This paper aimed to use social media impact on student studies in higher education. Apart from enjoyment and academic purposes, many educational practices and processes have been influenced by social networks. This paper highlighted the use of media tools in higher education as well as indicates out some of the factors. Moreover, through a literature review of related articles, we aim to provide insights into the impacts of a social network on educational quality, actual use of social media, and performance impact in higher education. A questionnaire survey on constructivism was circulated among a total of 206 university students as the key method for collecting data. This research hypothesizes educational quality and actual social media use indicates a positive effect in education, all of which also hypothesizes constructivism for educational quality and actual social media that in turn improve students’ satisfaction, and performance impact. Moreover, all research findings were attained through a quantitative method using the Structural Equation Modeling (SEM-AMOS). Findings of this research to indicate a positive effects students on their academic through behavioral intention to utilize social media to actual social media use for teaching and learning on higher education. Moreover, the results mention the use of social media for learning purpose, as well as social media to enables the sharing of knowledge, discussions, and information to enhance students' learning activities, Further studies are recommended which universities educators should take this into consideration when planning their curricula; it comes to the inclusion of technology in the teaching process.

The basic idea is to expand the completed zeta function $\xi(s)$ in MacLaurin series (infinite polynomial), which can be further expressed as infinite product (Hadamard product) by conjugate complex roots. Finally, the functional equation $\xi(s)=\xi(1-s)$ leads to $(s-\alpha_i)^2 = (1-s-\alpha_i)^2, i \in \mathbb{N}$ with solution $\alpha_i= \frac{1}{2}, i \in \mathbb{N}$, where $\alpha_i$ are the real parts of the zeros of $\xi(s)$, i.e., $s_i =\alpha_i\pm j\beta_i, i\in \mathbb{N}$. Therefore, a proof of the Riemann Hypothesis is achieved.

In this era of technology, programming has become more significant than ever before. Python and C++ are both widely used programming languages. Python, the most popular programming language in today’s world, is a high-level object-oriented language whereas C++, the language behind most operating systems, is a low-level object-oriented language. In this paper, we present a comparative study of Python and C++. This paper discusses the introduction to these languages, their memory management techniques, and the reasons behind their program execution speed. Furthermore, we analyzed the execution time and memory used by multiple algorithms in both the languages with best, average, and worst cases. They are also compared with respect to the benefits and issues related to them. Results indicate that C++ is faster than Python in execution speed but Python serves as a better language for beginners due to its simplicity. Moreover, for the best results, the language should be selected according to the type of project.

A concise proof of the Riemann Hypothesis is presented by clarifying the Hadamard product expansion over the zeta zeros, demonstrating that the Riemann Hypothesis is true.

Electronic Health Record (EHR) is being used in most healthcare institutions to preserve and share health records instead of a paper-based method. Data records must be exchanged amongst various parties and users' privileges to manage access to their records should also be provided. In addition to the basic standards of secrecy, confidentiality and integrity of information, these facts further demonstrate the need for interoperability and consumer control to access their personal data. Electronic Health Record (EHR) system faces issues of protection of data, trust and management issues. In recent Covid-19 pandemic, various applications, tools and websites were launched that stores records. Also, many personal records related to health need to be shared among different parties for early detection, contact tracing, monitoring and the future prediction that requires accurate and reliable data. Simultaneously, the citizens will be hesitant in providing their personal details due to privacy concerns and social stigma. Blockchain technology has arisen as a powerful technology that can offer the immutability, confidentiality and user access properties of stored information and provided distributed storage. This paper analyses the blockchain suitability in EHR and its further applications in efficient Covid-19 pandemic management.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

The Collatz conjecture (or 3n+1 problem) has been explored for about 86 years. In this article, we prove the Collatz conjecture. We will show that this conjecture holds for all positive integers by applying the Collatz inverse operation to the numbers that satisfy the rules of the Collatz conjecture. Finally, we will prove that there are no positive integers that do not satisfy this conjecture.

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.

Relationships between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem are discussed. Whether a function similar to Chebyshev’s second function is square-root close to a line having a slope different from 1 is discussed. The nontrivial zeros of the Riemann zeta function can be used to approximate many functions in analytic number theory. For example, it could be said that the nontrival zeta function zeros and the Möbius function generate in essence the same function - the Mertens function. A different approach is to start with a sequence that is analogous to the nontrivial zeros of the zeta function and follow the same procedure with both this sequence and the nontrivial zeros of the zeta function to generate in essence the same function. A procedure for generating such a function is given.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

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

We approximate the trigonometric function sine and cosine on the interval . This analysis provides two formulas to approximate sine and cosine. At first, we try to derive the formula which involves a square root, and then we derive another formula that does not require any use of a square root. Nevertheless, after deriving the procedure which requires no square root, we further try to increase its accuracy and then derive another formula that approximates trigonometric functions more accurately on the interval [0, pi/2]. So, this analysis provides mainly two types of procedures. One uses square roots, whereas the other does not. We also focus on ensuring the accuracy of these trigonometric functions in the interval [0,pi/2]. This accuracy analysis is portrayed using the graph. This graph shows the difference between the values generated by the functions defined here and the actual value of these functions. So, these graphs also indicate the error of these functions on that interval. Finally, we compare our approximation with the approximation formula of the 7th-century Indian Mathematician Bhaskara I.

The developments of confirmed daily Sars-CoV-2 infections can be modeled a posteriori in a comparatively simple and satisfactory way by means of a special exponential function: its exponential coefficient varies exponentially with time itself. This property enables the function to directly simulate the „daily case“ curve fragments observed for the first waves of the current epidemics in a number of counties and countries. Linear combinations of two or more of the functions allow for the modeling of the complete curves observed in the vast majority of all regions for which case number developments have been tabulated.

