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.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

Crop yield prediction is relevant subject of current agricultural science. There are various mathematical approaches to crop yield prediction, and regression analysis, notwithstanding the fact that it is somewhat outdated, is still one of the most used ones in this purpose. The quality of predictive model is of great importance, and it is strongly dependent on the rational choice of the target function. The goal of this study is to find out the best regression model for winter wheat, soybeans, and grain corn yield prediction depending on the crops’ water use. The data on true crops’ yields and water use were collected within 1970-2020 at the experimental fields of the Institute of Climate-Smart Agriculture, Kherson region, Ukraine. In total, 145 data pairs were processed by the best subsets regression to find out the best model in terms of fitting quality (assessed by the Pearson’s coefficient of correlation), and prediction accuracy (assessed by the values of the minimum and maximum absolute errors and mean average percentage error). As a result, it was established that the best fitting quality for all the studied crops is attributed to cubic function, while the best accuracy is recorded for hyperbolic (reverse) function in soybeans (mean absolute percentage error is 12.27%), quadratic and hyperbolic functions in winter wheat (mean absolute percentage error is 20.54%), and cubic function in grain corn (mean absolute percentage error is 14.92%). To sum up the results of the study, it is recommended to apply cubic regression function for modeling crops’ yields in agricultural studies.

Abstract: Background: Restless Legs Syndrome /Willis-Ekbom disease (RLS/WED) has occasionally -but not consistently- been associated with cognitive, and most notably, language and executive impairment. The present study was conducted to investigate the cognitive trajectories of older individuals with RLS/WED. Methods: Participants were drawn from the randomly selected, older (>64 years), population-based HELIAD cohort. Individuals without dementia, with available neuropsychological evaluations at baseline and follow-up were considered for potential eligibility. A comprehensive assessment examining five principal components of cognition (memory, visuo-spatial ability, attention, executive function, and language) was administered to the partici-pants. Generalized estimating equations analysis was used to examine the unadjusted and adjusted (for critical factors and covariates) effects of RLS/WED on cognition over time. Results: A total of 1003 predominantly female, older (72.9 ±4.9 years) partici-pants, with follow-up evaluations after a mean of 3.09 ±0.85 years and without demen-tia at baseline and follow-up were included in the present study. Among them, 81 were diagnosed with RLS/WED at baseline. Global cognition, memory, attention, executive and visuo-perceptual skills did not differ between those with and without RLS/WED. However, the RLS/WED group performed worse on language at baseline by 0.249 of a standard deviation, while demonstrating a mitigated language decline over time, by 0.063 of a standard deviation. The unadjusted models yielded similar results. Conclu-sions: Our findings were indicative of a baseline language disadvantage among older individuals with RLS/WED, but the initial discrepancy tends to dissolve over time.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

The implementation of sentinel lymph node (SLN) biopsy is changing the scenario in the surgical treatment of early-stage cervical cancer and the oncologic safety of replacing bilateral pelvic lymphadenectomy with SLN biopsy is currently under investigation. One of the undisputed values of SLN biopsy is its diagnostic accuracy in detecting low-volume metastases (LVM) via pathologic ultrastaging. In early-stage cervical cancer, the reported incidence of LVM ranges from 4 to 20%. The prognostic impact and the role of adjuvant treatment in patients with LVM is still unclear. Some non-prespecified analyses in prospective studies showed no impact on the oncologic outcomes compared to node-negative disease. However, the heterogeneity of the studies, the differences in the disease stage and the use of adjuvant treatment, and the concomitant pelvic lymphadenectomy (PLND) make any conclusion on this topic hard. Current guidelines suggest considering micrometastasis (MIC) as a node-positive disease, while isolated tumor cells (ITC) as a node-negative disease, with a low level of evidence. This review aims to highlight the unanswered questions about the definition, identification, prognostic and therapeutic role of LVM and underline the present and future challenges we are facing. We hope this review will guide further research, giving robust evidence on LVM and their impact on clinical practice.

In wireless sensor networks (WSNs) deployed in smart agriculture systems, accurately determining the locations of sensor nodes is crucial for efficient monitoring and control. However, in many cases, the exact positions of certain sensor nodes may be unknown. To address this challenge, this paper presents a novel method for localizing unknown sensor nodes in WSN-based smart agriculture systems using range measurements. The proposed method utilizes the Levenberg-Marquardt optimization algorithm to solve a nonlinear least squares problem and minimize the error in estimating the unknown node locations. By leveraging the known positions of a subset of sensor nodes and the inexact distance measurements between pairs of nodes, the localization problem is transformed into a nonlinear optimization problem. To validate the effectiveness of the approach, extensive simulations and experiments were conducted. The results demonstrate that the proposed method achieves accurate localization of the unknown sensor nodes, effectively enhancing the overall performance of the WSN-based smart agriculture system. Furthermore, the method demonstrates robustness against measurement noise and scalability for large-scale networks. The practical implications of this research extend beyond smart agriculture systems, as the proposed method can be applied to various WSN applications where precise node localization is essential.

Investigating the network response to node removal and the efficacy of the node removal strategies are related and fundamental questions in network science. Research studies proposed many node centralities based on the network structure ranking node to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks, and an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node removal strategies to network dismantle with effective node removal strategies from the literature, such as betweenness and closeness node removal over synthetic and real-world networks. We evaluate the network dismantle along node removal using the size of the largest connected component (LCC). We find that, hence the betweenness nodes attack is the best strategy overall, the new node removal strategies based on RW show the highest efficacy in peculiar network topology. Specifically, RW strategies based on covering times emerge as the most effective strategy on a synthetic lattice network and two real-world road networks. Our results may be useful in selecting the best node attack strategies in a specific class of networks and in building more robust network structures.

Abstract Objective: To review the relevant literature on the use of atrioventricular node ablation and pacing in patients with heart failure and atrial fibrillation. Methods: A PubMed/MEDLINE and SCOPUS search was performed in order to assess the clinical outcomes of atrioventricular node ablation and pacemaker implantation, as well as the complications that may occur. Results: Several clinical trials, observational analyses and meta-analyses have shown that “pace and ablate” strategy not only improves symptoms but also can enhance cardiac performance in patients with heart failure and atrial fibrillation. Although this procedure is effective and safe, some complications may occur including worsening of heart failure, permanent fibrillation, arrhythmias and sudden death. Regarding the implantation of pacemaker, cardiac resynchronization therapy is shown to be the optimal choice compared to right ventricle apical pacing. His bundle pacing is a promising alternative to cardiac resynchronization therapy and has shown beneficial effects, while left bundle brunch pacing is an innovative modality. Conclusions: Atrioventricular node ablation and implantation of pacemaker is shown to have beneficial effects on clinical outcomes of patients with atrial fibrillation ± heart failure who do not respond or are intolerant to medical treatment. Cardiac resynchronization therapy is the treatment of choice and His bundle pacing seems to be an effective alternative way of pacing in these patients.

This paper analyzed the main diseases of the friction high-strength bolt (FHSB) joints in order to study the characteristics of the corrosion products of the joints in steel bridge and the influence factors. Seven representative FHSB connection pairs and eight steel plate samples were selected from the Dongying Shengli Yellow River Bridge, which has been in operation for 33 years. Then Scanning Electron Microscope (SEM), Energy Dispersive Spectroscopy (EDS) and X-Ray Diffraction (XRD) were used to analyze the microscopic morphology and chemical composition of the corroded surface of the samples. Finally, this paper discussed the relationship between the corroded sample surface and the environmental corrosion. The research results showed that construction quality problems, such as non-standard hole expansion, segmental slab joint dislocation and contact surface pollution, accelerated corrosion of the contact surface. With the increase of corrosion degree of joints, the contact surface of aluminum spraying layer gradually changed from a rugged and dense state to a smooth and porous powder state. With the corrosion of the steel plate substrate, the contact surface gradually changed from a fluffy stratified state to a surface bonding state. It was inferred that the friction coefficient of the FHSB connection node on the corroded aluminum sprayed contact surface first decreased and then increased. The corroded node samples detected not only a large number of S and Cl elements, but also the oxides of Mn, Si and other elements as well as FeS. It was speculated that node corrosion was also related to atmospheric (acid rain) and industrial dust and other corrosive environments. Almost all samples detected the component SiO2 of the Yellow River soil, as well as Mg, Ca, K, Na and other elements at the same time, which is basically consistent with the component elements of the Yellow River soil. Therefore, it was inferred that it was related to the inclusion of the Yellow River soil.

