion which physical system is considered. In this work we revisit the baryon physics and address all the above mentioned issues, based solely on conservation of stress-energy tensor, resulting in taking into account a correction that is usually neglected and that is numerically small. We also study the tight coupling approximation up to the second order without choosing any gauge. We implement the improved baryon equations in a Boltzmann code and investigate the change in the estimate of cosmological parameters by performing an MCMC analysis. While in this paper we study the Lambda-CDM model only, our baryon equations can be easily implemented in other models and various modified gravity theories.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

We develop an 1/n expansion method for the systematic approxi- mation of the solutions of classical spin systems (tri-dimensional vec- tors) which can describe general spin-spin interactions and phases with complex magnetization pattern. This method is applied to study the phase transitions observed in pyrochlore crystals (e.g. Gd₂ Ti₂ O₇ ) and the results have qualitative agreement with the experimental ones.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Paleoclimate information is key to understanding the climate system and predicting future climate. Currently, stable isotope analysis of whole molecules in tree rings is among the most advanced paleoclimate tools. Still, it only enables reconstructions of one climate parameter at a time (univariate climate reconstruction), a fundamental limitation. Here, we investigated whether this limitation can be overcome by analysing isotope variability at the level of intramolecular carbon positions in tree-ring glucose. We found that drought governs isotope variability at glucose C-1 to C-3, whereas radiation governs isotope variability at glucose C-5 to C-6. These isotope-climate relationships are statistically and mechanistically robust. According to cross-validation analysis, they can be reconstructed with high accuracy and precision. Thus, intramolecular isotope analysis enables multivariate climate reconstructions (proof of concept).

The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) in general differ from the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue a robust alternative is introduced which estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to detect which claims have an abnormally large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.

The aim of this work is to introduce new ways to model the I-V characteristic of a PV cell or PV module using straight lines and Bézier curves. This is a complete novel approach, Bézier curves being previously used mainly for computer graphics. The I-V characteristic is divided in three sections, modeled with lines and a quadratic Bézier curve in the first case and with three cubic Bézier curves in the second case. The result proves to be accurate and relies on the fundamental points usually present in the PV cell datasheets: Voc (the open circuit voltage), Isc (the short circuit current), Vmp (the maximum power corresponding voltage) and Imp (the maximum power corresponding current) and the parasitic resistances Rsh0 (shunt resistance at Isc) and Rs0 (series resistance at Voc). The proposed algorithm completely defines all the implied control points and the error is analyzed. The temperature and irradiance influence is also analyzed. The model is also compared using the least squares fitting method. The final validation shows how to use Bézier cubic curves to accurately represent the I-V curves of an extensive range of PV cells and arrays.

The purpose of this paper is threefold: (i) to introduce and study the Euler-Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemannian manifolds; (ii) to analyze some decomposable multivariate dynamics represented by Euler-Lagrange PDEs of least squares Lagrangians generated by flatness PDEs and Riemannian metrics; (iii) to give examples of explicit flat extremals and non-flat approximations.

In this review paper, we present a pellucid proof of how x tanh(x/µ) approximates |x|and is better than √x² +µ  when we are concernedwith accuracy.

An empirical investigation was carried out to study the relationship between the soil characteristics, including the Nitrogen (N), Phosphorus (P), Potassium (K), potential of Hydrogen (pH), Electrical conductivity (EC), Sulfur (S,), Zinc (Zn), Iron (Fe), Copper (Cu), Manganese (Mn) and Boron (B) using principal component analysis (PCA), Factor Analysis (FA), and Canonical Correlation analysis (CCA) for data reduction multivariate techniques. The first five main components accounted for 24.22%, 18.52%, 16.1%, 9.97%, and 9.27% of sample variances, respectively. All five principal components (PCs) accounted for 78.07% of the sample variance. The soil characteristics viz., P and K have highly dominated the first PC; the soil characteristics N and pH have dominated the second PC; K, EC, and Cu have dominated the third PC; Fe, Mn, and pH have dominated in the fourth PC; whereas the parameter Cu dominated the fifth PC. The first factor showed a strong negative loading on S and a strong favorable loading on Cu; P, K, and EC have substantial positive loadings in the second factor. Significant positive loadings on Mn, Fe, Cu, pH, N, and K are present in the third component. The fourth factor had a significantly positive pH, Fe, N, P, K, and B loadings. Fe, P, and B have much weight in the fifth factor. The soil characteristics viz., N, Zn, pH, K, Fe, and Mn have dominated the first PC; the soil characteristics B, P, S, Zn, and Fe have dominated the second PC; B and P have dominated the third PC whereas the only character Cu dominated the fourth PC. Cu and OC have much weight in the fourth factor. The canonical redundancies for dependent and independent sets are 12% and 17%, respectively. The Stewart-Love canonical redundancy index is 70.58%, which means that the first linear combination of the X-set explains 70.58% of the total variance in the Y-set.

The only cases where exact distributions of estimates are known is for samples from exponential families, and then only for special functions of the parameters. So statistical inference was traditionally based on the asymptotic normality of estimates. To improve on this we need the {\it Edgeworth expansion} for the distribution of the standardized estimate. This is an expansion in $n^{-1/2}$ about the normal distribution, where $n$ is typically the sample size. The 1st few terms of this expansion were originally given for the special case of a sample mean. In earlier work we derived it for {\it any } standard estimate, hugely expanding its application. We call an estimate $\hat{w}$ of an unknown vector $w\in R^p$, a {\it standard estimate}, if $E\ \hat{w}\rightarrow w$ as $n\rightarrow \infty$, and for $r\geq 1$ the $r$th order cumulants of $\hat{w}$ have magnitude $n^{1-r}$ and can be expanded in $n^{-1}.$ Here we give another huge extension. We give the expansion of the distribution of {\it any smooth function} of $\hat{w}$, say $t(\hat{w})\in R^q,$ giving its distribution to $n^{-5/2}$. We do this by showing that $t(\hat{w})$, is a standard estimate of $t(w)$. This provides far more accurate approximations for the distribution of $t(\hat{w})$ than its asymptotic normality. %NOT USED: The building blocks of the Edgeworth expansions are the {\it cumulant coefficients } of the estimate. These cumulant coefficients are also needed for bias reduction, Bayes estimates and confidence regions. We give {\it chain rules} for the cumulant coefficients of $t(\hat{w})$ in terms of those of $\hat{w}$ and the derivatives of $t(w)$, up to those needed for 5th order Edgeworth expansions for $t(\hat{w})$ and its {\it tilted expansion}, useful for the tail of the distribution.

The understanding of water quality and its underlying processes is important for the protection of aquatic environments enabling the rare opportunity of access to a domain expert. Hence, an explainable AI (XAI) framework is proposed that is applicable to multivariate time series resulting in explanations that are interpretable by a domain expert. The XAI combines in three steps a data-driven choice of a distance measure with explainable cluster analysis through supervised decision trees. The multivariate time series consists of water quality measurements, including nitrate, electrical conductivity, and twelve other environmental parameters. The relationships between water quality and the environmental parameters are investigated by identifying similar days within a cluster and dissimilar days between clusters. The XAI does not depend on prior knowledge about data structure, and its explanations are tendentially contrastive. The relationships in the data can be visualized by a topographic map representing high-dimensional structures. Two comparable decision-based XAIs were unable to provide meaningful and relevant explanations from the multivariate time series data. Open-source code in R for the three steps of the XAI framework is provided.

An oil and vinegar scheme is a signature scheme based on multivariate quadratic polynomials over finite fields. The system of polynomials contains $n$ variables, divided into two groups: $v$ vinegar variables and $o$ oil variables. The scheme is called balanced (OV) or unbalanced (UOV), depending on whether $v = 0$ or not, respectively. These schemes are very fast and require modest computational resources, which make them ideal for low-cost devices such as smart cards. However, the OV scheme has been already proven to be insecure and the UOV scheme has been proven to be very vulnerable for many parameter choices. In this paper, we propose a new multivariate public key signature whose central map consists of a set of polynomials obtained from the multiplication of block matrices. Our construction is motivated by the design of the Simple Matrix Scheme for Encryption and the UOV scheme. We show that it is secure against the Separation Method, which can be used to attack the UOV scheme, and against the Rank Attack, which is one of the deadliest attacks against multivariate public-key cryptosystems. Some theoretical results on matrices with polynomial entries are also given, to support the construction of the scheme.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

The current work reveals the fine tuning between stability zones and randomness of Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary queueing D/M/1 system. More specifically, this clearly provides more insights into developing a contemporary PSFFA theory that unifies non-stationary queueing theory with chaos theory and fields in both theoretical physics and chaotic systems. This opens new grounds for stability analysis of non-stationary queueing systems.

