The conformity assessment of products or a measured value with the given standards is carried out based on the global risk of producers and consumers calculation. A product may conform to specifications but be falsely rejected as non-conforming. This is about the producer's risk. If a product doesn't meet the requirements but is falsely accepted as conforming, that poses a risk to the consumer. The conventional approach to risk assessment, which yields only a single numerical value for the global risk of producers and consumers, is naturally extended, and utilized for assessing risk in measurement models with linear regression. The outcomes of the two-dimensional extension, along a moderate scale, are the parabolas with an opening upwards. Risk surfaces were obtained through three-dimensional extension over the area limited by the moderate scale and guard band axes. Four models with different ranges of tolerance intervals were used to test this innovative method of risk assessment in linear regression. The corresponding standard measurement uncertainties are determined by applying a simplified measurement model with the use of comprehensive data on the measurement performance and by determining measurement uncertainty derived from consideration of the functional relationship obtained by linear regression analysis. Models that utilize information from linear regression analysis to determine measurement uncertainty are biased towards risks at the edges of the moderate scale. Testing the model's performances with metrics related to the confusion matrix, such as the F1 score, further substantiated this assertion. The diagnostic odds ratio has been proven to be extremely effective in identifying the curve along the guard band axis, along which the global risks of producers and consumers are at their lowest.

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested by generalizing the uniform shrinkage of ridge regression to the non-uniform shrinkage, which was shown to perform well under sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (the first version published on 2023-12-07 at https://cran.r-project.org/package=g.ridge) that implements both the ridge estimator and generalized ridge estimators. The package equips with the generalized cross-validation for automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with the normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on “glmnet”, and hence, it can be the most recommended estimator under sparse and high-dimensional models. We demonstrate the package using the intracerebral hemorrhage data.

This study investigated the trends of registered Death and Birth in Nigeria using Generalized Linear Models. Annual data on Death and Birth was collected from National Population Commission for the period of 2004 to 2017. The Natural increase calculated revealed a positive trend in the natural increase in Nigeria from 2004 to 2017. Evidence from summary statistics revealed some level of over dispersion (variance > mean). This study explored Poisson Regression Models and Negative Binomial Regression Models using two links (identity and log). The results revealed a positive increase in registration of birth and death rates in Nigeria and among the competing the models, Negative Binomial regression model with identity link emerged as the best model for modeling birth and death rates registration in Nigeria. Data on numbers of deaths and causes of death are essential if countries are to determine priorities, formulate and monitor policies for public health care as well as other government policies that may be based on such data

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

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

In this work, we propose a generalized partially functional linear model, which not only models the relationship between multiple scalar and functional predictors and response, but also automatically estimates the link function. Specifically, we use the functional principal component analysis method to reduce the dimensionality of functional predictors, estimate the regression coefficients using the maximum likelihood estimation method, estimate the link function using the method of local linear regression, iteratively obtain the final estimator, and prove the asymptotic normality of the estimator. The asymptotic normality is illustrated through simulation experiments. Finally, the proposed model is applied to study the influence of environmental, economic, and medical levels on life expectancy in China. In the study functional predictors are the daily air quality index, temperature, and humidity of 58 cities in 2020 and scalar predictors are GDP and number of beds in hospitals.

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

The particulars of stimulus-response experiments done on dynamic biosystems clearly limit what one can learn and validate about their structural interconnectivity (topology), even when collected kinetic output data are perfect (noise-free). As always, available access ports and other data limitations rule. For linear systems, exponential modes, visible and hidden, play an important role in understanding data limitations, embodied in what we call dynamical signatures in the data. We show here how to circumscribe and analyze modal response data in compartmentalizing model structures – so that modal analysis can be used constructively in systems biology model building – for nonlinear (NL) as well as linear biosystems. We do this by developing and exploiting the modal basis for dynamical signatures in hypothetical (perfect) input-output data associated with a structural model – one that includes inputs and outputs explicitly – and for NL as well as linear biosystems. The methodology establishes model dimensionality (size, complexity) from particular data sets; helps select among multiple candidate models (model distinguishability); helps in designing new experiments to extract “hidden” structure; and helps to simplify (reduce) models to their essentials. For NL biosystems, results are not as comprehensive, similarly informative about their dominant dynamical properties, and unified with linear models on invariant 2-dimensional manifolds in phase space. Some automation of these highly technical aspects of biomodeling is also introduced.

Reliable fatigue design rules affect the proactive identification of safety parameters in aerospace industry. Numerous fatigue crack initiation and propagation models, linear and nonlinear, have been developed for designing purposes or estimation of the remaining life of aging airplanes. Depending on the adopted assumptions, the accuracy varies for different loading histories, loading types, and materials. Semi empirical models are simple but yield significant inaccuracies. Models with better theoretical basis provide better accuracy, but implementation in real conditions is problematic. In the present work, a review of author’s recent fatigue crack initiation and propagation models based on physical mechanisms is presented and improvements are proposed. Verification of the models on test results is provided and discussed.

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

Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

Byers Peninsula (62°34’-62°40’S-60°54’61°13’W), 60 km2 in size, is considered one of the largest ice-free areas in Antarctica. Since 2006, the Spanish Polar Program has taken part in a large number of environmental studies involving effects of climate changes, limnology and microbiology, live cycles, but not albedo. Surface albedo is one of the key physical parameters in the surface energy budget of polar regions. Most of Antarctica is covered by ice sheets; only about 0.44% of the area is permanently ice-free. However, in maritime Antarctica, the ice-free areas, corresponding to small islands, peninsulas, and coastal beaches, account for about 3% of the territory. To incorporate the contribution of these areas into global albedo models, it is necessary to relate the soil properties of the ice-free areas to the surface albedo response. Also, mapping soil properties and albedo have and special interest in these ice-free areas. Image classification using machine learning methods trained with georeferenced soil data could be useful for mapping soil properties and albedo in multispectral optical satellite images. A shallow neural network implemented using the Keras Python module was used to define and train models of soil properties using 15 explanatory variables corresponding to bands and spectral indices of a Sentinel image and a population of 49 soil samples taken from the top 5 centimeters of the soil profile. The soil samples were analyzed in the laboratory and a spectral library in the Vis-Nir range (350-2500 nm) was created. The albedo of the samples was integrated from the ADS spectra. At the same time, a linear regression model of albedo using the soil properties as explanatory variables was performed. The R2 fit of this new model was about 0.82 and the error of estimation was 4.1. The model was extended to the entire Byers Peninsula using the ML soil property models as explanatory variables. The RMSE of the extended models increased up to 8.2. We think that the main cause of this increase (2.6 points) is related to the error propagation, phenomenon due to the use of models as explanatory variables. However, another important part of the error increase could be due, among other reasons, to the use of an image that, although corrected, is not completely free of clouds.