Targeted radioisotope-guided sentinel lymph node dissection (sLND) has shown high diagnostic accuracy in prostate cancer (PCa). To overcome the downsides of the radioactive tracers, magnetometer-guided sLND using superparamagnetic iron oxide nanoparticles (SPIONs) was successfully applied in PCa. This prospective study (SentiMag Pro II, DRKS00007671) determined the diagnostic accuracy of magnetometer-guided sLND in intermediate- and high-risk PCa. Fifty intermediate- or high-risk PCa patients (PSA≥10 ng/ml and/or Gleason score ≥7; median PSA 10.8 ng/ml, IQR 7.4–19.2 ng/ml) were enrolled. After intraprostatic SPIONs injection a day earlier, patients underwent magnetometer-guided sLND and eLND, followed by radical prostatectomy. SLNs were detected in vivo and in ex vivo samples. Diagnostic accuracy of sLND was assessed using eLND as the reference. SLNs were detected in all patients (detection rate 100%), with 447 SLNs (median 9, IQR 6–12) being identified and 966 LNs (median 18, IQR 15-23) being removed. Thirty-six percent (18/50) of patients had LN metastases (median 2, IQR 1–3). Magnetometer-guided sLND had 100% sensitivity, 97.0% specificity, 94.4% positive predictive value, 100% negative predictive value, 0.0% false negative rate, and 3.0% additional diagnostic value (LN metastases only in SLNs outside the eLND template). In vivo, one positive SLN/LN-positive patient was missed, resulting in a sensitivity of 94.4%. In conclusion, this new magnetic sentinel procedure has high accuracy for nodal staging in intermediate- and high-risk PCa. The reliability of intraoperative SLN detection using this magnetometer system requires verification in further multicentric studies.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

Excessive high fat diet (HFD) consumption can induce food addiction which is believed to involve the communication between the hypothalamus and mesolimbic dopaminergic neurons, originating in the ventral tegmental area (VTA) and projecting to the nucleus accumbens (NAc). These brain regions are densely populated with opioid receptors, raising the possibility that these receptors, and particularly mu opioid receptors (MORs), are involved in mediating reward induced by palatable foods. This study sought to investigate the involvement of MORs in high fat diet (HFD)-induced reward and if there is any difference between male and female subjects in this response. We also assessed if exposure to HFD would potentiate the rewarding action of oxycodone, a relatively selective MOR agonist. The place conditioning paradigm was used to determine if conditioning for a short time (STC, 2 h) or long time (LTC, 16 h) with HFD induces reward or alters the rewarding action of oxycodone. Male and female C57BL/6J mice as well as MOR knockout and wildtype mice of both sexes were tested for basal place preference on day 1 and then conditioned with HFD in one chamber and regular chow diet (RCD) in another chamber and tested for place preference again after three sets of STC and again after a set of LTC. Each set consisted of two conditioning with RCD and two conditioning with HFD. Controls were conditioned with RCD in both conditioning chambers. Following the last place preference test, mice were treated with oxycodone and conditioned in the HFD-paired chamber and saline in the RCD-paired chamber for one hour once a day to explore the possibility if the HFD could alter oxycodone reward. The result showed that HFD induced conditioned place preference (CPP) in both male and female subjects following the LTC. This response was further potentiated after oxycodone conditioning. The latter response was mediated via MORs, as it was blunted in MOR knockout mice. However, HFD-induced CPP was observed following LTC in only female MOR knockout mice, suggesting for sexual dimorphism in this response.

Place-based education (PBE) and active learning are effective strategies for geoscience education. However, traditional PBE via field trips requires significant resources, time, physical abilities, and expertise of teachers. We provide an alternative PBE experience by showing how different kinds of geoscience videos can be spatially organized into one digital interactive virtual environment. Here, we present the Google Earth Geoscience Video Library (GEGVL) which uses Google Earth and location specific videos about Earth events to create a virtual PBE experience. Using Google Earth, GEGVL organizes place-based videos by locations and links pertinent non-place-based videos and allows users to roam the globe in search of geoscientific videos that are pertinent to them or their students. Currently GEGVL contains 150 videos organized into ten different geoscience disciplines: Plate Tectonics, Minerals, Structural Geology, Metamorphism, Magmatism, Hydrology, Environmental Science, Sedimentology, Paleontology, and Paleomagnetism. Despite stability challenges with Google Earth integration, results of user surveys among lower division undergraduates show that the design logic of GEGVL is promising virtual PBE organizer for interesting students in and helping them learn about Earth sciences.

The differential-equation of second order for space-time oscillation in flat tangential-spacetime of Minkowski-type can be written as an energy-equation. For this energy-equation the analogon of damping energy in two coupled Minkoswki-spacetimes with ftl can be calculated and formulated over Lamberts W-function or via Euler-equation.

In recent times, using image-based deep learning techniques has been very useful for classifying fruits. However, mango is a particular challenge because its shelf life is directly related to the degree of maturity at the time of harvest, which is determined mainly through the visual assessment of the operators when sorting them, doing it incorrectly, coupled with the blows and compressions exposed during storage and transport, trigger the deterioration in their quality, hence the importance of this operation. In this sense, the purpose of this study focuses on designing a computational model based on Deep Learning that uses a convolutional neural network (CNN) parameterized to select mangoes according to their color tone based on their maturity stage. A dataset was established from 201 labeled images, then a CNN architecture was built, obtaining a model on which 3 criteria were evaluated: the number of convolution and grouping layers, the resolution of the input images and the number of training epochs required. As a result, an input image resolution of 32 x 32 pixels was achieved, the process included a convolution layer followed by pooling that fed another layer that processed the results and ended in an output layer with 2 neurons under the One Hot Encoding representation. The model required 20 epochs to perfect its training, achieving 96.04 % accuracy in mango image selection. This study supports the potential of CNNs in quality analysis through mango color selection, even in uncertainty scenarios.

In this article, we present two topics related to mathematical economics. We offer an intriguing proposal for securing cost and production functions in the face of uncertainty and risk. We discuss the relationship between individual and social preferences. This is important because traditional revealed preference theory does not account for such factors.

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

In this paper, we establish some inequalities bounding the ratio Г_p,k(x)/Г_p,k(y), where Г_p,k(.) is the (p,k)-analogue of the Gamma function. Consequently, some previous results are recovered from the obtained results.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

The primary purpose of this article is to deduce specific order estimates for the \textit{Mertens Function} $M(n)$, which facilitates us to analyze the location of zeros of the \textit{Riemann Zeta function} $\zeta(s)$. The paper also provides a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$. In addition to learning about various \textit{spectral properties} of $ \mathbb{A}_{n}$, we shall also deduce the relation between these two, which, eventually would lead us to establish a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true, as justified by \textit{Redheffer} himself. We shall also observe several numerical evidence as well as theoretical justification behind the falsity of the famous \textit{Mertens Hypothesis}, along with how researchers over the years have approached towards deriving an estimate of the smallest possible natural number $n$ for which the first such violation of the theorem occurs, utilizing numerous conjectures annotating about the order of $M(n)$. Readers who are highly motivated in pursuing research in any of the topics relevent to the contents of this paper will surely find the \texttt{References} section to be extremely resourceful.