This article presents a dataset of tweets in the Urdu language. There are 1,140,824 tweets in the dataset, collected from Twitter for September and October 2020. This large-scale corpus of tweets is generated by performing pre-processing which includes removing columns containing user information, retweet’s count, followers information, duplicate tweets, removing unnecessary punctuation, links, symbols, and spaces, and finally extracting emojis if present in the tweet text. In the final dataset each tweet record contains columns for tweet id, text, and emoji extracted from the text with a sentiment score. Emojis are extracted to validate Machine Learning models used for the multilingual sentiment and behavior analysis. These are extracted using a Python script that searches for an emoji from the list of 751 most frequently used emojis. If an emoji is present in the text, a column with the emoji description and sentiment score is added.

In the paper, the authors nd a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

Decentralized Finance (DeFi) takes the promise of blockchain a step further and aims to transform traditional financial products into trustless and transparent protocols that run without involving intermediaries. Similar to how 2017 was the year of ICOs, 2020 was the year of DeFI with more than $15 billion of total investments. The decentralized platforms utilize oracles to retrieve asset data from the external world, but their choice and management criteria are often unknown to the end-users. If oracles are poorly selected or managed, the funds of a rising number of investors are inevitably in danger. The issue known as “the oracle problem,” which makes real-world applications controversial and debated due to the loss of decentralization, had recently drawn attention to DeFi given the crescent number of related hacks that caused the loss of millions of dollars held in DeFi projects. With a multivocal approach, this paper aims to shed light on the pattern that identifies the oracle problem in DeFi and outline the most promising ways to overcome the related weaknesses. This research supports the view that the oracle problem in decentralized finance bears specific characteristics which require standardization and appropriate economic incentives to be addressed.

We demonstrate a new quantitative method to the sieve of Eratosthenes, which is an alternative to the sieve of Legendre. In this method, every element of a given set is sifted out once only, and therefore, this method is free of the Mobius function and of the parity barrier. Using this method, we prove that every sufficiently large even number is the sum of two primes, and that every even number is the difference of two primes in infinitely many ways.

Now when the whole world is still under COVID-19 pandemic, many schools have transferred the teaching from physical classroom to online platforms. It is highly important for schools and online learning platforms to investigate the feedback to get valuable insights about online teaching process so that both platforms and teachers are able to learn which aspect they can improve to achieve better teaching performance. But handling reviews expressed by students would be a pretty laborious work if they were handled manually as well as it is unrealistic to handle large-scale feedback from e-learning platform. In order to address this problem, both machine learning algorithms and deep learning models are used in recent research to automatically process students' review getting the opinion, sentiment and attitudes expressed by the students. Such studies may play a crucial role in improving various interactive online learning platforms by incorporating automatic analysis of feedback. Therefore, we conduct an overview study of sentiment analysis in educational field presented in recent research, to help people grasp an overall understanding of the sentiment analysis research. Besides, according to the literature review, we identify three future directions that researchers can focus on in automatically feedback processing: high-level entity extraction, multi-lingual sentiment analysis, and handling of figurative language.

Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order on all finite groups, that is well behaved with respect to cardinality. In fact, if $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G$. There is also a canonical order for the elements of $G$ and we can define equivalent objects of $G$. This allows us to find the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and a minimal set of independent equations that define the group is obtained. We show how to find all groups of order $n$, and order them. Examples are given using all groups with order smaller than $10$. The canonical block form of the symmetry group $\Delta_4$ is given and we find its automorphisms. These results are extended to the infinite case. A real number is an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. We make brief comments on treating the calculus of real numbers. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational and physical aspects of these representations.

Information security plays a major role in the dynamics of today’s interconnected world. Despite the successful implementation and effectiveness of modern cryptographic techniques, their inherent limitations can be exploited by quantum computers. In this article we discuss Grover’s quantum searching algorithm and its impact on the security of modern symmetric ciphers. More specifically, we present its formal description and give an implementation of the algorithm using IBM’s Qiskit framework, which allows us to simulate and run the program on a real device. The developed program is modular and scalable, managing to properly run on any input state. We compare the performance of the algorithm running on the local simulator against its execution on a quantum processor from IBM’s lineup, noting the discrepancies between the results due to physical characteristics of the chip.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

The spread of the Coronavirus pandemic has been accompanied by an infodemic. The false information that is embedded in the infodemic affects people’s ability to have access to safety information and follow proper procedures to mitigate the risks. This research aims to target the falsehood part of the infodemic, which prominently proliferates in news articles and false medical publications. Here, we present NeoNet, a novel supervised machine learning text mining algorithm that analyzes the content of a document (news article, a medical publication) and assigns a label to it. The algorithm is trained by TFIDF bigram features which contribute a network training model. The algorithm is tested on two different real-world datasets from the CBC news network and Covid-19 publications. In five different fold comparisons, the algorithm predicted a label of an article with a precision of 97-99 %. When compared with prominent algorithms such as Neural Networks, SVM, and Random Forests NeoNet surpassed them. The analysis highlighted the promise of NeoNet in detecting disputed online contents which may contribute negatively to the COVID-19 pandemic.

Neural networks present the characteristics that the results are strongly dependent on the training data, the weight initialisation, and the hyper-parameters chosen. The determination of the distribution of a statistical estimator, as the Mean Squared Error (MSE) or the accuracy, is fundamental to evaluate the performance of a neural network model (NNM). For many machine learning models, as linear regression, it is possible to analytically obtain information as variance or confidence intervals on the results. Neural networks present the difficulty of being not analytically tractable due to their complexity. Therefore, it is impossible to easily estimate distributions of statistical estimators. When estimating the global performance of an NNM by estimating the MSE in a regression problem, for example, it is important to know the variance of the MSE. Bootstrap is one of the most important resampling techniques to estimate averages and variances, between other properties, of statistical estimators. In this tutorial, the application of two resampling (including bootstrap) techniques to the evaluation of neural networks’ performance is explained from both a theoretical and practical point of view. Pseudo-code of the algorithms is provided to facilitate their implementation. Computational aspects, as the training time, are discussed since resampling techniques always require to run simulations many thousands of times and, therefore, are computationally intensive. A specific version of the bootstrap algorithm is presented that allows the estimation of the distribution of a statistical estimator when dealing with an NNM in a computationally effective way. Finally, algorithms are compared on synthetically generated data to demonstrate their performance.