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

An evolutionary game is introduced which considers game-theoretic strategies in the context of non-linear population matrix models. This game considers the states and actions of the organisms of the evolving population, and a notion of dynamic equilibrium between strategies is described. The game’s formalism is expounded and a proof about equilibrium is given; specifically that any stable equilibrium can be described by proportions of pure strategies; particularly when population matrices are not defective.

A variable annuity is a popular life insurance product that comes with financial guarantees. Using Monte Carlo simulation to value a large variable annuity portfolio is extremely time-consuming. Metamodeling approaches have been proposed in the literature to speed up the valuation process. In metamodeling, a metamodel is first fitted to a small number of variable annuity contracts and then used to predict the values of all other contracts. However, metamodels that have been investigated in the literature are sophisticated predictive models. In this paper, we investigate the use of linear regression models with interaction effects for the valuation of large variable annuity portfolios. Our numerical results show that linear regression models with interactions are able to produce accurate predictions and can be useful additions to the toolbox of metamodels that insurance companies can use to speed up the valuation of large VA portfolios.

Linear mixed models are frequently used for analysing heterogeneous data in a broad range of applications. The restricted maximum likelihood method is often preferred to estimate co-variance parameters in such models due to its unbiased estimation of the underlying variance parameters. The restricted log-likelihood function involves log determinants of a complicated co-variance matrix. An efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the first derivatives and the second derivatives of the restricted log-likelihood function, i.e., the observed information. Standard approaches to compute the observed information and its expectation, the Fisher information, is computationally prohibitive for linear mixed models with thousands random and fixed effects. Customized algorithms are of highly demand to keep mixed models analysis scalable for increasing high-throughput heterogeneous data sets. In this paper, we explore how to leverage an averaged information splitting technique and dedicate matrix transform to significantly reduce computations and to accelerate computing. Together with a fill-in reducing multi-frontal sparse direct solver, the averaged information splitting approach improves the performance of the computation process.

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

In this study, the focus is on the drop test simulation of an MR (Magnetorheological) damper-based main landing gear (MRMLG), aiming to explore multi-degree-of-freedom (DOF) dynamic models during aircraft landing. Three different 6-DOF dynamic models are proposed in this work and their drop performances are compared with results achieved one of commercial softwares. The proposed models include a nonlinear aircraft model (NLAM), a linearized approximated aircraft model (LAAM) linearizing from the nonlinear equations of motion in NLAM, and a fully approximated aircraft model (FAAM) which linearizes the MRMLG's strut force model. In order to evaluate drop performance of the aircraft landing gear system with MR dampers, a 7-DOF aircraft model incorporating the nonlinear MRMLG is formulated using RecurDyn. The principal comparative param-eters are the coefficient of determination (R2) for system response of each model with Re-curDyn model and root mean square error (RMSE) which is the ensembles of CG dis-placement data for each model. In addition, the ensemble of time series data is created for diverse drop scenarios, providing valuable insights into the performance of the proposed drop test models of the aircraft landing gear system featuring MR dampers.

The development of plant-based meat analogues has become a significant challenge for the food industry in recent years due to the increasing demand for sustainable and healthier proteins in the context of a global protein transition. Plant-based meat analogues imitate the visual, textural, and chemical properties of traditional meat products and are required to closely resemble meat to appeal to consumers. In addition, consumers demand natural, clean-label, and nutritional and healthy products. To address these challenges, the food industry must develop highly healthy, nutritious, and E-number-free meat analogue products. Understanding the functionality of each ingredient and its role in the food matrix is crucial to being a key player in the innovation of the meat analogues market. This review provides updated information on the primary ingredients utilized for the development of plant-based burger meat alternatives and their functionality. The key components of meat analogue burgers are outlined, including plant proteins, binding agents, fats and oils, flavorings, colorings, preservatives, fortificants, and clean-label considerations.

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

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

Single particle tracking (SPT) is a powerful class of methods for studying the dynamics of biomolecules inside living cells. The techniques reveal the trajectories of individual particles, with a resolution well below the diffraction limit of light, and from them the parameters defining the motion model, such as diffusion coefficients and confinement lengths. Most existing algorithms assume these parameters are constant throughout an experiment. However, it has been demonstrated that they often vary with time as the tracked particles move through different regions in the cell or as conditions inside the cell change in response to stimuli. In this work, we propose an estimation algorithm to determine time-varying parameters of systems that discretely switch between different linear models of motion with Gaussian noise statistics, covering dynamics such as diffusion, directed motion, and Ornstein-Uhlenbeck dynamics. Our algorithm consists of three stages. In the first stage, we use a sliding window approach, combined with Expectation Maximization (EM) to determine maximum likelihood estimates of the parameters as a function of time. These results are only used to roughly estimate the number of model switches that occur in the data to guide the selection of algorithm parameters in the second stage. In the second stage, we use change detection (CD) techniques to identify where the models switch, taking advantage of the off-line nature of the analysis of SPT data to create non-causal algorithms with better precision than a purely causal approach. Finally, we apply EM to each set of data between the change points to determine final parameter estimates. We demonstrate our approach using experimental data generated in the lab under controlled conditions.