In order to overcome this problem our group designed a novel machine learning technique, multivariate linear method (MLM) which can capture convergent data from voxel-based morphometry, functional resting state and task-related neuroimaging and the relevant clinical measures. In this paper we report results from convergent cross-validation of biological signatures of disease in a sample of patients with schizophrenia as compared to depression. Our model provides evidence that the combination of the neuroimaging and clinical data in MLM analysis can inform the differential diagnosis in terms of incremental validity to reach 90 % accuracy of the prediction.

Model-based image reconstruction has brought improvements in terms of contrast and spatial resolution to imaging applications such as magnetic resonance imaging and emission computed tomography. However, their use for pulse-echo techniques like ultrasound imaging is limited by the fact that model-based algorithms assume a finite grid of possible locations of scatterers in a medium -- which does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure based on a truncated singular value decomposition. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit (OMP), that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of 2-dimensional ultrasound image reconstructions with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

Strawberry is produced in tropical regions using imported cultivars adapted to temperate and subtropical climates. These cultivars, under tropical conditions, produce below their genetic potential. Through multivariate analyses, the objective was to evaluate and select short-day strawberry genotypes based on intraspecific crosses, product characteristics, and fruit quality. The genotypes were obtained from the cross between 'Camino Real' (female parent) and the first-generation genotypes RVCA16, RVCS44, RVFS06, RVFS07, and RVDA11 (male parent), obtained in previous selections. The experimental design consisted of augmented blocks with standard controls, consisting of first-generation genotypes and commercial cultivars. The fruits were harvested and evaluated for productivity and post-harvest characteristics: Total Fruit Mass (MTF); Total Number of Fruits (TFN); Average Fruit Mass (AFM); Commercial Fruit Mass (CFM); Fruit Commercial Number (CFN); Average Commercial Mass of Fruits (ACFM); Total Soluble Solids (TSS); Firmness (F); Brightness (L); Hue Angle (°Hue); Chroma (C). The selection index of Mulamba and Mock (1978) was used with an intensity of 3% to obtain superior genotypes and submitted to multivariate analysis for comparative purposes. Of the 1500 genotypes evaluated, it was possible to select 44 genotypes with characteristics superior to the 13 controls. The RVDA11CR59 genotype showed better values for the attributes of interest, but the RVCS44CR population, from the cross between 'Camino Real' × RVCS44 ('Camarosa' × 'Sweet Charlie'), obtained the highest number (16) of individuals among those selected. Significant traits had high heritability but were not necessarily reflected in high selection gain. Coefficients of genetic variation were high, indicating sufficient genetic variability to select genotypes for these traits. When multivariate analyses were used, it was possible to group the selected genotypes into the same cluster according to the similarity and balance in the responses to the evaluated variables, demonstrating that these analyses help other parameters choose superior genotypes. The multivariate analysis allowed the selection of more balanced genotypes for production and post-harvest traits for tropical climates.

Information-related measures are useful tools for multi-variable data analysis, as measures of dependence among variables, and as descriptions of order and disorder in biological and physical systems. Measures, like marginal entropies, mutual / interaction / multi -information, have long been used in a number of fields including descriptions of systems complexity and biological data analysis. The mathematical relationships among these measures are therefore of significant inherent interest. Relations between common information measures include the duality relations based on Möbius inversion on lattices. These are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). While these relationships are of significant interest there has been, to our knowledge, no systematic examination of the full range of relationships of this diverse range of functions into a unifying formalism as we do here. In this paper we define operators on functions on these lattices based on the Möbius inversions that map functions into one another (Möbius operators). We show that these operators form a simple group isomorphic to the symmetric group S₃. Relations among the set of functions on the lattice are transparently expressed in terms of the operator algebra, and, applied to the information measures, can be used to derive a wide range of relationships among diverse information measures. The Möbius operator algebra is naturally generalized which yields extensive new relationships. This formalism now provides a fundamental unification of information-related measures, and the isomorphism of all distributive lattices with the subset lattice implies an even broader application of these results.

We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting in the weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of \texorpdfstring{$L_2$}{}-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on \texorpdfstring{$d$}{} and \texorpdfstring{$\va^{-1}$}{}. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and \texorpdfstring{$(t_1,t_2)$}{}-weak tractability (\texorpdfstring{$(t_1,t_2)$}{}-WT) for all \texorpdfstring{$t_1>1$}{} and \texorpdfstring{$t_2>0$}{} in terms of the introduced weights under the absolute error criterion or the normalized error criterion.

In this paper, we study a co-variational inequality problem involving Yosida approximation operators in real uniformly smooth Banach space and define an iterative method to obtain its solution. We prove some properties of Yosida approximation operator for our purpose, that is strongly accretivity and Lipschitz continuity. An existence as well as convergence result is proved for co-variational inequality problem involving Yosida approximation operators using the concept of nonexpansive sunny retraction.

In many Bayesian computations, first, we obtain the expression of the joint distribution of all the unknown variables given the observed data. In general, this expression is not separable in those variables. Thus, obtaining their marginals for each variable and computing the expectations are difficult and costly. This problem becomes even more difficult in high dimensional quandaries, which is an important issue in inverse problems. We may then try to propose a surrogate expression with which we can do approximate computations. Often a separable expression approximation can be useful enough. The Variational Bayesian Approximation (VBA) is a technique that approximates the joint distribution $p$ with an easier, for example separable, one $q$ by minimizing Kullback–Leibler Divergence $KL(q|p)$. When $q$ is separable in all the variables, the approximation is also called Mean Field Approximation (MFA) and so $q$ is the product of the approximated marginals. A first standard and general algorithm is alternate optimization of $KL(q|p)$ with respect to $q_i$. A second general approach is its optimization in the Riemannian manifold. However, in this paper, for practical reasons, we consider the case where $p$ is in the exponential family and so is $q$. For this case, $KL(q|p)$ becomes a function of the parameters $\thetab$ of the exponential family. Then, we can use any other optimization algorithm to obtain those parameters. In this paper, we compare three optimization algorithms: standard alternate optimization, a gradient-based algorithm and a natural gradient algorithm and study their relative performances on three examples.

In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.

Forest planners have traditionally used expected growth and yield coefficients to predict future merchantable timber volumes. However, because climate change affects forest growth, the typical forest planning methods using expected value of forest growth can lead to sub-optimal harvest decisions. We proposed in this paper to formulate the harvest planning with growth uncertainty due to climate change problem as a multistage stochastic optimization problem and use sample average approximation (SAA) as a tool for finding the best set of forest units that should be harvested in the first period even though we have a limited knowledge of what future climate will be. The objective of the harvest planning model is to maximize the expected value of the net present value (NPV) considering the uncertainty in forest growth and thus in revenues from timber harvest. The proposed model was tested on a small forest with 89 stands and the numerical results showed that the approach allows to have superior solutions in terms of net present value and robustness in face of different climate scenarios compared to the approach using the expected growth and yield. The SAA methods requires to generate samples from the distribution of the random parameter. Our results suggested that a sampling scheme that focuses on generating high number of samples in distant future stages is favorable compared to having large sample sizes for the near future stages. Finally, we demonstrated that, depending on the level of forest growth change, ignoring this uncertainty can negatively affect forest resources sustainability.

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

We present smooth approximations to $ \vert{x} \vert $ using sigmoid functions. In particular $ x\,erf(x/\mu) $ is proved to be better smooth approximation for $ \vert{x} \vert $ than $ x\,tanh(x/\mu) $ and $ \sqrt{x^2 + \mu} $ with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for error function.