Summary: Studying biological systems generally relies on computational modeling and simulation, e.g., for model-driven discovery and hypothesis testing. Progress in standardization efforts led to the development of interrelated file formats to exchange and reuse models in systems biology, such as SBML, the Simulation Experiment Description Markup Language (SED-ML), or the Open Modeling EXchange format (OMEX). Conducting simulation experiments based on these formats requires efficient and reusable implementations to make them accessible to the broader scientific community and to ensure the reproducibility of the results. The Systems Biology Simulation Core Library (SBSCL) provides interpreters and solvers for these standards as a versatile open-source API in Java™. The library simulates even complex bio-models and supports deterministic Ordinary Differential Equations (ODEs); Stochastic Differential Equations (SDEs); constraint-based analyses; recent SBML and SED-ML versions; exchange of results, and visualization of in silico experiments; open modeling exchange formats (COMBINE archives); hierarchically structured models; and compatibility with standard testing systems, including the Systems Biology Test Suite and published models from the BioModels and BiGG databases. Availability and implementation: SBSCL is freely available at https://draeger-lab.github.io/SBSCL/.

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.

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion formula for the Bell polynomials in terms of the Stirling numbers of the first and second kinds, with the aid of the above explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials; (3) constructs some determinantal and product inequalities and deduces the logarithmic convexity of the Bell polynomials, with the assistance of the complete monotonicity of generating functions of the Bell polynomials. These inequalities are main results of the paper.

The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.

This paper includes some new investigations and results for post quantum calculus, denoted by (p,q)-calculus. A chain rule for (p,q)-derivative is developed. Also, a new (p,q)-analogue of the exponential function is introduced and some its properties including the addition property for (p,q)-exponential functions are investigated. Several useful results involving (p,q)-binomial coefficients and (p,q)-antiderivative are discovered. At the final part of this paper, (p,q)-analogue of some elementary functions including trigonometric functions and hyperbolic functions are considered and some properties and relations among them are analyzed extensively.

The ongoing COVID-19 global pandemic is affecting every facet of human lives (e.g., public health, education, economy, transportation, and the environment). This novel pandemic and citywide implemented lockdown measures are affecting virus transmission, people’s travel patterns, and air quality. Many studies have been conducted to predict the COVID-19 diffusion, assess the impacts of the pandemic on human mobility and air quality, and assess the impacts of lockdown measures on viral spread with a range of Machine Learning (ML) techniques. This review study aims to analyze results from past research to understand the interactions among the COVID-19 pandemic, lockdown measures, human mobility, and air quality. The critical review of prior studies indicates that urban form, people's socioeconomic and physical conditions, social cohesion, and social distancing measures significantly affect human mobility and COVID-19 transmission. During the COVID-19 pandemic, many people are inclined to use private transportation for necessary travel purposes to mitigate coronavirus-related health problems. This review study also noticed that COVID-19 related lockdown measures significantly improve air quality by reducing the concentration of air pollutants, which in turn improves the COVID-19 situation by reducing respiratory-related sickness and deaths of the people. It is argued that ML is a powerful, effective, and robust analytic paradigm to handle complex and wicked problems such as a global pandemic. This study also discusses policy implications, which will be helpful for policymakers to take prompt actions to moderate the severity of the pandemic and improve urban environments by adopting data-driven analytic methods.

Buyer practices have changed as individuals are figuring out how to live with the new truth of COVID-19. Take-out and conveyance orders have expanded, and our customer has added new items to their menu because of new client inclinations. With every one of the continuous changes, the customer had numerous unanswered inquiries, for example, Smartbridge has broad involvement with café innovation development Café TECHNOLOGY CAPABILITIES :Are the most famous items as yet unchanged after COVID? :Which are the most sold item blends now? :What is the acknowledgment of new things? :What are clients purchasing alongside new things? :How have liquor deals changed? The customer previously had reports that followed item deals and operational measurements, notwithstanding, there was a need to get a more profound knowledge into item examination. The customer expected to recognize what items and introductions were being sold all the more frequently, measure the acknowledgment of new items, and figure out what items clients buy together to improve advertising efforts, advancements, and deals. he E-business industry is filling immensely in the Indian market. The modest 4G web bundles in India clearly gives a push to these ventures. Thus, as Covid19 first hit in Quite a while, individuals got terrified to go out from their homes in light of the fact that, in their mind, it's a dread of Covid. They even wonder whether or not to go out to purchase fundamental (FMCG) products. Frenzy purchasing additionally has seen and to stay away from this dread of COVID-19, individuals are offering inclinations to the E-Commerce destinations to purchase fundamental products and a few clients are new which joined to purchase fundamental merchandise during this Pandemic Lockdown period. Numerous clients are moving their purchasing conduct from disconnected retail locations to online stores. This paper examines the customer buying pattern during lockdown.

In today’s Industrial IoT (IIoT) environment, where different systems interact with the physical world, the state proposed by the Industry 4.0 standards can lead to escalating vulnerabilities, especially when these systems receive data streams from multiple intermediaries, requiring multilevel security approaches, in addition to link encryption. At the same time taking into account the heterogeneity of the systems included in the IIoT ecosystem and the non-institutionalized interoperability in terms of hardware and software, serious issues arise as to how to secure these systems. In this framework, given that the protection of industrial equipment is a requirement inextricably linked to technological developments and the use of the IoT, it is important to identify the major vulnerabilities, the associated risks and threats and to suggest the most appropriate countermeasures. In this context, this study provides a description of the attacks against IIoT systems, as well as a thorough analysis of the solutions against these attacks, as they have been proposed in the most recent literature.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

The COVID-19 pandemic has resulted in a wide range of spatial interventions to slow down the spread of the virus. The spatial limitations of narrow public circulation spaces within informal settlements, which house over one billion people around the world, make it impossible for pedestrians to practice physical distancing (or social distancing). In this paper, we propose a flexible mathematical method, named the Cluster Lane Method, for turning a planar circulation network of any size or complexity into a network of unidirectional lanes, making physical distancing possible in narrow circulation spaces by limiting face-to-face interactions. New notions and theorems about oriented graphs in graph theory are introduced. The paper ends with a discussion of the potential implementation of this cost-efficient, low-tech, sustainable solution, and with the introduction of a novel unidirectional tactile paving for the visually impaired.