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

The main aim of this study is to predict whether the type of breast cancer is “benign” or “malignant” by classical generalized linear model (GLM) approach and an extended family of GLM called generalized linear mixed model (GLMM) approach for binomially distributed response variable with binary link functions. In this study, an advanced statistical modeling approach based on the GLMM to the traditional statistical modeling approach based on the GLM for binomially distributed response variable with various binary link functions is proposed to investigate the relationships between the “malignant or benign diagnosis of the BC in patients” and “nine attributes” of 699 BC diagnosed patients. This study also focuses on the statistical significance of the accurate classification of the BC diagnosed patients in cancer studies in medicine in “benign” or “malignant” type based on the WBC dataset. In this study, the superiority of the GLMM approach over the GLM approach for the binary response variable especially belonging to the WBC dataset is emphasized in the field of cancer diagnosis in medicine. Also the importance and the power of the IC and performance metrics as the goodness-of-fit test statistics are strongly emphasized for accurate statistical inferences from the “best” fitted model. In this study, from the main findings, the best fitted model among the GLM and GLMM approaches for the binary response variable is determined as the GLMM under “logit” link function with “id” random effect with the most statistically significant odds of the occurance of the BC being “malignant” as 7.9104, 5.6888, 5.6643, 4.9842, 4.1212, 2.0679, 1.8755, and 1.3970 times more than being “benign” for every one-unit increase in the quantities of “clump thickness”, “bland chromatin”, “mitoses”, “bare nuclei”, “cell shape”, “marginal adhesion”, “epithelial cell size”, and “cell size”, respectively.

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

The abilities of quantitative description of noise are restricted due to its origin and only the statistical and spectral analysis methods can be applied while an exact time evolution cannot be defined or predicted. It emphasizes the challenges faced in many applications including communication systems where noise can play, on one hand, a vital role impacting signal-to-noise ratio but possessing, on the other hand, unique properties such as infinite entropy (infinite information capacity), exponentially decaying correlation function and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criteria, on which the main idea of the study is based on, is the Central Limit Theorem which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. The study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.) whose output signals are analyzed according to criteria that encompass the probability density functions of a chaotic signal itself and its envelope and phase, statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. The analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates Gaussian distribution. It allows generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

Antimicrobial peptides (AMPs) are considered as promising alternatives to conventional antibiotics in order to overcome the growing problems of antibiotic resistance. Computational prediction approaches receive an increasing interest to identify and design the best candidate AMPs prior to the in-vitro tests. In this study, we focused on the linear cationic peptides with non-hemolytic activity, which are downloaded from the Database of Antimicrobial Activity and Structure of Peptides (DBAASP). Referring to the MIC (Minimum inhibition concentration) values, we have assigned a positive label to a peptide if it shows antimicrobial activity; otherwise the peptide is labeled as negative. Here, we focused on the peptides showing antimicrobial activity against Gram-negative and against Gram-positive bacteria separately, and we created two datasets accordingly. Ten different physico-chemical properties of the peptides are calculated and used as features in our study. Following data exploration and data preprocessing steps, a variety of classification algorithms are used with 100-fold Monte Carlo Cross Validation to build models and to predict the antimicrobial activity of the peptides. Among the generated models, Random Forest has resulted in the best performance metrics for both Gram-negative dataset (Accuracy: 0.98, Recall: 0.99, Specificity: 0.97, Precision: 0.97, AUC: 0.99, F1: 0.98) and Gram-positive dataset (Accuracy: 0.95, Recall: 0.95, Specificity: 0.95, Precision: 0.90, AUC: 0.97, F1: 0.92) after outlier elimination is applied. This prediction approach might be useful to evaluate the antibacterial potential of a candidate peptide sequence before moving to the experimental studies.

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

This paper presents a two-stage ADC based on pseudo-differential operational transconductance amplifier (OTA), which is designed for the readout circuit of X-ray linear array sensor. This hybrid ADC employs an incremental sigma-delta ADC and a cyclic ADC, achieving a good trade-off between accuracy and conversion speed. The two stages share the same hardware to reduce power consumption and die area. A common-mood feedback module is used to suppress the influence of charge injection, and the effectiveness is demonstrated by detailed theoretical analysis. A test chip of 14-bit ADC is fabricated in 0.35μm CMOS technology. The measured root mean square (RMS) value of DNL is 0.254 LSB, and the maximum value of INL is -0.776/+1.56 LSB. The measured effective number of bits (ENOB) is 13.43 bits.

With the development of organizational biology and forced from the EU Cosmetic Regulation (EU/1223/2009) with the complete ban of animal testing for cosmetic purposes, 3D skin models have been widely developed due to their similar physiological structure and metabolic function to native human tissue. 3D skin models for in vitro cosmetic evaluation are still promising alternative methods for evaluating phototoxicity, corrosivity and irritation. These models have been used for early screening and later validation of toxicity and efficacy evaluation by many well-known cosmetic companies. 3D skin models have become an important tool in cosmetic evaluation research. This article reviews the development of 3D skin models and their application in cosmetic evaluation. An outlook on the current application and future technological development directions in the cosmetic field is also presented.

The assortment of low-cost 3D printers for “in-practice” use, e.g., for clear aligner therapies, is ever increasing. To address concerns about the accuracy of orthodontic models produced on such printers when cost efficient modes of 3D printing are employed, this study examined the effect of print model body type and print angulation on accuracy. Six printing-configuration groups were included: 2 model types (solid or hollow shell) combined with 3 print angles (0°, 70°, or 90°) with 10 models/group; all models were printed with 100-µm layer thickness using a digital light processing-based 3-dimensional printer. Eleven selected structures and distances were measured on the printed models with a digital microscope and compared to the same measures on a digitized master model. The clinically-acceptability range was set at ±0.25 mm difference from the master model for single tooth measurements (intra-tooth) and ±0.5 mm for cross-arch measurements (inter-tooth). For individual measurements across all models, 98% fell within clinical acceptability. For mean measurements within each model group, only canine height for the shell-0° model had a mean difference (0.26 mm ± 0.03) outside the clinically acceptable range for intra-tooth measurements. Standard deviations for all intra-tooth measurements were within 0.07 mm. While none of the mean inter-tooth measurements exceeded the acceptability range, the standard deviations were larger (0.04 to 0.30 mm). Accuracy of orthodontic models for clear aligner therapies was not impacted beyond the clinically acceptable range when altering model body type and print angulation to improve efficiency of 3D printing. These findings suggest greater flexibility of the practitioner to alter print settings to address time and cost efficiency in various clinical scenarios and still maintain clinically acceptable model accuracy.

There are many uncertainties and risks in residential electricity consumption during the economic development. Knowledge of the relationship between residential electricity consumption and its key determinant—income—are important to the sustainable development of electric power industry. Using panel data from 30 provinces for the 1995-2012 period, this study investigates how residential electricity consumption changes as incomes increase in China. Previous studies typically used linear or quadratic double-logarithmic models imposing ex ante restrictions on the indistinct relationship between residential electricity consumption and income. Contrary to those models, we employed a reduced piecewise linear model that is self-adaptive and highly flexible and circumvents the problem of “prior restrictions.” Robust tests of different segment specifications and regression methods are performed to ensure the conservatism of the research. The results provide strong evidence that the income elasticity was approximately one, and it remained stable throughout the estimation period. The income threshold at which residential electricity consumption automatically remains stable or slows has not been reached. To ensure the sustainable development of the electric power industry, introducing higher energy efficiency standards for electrical appliances and improving income levels are vital. And government should emphasize electricity conservation in industrial sector rather than in residential sector.