In recent decades, the Variational AutoEncoder (VAE) model has shown good potential and capabilities in image generation and dimensionality reduction. The combination of VAE and various machine learning frameworks has also worked effectively in different daily life applications, however its possibility and effectiveness in modern game design has seldom been explored nor assessed. The use of its feature extractor for data clustering was minimally discussed in literature neither. This paper first attempts to explore different mathematical properties of the VAE model, in particular, the theoretical framework of the encoding and decoding processes, the possible achievable lower bound and loss functions of different applications; then applies the established VAE model into generating new game levels within two well-known game settings; as well as validating the effectiveness of its data clustering mechanism with the aid of the Modified National Institute of Standards and Technology (MNIST) database. Respective statistical metrics and assessments were also utilized for evaluating the performance of the proposed VAE model in aforementioned case studies. Based on the statistical and spatial results, several potential drawbacks and future enhancement of the established model were outlined, with the aim of maximizing the strengths and advantages of VAE for future game design tasks and relevant industrial missions.

Additive manufacturing enables the realization of complex component designs that can not be achieved with conventional processes, such as the integration of lattice structures for weight reduction. To include lattice structures in component designs, an automated algorithm compatible to conventional CAD is required that is able to handle various lattice topologies as well as variable local shape parameters such as strut radii. Furthermore, smooth node transitions are desired since previous studies indicate advantages regarding reduced stress concentrations and the structural response to loadings such as fatigue performance. The surface patch-based algorithm developed in this work is able to solidify given lattice frames to smooth lattice structures without manual construction steps. The algorithm requires only a few seconds of sketching time for each node and favours paralellization. Automated special case workarounds as well as fallback mechanisms are considered for non-standard inputs. It is demonstrated on irregular lattice topologies and applied for the construction of a lattice infill of an aircraft component that was additively manufactured.

Background: Primary lymphedema is a chronic condition caused by a developmental abnormality of the lymphatic system and its malfunction. Different surgical options such as physiologic and excisional procedures have been proposed. The aim of this study was to present a complete algorithm for the treatment of primary lower extremity lymphedema: Primary LYmphedema Multidisciplinary Approach (P-LYMA). Methods: Nineteen patients were treated according to the P-LYMA. Patients underwent pre- and post-operative complex decongestive therapy (CDT). Different physiologic and excisional procedures were performed independently or in combination. The primary outcome was the circumferential reduction rate (CRR). The Lymphedema Quality of Life Score (LeQOLiS), reduction in the number of episodes of cellulitis, length of stay, and complications were recorded. Results: The mean CRR calculated was 72.8±19.6% after twelve months. The episodes of cellulitis per year decreased from a mean of 1.9±0.8 preoperative to 0.4± 0.6 throughtout follow-up. Two patients experienced minor complications. Mean hospitalization time was 5 days. Patients’ quality of life (LeQOLi score) drastically improved from 70.4±11.6 to 24.2 ±13.9 at twelve months post-op. Conclusion: The P-LYMA algorithm allows to maximize surgical results and improve the quality-of life in patients who suffer from primary lymphedema. CDT is mandatory to optimize results.

LoRa and its upper layers definition LoRaWAN is one of the most promising LPWAN technologies for implementing the Internet of Things (IoT). Although being a popular technology, several works in the literature have revealed various weaknesses regarding the security of LoRaWAN v1.0 (the official 1st draft). By using all these recommendations from the academia and industry, the LoRa-Alliance has worked on the v1.0 to develop an enhanced version and provide more secure and trustable architecture. The result of these efforts ended-up with LoRaWAN v1.1, which was released on Oct 11, 2017. This manuscript aims at demystifying the security aspects and provide a comprehensive Security Risk Analysis related to latest version of LoRaWAN. Besides, it provides several remedies to the recognized vulnerabilities. To the best of authors’ knowledge, this work is one of its first kind by providing a detailed security analysis related to latest version of LoRaWAN. According to our analysis, end-device physical capture, rogue gateway and replay attacks are found to be threating for safety operation of the network. Eventually, v1.1 of LoRaWAN is found to be less vulnerable to attacks compared to v1.0, yet possesses several security implications that need to be addressed and fixed for the upcoming releases.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

In this paper, the authors employ Mountain Pass Lemma, the method of weak solution regularization and Lyapunov function method to derive the unique existence of globally exponential stable positive stationary solution of a single-species model with diffusion and delayed feedback. The obtained stability criterion illuminates that under some suitable conditions, a certain internal competition is conducive to the overall stability of the population, and a certain amount of family planning is conducive to the overall stability of the population. A numerical example and three tables show the effectiveness of the proposed methods.

Mammography is often used as the most common laboratory method for the detection of breast cancer, yet associated with the high cost and many side effects. Machine learning prediction as an alternative method has shown promising results. This paper presents a method based on a multilayer fuzzy expert system for the detection of breast cancer using an extreme learning machine (ELM) classification model integrated with radial basis function (RBF) kernel called ELM-RBF, considering the Wisconsin dataset. The performance of the proposed model is further compared with a linear-SVM model. The proposed model outperforms the linear-SVM model with RMSE, R², MAPE equal to 0.1719, 0.9374 and 0.0539, respectively. Furthermore, both models are studied in terms of criteria of accuracy, precision, sensitivity, specificity, validation, true positive rate (TPR), and false-negative rate (FNR). The ELM-RBF model for these criteria presents better performance compared to the SVM model.

When extract building from high resolution remote sensing image with meter/sub-meter accuracy, the shade of trees and interference of roads are the main factors of reducing the extraction accuracy. Proposed a Bayesian Convolutional Neural Networks(BCNET) model base on standard fully convolutional networks(FCN) to solve these problems. First take building with no shade or artificial removal of shade as Sample-A, woodland as Sample-B, road as Sample-C. Set up 3 sample libraries. Learn these sample libraries respectively, get their own set of feature vector; Mixture Gauss model these feature vector set, evaluate the conditional probability density function of mixture of noise object and roofs; Improve the standard FCN from the 2 aspect:(1) Introduce atrous convolution. (2) Take conditional probability density function as the activation function of the last convolution. Carry out experiment using unmanned aerial vehicle(UVA) image, the results show that BCNET model can effectively eliminate the influence of trees and roads, the building extraction accuracy can reach 97%.

In history, theta function identities have been studied extensively and deeply. In this paper, applying the residue theorem of an elliptic function, we obtain a parameterized theta function identity. Then, by selecting the appropriate parameter, we derive some famous Jacobi identities, as well as other relatively simple theta function identities.

In this paper, an analytical form of the Unit Step Function (or Heaviside Step function) is presented. This important function constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics. In particular, Heaviside Step Function is performed in a very simple manner by the use of a finite number of standard operations, as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical expressions, is that the proposed exact formula contains two arbitrary single - valued continuous functions which satisfy only one restriction. In addition, the proposed representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Beta function, Logistic function. Besides, it is neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

In this paper, the author obtains an analytic exact form of Heaviside function, which is also known as Unit Step function and constitutes a fundamental concept of the Operational Calculus.In particulat, this function is explicitly expressed in a very simple manner by the aid of purely algebraic representations. The novelty of this work is that the proposed explicit formula is not performed in terms of non – elementary special functions, e.g. Dirac delta function or Error function and also is neither the limit of a function, nor the limit of a sequence of functions with point wise or uniform convergence. Hence, it may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.