The fundamental objective is to study the application of multivariate sets of data in Gaussian distribution. This paper examines broad measurements of structure for both Gaussian and non-Gaussian distributions, which shows that they can be described in terms of the infor-mation-theoretic between the given covariance matrix and correlated random variables (in terms of relative entropy). In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion supported by illustrations, both technically and statistically. The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic's science and implementations. It also helps readers grasp the themes' fundamental concepts. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis based on differential equations, a wide range of information is addressed, including basic to application concerns.

Multivariate Time Series Classification (MTSC) is one of most important tasks in time series analysis, aiding in activities such as human motion recognition and medical diagnostics. Existing methods for MTSC do not explicitly model temporal differences and generalize the idea of temporal difference into a efficient temporal module. Additionally, existing methods are not yet able to capture cross-variable relationships well during network training. As a result, they are unable to achieve convincing feature representation, leading to suboptimal classification accuracy. In this paper, we propose a novel MTSC model called Temporal Difference and Cross-variate Fusion Network (TDCFN), which integrates a two-stream differential LSTM network and a cross-variate feature extraction network to enhance feature representation. TDCFN achieves superior classification accuracy by capturing dynamic temporal evolution and inter-variable relationships. The experimental results show that TDCFN can achieve competitive performance with state-of-the-art multivariate time series classification approaches.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

Machine learning methods have widely been applied to detect anomalies in machine and cutting tool behavior during lathe or milling. However, detecting anomalies in the workpiece itself did not get the same attention by researchers. That is why in this article, the authors present a pub-licly available multivariate time series dataset which was recorded during milling of 16MnCr5. Due to artificially introduced, though realistic anomalies in the workpiece the dataset can be ap-plied for anomaly detection. By using a convolutional autoencoder as a first model good results in detecting the location of the anomalies in the workpiece were achieved. Furthermore, milling tools with two different diameters where used which led to a dataset eligible for transfer learn-ing. The objective of this article is to provide researchers with a real-world time series dataset of the milling process which is suitable for modern machine learning research topics like anomaly detection and transfer learning.

The use of principal components analysis provided information about the main characteristics of teams, based on a set of indicators, instead of displaying individualized information for each of these indicators. In this work we have considered reducing an extensive data matrix to improve interpretation, using the principal components analysis. Subsequently, with new components and with a multiple linear regression, we have carried out a comparative analysis between the best and bottom teams of LaLiga. The sample consisted of the matches corresponding to the 2015/16, 2016/17 and 2017/18 seasons. The results showed that the best teams were characterized and differentiated from bottom teams in the realization of a greater number of successful passes and in the execution of a greater number of dynamic offensive transitions. The bottom teams were characterized by executing more defensive than offensive actions and showing a fewer number of goals, a greater ball possession time in the final third of the field. Goals, ball possession time in the final third of the field, number of effective shots and crosses are the main performance factors that influence the offensive success of football. This information allows us to increase knowledge about the key performance indicators in football.

The aim of this research work was to provide model for predicting stock volatility in Nigeria Stock market. To achieve this, monthly data for Nigerian stock exchange, Exchange rate, Share index and inflation rate was collected for a period of January 1990 to December 2016.The descriptive statistics revealed these variables to exhibit volatility as a characteristics of financial time –varying series. DCC Model was fitted, were the coefficients for all the parameters and that of the correlation-Targeting (rho_21) are both negative and positive and tend very close to 1 and -1, indicating that high persistence in the conditional variances. The Model DCC, satisfied the properties of a good model of conditional mean and variance of the confidential Interval (C.I) of 1 and -1, that is, the conditional variances are finites and their series are strictly stationary. This therefore implies that the Nigerian Stock Exchange, Exchange rate, share index and Inflation rate will experience a non-steady shock in the Stock market. However Each of these variables have different length of recovery (volatility half- life) ranging from 1.5month, 6.5months, 6months to 2,4months for stock exchange, exchange rate, share index and inflation rate respectively. By implication, the volatility of these variables had a long memory, persistence and mean-reverting.

This work presents a novel approach to construct surrogate models of parametric Differential Algebraic Equations based on a tensor representation of the solutions. The procedure consists in building simultaneously, for every output of the reference model, an approximation given in tensor-train format. A parsimonious exploration of the parameter space coupled with a compact data representation allows to alleviate the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

We propose a new Mamdani fuzzy rule-based system in which the fuzzy sets in the antecedents and consequents are assigned in a discrete set of points and approximated by using the extended inverse fuzzy transforms, whose components are calculated by verifying that the dataset is sufficiently dense with respect to the uniform fuzzy partition. We test our system in the problem of spatial analysis consisting in the evaluation of the liveability of residential housings in all the municipalities of the district of Naples (Italy). Comparisons are done with the results obtained by using trapezoidal fuzzy numbers in the fuzzy rules.

This paper provides the first-time ever analytic modelling for Pointwise Stationary Fluid Flow Approximation(PSFFA) model of the non-stationary

There is immense variability in the postharvest quality of Hass avocados. However, there is a lack of knowledge to guaranteeing the robustness of fruit with consistent quality. The aims of this work were to develop a multivariate methodology for evaluating the postharvest quality of avocado and to determine predictive quality markers to manage fruit quality. Fruit samples produced under different nutrient management, elevation, date-to-harvest, and growing-cycle conditions were analyzed. The results highlighted soil and weather differences among orchards. Nutrient management practices based on index balancing in some samples increased both productivity and the fruit size. High variability was observed in the dry matter related to the age of the fruit at harvest. Ripening heterogeneity was very large in low-elevation orchards where the fruit was picked relatively early. High flesh mineral contents delayed fruit ripening. At low growing temperatures, more oleic and linoleic acids were present in fruits. The sensory texture and taste descriptors were affected by the fruit age and related to the flesh composition. Logistic, PLS-DA, and biplot models effectively represented the variabilities in the ripening pattern, composition, and sensory profile of avocado fruits and allowed the samples to be grouped according to the internal fruit quality.

We construct a novel family of summation-integral type hybrid operators in terms of shape parameter $\alpha\in \lbrack 0,1]$ in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre's K-functional, Lipschitz class, and second-order modulus of smoothness.

This letter aims to show the connection between the sinc approximation for high-energy absorption cross section and the shadow radius of the spherically symmetric black hole. This connection can give a physical interpretation of the absorption cross section in the eikonal limit parameters. Moreover, the use of this alternative way, one can extract its shadow radius from the absorption cross section in high energy limits to gain more information about the black hole spacetime. Our results indicate that the increasing the value of the shadow radius of the black hole, exponentially increase the the absorption cross section of the black hole in high-energy limits which can be captured by the Event Horizon Telescope (EHT) collaboration.

Non-neural Machine Learning (ML) and Deep Learning (DL) are used to predict system failures in industrial maintenance. However, only a few studies have assessed the effect of varying the amount of past data used to make a prediction and the extension in the future of the forecast. This study evaluates the impact of the size of the reading window and of the prediction window on the performances of models trained to forecast failures in three data sets of (1) an industrial wrapping machine working in discrete sessions, (2) an industrial blood refrigerator working continuously and (3) a nitrogen generator working continuously. A binary classification task assigns the positive label to the prediction window based on the probability of a failure to occur in such an interval. Six algorithms (logistic regression, random forest, support vector machine, LSTM, ConvLSTM and Transformers) are compared using multivariate time series. The dimension of the prediction windows plays a crucial role and the results highlight the effectiveness of DL approaches in classifying data with diverse time-dependent patterns preceding a failure and the effectiveness of ML approaches in classifying similar and repetitive patterns preceding a failure.

To detect aberrant human behaviors from large volume of passive data collected by smartphones in real time, we propose an online anomaly detection method using Hotelling’s T-squared test. The test statistic is a weighted average, with more weight on the between-individual component when there are little data available for the individual and more weight on the within-individual component when the data are adequate. The algorithm takes only O(1) run time in each update and the required memory usage is fixed after a pre-specified number of updates. The performance of the proposed method, in terms of accuracy, sensitivity and specificity, is consistently better than or equal to the offline method that it builds upon depending on the sample size of the individual data.

High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through Classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g. data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders / number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener-Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions.