As Artificial Intelligence (AI) technology, particularly Machine Learning algorithms, becomes increasingly ubiquitous, our abilities to understand and interpret AI and machine learning algorithms are becoming increasingly desirable. Visualization has been used as a common tool to view and understand complex machine learning processes. In this paper, we will focus on developing a general framework for the visualization of machine learning models as a scalar valued multi-dimensional function to help users understand how the models behave over different viewing spaces. We first give a formal definition of the visualization problem. Interpolation-based morphing and subspace sampling techniques are applied to generate various renderings through projections and cross-sections of the model space as 3D surfaces or heatmap images. This method will be applied to two real-world datasets and applications: the diagnosis of Alzheimer's Disease (AD) using a human brain networks dataset and a real-world benchmark dataset for predicting home credit default risks. The visualizations show that different machine learning algorithms can behave quite differently under different conditions.

Digital Elevation Models (DEMs) are widely used in geographic and environmental studies. In the current work, the fusion of multi-source DEMs is investigated to improve the overall accuracy of public domain DEMs. Multi-scale decomposition is an important analytical method in data fusion. Three multi-scale decomposition methods – the wavelet transform (WT), bidimensional empirical mode decomposition (BEMD) and nonlinear adaptive multi-scale decomposition (N-AMD) - are applied to the 1-arc-second Shuttle Radar Topography Mission Global digital elevation model (SRTM-1 DEM) and the Advanced Land Observing Satellite World 3D – 30 m digital surface model (AW3D30 DSM) in China. Of these, the WT and BEMD are popular image fusion methods. A new approach for DEM fusion is developed using N-AMD (which is originally invented to remove the cycle from sunspots). Subsequently, a window-based rule is proposed for the fusion of corresponding frequency components obtained by these methods. Quantitative results show that N-AMD is more suitable for multi-scale fusion of multi-source DEMs, taking the ice cloud and land elevation satellite (ICESat) global land surface altimetry data as a reference. The vertical accuracy of the fused DEM shows significant improvements of 29.6% and 19.3% in a mountainous region and 27.4% and 15.5% in a low-relief region, compared to the SRTM-1 and AW3D30 respectively. Furthermore, a slope position-based linear regression method is developed to calibrate the fused DEM for different slope position classes, by investigating the distribution of the fused DEM error with topography. The results indicate that the accuracy of the DEM calibrated by this method is improved by 16% and 13.6%, compared to the fused DEM in the mountainous region and low-relief region respectively, proving that it is a practical and simple means of further increasing the accuracy of the fused DEM.

We suppose that a Cooper pair (CP) will experience a damping force exerted by the condensed matter. A Langevin equation of a CP in two dimensional condensed matter is established. Following a method similar to Nelson's stochastic mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is derived. If the CPs move with a constant velocity, then the corresponding direct current (DC) electrical conductivity can be calculated. Therefore, a Drude like formula of resistivity of CPs is derived. We suppose that the damping coefficient of CPs in two dimensional cuprate superconductors is a linear function of temperature. Then the resistivity and scattering rate of CPs turn out to be also linear-in-temperature. The origin of linear-in-temperature resistivity and Planckian dissipation in cuprate superconductors may be the linear temperature dependence of the damping coefficient of CPs.

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

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

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

Fresnel incoherent correlation holography (FINCH) is a well-established incoherent imaging technique. In FINCH, three self-interference holograms are recorded with calculated phase differences between the two interfering, differently modulated object waves and projected into a complex hologram. The object is reconstructed without the twin image and bias terms by a numerical Fresnel back propagation of the complex hologram. A modified approach to implement FINCH by a single camera shot by pre-calibrating the system involving recording of the point spread function library and reconstruction by a non-linear cross-correlation has been introduced recently. The expression of the imaging characteristics from the modulation functions in original FINCH and the modified approach by pre-calibration in spatial and polarization multiplexing schemes are reviewed. The study reveals that a reconstructing function completely independent of the function of the phase mask is required for the faithful expression of the characteristics of the modulating function in the image reconstruction. In polarization multiplexing method by cross-correlation, a partial expression was observed, while in spatial multiplexing method by cross-correlation, the imaging characteristics converged towards a uniform behavior.

Predicting human trajectories poses a significant challenge due to the complex interplay of pedestrian behavior, which is influenced by environmental layout and interpersonal dynamics. This complexity is further compounded by variations in scene density. To address this, we introduce a novel dataset from the Festival of Lights in Lyon 2022, characterized by a wide range of densities (0.2-2.2 ped/m2). Our analysis demonstrates that density-based classification of data can significantly enhance the accuracy of predictive algorithms. We propose an innovative two-stage processing approach, surpassing current state-of-the-art methods in performance. Additionally, we utilize a collision-based error metric to better account for collisions in trajectory predictions. Our findings indicate that the effectiveness of this error metric is density-dependent, offering prediction insights. This study not only advances our understanding of human trajectory prediction in dense environments but also presents a methodological framework for integrating density considerations into predictive modeling, thereby improving algorithmic performance and collision avoidance.

The multiphase motors due to their reliability find new areas of application in the industry and transportation. Developing of any system with multiphase motors at first requires elaborate model of the system, define control mode and controllers. The model of control system for the six-phase drive is based on its conventional d-q mathematical model and indirect field-oriented control. Simulink model of six-phase drive with indirect field-oriented control and simulated with two types PID and PID fuzzy controllers. The simulation results, reflecting step response and provided speed reference law as well as load application at constant speed, are presented and analyzed. Fuzzy controller with 49 rules is considered and applied. Six-phase electric drive with field-oriented control at well-tuned PID controller has good step response specifications: settling time 0.13 s at starting without load, step response has no overshoot, small about 1 % short time decrease of speed at load of 5 Nm application. The system employing PID fuzzy controller shows slightly better results in response to torque application: the decrease in speed 1 % is eliminated in shorter time. Simulation results indicate the robustness of both systems with six-phase drive to disturbance and provide high quality transient specifications at determined reference speed.