Background: Upper extremities’ function impairments (UEFI) and gait impairment are frequently reported even in the early stages of Multiple Sclerosis (MS) disease. These motor deficits can negatively affect the quality of life (QOL) in MS patient. Exercise has been repeatedly introduced as a beneficial adjuvant therapy for MS, attenuating a wide range of physical and psychological symptoms without any side effects or increased risks of relapse or exacerbation in disease symptoms.Aim: This paper investigates the effect of multi-function swing suspension training (MFSST) program on upper and lower extremities’ function (ULEF), and QOL in MS women according to expanded disability status scale (EDSS) score.Design: Experimental method with a pre-test and post-test design with control group. Setting: The department of Sports Injuries and Corrective Exercise at the Shahid Bahonar University of Kerman.Population: Forty-seven MS women.Methods: Eligible subjects who matched the selection criteria were randomly assigned into three groups as follow: i. Intervention group A (EDSS of 2 – 4), ii. Intervention group B (EDSS of 4.5 – 6.5), and iii. Control group (EDSS of 2 – 6.5). The intervention groups have been trained by the SET program for a duration of 8 weeks. At baseline and after the intervention, the upper extremities’ function (UEF) and the lower extremities’ function (LEF) were assessed by 9-hole peg test (9HPT) and the timed 25-foot walk (T25FW) test, respectively. Moreover, participants’ QOL was measured using the Short Form questionnaire (SF-36).Results: A significant difference was found between the pre-test and post-test variables of walking speed and upper extremity endurance in intervention groups, and between the intervention groups and control group (P < 0.05). Compared to control group, both intervention groups showed improvements in all subscales of QOL, except emotional role limitation score.Conclusions: In summary, these results show that the present protocol of MFSST could be effective in improving ULEF and QOL in MS patients, showing the improvements after 4^th week. Moreover, this protocol was more useful for patients with an EDSS score of more than 4.5. Therefore, it seems that exercise therapy should be considered as a beneficial clinical intervention approach to improve ULEF and QOL in MS patients.

Experimental evidence suggests that chronic intermittent hypoxia (CIH), a major hallmark of obstructive sleep apnea (OSA), boosts carotid body (CB) responsiveness, thereby causing in-creased sympathetic activity, arterial and pulmonary hypertension, and cardiovascular disease. An enhanced circulatory chemoreflex, oxidative stress, and NO signaling appear to play im-portant roles in these responses to CIH in rodents. Since the guinea pig has a hypofunctional CB (i.e., it is a natural CB knockout), in this study we used it as a model to investigate the CB de-pendence of the effects of CIH on pulmonary vascular responses, including those mediated by NO, by comparing them with those previously described in the rat. We have analyzed pulmonary artery pressure (PAP), the hypoxic pulmonary vasoconstriction (HPV) response, endothelial function both in vivo and in vitro, and vascular remodeling (intima-media thickness, collagen fiber content, and vessel lumen area). We demonstrate that 30 days of exposure of guinea pigs to CIH (FiO2, 5% for 40 s, 30 cycles/h) induces pulmonary artery remodeling but does not alter en-dothelial function or the contractile response to phenylephrine in these arteries. In contrast, CIH exposure increased the systemic arterial pressure, and enhanced the contractile response to phenylephrine while decreasing endothelium-dependent vasorelaxation to carbachol in the aorta, without causing its remodeling. We conclude that since all of these effects are independent of CB sensitization, there must be other oxygen sensors, beyond the CB, with the capacity to alter the autonomic control of the heart and vascular function and structure in CIH.

In the dynamic interplay between people and their physical environments, the Global South stands as a mosaic undergoing a multitude of transformative influences in architecture and urbanism where examining social sustainability becomes imperative. While prevailing attention remains on environmental and economic sustainability, this study addresses a persistent gap in the urban literature by focusing on the dynamic and manifold nature of social sustainability. Positioning itself within the context of sustainable development, the study links the pursuit of social aspects of sustainability with selected unique urban contexts from the Global South. Five cases that include Alexandria (Egypt), Tripoli (Libya), Basra (Iraq), Lilongwe (Malawi), and Accra (Ghana) are discussed through multi-layered investigations that involve attitude surveys, interviews, focus groups, participatory systematic observations, and behavioral mapping, engaging directly with inhabitants and stakeholders. Uncovering people-place narratives in the identified contexts, the cases are developed into five knowledge typologies that serve as practical tools for planning and design decision-making, policy formulation, and academic discourse. Discussions are conceived to demonstrate the transformative role people-place narratives play in fostering a more sustainable and equitable urban future. Conclusions are drawn to offer practical insights for stakeholders involved in various capacities in shaping the urban landscape of the Global South.

Virtual reality (VR) describes a family of technologies which immerse users in sensorily-stimulating virtual environments. Such technologies have increasingly found applications in the treatment of neurological and mental health disorders. Depression, anxiety, and other mood abnormalities are of concern in the growing elderly population – especially those who reside in long-term care facilities (LTCFs). The transition from the familiar home environment to the foreign LTCF introduces a number of stressors that can precipitate depression. However, recent studies reveal that VR therapy (VRT) can promote positive emotionality and improve cognitive abilities in the elderly, both at home and in LTCFs. VR thus holds potential in allowing elderly individuals to gradually adapt to their new environments – thereby mitigating the detrimental effects of place attachment and social exclusion. Nevertheless, while the current psychological literature is promising, the implementation of VR in LTCFs faces many challenges. LTCF residents must gain trust in VR technologies, care providers require training to maximize the positive effects of VRT, and decision makers must evaluate both the opportunities and obstacles in adopting VR. Here, we concisely review the implications of depression related to place attachment in LTCFs, and explore the potential therapeutic applications of VR.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.

Elevated blood glucose levels, known as glycemia, play a significant role in sudden cardiac arrest, often resulting in sudden cardiac death, particularly among those with diabetes. Understanding this link has been a challenge for healthcare professionals, leading many research groups to investigate the relationship between blood glucose levels and cardiac electrical activity. Our hypothesis suggests that glucose-sensing mechanisms in cardiac tissue could clarify this connection. To explore this, we adapted a single-compartment, in-silico model of the human atrial node's action potential. We incorporated glucose-sensing mechanisms with voltage-gated sodium ion channels using ordinary differential equations. Parameters for the model were based on existing experimental studies to mimic the impact of glucose levels on atrial node action potential firing. Simulations using voltage clamp and current clamp techniques showed that elevated glucose levels decreased sodium ion channel currents, leading to a reduction in the sinoatrial node action potential frequency. In summary, our model provides a cellular-level understanding of how high glucose levels can lead to bradycardia and sudden cardiac death.

Background: The accurate diagnosis of regional lymph node metastasis is critical for guiding treatment decisions in head and neck cancer patients. Despite advances in imaging techniques, detecting nodal metastasis remains challenging, leading to potential undertreatment or overtreatment. This systematic review aims to identify molecular markers associated with occult metastasis in Head and Neck Squamous Cell Carcinoma (HNSCC) patients. Methods: The present research was conducted following PRISMA guidelines. Prospero registration nr. CRD42024522985. Results: Through a comprehensive literature search and review process, 634 articles were considered, 103 of them were finally included. Conclusions: Several promising markers were identified, including miR-205, DSG3, pan-CK AE1/AE3, HPV-16, Activin-A, Cyclin D1, and NPL that demonstrated effectiveness across multiple studies. Future research should focus on exploring combination scoring systems to improve diagnostic precision and optimize treatment selection in HNSCC patients.

Introduction: Flow-cytometry (FC) is a powerful tool that can assist in lymphoma diagnosis in lymph node (LN) specimens. Although lymphoma diagnosis and classification are mainly based on tumor cell characteristics, surrounding cells are less employed in this process.Methods: We retrospectively investigated alterations in the ploidy status, proliferative cell fraction (PF) and the percentages of surrounding immune cells in 62 consecutive LN specimens with B-Cell Non-Hodgkin Lymphoma (B-NHL) that were submitted for FC evaluation between 2019-2022.Results: Compared with indolent B-NHLs, aggressive B-NHLs show increased DNA aneuploidy and PF, increased monocytes, immature-granulocytes, mature granulocytes, CD8⁺ T-cells, Double-Negative-T-cells and Double-Positive-T-cells, and decreased total CD45⁺ cells, total lymphocytes, CD4⁺ T-cells and CD4/CD8 ratio. Receiver operating characteristic analysis determined PF > 6.8% and immature-granulocytes > 0.9% as optimal cutoffs with highest specificity and sensitivity in differentiating aggressive and indolent B-NHLs.Conclusions: These findings further strength the diagnostic value of DNA content analysis by FC and suggest the utilization of tumor surrounding immune cells in NHL diagnosis and classification.