For each non-prime odd number as F=pq , if we consider m/n as an approximation for q/p and choose k=mn , then by proving some lemmas and theorems, we can compute the values of m and n. Finally, by using Fermat’s factorization method for F and 4kF as difference of two non-consecutive natural numbers, we should be able to find the values of p and q. Then we introduce two new and powerful sieves for separating composite numbers from prime numbers.

Neural decoding from spiking activity is an essential tool for understanding the information encoded in population neurons, especially in applications like brain-computer interface (BCI). Various quantitative methods have been proposed and have shown superiorities under different scenarios respectively. From the machine learning perspective, the decoding task is to map the high-dimensional spatial &amp; temporal neuronal activity to the low-dimensional physical quantities (e.g., velocity, position). Because of the complex interactions and the abundant dynamics among neural circuits, good decoding algorithms usually have the capability of capturing flexible spatiotemporal structures embedded in the input feature space. Recently, the Transformer-based models are widely used in processing natural languages and images due to its superior performances in handling long-range and global dependencies. Hence, in this work we examine the potential applications of Transformers in neural decoding and introduce two Transformer-based models. Besides adapting the Transformer to neuronal data, we also propose a data augmentation method for overcoming the data shortage issue. We test our models on three experimental datasets and their performances are comparable to the previous state-of-the-art (SOTA) RNN-based methods. In addition, Transformer-based models show increased decoding performances when the input sequences are longer, while LSTM-based models deteriorate quickly. Our research suggests that Transformer-based models are important additions to the existing neural decoding solutions, especially for large datasets with long temporal dependencies.

A methodology for both accurate and smooth contour line generation from Light Detection and Ranging (LiDAR) point clouds is proposed in this paper. In order to improve the accuracy of contour lines in the area of forests, constrained triangulation networks with break lines are then constructed to generate contour lines. In break line extraction, a bi-threshold method for edge line detection is used to extract both complete and reliable break lines. A point clouds elevation adjustment with constrain of break lines and an interpolator considering a contour interval is proposed to improve the smoothness of contour lines. The proposed interpotator is also can avoid contour line intersection when contour lines are interpolated. Statistical parameters and shape index are then used to evaluate quantitatively the accuracy and smoothness of the resultant contour lines, which fill in the blank of contour lines evaluation in theory. The experiments show that high-quality contours in terms of smoothness and accuracy can be generated from LiDAR point clouds.

Ransomware is continually evolving. The most recent tactic is to combine crypto-ransomware with data exfiltration, mandate fraud, and other such schemes to steal from victims and attempt to blackmail them. This paper examines the new trend, its underlying motives, and proposes practical recommendations to help organizations defend against this menace

Paraphrase Generation is one of the most important and challenging tasks in the field of Natural Language Generation. The paraphrasing techniques help to identify or to extract/generate phrases/sentences conveying the similar meaning. The paraphrasing task can be bifurcated into two sub-tasks namely, Paraphrase Identification (PI) and Paraphrase Generation (PG). Most of the existing proposed state-of-the-art systems have the potential to solve only one problem at a time. This paper proposes a light-weight unified model that can simultaneously classify whether given pair of sentences are paraphrases of each other and the model can also generate multiple paraphrases given an input sentence. Paraphrase Generation module aims to generate fluent and semantically similar paraphrases and the Paraphrase Identification systemaims to classify whether sentences pair are paraphrases of each other or not. The proposed approach uses an amalgamation of data sampling or data variety with a granular fine-tuned Text-To-Text Transfer Transformer (T5) model. This paper proposes a unified approach which aims to solve the problems of Paraphrase Identification and generation by using carefully selected data-points and a fine-tuned T5 model. The highlight of this study is that the same light-weight model trained by keeping the objective of Paraphrase Generation can also be used for solving the Paraphrase Identification task. Hence, the proposed system is light-weight in terms of the model’s size along with the data used to train the model which facilitates the quick learning of the model without having to compromise with the results. The proposed system is then evaluated against the popular evaluation metrics like BLEU (BiLingual Evaluation Understudy):, ROUGE (Recall-Oriented Understudy for Gisting Evaluation), METEOR, WER (Word Error Rate), and GLEU (Google-BLEU) for Paraphrase Generation and classification metrics like accuracy, precision, recall and F1-score for Paraphrase Identification system. The proposed model achieves state-of-the-art results on both the tasks of Paraphrase Identification and paraphrase Generation.

We examine the extensions of the basic arithmetical operations of addition and multiplication on the natural numbers into higher-rank hyper-operations also on the natural numbers. We go on to define the concepts of prime and composite numbers under these hyper-operations and derive some results about factorisation, resulting in fundamental theorems analogous to the Fundamental Theorem of Arithmetic.

In Southern Asia, Bangladesh is a well-known developing country. Because of COVID-19, we continuously face challenges. Not only can these issues occur beyond economic or health concerns, but they also generate dangerous social problems, such as family abuse. Since the inception of this epidemic, multiple social crimes are looming. Remaining home during the lockout period enhances divorce rates. This research presents a customized forecast of family violence during the COVID-19 outbreak by using machine learning methods. In this paper, we have applied Random Forest, Logistic Regression, and Naive Bayes machine learning classifiers to predict family violence and discovered the feature importance. The performance of the classifiers is evaluated based on accuracy, precision, recall, and F-score. We have employed an oversampling strategy named synthetic minority oversampling technique (SMOTE) to solve the imbalance problem of our data. Even, we have tried to compare three machine learning model performances before and after balancing of normalization data. Finally, ROC analyses and confusion matrices were developed and analyzed by using data augmentation. Our proposed system with the random forest classifier performed better with 77% accuracy in comparison with other two machine learning classifiers.