Optinalysis, as a method of symmetry detection, is a new algorithm that intrametrically (within elements or variables) or intermetrically (between elements or variables) computes and compares two or more univariate or multi-clustered or multivariate sequences as a mirror-like reflection of each other (optics-like manner), hence the name is driven. Optinalysis is based by the principles of reflection and moment about a symmetrical line which detects symmetry that reflects a similarity measurement. This proposed methodology was validated in comparison with Pearson method of skewness detection, and also with some algorithms for pairewise alignment and comparison of genomic sequences (Needle, Stretcher, Water, Matcher) on EMBL-EBI website. A results comparison shows that optinalysis is more advance, more sensitive, more inferential and simple alternative approach of skewness detection and pairewise sequence comparison.

We study L_2-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters $\ga_j$ and $\az_j$ for $j=1,\,2,\dots,\,d$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the exponential convergence-(t,s)-weak tractability (EC-(t,s)-WT) of these L_2-approximation problems under the absolute or normalized error criterion. In particular, we obtain the sufficient and necessary conditions for EC-(1,1)-WT and EC-(t,1)-WT with t

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

4-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded, hence the symmetry between electronic and positronic solutions is not considered. These states are however needed in QED calculations, where furthermore charge conjugation symmetry becomes an issue. In this work we shall discuss the realization of charge conjugation symmetry of the Dirac equation in a central field within the finite basis approximation. Three schemes for basis set construction are considered: restricted, inverse and dual kinetic balance. We find that charge conjugation symmetry can be realized within the restricted and inverse kinetic balance prescriptions, but only with a special form of basis functions that does not obey the right boundary conditions of the radial wavefunctions. The dual kinetic balance prescription is on the other hand compatible with charge conjugation symmetry without restricting the form of the radial basis functions. However, since charge conjugation relates solutions of opposite value of the quantum number κ, this requires the use of basis sets chosen according to total angular momentum j rather than orbital angular momentum ` . As a special case, we consider the free-particle Dirac equation, where the solutions of opposite sign of energy are related by charge conjugation symmetry. We note that there is additional symmetry in those solutions of the same value of κ come in pairs of opposite energy.

The purpose of this paper is to prove strong convergent theorems for Browder's type iterations and Halpern's type iterations of a family of nonexpansive mappings in a complete geodesic space with curvature bounded above by a positive number. Moudafi's viscosity type methods are also discussed without the nice projection property.

This paper deals with bistatic subsurface probing of a horizontally layered dielectric half-space by means of ultra-wideband electromagnetic pulses. A receiver collects reflections from the air-ground interface and from the gradients of dielectric permittivity in the half-space. This scenario is of interest for ground penetrating radar (GPR) applications. For the analytical description of the received signal, we developed and implemented a novel time-domain version of the coupled-wave Wentzel–Kramers–Brillouin approximation. Our solution is in very good agreement with finite-difference time-domain results, radically accelerates calculations, and effectively accounts for the protracted return signals observed in the lower part of the GPR spectrum. The paper includes results showing the application of the proposed technique to two case studies: in particular, the method was employed for the post-processing of experimental radargrams collected on Lake Chebarkul, in Russia, and to simulate GPR probing of the Moon surface, to detect smooth gradients of the dielectric permittivity in lunar regolith.

This article presents a harmonic analysis of the stator currents of a squirrel-cage in-15 duction motor fed by a voltage source inverter with PWM space vector control (SV-PWM). The 16 influence of PWM switching frequency and dead time (dead-band) of controlled transistors on 17 THD and electromagnetic torque ripple is shown. The aim is to determine the lowest switching 18 frequency of the transistors for which the drive will operate correctly. Characteristics were de-19 termined as functions in the form of THD ( ), where the least square approximation was 20 used for stator current measurements when the PWM switching frequency is changed. The ap-21 proximations were realized for simulation and experimental results. To clarify the results, the 22 operation of hardware PWM circuits in microcontrollers was analyzed.

A tunable quantum cascade laser (QCL) spectrometer was used to develop methods for detecting and quantifying high explosives (HE) in soil based on multivariate analysis (MVA) and artificial intelligence (AI). For quantification, mixes of 2,4-dinitrotoluene (2,4-DNT) with concentrations from 0% to 20% w/w were investigated using three types of soils: bentonite, synthetic soil, and natural soil. A Partial least squares regression model was generated for predicting 2,4-DNT concentrations. To increase its selectivity, the model was trained and evaluated using additional analytes as interferences, including other HEs such as PETN, RDX, and TNT and non-explosives such as benzoic acid and ibuprofen. For detection, mixes of different explosives in soils were used to implement two AI strategies. In the first strategy, the spectra of the samples were compared with those of soils recorded in a database to identify the most similar soils based on QCL spectroscopy. Next, a Classical Least Squares preprocessing (Pre-CLS) was applied to soils spectra selected from the database. The parameter obtained based on the sum of the weights of Pre-CLS was then used to generate a simple binary discrimination model for distinguishing between contaminated and uncontaminated soils, achieving an accuracy of 0.877. In the second AI strategy, the same parameter was added to a principal component matrix obtained from spectral data of samples and used to generate multi-classification models based on different machine learning algorithms. A Random Forest model worked best with 0.997 accuracy and allowing to distinguish between soils contaminated with DNT, TNT, or RDX and uncontaminated soils.

Partial Information Decompositions (PIDs) aim to categorize how a set of source variables provide information about a target variable redundantly, uniquely, or synergetically. The original proposal for such an analysis used a lattice-based approach and gained significant attention. However, finding a suitable underlying decomposition measure is still an open research question, even at an arbitrary number of discrete random variables. This work proposes a solution to this case with a non-negative PID that satisfies an inclusion-exclusion relation for any f-information measure. The decomposition is constructed from a pointwise perspective of the target variable to take advantage of the equivalence between the Blackwell and zonogon order in this setting. The zonogons correspond to the Neyman-Pearson region for an indicator variable of one target state and f-information is the expected value of quantifying its boundary. We prove that the decomposition satisfies the axioms of the original decomposition framework and guarantees non-negative partial information results. We highlight that our decomposition behaves differently depending on the used information measure, which can be utilized for different applications. We additionally show how our proposal can be used to obtain a non-negative decomposition of Rényi-information at a transformed inclusion-exclusion relation, and for tracing partial information flows through Markov chains.

Energy distance is used to eigenvalue distributions in this new Wishart distribution study, providing a new perspective on high-dimensional data. Multivariate statistics relies on Wishart distribution to explain covariance matrices. This analysis shows how degrees of freedom and covariance matrix configurations affect eigenvalue dispersion. We use energy distance based on eigenvalue distributions to assess Wishart distribution differences without the "curse of dimensionality" via extensive simulation simulations. This approach improves measurement accuracy and processing efficiency in distribution comparisons and enables new analytical pathways in scientific fields that need data covariance comprehension. Our results show that degrees of freedom and matrix structure considerably affect energy distances, expanding the theoretical framework and practical applications of statistical models.

In the paper we present a new test for comparison of the means of multivariate samples with unknown distributions. The test is based on the comparison of the distributions of the distances between the samples’ elements and their means using univariate two-sample Kolmogorov-Smirnov test. The activity of the suggested method is illustrated by numerical analysis of the real-world and simulated data.

Paving blocks are concrete pieces placed in exposed places to the weather, which are sub-jected to loads and wear. Hence, quality control in the manufacture of paving blocks is es-sential to guarantee the properties and durability of the product in construction projects. In Ecuador, the requirements are described in the Ecuadorian technical standard "NTE INEN 3040", and tensile splitting strength is a fundamental requirement to guarantee product quality. It is analyzed using quality control measurements such as dimensions, the weight of the fresh paving block in the vibro-compacted process, and the percentage of water absorption in order to know how the variables influence and manage to predict the tensile splitting strength to avoid product non-conformity in advance, having a timely and better control of the manufacturing process. The data was obtained from a company that can produce 30 000 units per day of rectangular paving blocks with 6 cm thickness. Mul-tivariate models such as multiple linear regression, regression trees, random forests and neural networks are performed to predict the tensile splitting strength variable through two groups of predictors; the first group is the thickness mm, width mm, length mm, mass of fresh paving block g and percentage of water absorption %. The second group of pre-dictor variables is the density of the fresh paving block kg/m3 and the percentage of water absorption %. It is concluded that the multiple linear regression method performs better in predicting the first group of predictor variables with a mean square error (MSE) of 0.110086, followed by the neural network without hidden layers resulting in an MSE of 0.112198. The best method for the second set of predictors was the neural network with-out hidden layers with a mean square error ( MSE ) of 0.112402, closely followed by the multiple linear regression model with an MSE of 0.115044.