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

For a nonzero normed linear space X‎, ‎we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals‎. ‎Also separate continuity of the elements of each class are investigated‎. ‎The aim of this research is to introduce a source of examples and counterexamples in the field of fuzzy normed spaces‎.

Observed ENSO statistics exhibits a non-gaussian behavior, which is indicative of the presence of nonlinear processes. In this paper we use the Recharge Oscillator model (ROM), a largely used Low-Order Model (LOM) of ENSO, as well as methodologies borrowed from the field of statistical mechanics to identify which aspects of the system may give rise to nonlinearities that are consistent with the observed ENSO statistics. In particular, we are interested in understanding whether the nonlinearities reside in the system dynamics or in the fast atmospheric forcing. Our results indicate that one important dynamical nonlinearity often introduced in the ROM cannot justify a non-gaussian system behavior, while the nonlinearity in the atmospheric forcing can instead produce a statistics similar to the observed. The implications of the non-Gaussian character of ENSO statistics for the frequency of extreme El Nino events is then examined.

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

Electricity price forecasting has become a crucial element for both private and public decision-making. This importance has been growing since the wave of deregulation and liberalization of energy sector worldwide late 1990s. Given these facts, this paper tries to come up with a precise and flexible forecasting model for the wholesale electricity price for the Italian power market on an hourly basis. We utilize artificial intelligence models such as neural networks and bagged regression trees that are rarely used to forecast electricity prices. After model calibration, our final model is bagged regression trees with exogenous variables. The selected model outperformed neural network and bagged regression with single price used in this paper, it also outperformed other statistical and non-statistical models used in other studies. We also confirm some theoretical specifications of the model. As a policy implication, this model might be used by energy traders, transmission system operators and energy regulators for an enhanced decision-making process.

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

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

In this study, we investigated the features of co-infection with SARS-CoV-2 and nonpathogenic strain LEV8 of coxsackievirus A7 or enterovirus A71 for Vero E6 cells and Syrian hamsters. The investigation of co-infection with SARS-СoV-2 and LEV-8 or EV-A71 in the cell model was shown that a competitive inhibitory effect for these viruses were especially significant against SARS-CoV-2. Pre-infection with enteroviruses in animals caused more than a 100-fold decrease in the levels of SARS-CoV-2 virus replication in the respiratory tracts and more rapid clearance of the lower respiratory tract from infectious SARS-CoV-2. Co-infection with SARS-CoV-2 and LEV-8 or EV-A71 also reduced the severity of clinical manifestations of the SARS-CoV-2 infection for animals. Additionally, the histological data illustrated that co-infection with nonpathogenic coxsackievirus decreased the level of pathological changes by SARS-CoV-2 in the lungs. Research into the chemokine/cytokine profile demonstrated that the studied enteroviruses efficiently triggered this part of antiviral immune response, which can be associated with significant inhibition of SARS-CoV-2 infection. These results demonstrate that there exists a strong viral interference between the studied nonpathogenic strain of coxsackievirus A7 or enteroviruses A71 and SARS-CoV-2 pathogenic for humans in vitro and in vivo.

Molnupiravir, a prodrug known for its broad antiviral activity, demonstrated efficacy in animal models of Covid-19, prompting clinical trials where initial results indicated a significant effect against the disease. However, subsequent clinical studies did not confirm these findings, leading to the rejection of molnupiravir for permanent market authorization in many countries. This report critically assessed 19 studies published in 17 reports that investigated the efficacy of molnupiravir in animal models of Covid-19 with the purpose of determining how well the design of these models informed human studies. We found that the administered doses of molnupiravir in most studies involving animal Covid-19 models were disproportionately higher than the dose rec-ommended for human use. Specifically, when adjusted for body surface area, half of the doses of molnupiravir used in the animal studies were more than twice as high as the human dose. Addi-tionally, the drug was frequently given prophylactically or shortly after SARS-CoV-2 inoculation in these models, in contrast to clinical trials where such timing is not consistently achieved. Furthermore, the recommended five-day treatment duration for humans was exceeded in several animal studies. Collectively, we suggest that these design elements in the reported animal studies contributed to a bias favoring molnupiravir, and thus inflated expectations for its efficacy against Covid-19. Addressing these elements may offer avenues to enhance the clinical efficacy of mol-nupiravir for treatment of Covid-19 that include dose increment, early treatment, and admin-istration by inhalation along with use of molnupiravir in antiviral combination therapy.

Linear-width is a well-regarded width parameter in graph theory. The constructs of linear loose tangle and linear tangle present obstacles to attaining linear-width. In this succinct paper, our primary focus will be the exploration of maximal linear loose tangles.

This study considers an application of the first-order Grey Markov Model to foresee the values of Italian power generation in relation to the available energy sources. The model is used to fit data from the Italian energy system from 2000 to 2022. The integration of Markovian error introduces a random element to the model, which is able now to capture inherent uncertainties and misalignments between the Grey model predictions and the real data. This application provides valuable insights for strategic planning in the energy sector and future developments. The results show good accuracy of the predictions, which provides powerful information for the effective implementation of energy policies concerning the evolution of energy demand in the country. Despite advancements, Italy’s 2032 energy mix will still significantly rely on fossil fuels, emphasizing the need for sustained efforts beyond 2032 to enhance sustainability.