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

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly de…ned (q, r, w)-Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q, r, w)-Stirling numbers of the second kind and q-Bernoulli polynomials in w.

Motivated by Kurt's work [Filomat 30 (4) 921-927, 2016], we first consider a class of a new generating function for (p, q)-analog of Apostol type polynomials of order a including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order a. By making use of their generating function, we derive some useful identities. We also introduce (p, q)-analog of Stirling numbers of second kind of order v by which we construct a relation including aforementioned polynomials.

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

Since December 2019, the world is fighting against coronavirus disease (COVID-19). This disease is caused by a novel coronavirus termed as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). This work focuses on the applications of machine learning algorithms in the context of COVID-19. Firstly, regression analysis is performed to model the number of confirmed cases and death cases. Our experiments show that autoregressive integrated moving average (ARIMA) can reliably model the increase in the number of confirmed cases and can predict future cases. Secondly, a number of classifiers are used to predict whether a COVID-19 patient needs to be admitted to an intensive care unit (ICU) or semi-ICU. For this, classification algorithms are applied to a dataset having 5644 samples. Using this dataset, the most significant attributes are selected using features selection by ExtraTrees classifier, and Proteina C reativa (mg/dL) is found to be the highest-ranked feature. In our experiments, random forest, logistic regression, support vector machine, XGBoost, stacking and voting classifiers are applied to the top 10 selected attributes of the dataset. Results show that random forest and hard voting classifiers achieve the highest classification accuracy values near 98%, and the highest recall value of 98% in predicting the need for admission into ICU/semi ICU units.

There is a crucial need for advancement in the online educational system due to the unexpected, forced migration of classroom activities to a fully remote format, due to the coronavirus pandemic. Not only this, but online education is the future, and its infrastructure needs to be improved for an effective teaching-learning process. One of the major concerns with the current video call-based online classroom system is student engagement analysis. Teachers are often concerned about whether the students can perceive the teachings in a novel format. Such analysis was involuntarily done in the offline mode, however, is difficult in an online environment. This research presents an autonomous system for analyzing the students' engagement in the class by detecting the emotions exhibited by the students. This is done by capturing the video feed of the students and passing the detected faces to an emotion detection mode. The emotion detection model in the proposed architecture was designed by finetuning VGG16 pre-trained image classifier model. Lastly, the average student engagement index is calculated. We received considerable performance setting reliability of the use of the proposed system in real-time giving a future scope to this research.

This paper presents an effective heart disease prediction model through detecting the anomalies, also known as outliers, in healthcare data using the unsupervised K-means clustering algorithm. Most existing approaches for detecting anomalies are based on constructing profiles of normal instances. However, such techniques require an adequate number of normal profiles to justify those models. Our proposed model first evaluates an \textit{optimal} value of K using Silhouette method. Next, it intends to locate anomalies that are far from a certain threshold distance with respect to their clusters. Finally, the five most popular classification techniques such as K-Nearest Neighbor (KNN), Random Forest (RF), Support Vector Machines (SVM), Naive Bayes (NB), and Logistic Regression (LR) are applied to build the resultant prediction model. The effectiveness of the proposed methodology is justified using a benchmark dataset of heart disease.

The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers. This paper presents theoretical results which originated with a researchin the subject of the maximal prime gaps. the document presents the sharpest upper bound for the maximal prime gaps ever developed. The result becomes the Supremum bound on the maximal prime gaps and subsequently culminates with the conclusive proof of the Firoozbakht's Hypothesis No 30. Firoozbakht's Hypothesis implies quite a bold conjecture concerning the maximal prime gaps. In fact it imposes one of the strongest maximal prime gaps bounds ever conjectured. Its truth implies the truth of a greater number of known prime gaps conjectures, simultaneously, the Firoozbakht's Hypothesis disproves a known heuristic argument of Granville and Maier. This paper is dedicated to a fellow mathematician, the late Farideh Firoozbakht.

Introduced in 2009, Bitcoin has demonstrated a huge potential as the world’s first digital currency and has been widely used as a financial investment. Our research aims to uncover the relationship between Bitcoin prices and people’s sentiments about Bitcoin on social media. Among various social media platforms, micro-blogging is one of the most popular. Millions of people use micro-blogging platforms to exchange ideas, broadcast views, and to provide opinions on different topics related to politics, culture, science, and technology. This makes them a potentially rich source of data for sentiment analysis. Therefore we chose one of the busiest micro-blogging platforms, Twitter, to perform sentiment analysis on Bitcoin. We used ELMo embedding model to convert Bitcoin-related tweets into a vector form and SVM classifier to divide the tweets into three sentiment categories - positive, negative, and neutral. We then used the sentiment data to find its relation with Bitcoin price fluctuation using the linear mixed model.

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true. The equivalence theorems associated with the Riemann zeta--function are obtained in detail.

This article aims to identify the generating function of modi…ed Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modi…ed Apostol type q-Bernoulli polynomials are given. It is shown that aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications on q-Umbral calculus. From those applications, we derive some theorems in order to get Apostol type modi…ed q-Bernoulli polynomials as a linear combination of some known polynomials which we stated in the paper.

Stocks portfolio is a form of investment that can be used to minimize the risk of loss. In a stock portfolio, the value at risk (VaR) can be predicted through the portfolio return. If portfolio return variance is heteroscedastic risk prediction can be done by using VaR with ARIMA-GARCH or Ensemble ARIMA-GARCH model approach. Furthermore, the accuracy of VaR is tested through backtesting test. In this study, the portfolio formed from Astra Agro Lestari Ltd (AALI) and Indofood Ltd (INDF) stocks from 10/02/2012 to 10/01/2019. The results showed that the best model is ARIMA(0,0,[3])-GARCH(1,2) with AIC of -5.604 and MSE 1.874e-07.At confidence level of 95% and 1 day holding period, the VaR of the ARIMA(0,0,[3])-GARCH(1,2) was -0.3464. Based on the backtesting test, it is proven to be very accurate to predict the value of loss risk because the value of the violation ratio (VR) is equal to 0.