We have used Mass Multivariate Method on structural, resting state and task related fMRI data from two groups of patients with schizophrenia and depression, respectively, in order to define several regions of significant relevance to the differential diagnosis between those conditions. The regions included the left Planum polare, Left opercular part of the inferior frontal gyrus (OpIFG), Medial orbital gyrus (MOrG), Posterior Insula (PIns), and Parahippocampal gyrus (PHG). This study delivers evidence that multimodal neuroimaging approach can potentially enhance the validity of psychiatric diagnosis. Either structural, or resting state or task related functional MRI modality cannot provide independent biomarkers. Further studies need to consider and implement a model of incremental validity to combine clinical measures with different neuroimaging modalities to discriminate depressive disorders from schizophrenia. Biological signatures of disease on the level of neuroimaging are more likely to underpin broader nosological entities in psychiatry.

Soccer is the leading cause of all sports-related ocular injuries in Europe and Israel and leads to blindness at a disproportionately high rate, especially among children (Thompson et al., 2019). With soccer being the most popular sport in the world, it is surprising the only solution to ocular injuries are sports glasses which can cause direct damage to the eye and impair peripheral vision by 15%, calling for an alternative (Smith & Jones, 2020). This work, based on an imported facial model, focuses on both the qualitative and quantitative aspects of building a personalized, low-cost (through optimizing material needed), superior apparatus to conventional sports glasses. The quantitative side examines a modified and model-validated (through a SRS of thirty unique extrapolated points) multivariate linear regression equation, based on horizontal and vertical rotation angles (n=60) trained with residual and computer simulation data, that can accurately extrapolate and quantify ocular impact from all horizontal and vertical rotation angles and a modified Hertzian Contact Stress Equation to determine the thickness of the apparatus using the elasticity modulus, impact force, and geometrical facial and soccer-ball features. The qualitative side examines where firstly, ocular impact is most prevalent, and secondly, where most impact is seen from rotating the ball horizontally and vertically through analysis of Pearson’s Correlation Coefficient at the supraorbital, medial canthus, infraorbital, and lateral canthus regions from both regression equations as well as a cost-benefit analysis for comparison with conventional sports glasses. The findings discovered in this work lay the groundwork for future research to build a customized low-cost ocular injury prevention device which can simultaneously ensure complete ocular safety while enhancing athletic performance for over 250,000,000 players (Johnson & Garcia, 2022).

In this paper, we study a differential operator of parabolic type with a variable and unbounded coefficient, defined on an infinite strip. Sufficient conditions for the existence and compactness of the resolvent are established, and an estimate for the maximum regularity of solutions of the equation Lu=f∈L_2(Ω) is obtained. Two-sided estimates for the distribution function of approximation numbers are obtained. As is known, estimates of approximation numbers show the rate of best approximation of the resolvent of an operator by finite-dimensional operators. The paper proves the assertion about the existence of positive eigenvalues among the eigenvalues of the given operator and finds two-sided estimates for them.

Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon’s equation. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. The Part two deals with the Stress Energy tensor quantum, wherein the detail I linearized gravity of Einstein equation, and wherein I develop the tensor quantum energy pulse from the equivalence of equation einstein the linearized gravity and the Schrödinger equation relativistic described by Klein-Gordon’s equation.

This paper presents the light scattering matrices of atmospheric aggregated hexagonal ice particles appearing in cirrus clouds. In this work aggregates consist of the same particles with different spatial orientation and number of these particles. Two types of particle shape were studied: (1) hexagonal column; (2) hexagonal plate. For both shapes we study compact and non-compact cases of arrangement of particles in aggregates. As a result, four sets of aggregates were made: (1) compact columns; (2) non-compact columns; (3) compact plates; (4) non-compact plates. Each set consists of eight aggregates with different number of particles from 2 to 9. For practical reason the bullet-rosette and the aggregate of hexagonal columns with different sizes was also calculated. The light scattering matrices were calculated for the case of arbitrary spatial orientation within the geometrical optics approximation for sets of compact and non-compact aggregates and within the physical optics approximation for two additional aggregates. It was found that light scattering matrix elements for aggregates are depend on arrangement of particles they are consisted.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

A complete MAPLE procedure is designed to implement effectively an algorithm for approximating the trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval-polynomial as its output that we can easily explore in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both of rational and irrational arguments as well as drawing the graph of the piecewise approximate functions will be presented. Moreover, from the approximate integration of integrands of the form $x^m\sin x$ on $[a,b]$, another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best $L^2$-approximation of the sine function in the vector space $\mathcal{P}_{\ell}$ of polynomials of degree at most $\ell$, a subspace of $L^2(a,b)$.

Grinding processes’ stochastic nature poses a challenge in predicting the quality of the resulting surfaces. Post-production measurements for form, surface roughness, and circumferential waviness are commonly performed due to infeasibility in measuring all quality parameters during the grinding operation. Therefore, it is challenging to diagnose the root cause of quality deviations in real-time resulting from variations in the machine’s operating condition. This paper introduces a novel approach to predicting the overall quality of the individual parts. The grinder is equipped with sensors to implement condition-based maintenance and is induced with five frequently occurring failure conditions for the experimental test runs. The crucial quality parameters are measured for the produced parts. Fuzzy c-means (FCM) and Hotelling’s T-squared (T2) have been evaluated to generate quality labels from the multi-variate quality data. Benchmarked random forest regression models are trained using fault diagnosis feature set and quality labels. Quality labels from the T2 statistic of quality parameters are preferred over FCM approach for their repeatability. The model, trained from T2 labels achieves more than 94% accuracy when compared to the measured ring disposition. The predicted overall quality using the sensors’ feature set is compared against the threshold to reach a trustworthy maintenance decision.

The global financial crisis of 2008, triggered by the collapse of Lehman Brothers, highlighted a banking system that was widely exposed to systemic risk. The minimization of the systemic risk via a close and detailed monitoring of the entire banking network became a priority. This is a complex and demanding task considering the size of the banking systems: in the US and the EU they include more than 10000 institutions. In this paper, we introduce a methodology which identifies a subset of banks that can: a) efficiently represent the behavior of the whole banking system and b) provide, in the case of a failure, a plausible range of the crisis dispersion. The proposed methodology can be used by the regulators as an auxiliary monitoring tool, to identify groups of banks that are potentially in distress and try to swiftly remedy their problems and minimize the propagation of the crisis by restricting contagion. This methodology is based on Graph Theory and more specifically Complex Networks. We termed this setting a “multivariate Threshold – Minimum Dominating Set” (mT–MDS) and it is an extension of the Threshold – Minimum Dominating Set methodology (Gogas e.a., 2016). The method was tested on a dataset of 570 U.S. banks: 429 solvent and 141 failed ones. The variables used to create the networks are: the total interest expense, the total interest income, the tier 1 (core) risk-based capital and the total assets. The empirical results reveal that the proposed methodology can be successfully employed as an auxiliary tool for the efficient supervision of a large banking network.

In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

Due to their contribution to human health, the production of healthy snacks has garnered the attention of both the scientific community and the food industry. This study was conducted to determine the suitability of frying and baking processing methods for producing green banana chips using two varieties: Barraganete and Dominico. The aim was to identify a treatment geared towards producing healthy snacks. Initially, the physicochemical properties of the raw materials were analyzed, revealing significant differences in starch, fat, fiber, and protein content. Subsequently, the bananas were processed into baked and fried chips. Multivariate statistical techniques such as ANCOVA, MANOVA, and post-hoc tests were applied to examine the influence of initial characteristics and detect variations attributable to the cooking method. The main findings showed that the initial protein level had a significant covariate effect on the final content in the chips. The Dominico variety generally proved more suitable for making baked chips, retaining higher percentages of protein, starch, fiber, and lower fat content than Barraganete. Baked chips showed significantly lower sodium and fat values than fried ones when differentiated by processing method. The "Dominico + Baked" treatment emerged as the superior alternative, with favourable levels of protein, starch, and low sodium and fat, positioning it as the most suitable for producing a healthy snack.