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

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

The pursuit of Artificial Intelligence (AI) that emulates human cognitive processes is a cornerstone of ethical AI development, ensuring that emerging technologies can integrate seamlessly into societal frameworks requiring nuanced understanding and decision-making. Zero-Shot Instance Retrieval (ZSIR) stands at the forefront of this endeavour, potentially providing a robust platform for AI systems, particularly large visual language models, to demonstrate and refine cognition-aligned learning without the need for direct experience. In this paper, we critically evaluate current cognition alignment methodologies within traditional zero-shot learning paradigms, using visual attributes and word embedding generated by large AI models. We propose a unified similarity function that quantifies the cognitive alignment level, bridging the gap between AI processes and human-like understanding. Through extensive experimentation, our findings illustrate that this similarity function can effectively mirror the visual-semantic gap, steering the model towards enhanced performance in zero-shot instance retrieval. This work not only benchmarks the cognition alignment of AI, but also sets a new precedent for the development of visual language models attuned to the complexities of human cognition.}

The speed-density or flow-density relationship is a fundamental aspect of traffic flow theory. Single-regime models often face challenges in consistently fitting empirical data under diverse traffic conditions. This paper addresses the inaccuracies of single-regime models, attributing them not only to their functional forms but also to data dispersion and sample selection bias. To mitigate these issues, the data is segmented into day and night periods, leading to the creation of separate models for each. Calibration results, conducted on data from two freeways, Tehran-Karaj and Tehran-Qom, reveal distinct challenges, with the former exhibiting high dispersion and the latter showing low dispersion. Surprisingly, single-regime models demonstrate notable effectiveness when applied to distinct day and night data. Further analysis, categorizing data into day and night, results in reduced errors (20-60% improvement in R-Square), emphasizing the potential for enhanced accuracy by considering distinct regimes. Overall, the study underscores the significance of regime-specific considerations for accurate traffic flow modeling. Upon thorough evaluation, the study highlights the superiority of the neural network Multi-layer Perceptron (MLP) over traditional models. The research discusses the implications of incorporating day and night parameters into the models, emphasizing their potential for accuracy enhancement.

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

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

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

The article presents a model for optimizing biomass supply chains using the linear programming framework integrated with a Geographic Information System. Based on the distance from a given type of biomass resource, its calorific value, price, and transportation costs, the model identifies the optimal source of biomass, allowing it to cover the demand for the required total energy value with the lowest possible costs. The case study includes the Połaniec power plant in southeastern Poland and potential sources of forest biomass and agricultural straw within 100 km of the plant. Unit costs of biomass varied depending on biomass availability and energy demands. For energy demand on the level of 1 PJ yearly, the lowest unit costs of biomass (4.08 €/MJ) were when all kinds of biomass were available, and the highest (5.47 €/MJ) was when only stacked wood was available. As energy demand increased, unit costs increased, and the ability to meet this demand with just one type of biomass decreased. The energy biomass sector can utilize the model to benefit both biomass producers and their final buyers.

When dealing with limited sample sizes or missing values in time series data, achieving high accuracy in forecasting becomes challenging. This challenge is particularly common in wind energy forecasting, where many wind farms lack complete data. In this paper, we employ the widely-used ARIMA (Autoregressive Integrated Moving Average) model for time series forecasting. To address the difficulties posed by limited sample sizes and missing values, we adopt a unique approach by utilizing multiple ARIMA models for different datasets. A key distinction from other multiple models methods for time series forecasting lies in each model within our approach using its own dataset, making the fusion process more intricate. To overcome this, we incorporate neural networks and two techniques for model fusion: direct fusion with a learning mechanism and compensation for missing data through training. For each ARIMA model, we introduce a noise estimation method to circumvent the white noise assumptions inherent in ARIMA models. Finally, we apply these methods to wind energy prediction, and our experimental results showcase a significant enhancement in forecasting accuracy.

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

Previously, we described a 19-base pair double-stranded RNA with 3'-trinucleotide overhangs, acting as immunostimulatory RNA (isRNA). This molecule demonstrated notable antiproliferative effects on cancer cells, inhibited tumor growth, and elicited immunostimulatory and antiviral responses by inducing cytokine and interferon production. Within this study, we compared the efficiency of lung fibrosis development, initiated in mice by BLM or LPS using different schemes of induction. Then we compared the effect of isRNA used in a preventive or therapeutic regimen on the development of fibrosis in selected BLM- and LPS-induced mouse models and showed that isRNA can be used in pathological conditions accompanied by the development of inflammation and the risk of fibrosis formation, without adverse side effects. Prophylactic regimen of isRNA application is beneficial for prevention of the development of pulmonary fibrosis.

Count data analysis presents unique challenges due to its discrete nature, often exhibiting excessive zeros and overdispersion. To address these complexities, count models, such as Poisson regression and Negative Binomial regression, have been developed, enabling modeling and prediction of count-based phenomena. Additionally, it’s important to notice that zero inflation, a phenomenon commonly observed in count data, requires specialized techniques for robust analysis. This article provides an overview of count data and count models, explores zero inflation, introduces Likelihood Ratio Tests, and explains how the Vuong Test can be used as a model selection criteria. Furthermore, we created a Vuong Test implementation from scratch using the Python programming language. This implementation enhances the accessibility and applicability of the Vuong Test in real-world scenarios, providing a valuable contribution to the academic community, since Python didn’t have an implementation of this statistical test.

This paper is aimed at studying the temporal evolution of the surface displacements occurred over the past few years in the ocean-reclaimed platforms of the Shanghai megacity (China), which are mainly ascribable to consolidation processes of large dredger fills and alluvial deposits. With respect to previous analyses carried out over the same area, this work provides a joint multi-platform differential interferometry synthetic aperture radar (DInSAR) analysis, based on the application of the advanced Small BAseline Subset (SBAS) algorithm. This led us to retrieve long-term deformation time-series that are helpful for a better understanding of the on-going deformation phenomena. To this aim, we have exploited two sequences of SAR data collected by the ASAR/ENVISAT and by the COSMO-SkyMed (CSK) sensors, respectively, spanning the whole time period from 2007 to 2016. Unfortunately, the large time gap (of about three years) existing between the available ASAR/ENVISAT and CSK datasets gave rise to additional difficulties for their combination. Nevertheless, this problem has been faced by benefiting from the knowledge of a time-dependent model describing the temporal evolution of the expected deformations affecting the Shanghai ocean-reclaimed platforms.