For equivalent modeling of mixed wind farms (WFs), existing clustering indicators cannot consider the complex coupling characteristics between different types of wind turbines (WTs). This paper proposes a refined equivalent modeling method for mixed WFs based on artificial intelligence technology. Firstly, the electromechanical transient performance of mixed WFs is analyzed. The WT type, wind speed and direction, and voltage dip are considered the main factors affecting the external dynamic response of mixed WFs. Secondly, the equivalent node model is established, including the selection of independent and dependent variables. Then, the multiple artificial neural networks (ANNs) are trained one by one based on sample data, to explore the nonlinear relationship between the dependent variables and the independent variables. Finally, the electromechanical transient simulations of the power systems with a mixed WF is carried out by using the MATLAB platform. Simulation results show that the proposed model can reflect the external characteristics of the mixed WF in different wind scenarios and voltage dips.

Recently, the Internet of Things (IoT) has attracted wide attention from many fields, especially healthcare, because of its large capacities of information perception and collection. In this paper, we present an IoT-based home telehealth system for providing smart healthcare management for individuals, especially older people. Each client node of the system is mainly composed of an electronic water meter that records the user's daily water usage and an unobtrusive sleep sensor that monitors the user's physiological parameters during sleep such as heart rate (HR), respiratory rate (RR), body movement (BM), and states on the bed or outside the bed. The sleep sensor senses the biosignals and states by a sensor matrix composed of 12 piezoelectric sensors. The collected data can be transmitted to a remote centralized cloud service by a wireless home gateway for analyzing the living pattern and rhythm of users. Furthermore, the periodic feedback of results can be provided to users themselves as well as their family and health advisers. In the present study, data collections from a total of 18 older subjects were made for one year to evaluate the effectiveness of the proposed system. By analyzing living pattern and rhythm, preliminary results indicate the effectiveness of the telehealth system and suggest the potential of the system regarding improvement of quality of life (QoL) of older people and promotion of their health.

The objective of this study was to evaluate the efficacy of one-step nucleic acid amplification (OSNA) for the detection of sentinel lymph node (SLN) metastasis compared to standard pathological ultrastaging in patients with early-stage endometrial cancer (EC). A total of 526 SLNs from 191 patients with EC were included in the study. 379 SLNs (147 patients) were evaluated by both methods, OSNA and standard pathological ultrastaging. The central 1-mm portion of each lymph node was subjected to semi-serial sectioning at 200-μm intervals and examined by hematoxylin-eosin and immunohistochemistry with CK19; the remaining tissue was analysed by OSNA for CK19 mRNA. The OSNA assay detected metastases in 19.7% of patients (14.9% micrometastasis and 4.8% macrometastasis), whereas pathological ultrastaging detected metastasis in 8.8% of patients (3.4% micrometastasis and 5.4% macrometastasis). Using the established cut-off value for detecting SLN metastasis by OSNA in EC (250 copies/μl), the sensitivity of the OSNA assay was 92%; specificity was 82%; diagnostic accuracy was 83%, and the negative predictive value was 99%. Discordant results between both methods were recorded in 20 patients (13.6%). OSNA resulted in an upstaging in 12 patients (8.2%). OSNA could aid in the identification of patients requiring adjuvant treatment at the time of diagnosis.

In zebrafish inner ear, hair cell orientation in anterior and posterior maculae of the embryonic otic vesicle is different (about 30–40 degrees): this is rather unusual in planar polarity mechanism of action, instead suggests that kinocilia may be rotationally polarized. In mice node, the innermost monociliated cells generate a left-ward fluid flow sensed by the immotile primary cilia of Left peri-nodal cells: the Nodal signaling pathway is then expressed asymmetrically, in the Left lateral plate mesoderm, breaking symmetry in visceral organs (situs solitus); however, Right peri-nodal cells also, if artificially excited by a right-ward flow, break symmetry and activate the Nodal cascade, though inverting visceral organ asymmetry (situs inversus); surprisingly, peri-nodal cells prove to be adept at distinguishing flow directionality. Recently, in the Kupffer vesicle (the zebrafish laterality organ), chiral primary cilia orientation has been described: primary cilia, in the left and right side, are symmetrically oriented, showing a mirror average divergence of about 15–20 degrees from the midline. This finding, taken together with the mirror behavior of mouse perinodal cells and zebrafish hair cells, champions the idea of primary cilia enantiomerism.

Dry eye syndrome (DES) has become increasingly prevalent due to the prolonged use of digital devices in modern society. Individual supplementation with lutein or docosahexaenoic acid (DHA) demonstrated potential benefits for eye health. This study aimed to investigate the effects of lutein plus DHA complex supplementation on DES, visual function, and memory in healthy individuals. Thirty-four participants, aged 40~60 years, received lutein/DHA complex supplements (containing 10 mg free-form lutein, 200 mg DHA, 30 mg red algae extract (astaxanthin), phosphatidylserine, and vitamin A) for 12 weeks. Ophthalmological examinations and memory tests were carried out, and a questionnaire was administered at weeks 0, 6, and 12 of the study. After 12 weeks of the intervention, the tear break-up time had significantly increased, and intraocular pressure (IOP) had significantly decreased. This suggests that lutein/DHA complex supplementation may reduce the IOP and offer potential benefits for DES, as indicated by improved tear stability.

This work uses a new approach to investigate the Riemann hypothesis, drawing conclusions about its trueness. It is based on the more general method presented in a very recent publication, by the same author, showing in detail how to approach that very well-known and interesting problem. This is achieved by means of the theory of dynamical systems (Poincaré index associated to equilibria of 2-dimensional systems) and the study of the zeros of the Dirichlet eta function, defined by a Dirichlet series. By using the well-known fact that the zeros of the eta function include all zeros of the Riemann zeta function in the (open) critical strip, excluded the critical line, ((0,1/2) ∪ (1/2,1)) × (−∞,∞), the development proceeds using only the eta function. In addition, the open and simply connected region (1/2,1) × (0,∞) is used along the text, taking into account the symmetries of zeros of the functions under analysis in the critical strip. The basic line of proof is to find the mathematical expression for the Poincaré index of the vector field associated to the eta function, assuming the existence of a zero of the eta function outside the critical line (in (1/2,1) × (0,∞)), and investigating the resulting unfoldings. Eventually, an inconsistency occurs and the proof ends by contradiction.

This paper presents a novel algorithm, the multi-objective nonlinear interval PageRank (MONIPR) Algorithm. This algorithm extends the conventional PageRank (PR) algorithm, integrating nonlinear interval computation and multi-objective considerations into the computation process. The MONIPR algorithm bridges a research gap in integrating nonlinear interval approaches and multi-objective problems into the PR algorithm, which were traditionally treated separately. In addition, this research adopts the constrained interval arithmetic proposed to address the limitations of the conventional PR algorithm, which tends to overlook uncertainties and results in deterministic outcomes. In addition, we use a numerical example to demonstrate the proposed algorithm, contrasting it with the conventional approaches. A numerical example demonstrates the algorithm's performance by comparing the rank intervals obtained with the traditional crisp Markov chain and PR algorithm. The results highlight the ability of the proposed algorithm to provide a range of possible rank intervals, considering both uncertainty and multi-objectives. The findings suggest potential applications in decision-making, uncertainty quantification, and systems analysis.