Volatility is the most widespread measure of risk. Volatility modeling allows investors to capture potential losses and investment opportunities. This work aims to examine the impact of the two waves of COVID-19 infections on the return and volatility of the stock market indices of the euro area countries. The study also focuses on other important aspects such as time-varying risk premium and leverage effect. Thus, this investigation employed the Threshold GARCH(1,1)-in-Mean model with exogenous dummy variables. Daily returns of ten euro area stock indices from 4th January 2016 to 31th December 2020 has been used for the analysis. The results reveal that euro area stock markets respond differently to the COVID-19 pandemic. Specifically, the first wave of COVID-19 infections had a notable impact on stock market volatility of euro area countries with large and middle financial centres while the second wave had a significant impact only on stock market volatility of Belgium.

The virus SARS-CoV-2 has resulted in numerous modelling approaches arising rapidly to understand the spread of the disease COVID-19 and to plan for future interventions. Herein, we present an SEIR model with a spatial spread component as well as four infectious compartments to account for the variety of symptom levels and transmission rate. The model takes into account the pattern of spatial vulnerability in South Africa through a vulnerability index that is based on socioeconomic and health susceptibility characteristics. Another spatially relevant factor in this context is level of mobility throughout. The thesis of this study is that without the contextual spatial spread modelling, the heterogeneity in COVID-19 prevalence in the South African setting would not be captured. The model is illustrated on South African COVID-19 case counts and hospitalisations.

A novel domination invariant defined by Boutrig and Chellali in the recent: total vertex-edge domination. In this paper we obtain an improved upper bound of total vertex edge-domination number of a tree. If is a connected tree with order , then with and we characterize the trees attaining this upper bound. Furthermore we provide a characterization of trees with

Machine learning is an established and frequently used technique in industry and academia but a standard process model to improve success and efficiency of machine learning applications is still missing. Project organizations and machine learning practitioners have a need for guidance throughout the life cycle of a machine learning application to meet business expectations. We therefore propose a process model for the development of machine learning applications, that covers six phases from defining the scope to maintaining the deployed machine learning application. The first phase combines business and data understanding as data availability oftentimes affects the feasibility of the project. The sixth phase covers state-of-the-art approaches for monitoring and maintenance of a machine learning applications, as the risk of model degradation in a changing environment is eminent. With each task of the process, we propose quality assurance methodology that is suitable to address challenges in machine learning development that we identify in form of risks. The methodology is drawn from practical experience and scientific literature and has proven to be general and stable. The process model expands on CRISP-DM, a data mining process model that enjoys strong industry support but lacks to address machine learning specific tasks. Our work proposes an industry and application neutral process model tailored for machine learning applications with focus on technical tasks for quality assurance.

Rice is the grain feeds more than half of the world population. It is an important staple food provides twenty percent of the calories consumed worldwide. Food safety affects the health of consumers. Establishing an effective traceability system is one of the primary measures to protect rice quality and food safety. Blockchain-based traceability system has the characteristics of data tamper-proofing, decentralization, and co-governance. This paper proposed a rice traceability scheme based on blockchain technology that selects the critical nodes in the rice industry chain to construct a blockchain network to achieve transparent data sharing. It is meaningful for both enterprises and consumers. It can let enterprises get the real quality information of rice and related raw materials. Consumers can get the true information of rice and rice products to buy safe and healthy food. The scheme is proved feasible by simulating the traceability of the rice supply chain.

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

Agile methods promise to achieve high productivity and provide high-quality software. Agile software development is the most important approach that has spread through the world of software development over the past decade. The software team’s productivity measurement is essential in agile teams to increase the performance of Software development. Due to the increasing competition of software development companies, software team productivity has become one of the crucial challenges for software companies and teams. Awareness of the level of team productivity can help them to achieve better estimation results on the time and cost of the projects. However, to measure software productivity, there is no definitive solution or approach whether in traditional and agile software development teams that lead to the occurrence of many problems in achieving a reliable definition of software productivity. Hence, this study aims to propose a statistical model to assess the team’s productivity in agile teams. A survey was conducted with forty software companies and measured the impact of six factors of the team on productivity in these companies. The results show that team effectiveness factors including inter-team relationship, quality conformance by the team, team vision, team leader, and requirements handled by the team had a significant impact on team productivity. Moreover, the results also state that inter-team relations affect the most on software teams’ productivity. Finally, the model fit test showed that 80% of productivity depends on team effectiveness factors.

Advancements in deep learning and availability of medical imaging data have led to use of CNN based architectures in disease diagnostic assisted systems. In spite of the abundant use of reverse transcription-polymerase chain reaction (RT-PCR) based tests in COVID-19 diagnosis, CT images offer an applicable supplement with its high sensitivity rates. Here, we study classification of COVID-19 pneumonia (CP) and non-COVID-19 pneumonia (NCP) in chest CT scans using efficient deep learning methods to be readily implemented by any hospital. We report our deep network framework design that encompasses Convolutional Neural Networks (CNNs) and bidirectional Long Short Term Memory (biLSTM) architectures. Our study achieved high specificity (CP: 98.3%, NCP: 96.2% Healthy: 89.3%) and high sensitivity (CP: 84.0%, NCP: 93.9% Healthy: 94.9%) in classifying COVID-19 pneumonia, non-COVID-19 pneumonia and healthy patients. Next, we provide visual explanations for the CNN predictions with gradient-weighted class activation mapping (Grad-CAM). The results provided a model explainability by showing that Ground Glass Opacities (GGO), indicators of COVID-19 pneumonia disease, were captured by our CNN network. Finally, we have implemented our approach in three hospitals proving its compatibility and efficiency.