The development of new turbomachinery designs requires numerous time-consuming and computationally intensive computational fluid dynamics (CFD) calculations. However, most of the generated high spatial resolution data remains unused at later development steps. That is also the case with automated optimization processes that use only a few integral values to determine objectives and constraints. Therefore the development of a data-driven AI model was initiated to ensure the potential of further use of the CFD data which is also used to train the AI model. The presented method subsequently provides a fast approximation of the 3D flow for new designs. In this paper, the structure of the developed AI model is presented and the approximation quality is analysed using a complex, state-of-the-art compressor test case. It is shown that the AI model can reproduce many characteristics of the 3D flow of new designs, and performance measures such as efficiency can be derived from these flow predictions. In addition, the complex test case revealed that greater design variation reduces the AI approximation quality which can lead to undesirable exploratory behaviour in an optimisation setup. Overall, the test case has shown promising results and has provided hints for further improvements of the AI model.

Elucidating physicochemical processes in the degradation of pollutants may optimize their removal from water sources. This work presents a set of elementary steps in the photocatalytic degradation of carbamazepine (CBZ), assuming a steady state approximation in an Advanced Oxidation Process (AOP) combining short-wave ultraviolet radiation (UVC), homogeneous reagent (H₂O₂) and heterogeneous (TiO₂) catalyst. Elementary steps include excitation of both reagent/catalysts by UVC photons, adsorption of CBZ on the excited TiO₂, or its oxidation by hydroxyl radicals. Assuming the steady state approximation on the intermediate products (excited TiO₂, CBZ- excited TiO₂ complex, and hydroxyl radicals), leads to rate laws for degradation of CBZ, in which UVC radiation, TiO₂, and H₂O₂ are pseudo first order at all concentrations or intensities having no direct influence on CBZ pseudo-order, whereas CBZ shifts from pseudo first order at low concentrations to pseudo-zero order at high concentrations. Several experiments to test the mechanism were conducted, by varying CBZ, H₂O₂, and TiO₂ concentrations, and UVC radiation intensities. Measured results indeed fit the suggested mechanism for the first three, but irradiation intensity appears to shift CBZ influence from pseudo-second to pseudo-first order with increased intensities. Corrected elementary steps are proposed to fit the results.

Up-conversion nanoparticles (UCNP) under near-infrared (NIR) light irradiation have been well investigated in the field of bio-imaging. However, the low up-conversion luminescence (UCL) intensity limits applications. Plasmatic modulation has been proposed as an effective tool to adjust the luminescence intensity and lifetime. In this study discrete dipole approximation (DDA) was explored concerning guiding the design of UCNP@mSiO2-Au structures with enhanced UCL intensity. The extinction effects of gold shells could be changed by adjusting the distance between the UCNPs and the Au NPs by synthesized tunable mesoporous silica (mSiO2) spacers. Enhanced UCL was obtained under 808 nm irradiation. Theoretical predictions could not be demonstrated to full extend by experimental data, indicating that better models for simulation need to better take into account inhomogeneities in particle morphologies.

In this work, a novel approach is presented for the multivariate prediction of hydrological variables, employing a specialized type of recurrent neural network (RNN) known as the long-term memory network (LSTM).The central objective is to develop a flood prediction model using data collected from two hydrological stations situated along the Atrato River in the Choc´o Department, Colombia. The interconnected variables of water level, water flow, and water precipitation are analyzed in this model to enhance flood prediction accuracy. The LSTM model, integrated into an RNN structure, is designed to capture the complex dynamics and cross-correlations inherent in these hydrological variables. Validation involves a comparison with linear and nonlinear Nonlinear AutoRegressive with eXogenous input (NARX) models, considering factors such as estimation error and computational time. Additionally, the study conducts further analysis for water level prediction under two scenarios: utilizing only outflow and inflow measurements or predicting outflow alongside measuring inflow, with the objective of utilizing the proposed approach as a flood early warning system. † This article is a revised and expanded version of a paper entitled Multivariable NARX based Neural Networks Models for Short-term Water Level Forecasting, which was presented at International Conference on Time Series and Forecasting (ITISE-2023), Gran Canaria, Spain, 12th-14th July, 2023.

The study analyzed Ecuador's presence in the Web of Science (WoS) post-pandemic from a multivariate dynamic, highlighting a significant transformation in scientific communication towards open access (OA). The methodology integrated multivariate statistical techniques, using R and specialized tools, to process 9,085 relevant articles, 52% of the Ecuadorian publications in WoS between 2019 and 2021 were open access. This movement reflects a commitment to quality research and accessibility, showing an increase in publications and citations under OA. The research underscores the importance of establishing robust national OA policies in Ecuador to promote scientific collaboration and an equitable distribution of knowledge. Despite funding challenges and the lack of specific regulations, educational institutions in Ecuador have maintained a constant scientific output, adapting to the global environment and the demand for transparent information. The study concludes that there is an urgent need for a holistic approach to OA in the country, recognizing the progress made despite the difficulties.

Time series (TS)-based predictions are made by examining the behaviour of historical data to forecast future values. Multiple industries; such as stock market trading, power load forecasting, medical monitoring, and intrusion detection; frequently use it. Several variables; such as the performance of other markets as well as the economic situation of a country which affect its market performance; significantly affect the prediction of stock market prices. Therefore, this present study uses numerous variables; such as the opening, lowest, highest, and closing prices; to predict the indices of the stock market of the Kingdom of Saudi Arabia (KSA). Successfully accomplishing an investment goal largely depends on choosing the right stocks to buy, sell, or maintain. The project's output is the projected closing prices (regression) over the next seven days, which helps investors make the best decisions. This present study used exponential smoothing (ES) to remove noise from the input data obtained from the Saudi Stock Exchange, or Tadawul, before using a multivariate long short-term memory (LSTM) deep learning (DL) algorithm to forecast stock market prices. The proposed multivariate LSTMDL model had satisfactory prediction rates of 97.49% and 92.19% for the univariate model. Therefore, it can be used to effectively predict stock market prices. The results also indicate that DL as well as multiple sources of information can be used to accurately predict stock markets.

Despite the wide variety of variables commonly applied to measure different aspects of rehabilitation, the assessment and subsequent definition of indicators of environmental rehabilitation status are not simple tasks. The main challenges are comparing rehabilitated sites with target ecosystems as well as integrating individual environmental and eventually collinear variables into a single tractable measure of the state of a system before effective indicators that track rehabilitation may be modeled. For that, a consensus is lacking regarding which and how many variables need to be surveyed. Our approach considered ecological processes, vegetation structure, and community diversity from nonrehabilitated, rehabilitating and reference sites. We applied this approach to a curated set of 32 environmental variables retrieved from nonrevegetated, rehabilitating and reference sites associated with iron ore mines from the Urucum Massif, Mato Grosso do Sul, Brazil. By integrating variables from a single attribute or the entire set of variables into a single estimation of rehabilitation status, the proposed multivariate approach is straightforward and able to adequately address collinearity among variables. The proposed approach allows for the identification of biases towards single variables, surveys or analyses, which is necessary to rank environmental variables regarding their importance to the assessment. Furthermore, we show that bootstrapping permitted the detection of the minimum number of environmental variables necessary to achieve reliable estimations of the rehabilitation status. Finally, we show that the proposed variable integration enables the definition of environmental indicators for more comprehensive monitoring of mineland rehabilitation. Thus, the proposed multivariate ordination represents a powerful tool to outline the benefits of rehabilitating sites for the maintenance of biodiversity and ecosystem functions and services provided that sufficient environmental variables related to ecological processes, diversity and vegetation structure are gathered from nonrehabilitated, rehabilitating and reference study sites. By identifying deviations from predicted rehabilitation trajectories and providing assessments for environmental agencies, this proposed multivariate ordination increases the effectiveness of (mineland) rehabilitation.

Durum wheat is an important staple food used to obtain several products. At first the wheat is milled to obtain different products: bran, semolina and flour. These products are the base of several artifacts with varying properties both from a nutritional point of view and flavoring characteristics. It is known that most elements concentrate in the outer layers of the wheat seed (pericarp and aleurone) so that the content of the elements vary a lot in the ground products. The present study investigates the characterizing elements of the milled products and the effect of cultivation protocol applied. We measured, by ICP-OES, the concentration of 28 elements in the whole seed and in any grinding products; the results show that only few elements characterize each product. Few elements, but different for each product, permit to disclose the kind of agri-cultural method used: organic or conventional protocol. Five elements: B, Cd, Cu, K, Se, are the most important to distinguish between organic and conventional agriculture by PCA and PLS analysis; these elements also permit some differentiation of products.