The Marchenko method is a data-driven way which makes it possible to calculate Green's functions from virtual points in the subsurface by the reflection data at the surface, only requiring a macro velocity model. This method requires collocated sources and receivers. However, in practice, subsampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green's functions. To solve this problem, this paper proposes to integrate sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply sparse inversion during the iterative process. Our work not only reduces the strict requirements on acquisition geometries, but also avoids the complexity and instability of direct inversion for Marchenko equations. This new method is applied to a two-dimensional numerical example with irregular sampled data. The result shows that it can effectively fill gaps of the obtained focusing functions and Green's functions in the Marchenko method.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to find the sums over inverse powers of zeroes for the incomplete Gamma- and Riemann zeta- functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeroes of the Hurwitz zeta-function , including the sum over the inverse first power of its appropriately defined non-trivial zeroes. We also study some related properties of the Hurwitz zeta-function zeroes. In particular, we show that for any natural N and small real epsilon, when z tends to n=0, -1, -2… we can find at least N zeroes of zeta in the - vicinity of 0 for sufficiently small epsilon, as well as one simple zero tending to 1, etc.

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

The objective of this study is to examine a nonparametric estimate , using the kernel approach, of the conditional distribution function of a scalar response variable that is given a random variable whose values take place in a separable real Hilbert space. The observations will be dependent on one another in a quasi-associated fashion. The pointwise practically perfect consistencies with rates of this estimator are established by us under some broad conditions. The study’s major objective is to investigate the convergence rate of the proposed estimator and its application in the convergence rate and asymptotic normality of the hazard function. The asymptotic normality of the developed estimator is established precisely. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data.

We developed a novel hybrid approach for solving global optimization, computer science, bio-medical and engineering real life applications that is based on the coupling of the Whale Optimizer and Sine Cosine Algorithms via a surrogate model. We relate the whale optimizer algorithm to balance between the exploitation and the exploration process in the proposed method. There exist confirmed techniques for searching approximate best optimal solutions, but our algorithm will further guarantee that such numerical and statistical solutions satisfy physical bounds of the standard and real life functions. Our experiments with the benchmark, bio-medical, computer science and engineering real life problems have illustrated the advantages of using a newly hybrid approach based on mixing Whale Optimizer and Sine Cosine algorithms. It holds considerable potential for reducing execution time for solving standard and real life problems and at the same time improving the quality of the solution.

Motivated by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim, in the present paper, we consider a class of new generating function for the Frobenius-Genocchi polynomials, called the type 2 poly-Frobenius-Genocchi polynomials, by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Frobenius-Genocchi polynomias equal a linear combination of the classical Frobenius-Genocchi polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Frobenius-Genocchi polynomials and Bernoulli polynomials of order k. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim, we introduce the unipoly-Frobenius-Genocchi polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Frobenius-Genocchi polynomials and the classical Frobenius-Genocchi polynomials.

In the paper, the author finds bounds of the sine and cosine along a circle on the complex plane in terms of two double inequalities for the norms of the sine and cosine along a circle on the complex plane.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

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.

In the paper, by virtue of some properties for the Riemann zeta function, the author finds a double inequality for the ratio of two consecutive Bernoulli numbers with even indexes and analyzes the approximating accuracy of the double inequality.

The role of postmastectomy radiotherapy and regional nodal irradiation after radical mastectomy is defined in high-risk patients with locally advanced tumors, positive margins, and unfavorable biology. The benefit of postmastectomy radiotherapy in intermediate-risk patients (T3N0 tumors) remains a matter of controversy. It has been demonstrated that radiotherapy after breast-conserving surgery lowers the locoregional recurrence rate compared with surgery alone and improves the overall survival rate. In patients with 4 or more positive lymph nodes or extracapsular extension regional lymph node irradiation is indicated regardless of the surgery type (breast-conserving surgery or mastectomy). Despite the consensus that patients with more than 3 positive lymph nodes should be treated with radiotherapy, there is a controversy regarding the recommendations for patients with one to three involved lymph nodes. In patients with N0 disease with negative findings on axillary surgery, there is a trend to administer regional lymph node irradiation in patients with a high risk of recurrence. In patients treated with neoadjuvant systemic therapy and mastectomy, adjuvant radiotherapy should be administered in case of clinical stage III and/or ≥ypN1. In patients treated with neoadjuvant systemic therapy and breast-conserving surgery, postoperative radiotherapy is indicated irrespective of pathological response.

Over the past several years there has been much debate with regards to the prognostic and clinical significance of pancreatic ductal adenocarcinoma (PDAC) with lymph nodes metastasis. The PDAC gene-expression knowledge and the biologic alterations underlying the lymph node involvement convey a clinical implication in dealing with the theranostic window.To this end, we provide an original bioinformatic dissection of the gene-expression differences of PDAC according to the nodal involvement from a large public available dataset. Comprehensive transcriptomic analysis from 143 RNA-seq patient’s derived samples indicated that WNT increased activation and a peculiar immune-microenvironment identify subjects with nodal involvement.In frame of this thinking, we validated the WNT pathway role in increasing the likelihood of lymphatic dissemination in vitro. Moreover, we demonstrated for the first time in a PDAC model the potential therapeutic window that XAV-939, a specific WNT pathway inhibitor, has in re-educating a tumour permissive immune system. Finally, we outline the potential implication on bystander molecular drivers exerted by WNT molecular inhibition, providing a picture of the proteomic oncogenic landscape changes elicited by XAV-939 on PDAC cells and their clinical implication. Our findings hold the promise to identify novel immune-based therapeutic strategies targeting WNT to enhance PDAC cytotoxicity and restore anti-PDAC immunity in nodes-positive disease.

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

When training deep neural networks tasks, the most popular choices are cross-entropy loss. On the other hand, in general speaking, a decent loss function can take on shapes that are considerably more flexible and ought to be adapted for different activities and datasets. In most of the classification tasks, generally if the true class is not correctly recognized by the network (top1), that class is placed among the five classes with the highest probability (top5). This shows that the network does not necessarily recognize the correct class with a low probability, but a class similar to it (such as 3 vs. 8 in mnist) assigns a higher probability and this causes a mistake in that task. Accordingly, we proposed a loss function deals with the error of class that the neural network incorrectly recognized as correct, in addition to the correct class error. We call our proposed loss as False Positive Loss (FPL), with the intention of viewing and designing loss functions not only through the utilization of true class but also through the utilization of the value of false positive classes. One of the core properties of our proposed loss is full adaptability, which makes False Positive Loss be fully capable of getting reformulated by using other widely used loss functions formulas based on the task or the need of the users. Extensive experimental results demonstrate that our suggested loss function outperforms other well-known losses on a variety of tasks and datasets. As can be observed, the performance of our False Positive Loss is superior to that of the cross-entropy loss when it comes to tasks involving 2D picture classification. We have compared our loss with cross entropy as the most common classification loss function on some models (such as ResNet-18, ResNet-50 and Efficientnet-V2) through classification known as a basic computer vision task. with both random or pre-trained initial weights. As a result, in some cases the models with our loss outperform the same tasks with cross entropy from the viewpoint of some metric (i.e. accuracy and FP). For example, the resnet-50 on cifar-10 dataset with random initialization indicated a top1 accuracy of 94.93 with cross entropy and 95.25 with our loss, while for top5 accuracy the results are 99.86 and 99.87, respectively.