Due to the unanticipated, forced migration of classroom activities to a fully remote format because of the coronavirus pandemic, there is a critical need for progress in the online education system. Not only that, but online education is the way of the future, and its infrastructure must be enhanced for teaching and learning to be effective. Engaging the students and enhancing their focus is one of the major concerns in the current video calling-based system. In this research, we propose a VR and AR-based virtual classroom environment system called "Edu VR" which encourages students to learn with a high level of involvement and attentiveness. We have divided the system into 2 distinct categories. one amongst which incorporates the virtual reality classroom, wherever the students can have a similar feel of actual school with peer-to-peer-based interactions and student-to-teacher interactions with Unity3D. We are able to conjointly deploy AR models with Vuforia, which permits the teachers to take classes more efficiently with student’s engagement. The other category involves the AI-based classroom assessment system, which enables teachers to produce assessments, which in turn are proctored by Artificial Intelligence. The results are automatically sent to the student within a short period, with the assistance of text similarity analysis for evaluating the answer scripts with Machine learning. This approach solves the drawbacks of video call-based systems with enhanced focus and engagement.

Coronavirus, also known as COVID-19, has been declared a pandemic by the World Health Organization (WHO). At the time of conducting this study, it had recorded over 1.6 million cases while more than 105,000 have died due to it, with these figures rising on a daily basis across the globe. The burden of this highly contagious respiratory disease is that it presents itself in both symptomatic and asymptomatic patterns in those already infected, thereby leading to an exponential rise in the number of contractions of the disease and fatalities. It is therefore crucial to expedite the process of early detection and diagnosis of the disease across the world. The case-based reasoning (CBR) model is an effective paradigm that allows for the utilization of cases’ specific knowledge previously experienced, concrete problem situations or specific patient cases for solving new cases. This study therefore aims to leverage the very rich database of cases of COVID-19 to solve new cases. The approach adopted in this study employs the use of an improved CBR model for state-of-the-art reasoning task in classification of suspected cases of Covid19. The CBR model leverages on a novel feature selection and semantic-based mathematical model proposed in this study for case similarity computation. An initial population of the archive was achieved with 68 cases obtained from the Italian Society of Medical and Interventional Radiology (SIRM) repository. Results obtained revealed that the proposed approach in this study successfully classified suspected cases into their categories at an accuracy of 97.10%. The study found that the proposed model can support physicians to easily diagnose suspected cases of Covid19 base on their medical records without subjecting the specimen to laboratory test. As a result, there will be a global minimization of contagion rate occasioned by slow testing and as well reduce false positive rates of diagnosed cases as observed in some parts of the globe.

Automatic Number Plate Recognition is a computer vision technology that provides a way to recognize the vehicles number plates without direct human intervention. Developing Automatic Number Plate Recognition methodologies is a widely studied topic among the computer vision community to increase the accuracy rates. Although there are many studies, the research in character segmentation and improving the recognition accuracy remains limited. In this study, a new methodology is proposed to reduce the character recognition errors of Automatic Number Plate Recognition systems. To achieve this, it will be determined whether the characters are letters or numbers, and the number plates will be expressed in the form of letters - digit. The method suggested for segmenting blobs correctly worked with an accuracy of 96.12% on the test dataset. The method suggested for generating letter-digit expression for the number plates correctly worked with an accuracy of 99.28% on the test dataset. The proposed methodology can work only on Turkish number plates. In the future studies, the proposed methodology can be expanded by using the number plate dataset of a different country.

We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give someof their basic properties including not only addition property, but also derivative properties and integralrepresentations. We also de.ne the Hermite based λ -Stirling polynomials of the second kind, and thenprovide some relations. Moreover, we derive several correlations and identities including the Hermite-Kampéde Fériet (or Gould-Hopper) family of polynomials, the Hermite based poly-Bernoulli polynomials with a qparameter and the Hermite based λ -Stirling polynomials of the second kind.

The purpose of this study is to present a systematic review of the literature on public blockchain consensus algorithms. Blockchain consensus algorithms have gain much popularity in last few years especially in the cryptocurrency field. Based on a systematic review of the relevant literature, we provide a classification of blockchain consensus algorithms, philosophy behind creation of blockchain consensus algorithms and as well as the rewards and incentive strategies of various public blockchain consensus algorithms. On the basis of these results, the research gaps and future work directions are identified for further study.

The Galvanic Skin Response (GSR, also widely known as electrodermal activity EDA) is one of the signals related to this emotional reaction. Given the sparsity of studies related to and the variety of devices, we experimented at the Human Health Activity Laboratory with 17 healthy subjects. The goal is to know the variability of detection changes in the electrodermal activity among a test group with heterogeneous respondents in response to valence and arousal stimuli, correlating GSR biosignals measured from different body sites. We experiment with the right and left wrist, left fingers, the right foot's inner side using Shimmer3GSR, and Empatica E4 sensors. Results indicate as the most promising homogeneous GSR measure place the left fingers and right foot. Results suggest that due to a significantly strong correlation among the inner side of the right foot and left fingers and moderate correlations with the right and left wrist, the foot is a good place to measure EDA. This paper also contributes knowledge about some wearable sensor technologies available in the market. Shimmer3GSR sensor may be better reliable to homogenous detecting electrodermal activity changes, as these have fewer anomalies among the respondents. However, we found some anomalies in signals from the Empatica E4 sensor, which we discuss in this work.

The aim of this article is introduced the concept of double framed T-soft fuzzy set (DFT-soft fuzzy set) which is the combination of soft set and fuzzy set. We also defined the notions and apply this concept in BCK/BCI-algebras. By using example, we also discussed the concept of double framed T-soft fuzzy algebra (DFT-soft fuzzy algebra) and double framed B-soft fuzzy algebra (DFB-soft fuzzy algebra) and also investigated their properties. Each double framed T-soft fuzzy algebra is double framed B-soft fuzzy algebra but by using example, we proved that converse may or may not be possible.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ω-function). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.