The utilization for water resource has been of great concern to human life. To assess the natural water system in Kangding County, the integrated methods of hydrochemcial analysis, multivariate statistics and geochemical modelling were conducted on surface water, groundwater and thermal water samples. Surface water and groundwater were dominated by Ca-HCO₃ type, while thermal water belonged to Ca-HCO₃ and Na-Cl type. The analyzing results concluded the driving factors that affect hydrochemical components. Following the results of the combined assessments, hydrochemcial process was controlled by the dissolution of carbonate and silicate minerals with slight influence from anthropogenic activity. The mixing model of groundwater and thermal water was calculated using silica-enthalpy method, yielding cold-water fraction of 0.56-0.79 and estimated reservoir temperature of 130-199 ^oC, respectively. δD and δ¹⁸O isotopes suggested surface water, groundwater and thermal springs were of meteoric origin. Thermal water should have deep circulation through the Xianshuihe fault zone, while groundwater flows through secondary fractures where it recharges with thermal water. Those analytical results were used to construct a hydrological conceptual model, providing a better understanding of the natural water system in Kangding County.

Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric) nature of averaging. The original concept of PMA was motivated by the practice of matrix population models as a tool to assess the population viability from long-term monitoring data. The task has reduced to searching for an approximate solution to an overdetermined system of polynomial equations for unknown elements of the average matrix (G), hence to a nonlinear constrained minimization problem for the matrix norm. Former practical solutions faced certain technical problems, which required sophisticated algorithms but returned acceptable estimates. Fresh idea to use the eigenvalue approximation ensues also from the basic equation of averaging, which determines the exact value of λ1(G), the dominant eigenvalue of matrix G, too, and the corre-sponding eigenvector. These are bound by the well-known linear equations, which reduce the task to a standard problem of linear programing (LP). The LP approach is realized for 13 fixed-pattern matrices gained in a case study of Androsace albana, an alpine short-lived perennial, monitored on permanent plots during 14 years. A standard software routine reveals the unique exact solution, rather than an approximate one, to the PMA problem, which turns the LP approach into ‘’the best of versatile optimization tools”. The exact solution turns out to be peculiar in reaching zero bounds for certain nonnegative entries of G, which deserves a modified problem formulation separating the lower bounds from zero.

Intrusion detection is generally carried out by matching network traffic patterns with known attack patterns or by identifying abnormal network traffic patterns. One statistical methodological approach used in intrusion detection is Statistical Process Control (SPC) by constructing a control chart. Hotelling’s T2 control chart is a multivariate control chart commonly used to monitor the mean process. The performance of the T2 chart in monitoring mean shifts can be increased if a robust estimator is utilized. Based on previous research, T2 based on the Fast-MCD estimator has good performance in monitoring low to medium outlier contaminated data. Therefore, the MRCD estimator can be used to detect intrusion. On the other hand, this research focuses on developing a bootstrap-based robust Hotelling’s T2 charts with Fast-MCD and MRCD estimators for evaluating performance in detecting intrusion on intrusion detection datasets. Based application of UNSW-NB15, the proposed chart has better performance than the conventional T2 and Fast-MCD-based T2 despite the longer execution time.

Recent work on heavy metal pollution in Manila Bay suggests elevated concentration in the surface sediments. It is critical to identify the sources of these heavy metals to effectively rehabilitate the bay. Our study investigated the sources of the heavy metal pollution that ended up in Manila Bay and the risks associated with these toxic metals based on a recent survey conducted. Surface sediment samples with higher heavy metal concentrations were found in the upper to middle parts of the bay while lower concentrations were in the southeast areas. Multivariate analyses such as hierarchical cluster analysis (HCA), principal component analysis (PCA), and Pearson correlation analysis were used to identify the sources of the heavy metals. The heavy metal pollution in Manila Bay is attributed to several rivers draining northeast of Manila Bay, particularly the Marilao-Meycauayan-Obando River System (MMORS) which is cited as one of the 30 dirtiest river systems in the world. The ecological risks associated with heavy metals in the sediments found higher incidences of toxicity in north and middle parts of Manila Bay. Cu and Cr posed the highest risks of toxicities than any other heavy metals. Based on our analysis, the counterclockwise water gyre of the bay can explain the distribution and ecological risks associated with the heavy metals as supported by the findings of the PCA. Given the high priority by the Philippine government to rehabilitate the bay, our study strongly shows that efforts to restore the ecological status of Manila Bay will only succeed if the pollution from major rivers draining to it will be properly addressed.

In this paper we describe a nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions. Given $N$ independent observations, convexity theory shows that the NPML estimator is discrete with at most $N$ support points. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. The probability of the support points is found by a Primal-Dual Interior-Point method; the location of the support points is found by an Adaptive Grid method. Our method is able to handle high-dimensional and complex multivariate mixture models.An important application is discussed for the problem of population pharmacokinetics and a non-trivial example is treated.Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics.

This study assessed farmers’ perception of climate change, estimated the determinants of, and evaluated the relationship among adaptation practices using the multivariate probit model. A survey in 300 agricultural households was carried out covering 10 sample districts considering five agro-ecological zones and a vulnerability index. Four adaptation choices (change in planting date, crop variety, crop type and investment in irrigation) were deemed as outcome variables and socioeconomic, demographic, institutional, farm-level and perceptions variables were deployed as explanatory variables. Their marginal effects were determined for three climatic variables—temperature, precipitation and drought. Age, gender and education of head of household, credit access, farm area, rain-fed farming and tenure, are found to be more influential compared to other factors. All four adaptation-options are found to be complimentary to each other. Importantly, the intensity of impact of dependent variables in different models, and for available adaptation-options, are found to be unequal. Therefore, policy options and support facilities should be devised according to climatic variables and adaptation options to achieve superior results.

The extensive deployment of wireless infrastructure provides a low-cost way to track mobile users in indoor environment. This paper demonstrates a prototype model of an accurate and reliable room location awareness system in a real public environment, where three typical problems arise. First, a massive number of access points (APs) can be sensed leading to a high-dimensional classification problem. Second, heterogeneous devices record different received signal strength (RSS) levels due to the variations in chip-set and antenna attenuation. Third, APs are not necessarily visible in every scanning cycle leading to missing data. This paper presents a probabilistic Wi-Fi fingerprinting method in a hidden Markov model (HMM) framework for mobile user tracking. Considering the spatial correlation of the signal strengths from multiple APs, a Multivariate Gaussian Mixture Model (MVGMM) is fitted to model the probability distribution of RSS measurements in each cell. Furthermore, the unseen property of invisible AP has been investigated in this research, and demonstrated the efficiency of differentiation between cells. The proposed system is able to achieve comparable localization performance. The filed test results present a reliable 97% localization room level accuracy of multiple mobile users in a real university campus WiFi network without any prior knowledge of the environment.

Zero-Knowledge Proofs ZKP provide a reliable option to verify that a claim is true without giving detailed information other than the answer. A classical example is provided by the ZKP based in the Graph Isomorphism problem (GI), where a prover must convince the verifier that he knows an isomorphism between two isomorphic graphs without publishing the bijection. We design a novel ZKP exploiting the NP-hard problem of finding the algebraic ideal of a multivariate polynomial set, and consequently resistant to quantum computer attacks. Since this polynomial set is obtained considering instances of GI, we guarantee that the protocol is at least as secure as the GI based protocol.

Currently, the pesticides are the global core concern because it is a boon to farmers against increasing disease-pest and simultaneously, pesticide residue is the major anxiety regarding human health. For that reason, identification and determination of factors affecting the application of pesticides are essential. To identify and evaluate determinants of pesticides application in Nepal, a household survey of 300 households was carried-out and an empirical analysis was done using multivariate probit model. Moreover, powder and liquid forms of pesticides were considered for summer and winter season in vegetable farming, which was assigned as outcome variables. Likewise, socio-economic, demographic, farm-level and perception data were considered as explanatory variables. Use of chemical fertilizers, age and gender of head of household, household size and access to weather information were found the most influencing factors. Moreover, forms of pesticides and growing seasons were found complementary to each other. Therefore, devising the policy options accordingly should balance needs of farmers and health of consumers.