Rats, including those of the Sprague Dawley strain, may kill mice. Because of this muridical behavior, it is standard practice in many research animal housing facilities to separate mice from rats (i.e., the predators) to minimize stress for the mice. We therefore tested the effect of cohousing on the stress levels of mice from either the C57BL/6J (BL6) or the CD1 strain and Sprague Dawley (SD rat) by determining their fecal corticosterone or cortisol metabolites (FCM) concentration and investigated how cohousing impacts a behavioral assay, i.e., conditioned place preference for intragenus (i.e., mouse-mouse or rat-rat) dyadic social interaction (DSI CPP) that had been shown be sensitive to social factors, especially to handling by humans. We found that the two delivery batches of BL6 mice or SD rats, respectively, had different stress levels at delivery that were statistically significant for the BL6 mice. Even so, the BL6 mice cohoused with rats had significantly increased FCM concentrations, indicative of higher stress levels, as compared to (1) BL6 mice housed alone or (2) BL6 mice at delivery. In contrast to their elevated stress levels, the attractiveness for contextual cues associated with mouse-mouse social interaction (DSI CPP) even increased in rat-cohoused BL6 mice, albeit nonsignificantly. Thus, cohousing BL6 mice and rats did not impair a behavioral assay in BL6 mice that had proved to be sensitive to handling stress by humans in our laboratory. SD rats cohoused with BL6- or CD1 mice and CD1 mice cohoused with SD rats showed DSI CPP that was not different from our previously published data on SD rats and BL6 mice of the Jackson- or NIH substrain obtained in the absence of cohousing. Our findings suggest that the effect of cohousing rats and mice under the conditions described above on their stress levels as opposed to their behavior might be less clearcut than generally assumed and might be overriden by conditions that cannot be controlled, i.e., different deliveries. Our findings can help to use research animal housing resources, which usually are limited, more efficiently.

Understanding brain function is one of the most important open problems in science today. At present, there is no concrete theory for how the brain works. Here, a theory is presented that provides a detailed mechanistic biological account of the brain’s capacities. Brain function is managed by a response (R) process that is structurally similar to the immune response, and shows anatomical and molecular specificity. Different R process stages utilize different cortical layers, hippocampus fields, basal ganglia paths, GABAergic interneurons, cerebellum paths, and molecular agents such as dopamine, serotonin and opioids. We show how the R process supports hierarchical action sequences, language and thought. The theory is supported by a large body of experimental evidence in many modalities, and accounts for virtually all of the major facts known about the brain at the system level.

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

The closed forms of the non-resonant thermonuclear function in the Maxwell-Boltzmann and Tsallis case with depleted tail are obtained in generalized special functions. The results are written in terms of H-function of two variables. The importance of the results in this paper lies in the fact that the reaction rate probability integrals in Maxwell-Boltzmann and Tsallis cases are not obtained by the conventional method of approximation or by means of a single variable transform technique but by means of a two variable transform method. The Behaviour of the depleted non-resonant thermonuclear functions are examined using graphs. The results in the paper are of much interest to astrophysicists and statisticians in their further work in this area.

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

Financial system is essentially chaotic and unstable if there is not any external inputs. By means of Lyapunov function method, design of switching law, novel fuzzy assumption, $L^p$ estimation technique and Laplace semigroup theory, the author presents the boundedness and LMI-based (globally) asymptotical input-to-state stability criteria of financial systems. Particularly, the globally asymptotical stability in the meaning of switching implies that when the time $t$ is big enough, the dynamic of any subsystem must approach its unique equilibrium point. Besides, the global financial crisis often erupts periodically, which illuminates that the global stability in the classical sense is actually meaningless. So the stability in the meaning of switching proposed in this paper is suitable and appropriate. Numerical examples illuminate the effectiveness of the obtained results.

Kim(2015) introduced the degenerate Cauchy numbers of the second kind and gave some identities of them. In this paper, by using the modified polyexponential functions which are introduced by Kim-Kim(2019), we define the degenerate poly-Cauchy polynomials of the second kind and investigate some properties of them. Furthermore, we consider the degenerate unipoly-Cauchy polynomials of the second kind and discuss some properties of them.

This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the $p$-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the "broom topology'' type.

(1) Background: Sentinel lymph node (SLN) mapping represents an accurate and feasible technique for the surgical staging of endometrial and cervical cancer. This is commonly performed by conventional laparoscopy or robotic-assisted laparoscopy, but in recent years, a new retroperitoneal transvaginal natural orifice transluminal endoscopic surgery (vNOTES) approach has been described. This technique provides easy visualization of lymphatic afferent vessels and pelvic lymph nodes, early SLNs assessment, and a coherent mapping methodology following the lymphatic flow from caudal to cranial. However, only a few publications have reported it. Following the IDEAL (Idea Development Exploration Assessment Long-term follow-up) framework, research concerning this technique is at stage 2a, with only small case series as evidence of its feasibility. Its standardized description appears necessary to provide the surgical homogeneity required to move further. (2) Methods: description of a standardized approach for retroperitoneal pelvic SLN mapping by vNOTES. (3) Results: we described a 10-step approach to successfully perform retroperitoneal vNOTES SLN mapping, including pre-, intra-, and postoperative management. (4) Conclusions: This IDEAL stage 2a study could help other surgeons approach this new technique, and it proposes a common methodology necessary to evolve through future IDEAL stage 2b (multi-center studies) and stage 3 (randomized controlled trials) studies.

This study examines the prospective association of egg consumption with multiple domains of cognitive function in older, community-dwelling men and women followed 16.3 years. Participants were 617 men and 898 women from the Rancho Bernardo Cohort aged 60 and older who were surveyed about egg intake/week in 1972-74, and attended a 1988-91 research visit when cognitive function was assessed with 12 tests. Analyses showed that egg intake ranged from 0-24/week (means: men=4.23.2, women=3.52.7, p<0.0001). In men, covariate-adjusted regressions showed egg intake was associated with better performance on Buschke total (p=0.04), long-term (p=0.02) and short-term (p=0.05) recall. No significant associations were observed in women (p’s>0.05). Analyses in those <60y at in 1972-74 showed egg intake was positively associated with scores on Heaton copying(p<.04) and the Mini-Mental Status Exam(MMSE;p<.02) in men, and category fluency(p<0.05) in women. Egg intake was not significantly associated with odds of poor performance on MMSE, Trails B, or category fluency in either sex. These reassuring findings suggest there are no long-term detrimental effects of egg consumption on multiple cognitive function domains, and for men, there may be beneficial effects for verbal episodic memory. Egg consumption in middle-age may also be related to better cognitive performance later in life.

Spectral calibration consists of the calibration of wavelengths and the measurement of the instrument's spectral response function (SRF). Unlike conventional slits, the absorbed aerosol sensors (AAS) are used as a slit homogenizer, in which the spectral response function (SRF) is not a conventional Gaussian curve. To be more precise, the SRF is the convolution of the slit function of the spectrometer, the line spread function of the optical system, and the detector response function. The SRF of the slit homogenizer is a flat-topped multi-Gaussian function. Considering the convenience of fitting, a super-Gaussian function, which looks like a similar distribution to the flat-topped multi-Gaussian function, is used to fit the measured data in a spectral calibration. According to the results, the SRF’s shapes, due to the Earth port, resemble a Gaussian curve with a flatted top could be concluded, which contains an FWHM of 1.78–1.82 nm for the AAS. The results show that the correlation coefficients are about 0.99, which proves that the fitting function could better characterize the SRF of the instrument.

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

This paper addresses a variant of the product for the Dirichlet $L$--functions. We propose a completely detailed proof for the truth of the generalized Riemann conjecture for the Dirichlet $L$--functions, which states that the real part of the nontrivial zeros is $1/2$. The Wang and Hardy--Littlewood theorems are also discussed with removing the need for it. The results are applicable to show the truth of the Goldbach's conjecture.

In this study, we investigate the performance of the saddlepoint approximation of the probability mass function and the cumulative distribution function for the weighted sum of independent Poisson random variables. The goal is to approximate the hazard rate function for this complicated model. The better performance of this method is shown by numerical simulations and comparison with a performance of other approximation methods.