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

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

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine both partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions. On the way, an accurate description of the deformation of the integration paths defining the analytic solutions and the knowledge of Lambert W function are needed in order to provide the asymptotic behavior of the solution near the origin, regarding the perturbation parameter. Such deformation varies depending on the analytic solution considered, which lies in two families with different geometric features.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

A review of quantitative risk assessment (QRA) models of L. monocytogenes in produce was carried out, with the objective of appraising and contrasting the effectiveness of the control strategies placed along the food chains. Despite nine of the thirteen QRA models recovered focused on fresh or RTE leafy greens, none of them represented important factors or sources of contamination in the primary production, such as type of cultivation, water, fertilisers or irrigation method/practices. Cross-contamination at processing and during consumer’s handling was modelled using transfer rates, which were shown to moderately drive the final risk of listeriosis; highlighting therefore the importance of accurately representing the transfer coefficient parameters. Many QRA models coincided in the fact that temperature fluctuations at retail or temperature abuse at home were key factors contributing to increasing the risk of listeriosis. In addition to a primary module that could help assess current on-farm practices and potential control measures, future QRA models for minimally-processed produce should also contain a refined sanitisation module able to estimate the effectiveness of various sanitisers as a function of type, concentration and exposure time. Finally, L. monocytogenes growth in the products down the supply chain should be estimated by using realistic time-temperature trajectories, and validated microbial kinetic parameters, both of them currently available in the literature.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

The concept of green energy is now at the forefront of development discourse, with the United Nations Sustainable Development Goals (SDGs) 7, 11, and 12 all aimed at promoting green energy consumption to combat the three planetary crises: climate change, biodiversity loss, and pollution. Similarly, issues regarding Africa’s natural resource curse have caused a stir in the growth and development literature for some time now and there is no sign that it will die out. This study, the first of its kind, simultaneously assesses the impact of green energy consumption and Africa’s natural resources rents on economic growth by applying the Feasible Generalized Least Square (FGLS) estimator and the dynamic panel models of the Pooled Mean Group (PMG) and Mean Group (MG) estimators on data from 1990 to 2020 for 24 selected African countries. The results show that green energy consumption has a short-run growth-limiting effect and a long-run growth-enhancing effect in Africa. The study also found evidence of the natural resource curse phenomenon in Africa. The study, therefore, calls for the advancement and usage of green energy for both domestic and industrial production in Africa. The study further calls for a revamp in the global tax policy to curb illicit financial activities and strengthening institutional quality for transparency and accountability in the entire value chain of natural resource management in Africa.

Natural language Processing (NLP) has significantly transformed in the last decade, especially in the field of Language Modeling. Large Language Models (LLMs) have achieved SOTA performances on Natural Language Understanding (NLU) and Natural Language Generation (NLG) tasks by learning language representation in self-supervised ways. This paper provides a comprehensive survey to capture the progression of advances in Language Models. In this paper, we examine the different aspects of Language Models, which started with a few million parameters but have reached the size of a trillion in a very short time. We also look at how these LLMs transitioned from task-specific to task-independent to task-and-language-independent architectures. This paper extensively discusses different pre-training objectives, benchmarks, and transfer learning methods used in LLMs. It also examines different fine-tuning and In-Context learning techniques used in downstream tasks. It also explores how LLMs can perform well across many domains and datasets if sufficiently trained on a large and diverse dataset. Next, it discusses how, over time, the availability of cheap computational power and large datasets have improved LLM’s capabilities and raised new challenges. As part of our study, we also inspect LLMs from the lens of scalability to see how their performance is affected by the model’s depth, width, and data size. Lastly, we provide an empirical comparison of existing trends and techniques and a comprehensive analysis of where the field of LLM currently stand.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

Responding to changing value creation processes in the sheet metal working sec-tor, where the complexity and interchangeability of products challenge traditional dif-ferentiation strategies, this empirical analysis explores integrating service-oriented and data-driven business models as new paths to ensure competitiveness, especially for small and medium-sized enterprises (SMEs). This study aims to capture the current state and challenges associated with the implementation of these business models in this sector. The research was conducted through semi-structured interviews with SMEs in the industry. The findings indicate that service-oriented and data-driven business models are not yet widely adopted and that manufacturing companies re-quire support in their implementation. Fields of action were identified for the industry. These are "Creating awareness and understanding", "Recognizing added value", "In-creasing company maturity" and "Understanding the change process". Cooperation between science and industry is essential in tackling these fields of action to ensure the successful integration of such business models in manufacturing companies. This pa-per identifies challenges in the fields of action that companies must address through a structured approach promoting awareness, recognizing value, improving organiza-tional maturity, and understanding the change process to successfully implement ser-vice-oriented and data-driven business models.

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

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

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

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

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

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

Herein, we examined the effects of weather parameters and individual clinicodemographic risk factors on hemorrhagic stroke (HS) incidence, severity on admission, and disability at discharge in a harsh desert climate. In a retrospective design we studied patients admitted to a stroke unit in Arab Emirates in 2016-2019. With a distributed lag nonlinear model we explored immediate and delayed effects of weather on stroke incidence. Supervised machine learning was used to build models predictive of scores in NIHSS and mRS scales. We assessed model performance by calculating ROC AUC, F1 scores, specificity, and sensitivity. HS risk increased after a significant change in any weather parameter. The risk was reduced below baseline after 1-week adjustment to environmental changes. Climate input from the previous 3 days yielded reliable classification models. Humidex was a better predictor of severity than air temperature, whereas body mass index, age, and time of day at stroke onset were the strongest clinical predictors. Weather parameters before admission were stronger predictors of disease severity than individual clinical factors. We addressed limitations of previous studies by analyzing a full set of climate parameters: ambient temperature, relative humidity, humidex, atmospheric pressure, and wind speed. Predictive models may help to optimize patient management and develop preventative strategies.

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how we can get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are analyzed.

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

Effective agricultural management in maize production operations starts with the early quantification of seedlings. Accurately determining plant presence allows growers to optimize planting density, allocate resources, and detect potential growth issues early on. This study presents an in-depth analysis of multiple object detection models used by drones to count maize seedlings, while concurrently investigating the influence of planting density, flight altitude, and plant growth stage. The findings of this study demonstrate that one-stage models are able to more accurately detect maize seedlings than two-stage models. In particular, YOLOv8n exhibits outstanding performance, achieving an F1-score of over 0.92 under various density conditions and maintaining a stable performance, especially under densities below 105,000 plants/ha. Additionally, planting density and growth stage were observed to significantly affect detection accuracy, with performance declining as density and growth stage increased. Image resolution and detection were impacted by flight altitude, with lower flights producing higher-quality results. Ultimately, YOLOv8n displays optimal performance under various conditions, providing crucial data to support intelligent decision-making. This research offers valuable insights into the application of object detection technology and provides a basis for the future development of precision agriculture.