Currently the majority of studies on vision-based measurement has been conducted under ideal environments so that an adequate measurement performance and accuracy is ensured. However, vision-based systems may face some adverse influencing factors such as illumination change and fog interference, which can affect the measurement accuracy. This paper develops a robust vision-based displacement measurement method which can handle the two common and important adverse factors given above and achieve sensitivity at the subpixel level. The proposed method leverages the advantage of high-resolution imaging incorporating spatial and temporal context aspects. To validate the feasibility, stability and robustness of the proposed method, a series of experiments was conducted on a two-span three-lane bridge in the laboratory. The illumination change and fog interference are simulated experimentally in the laboratory. The results of the proposed method are compared to conventional displacement sensor data and current vision-based method results. It is demonstrated that the proposed method gives better measurement results than the current ones under illumination change and fog interference.

Black ginseng is a type of processed ginseng that is traditionally used as herbal medicine in East Asian countries. It is prepared from fresh, white, or red ginseng by undergoing a process of steaming and drying nine times. However, the chemical differentiation of black ginseng with different processing levels is not well understood. The aim of this study is to propose a new method for discriminating and quantifying black ginseng. Six ginsenosides from black ginseng were accurately quantified, and based on this, the black ginseng samples were divided into uncompleted and completed black ginseng. Ultra-high-performance liquid chromatography-quadrupole-time of flight/mass spectrometry (UPLC-Q-TOF/MS) combined with a multivariate statistical analysis strategy was then employed to differentiate the two groups. A total of 141 ions were selected as analytical markers of black ginseng, with 45 of these markers being annotated by matching precise m/z and MS/MS data from prior studies.

Omega-3 fatty acids (ω-3 FAs) are important fatty acids having the beneficial roles in human health including reducing blood pressure, lowering the risk of cardiovascular disease and exerting anti-inflammation activities. Omega-3 FAs were mainly found in fish oils, therefore, determination of these FAs is very important. This study highlighted the employment of FTIR spectroscopy combined with multivariate data analysis for determination of ω-3 FAs in fish oils. Fish oils were obtained from the extraction of corresponding fishes and subjected to purification. The oils were further subjected to FTIR spectroscopic measurement at mid infrared region (4000-450 cm-1). Fatty acid compositions of ω-3 FAs namely eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) were determined using gas chromatography with flame ionization (GC-FID), and the results from GC-FID were used as actual values. Two multivariate regressions along with wavenumbers regions or their combinations were optimized and compared to provide the best condition for prediction of EPA and DHA in fish oils. The results showed that partial least square regression (PLSR) was suitable for prediction of DHA applying the variable of absorbance values of the second derivative spectra, with the values of coefficient of determination (R2) of 0.9916 and 0.9316 in calibration and validation models, respectively. The values of root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) obtained were 0.789 and 2.53. While, prediction of EPA was performed using principal component regression with R2 value of &gt; 0.72 and low values of RMSEC and RMSEC. It can be concluded that the combination of FTIR spectra and multivariate regression provides the effective tools and alternative GC-FID method for the prediction of EPA and DHA in fish oils.

Abstract Women victims of abuse can suffer neuropsychological sequelae that affect memory and attention, as well psychopathological disorders such as depression. These consequences affect their daily life and physical and psychological health. Objective: To analyze sequelae that affect attention and memory, as well a possible association of these sequelae to depression. Method: A total of 68 women victims of gender-based violence participated in the study. The participants were between 15 and 62 years of age and resided in Spain at the time of data collection. The Luria DNA Battery (Neuropsychological Diagnosis of Adults) by Manga and Ramos (2000); and the Beck Depression Inventory were applied. Results: Women victims of gender-based violence suffer neuropsychological sequelae, presenting low short-term memory and attentional control; and score low on the Luria-DNA battery. Of these women, 60% suffer from some relevant type of depression, and there are significant differences according to their degree of memory. Through the HJ-Biplot, a direct relationship was found between memory and attentional control with the total score of the Luria battery. On the other hand, an inverse relationship was found between short-term memory and depression. Lastly, three well-differentiated gender clusters of women victims of gender-based violence were identified. Conclusions: A lower rate of depression is observed in women victims of abuse when they have a more intact short-term memory.

Background: High blood pressure (BP) has been implicated as a major risk factor for cardiovascular diseases in several global populations, including in individuals of African ancestry. Despite the elevated burden of high BP-induced cardiovascular diseases in Africa and other global populations with African ancestry, limited genetic studies have been carried out to explore the genetic machinery driving this phenomenon. Methods: We performed univariate and multivariate analyses using Genome-wide association studies (GWAS) and summary statistics data of 77,850 individuals of African ancestry for systolic (SBP) and diastolic blood pressure (DBP) traits. The six independent cohorts used included individuals derived from the African Partnership for Chronic Disease Research (APCDR), the UK Biobank, and the Million Veteran Program (MVP). Subsequently, we annotated, prioritized, visualized, and interpreted our meta-analyses results using FUMA, to gain further insight into the molecular mechanism(s) that contribute to the genetics of BP traits. Finally, loci attaining genome-wide significance, GWS (p<5x10-8) were also followed up with Bayesian fine-mapping to identify potential causal variants. Results: Our meta-analyses altogether identified 350 GWAS SNPs for SBP (166 SNPs) and DBP (184 SNPs, including two novel loci) whilst our multivariate GWAS method identified 166 SNPs (including three novel loci). Interestingly, in FUMA there was significant tissue enrichment of up-regulated differentially expressed genes (DEGs) in the sigmoid and transverse colon for SBP, as well as 10 significant gene sets from MAGMA gene set analyses, However, for DBP, no significant DEGs nor gene sets in MAGMA were found; instead, in DBP for gene property analysis for tissue specificity nine candidates were found to be significant and all nine were in different brain regions. Finally, Bayesian fine-mapping revealed that only 11 variants from the lead SNPs had >50% posterior probability (PP) of being causal and they included novel variant rs562545 (MOBP, PP = 77%) and 10 other previously published variants. Conclusion: Our results demonstrate the importance of performing GWAS in large sample sizes of global populations of African ancestry, including continental Africans; which yield novel insights, from novel loci to novel pathways/tissue expression candidates. Large-scale genomic datasets are required to enhance further discovery and fine-mapping of high-risk loci/variants in highly susceptible groups for cardiovascular disease and other related traits. Our study highlights the need for diversity in genetic research and the importance of expanding large GWASs to include ancestrally diverse populations.

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.

Solar flares are characterized by sudden bursts of electromagnetic radiation from the Sun’s surface, and caused by the changes in magnetic field states in solar active regions. Earth and its surrounding space environment can suffer from various negative impacts caused by solar flares ranging from electronic communication disruption to radiation exposure-based health risks to the astronauts. In this paper, we address the solar flare prediction problem from magnetic field parameter-based multivariate time series (MVTS) data using multiple state-of-the-art machine learning classifiers that include MINImally RandOm Convolutional KErnel Transform (MINIROCKET), Support Vector Machine (SVM), Canonical Interval Forest (CIF), Multiple Representations SEQuence Learner (Mr-SEQL), and Long Short-Term Memory (LSTM)-based deep learning model. Our experiment is conducted on the on the Space Weather ANalytics for Solar Flares (SWAN-SF) benchmark data set, which is a partitioned collection of MVTS data of active region magnetic field parameters spanning over 9 years of operation of the Solar Dynamics Observatory (SDO). The MVTS instances of the SWAN-SF dataset are labeled by GOES X-ray flux-based flare class labels, and attributed to extreme class imbalance because of the rarity of the major flaring events (e.g., X and M). As a performance validation metric in this class-imbalanced dataset, we used the true skill statistic (TSS) score. Finally, we demonstrate the advantages of the MVTS learning algorithm MINIROCKET, which outperformed the aforementioned classifiers without the need for essential data preprocessing steps such as normalization, statistical summarization, and class imbalance handling heuristics.