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E. T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to $SL(2,R)$. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2. We also derive more representations of the p-adic (ρ,q)-gamma function in general case. Moreover, we consider the p-adic (ρ,q)-Euler constant derived from the derivation of p-adic (ρ,q)-gamma function at x = 1. Furthermore, we provide a limit representation of aforementioned Euler constant based on (ρ,q)-numbers. Finally, we consider (ρ,q)-extension of the p-adic beta function via the p-adic (ρ,q)-gamma function and we then investigate various formulas and identities.

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A—which is the area of the event horizon of the black hole-, a length L_P—which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function, with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local, statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations.

Background: Tuberculosis (TB) manifests itself primarily in the lungs as pulmonary disease (PTB) and sometimes disseminates to other organs to cause extra-pulmonary TB, such as lymph node TB (LNTB). This study aimed to investigate the role of host genetic polymorphism in immunity related genes to find a genetic basis for such differences. Methods: Sixty-three, Single nucleotide polymorphisms (SNPs) in twenty-three, TB-immunity related genes including eleven innate immunity (SLCA11, VDR, TLR2, TLR4, TLR8, IRGM, P2RX7, LTA4H, SP110, DCSIGN and NOS2A) and twelve cytokine (TNFA, IFNG, IL2, Il12, IL18, IL1B, IL10, IL6, IL4, IL1RA, IL8 and TNFB) genes were investigated to find genetic associations in both PTB and LNTB as compared to healthy community controls. The serum cytokine levels were correlated for association with the genotypes. Results: PTB and LNTB showed differential genetic associations. The genetic variants in the cytokine genes (IFNG, IL12, IL4, TNFB and IL1RA and TLR2,4 associated with PTB susceptibility and cytokine levels but not LNTB (p &lt; 0.05). Similarly, genetic variants in LTA4H, P2RX7, DCSIGN and SP110 showed susceptibility to LNTB and not PTB. Pathway analysis showed abundance of cytokine related variants for PTB and apoptosis related variants for LNTB. Conclusions: PTB and LNTB outcomes of TB infection have a genetic component and should be considered for any future susceptibility and functional studies.

This research takes Cuiwei Village in Qianshan District of Zhuhai City as an example. Through field research, the village is investigated and analyzed, and the street scale, spatial structure, functional characteristic streets, internal commercial distribution forms, and functions of Cuiwei Historic District are studied. analysis. On this basis, based on the convex space method and the line-of-sight analysis method in the space syntax theory, with the help of Depthmap software, the complex street node, that is, the space of the two nodes A and B, is established through the establishment of a visual field model. It includes the analysis of the integration degree of the horizon, the concentration of the horizon, the connection value of the horizon and the spatial characteristics of the historical area, as well as the traditional buildings that are the most representative of the village, namely the Three Kings Temple and the Webster's Mansion. When R=N and radius R=3, observe the changes in the two parameters of the visual integration and visual depth of the two historical buildings. And with the help of Baidu Time Machine photos in different periods to observe and record the changes in the store and the characteristics of people's behavior, and draw conclusions.

In this paper, the methodology using Insect Intelligent Building (I^2B) technology for establishing energy consumption monitoring system of public buildings is prevailed. The computing process node and distributed algorithm are utilized to implement the energy consumption collection and data transmission and data pre-processing. Taking a commercial building as a case study, CPNs are applied to set up the building energy consumption monitoring system, with the Spanning Tree Algorithm for generating network topology，and BPNN method for solving abnormal data and recovering missing data. The research results demonstrate the proposed method can effectively improve the performance of plug-and-play and self-identified and self-configuration of energy consumption monitoring system.

In this study we discuss critical issues in modelling the structure and function of lymph nodes (LNs), with emphasis on how LN physiology is related to its multi-scale structural organization. In addition to macroscopic domains such as B-cell follicles and the T cell zone, there are vascular networks which play a key role in the delivery of information to the inner parts of the LN, i.e., the conduit and blood microvascular networks. We propose object-oriented computational algorithms to model the 3D geometry of the fibroblastic reticular cell (FRC) network and the microvasculature. Assuming that a conduit cylinder is densely packed with collagen fibers, the computational flow study predicted that the diffusion should be a dominating process in mass transport than convective flow. The geometry models are used to analyze the lymph flow properties through the conduit network in unperturbed- and damaged states of the LN. The analysis predicts that elimination of up to 60–90 % of edges is required to stop the lymph flux. This result suggests a high degree of functional robustness of the network.

Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$. By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.

This paper presents a theorem in factorial functions with the sum of any two nonnegative integers that is equal to multiple of the product of factorial of the same two nonnegative integers.

Abstract: Background: Of the many side effects suffered by cancer patients, those related to cognitive performance have become increasingly prominent in clinical practice. We know that chemotherapy generates a series of side effects, such as nausea and vomiting, alopecia, and so on, which can be counteracted by complementary medication. However, in the case of post-chemotherapy cognitive impairment, or chemo brain, these cannot be controlled with drug therapies. However, before any intervention can be considered, it is necessary to know exactly what cognitive impairment is being triggered. For this reason, we decided to study the cognitive status of breast cancer patients. Methods: analytical, prospective, three-measure longitudinal, intrasubject unifactorial, non-probabilistic and accidental assignment study. The sample came from the Medical Oncology Department at Hospital de Salamanca, in Spain. Cognitive function (Trail Making Test and Stroop Test) was established as the primary variable; the presence of sleep disorders (Insomnia Severity Index, ISI) and anaemia (haemoglobin levels in blood) were analysed as secondary variables, in addition to sociodemographic variables (age, stage, type of carcinoma, radiotherapy, menopause, social support network, marital status, years of schooling and employment status). Results: We recruited 151 individuals according to the selection criteria. We can confirm that factors including anaemia, menopause, patient support network and marital status, years of schooling, and employment status did affect the cognitive performance of the patients in active chemotherapy treatment in the study. In contrast, sleep disorders, age, radiotherapy treatment, stage of disease, and type of carcinoma did not affect the cognitive performance of the cancer patients. Conclusions: Chemotherapy does impact the cognitive performance of breast cancer patients.

Let $f(t)$ be a characteristic function. The question on infinite divisibility of $g_{2k}(t)=f^{(2k)}(t)/f^{(2k)}(0)$ is considered. There are given the condition for that function not to be infinite divisible. Some examples of infinite divisibility of $g_{2k}(t)$ are given.

Background: Of the many side effects suffered by cancer patients, those related to cognitive performance have become increasingly prominent in clinical practice. We know that chemotherapy generates a series of side effects, such as nausea and vomiting, alopecia, and so on, which can be counteracted by complementary medication. However, in the case of post-chemotherapy cognitive impairment, or chemo brain, these cannot be controlled with drug therapies. However, before any intervention can be considered, it is necessary to know exactly what cognitive impairment is being triggered. For this reason, we decided to study the cognitive status of breast cancer patients. Methods: analytical, prospective, three-measure longitudinal, intrasubject unifactorial, non-probabilistic and accidental assignment study. The sample came from the Medical Oncology Department at Hospital de Salamanca, in Spain. Cognitive function (Trail Making Test and Stroop Test) was established as the primary variable; the presence of sleep disorders (Insomnia Severity Index, ISI) and anaemia (haemoglobin levels in blood) were analysed as secondary variables, in addition to intervening variables (age, stage, type of carcinoma, radiotherapy, menopause, social support network, marital status, years of schooling and employment status). Results: We recruited 151 individuals according to the selection criteria. We can confirm that factors including anaemia, menopause, patient support network and marital status, years of schooling, and employment status did affect the cognitive performance of the patients in the study. In contrast, sleep disorders, age, radiotherapy treatment, stage of disease, and type of carcinoma did not affect the cognitive performance of the cancer patients. Conclusions: Chemotherapy does impact the cognitive performance of breast cancer patients.