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

Although researchers have proposed various indentation size effect (ISE) models, these models often involve different form and number of parameters that can make our wonder which is the best in existed ISE models. Three types of ISE test data, namely, normal ISE, reverse ISE and transition of normal to reverse ISE, are used to evaluate the sixteen ISE models. The comparatively study indicates that H-J, N-G-Fs, N-G-H, N-G-A and N-G-Qs models can accurately predict the normal ISE. The reason for this is that the friction stress that is not related to dislocation activities or the indentation size effect of plastic zone has been introduced into these models. Therefore, these two factors should be considered in future ISE models. The sixteen ISE models are originally proposed to describe the normal ISE of different materials. However, to our surprise, some of these models are able to capture the reverse ISE and the transition of normal to reverse ISE of different materials. The determination coefficients (DC) of the sixteen ISE models are also determined for different materials. For reverse ISE, the highest DC value for NiCSi, TC4 and PED Ni are given by the EXP, N-G-Fs and N-G-A models, respectively. For the transition of normal to reverse ISE, the N-G-YC, N-G-Fs, and N-G-H models produce the maximum DC for ZrO2, Cu and Y2O3-ZrO2, respectively. Moreover, the mean DC of the N-G-Fs model is the maximum among the sixteen ISE models, followed by the N-G-H model, but they cannot accurately predict the reverse ISE. Therefore, the N-G-Fs and N-G-H models should be further modified to accurately predict the reverse ISE.

We introduce linear probing hashing schemes that construct a hash table of size $n$, with constant load factor $\alpha$, on which the worst-case unsuccessful search time is asymptotically almost surely $O(\log \log n)$. The schemes employ two linear probe sequences to find empty cells for the keys. Matching lower bounds on the maximum cluster size produced by any algorithm that uses two linear probe sequences are obtained as well.

A numerical application of linear-molecule symmetry properties, described by the D_∞h point group, is formulated in terms of lower-order symmetry groups D_nh with finite n. Character tables and irreducible representation transformation matrices are presented for D_nh groups with arbitrary n-values. These groups are subsequently used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules as part of the variational nuclear motion program TROVE. The TROVE symmetrisation procedure is based on a set of "reduced" vibrational eigenvalue problems with simplified Hamiltonians. The solutions of these eigenvalue problems have now been extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator ${\widehat{L}}_z$ . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D_nh. ¹²C₂H₂ is used as an example of a linear molecule of D_∞h point group symmetry to illustrate the symmetrisation procedure.

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

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

The advent of deep learning (DL) has revolutionized medical imaging, offering unprecedented avenues for accurate disease classification and diagnosis. DL models have shown remarkable promise for classifying brain tumor from Magnetic Resonance Imaging (MRI) scans. However, despite their impressive performance, the opaque nature of DL models poses challenges in understanding their decision-making processes, particularly crucial in medical contexts where interpretability is essential. This paper explores the intersection of medical image analysis and DL interpretability, aiming to elucidate the decision-making rationale of DL models in brain tumor classification. Leveraging state-of-the-art DL frameworks with transfer learning, we conduct a comprehensive evaluation encompassing both classification accuracy and interpretability. Using state-of-the-art DL frameworks with transfer learning, we conduct a thorough evaluation covering both classification accuracy and interpretability. We employ adaptive path-based techniques to understand the underlying decision-making mechanisms of these models. Grad-CAM and Grad-CAM++ highlight critical image regions where the tumors are located.

Crop yield estimation supported by satellite remote sensing data can provide expeditious and strategic information for farmers’ decision-making. Most recent forecasting methods have indicated a promising pathway based on machine learning algorithms. However, validation performances, demand for big data and their inherent inexplicability have not yet consolidated a substantial differential to replace methods based on simpler and more understandable models. This paper proposes an approach based on simple linear models fitted from vegetation indices (VIs) assessed at regular intervals of time series derived from MODIS satellite images, aiming to forecast cotton yields in representative areas of the Brazilian Cerrado. Data from 281 commercial production plots were taken to train (167 plots) and test (114 plots) linear regression models relating seed cotton yield and nine well-known VIs averaged in 15-days intervals. Among the evaluated VIs, EVI (Enhanced Vegetation Index) and TVI (Triangular Vegetation Index) showed the lowest root mean square errors (RMSE) and the highest determination coefficients. The best periods for in-season yield prediction were from the 90-105 to 135-150 days after sowing (DAS), i.e. phenological phases corresponding to boll development, open boll and fiber maturation, with lowest RMSE of about 750 kg ha-1 and R2=0.70. The best forecasts for early crop stages were provided by models at the peaks (maximum value of the VI time-series) for EVI and TVI, which occurred around 80-90 DAS. The proposed approach makes the yield predictability more inferable along the crop time series just by providing sowing dates, contour maps and its respective VIs.

A hallmark of Alzheimer’s disease (AD) are the proteinaceous aggregates formed by the amyloid-beta peptide (Aβ) that is deposited inside the brain as amyloid plaques. The accumulation of aggregated Aβ may initiate or enhance pathologic processes in AD. According to the amyloid hypothesis any agent that has the capability to inhibit Aβ aggregation and/or destroy amyloid plaques represents a potential disease modifying drug. In 2023, a humanized IgG1 monoclonal antibody (lecanemab) against the Aβ soluble protofibrils was approved by US FDA for AD therapy thus providing compelling support to the amyloid hypothesis. To acquire a deeper insight on the in vivo Aβ aggregation, various animal models, including aged herbivores and carnivores, non-human primates, transgenic rodents, fish and worms are widely exploited. This review is based on the recent data obtained using transgenic animal AD models and presents experimental verification of the critical role in Aβ aggregation seeding of the interactions between zinc ions, Aβ with the isomerized Asp7 (isoD7- Aβ) and the α4β2 nicotinic acetylcholine receptor.

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

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

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

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of the generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss generating function approach using which we derive different entropy measures. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

While the simple model of the total atmospheric carbon sink effect as a linear function of concentration has provided excellent prediction results, several problems remained to be investigated and solved. The most obvious open issue is the correct treatment of land use change emssions. It turns out that the model improves by mostly neglecting them after 1959. This effectively implies that land use change emissions have been constant and small since then. The key investigation starts with the observation, that the total carbon sink has a short term component which be explained by temperature changes commonly known as El Nin˜o. The apparent paradox is analysed and explained, why contrary to the short term changes no temperature caused trend can be detected in the model, despite the fact that several contributing processes exhibit temperature dependency. The result of this analysis leads to the model extension, where the total effect of sinks and natural emissions are a linear function of concentration and temperature. This model not only explains current measurements but also paleo climate from ice-core time series.