Melanoma is considered the most serious and aggressive type of skin cancer, and metastasis appears to be the most important factor in prognosticating this type of cancer. With the emergence of new therapeutic strategies for metastatic melanoma that have shown improvement in patient survival, we developed a transfer learning-based biomarker discovery model that could help in the diagnosis and prognosis of this disease. After applying it to the ensemble machine learning model, results reveal that the genes we found show consistency with other methodologies previously applied to the same TCGA (The Cancer Genome Atlas) data set, and our methods found novel biomarker genes as well. Our ensemble model achieved Area Under the Receiver Operating Characteristic (AUC) of 0.9861, an accuracy of 91.05, and an F1 score of 90.60 using an independent validation data set. This study was able to identify potential genes for diagnostic classification (C7 and GRIK5) and diagnostic and prognostic biomarkers (S100A7, S100A7, KRT14, KRT17, KRT6B, KRTDAP, SERPINB4, TSHR, PVRL4, WFDC5, IL20RB). We also assessed the potential sources of bias for our model and confirmed some of them by the model's performance.

This article contains the theorems concerning the algebraic dependence of polynomial mappings with the constant Jacobian having two zeros at infinity. The work is related to the issues of the classical Jacobian Conjecture. This hypothesis affirm that the polynomial mapping of two complex variables with constant non-zero Jacobian is invertible. The Jacobian Conjecture is equivalent to the fact that polynomial mappings with constant non-zero Jacobian do not have two zeros at infinity, therefore it is equivalent to the two theorems given in the work. The proofs of these theorems proceeds by induction.

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

Bounce Back Loan is amongst a number of UK business financial support schemes launched by UK Government in 2020 amidst pandemic lockdown. Through these schemes, struggling businesses are provided financial support to weather economic slowdown from pandemic lockdown. £43.5bn loan value has been provided as of 17^th Dec2020. However, with no major checks for granting these loans and looming prospect of loan losses from write-offs from failed businesses and fraud, this paper theorizes prospect of applying spatiotemporal modelling technique to explore if geospatial patterns and temporal analysis could aid design of loan grant criteria for schemes. Application of Clustering and Visual Analytics framework to business demographics, survival rate and Sector concentration shows Inner and Outer London spatial patterns which historic business failures and reversal of the patterns under COVID-19 implying sector influence on spatial clusters. Combination of unsupervised clustering technique with multinomial logistic regression modelling on research datasets complimented by additional datasets on other support schemes, business structure and financial crime, is recommended for modelling business vulnerability to certain types of financial market or economic condition. The limitations of clustering technique for high dimensional is discussed along with relevance of an applicable model for continuing the research through next steps

In this paper, we represent the generating function of w-torsion Fubini polynomials by fermionic p-adic integral on Z_p. Then we consider a quotient of such fermionic p-adic integrals on Z_p, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

One of the oldest and common methods of diagnosing heart abnormalities is auscultation. Even for experienced medical doctors, it is not an easy task to detect abnormal patterns in the heart sounds. Most of the digital stethoscopes are now capable of recording and transferring the heart sounds. Moreover, it is proven that auscultation records can be classified as healthy or unhealthy via artificial intelligence techniques. In this work, an artificial intelligence-powered mobile application that works in a connectionless fashion is presented. According to the clinical experiments, the mobile application can detect heart abnormalities with approximately 92% accuracy which is comparable if not better than humans since only a small number of well-trained cardiologists can analyze auscultation records better than artificial intelligence. Using the diagnostic ability of artificial intelligence in a mobile application would change the classical way of auscultation for heart disease diagnosis.

Multi-objective optimization (MOO) is an optimization involving minimization or maximization of several objective functions more than the conventional one objective optimization, which is useful in many fields. Many of the current methodologies addresses challenges and solutions that attempt to solve simultaneously several Objectives with multiple constraints subjoined to each. Often MOO are generally subjected to linear inequality, equality and or bounded constraint that prevent all objectives from being optimized at once. This paper reviews some recent articles in area of MOO and presents deep analysis of Random and Uniform Entry-Exit time of objectives. It further break down process into sub-process and then provide some new concepts for solving problems in MOO, which comes due to periodical objectives that do not stay for the entire duration of process lifetime, unlike permanent objectives which are optimized once for the entire process duration. A methodology based on partial optimization that optimizes each objective iteratively and weight convergence method that optimizes sub-group of objectives are given. Furthermore, another method is introduced which involve objective classification, ranking, estimation and prediction where objectives are classified based on their properties, and ranked using a given criteria and in addition estimated for an optimal weight point (pareto optimal point) if it certifies a coveted optimal weight point. Then finally predicted to find how far it deviates from the estimated optimal weight point. A Sample Mathematical Tri-Objectives and Real world Optimization was analyzed using partial method, ranking and classification method, the result showed that an objective can be added or removed without affecting previous or existing optimal solutions. Therefore suitable for handling time governed MOO. Although this paper presents concepts work only, it’s practical application are beyond the scope of this paper, however base on analysis and examples presented, the concept is worthy of igniting further research and application.

Coronavirus disease (COVID-19) is a pandemic infectious disease that has a severe risk of spreading rapidly. The quick identification and isolation of the affected persons is the very first step to fight against this virus. In this regard, chest radiology images have been proven to be an effective screening approach of COVID-19 affected patients. A number of AI based solutions have been developed to make the screening of radiological images faster and more accurate in detecting COVID-19. In this study, we are proposing a deep learning based approach using Densenet-121 to effectively detect COVID-19 patients. We incorporated transfer learning technique to leverage the information regarding radiology image learned by another model (CheXNet) which was trained on a huge Radiology dataset of 112,120 images. We trained and tested our model on COVIDx dataset containing 13,800 chest radiography images across 13,725 patients. To check the robustness of our model, we performed both two-class and three-class classifications and achieved 96.49% and 93.71% accuracy respectively. To further validate the consistency of our performance, we performed patient-wise k-fold cross-validation and achieved an average accuracy of 92.91% for three class task. Moreover, we performed an interpretability analysis using Grad-CAM to highlight the most important image regions in making a prediction. Besides ensuring trustworthiness, this explainability can also provide new insights about the critical factors regarding COVID-19. Finally, we developed a website that takes chest radiology images as input and generates probabilities of the presence of COVID-19 or pneumonia and a heatmap highlighting the probable infected regions. Code and models' weights are availabe.

Ongoing COVID-19 Pandemic has resulted into massive damage to various platforms of global economy which has caused disruption to human livelihood. Natural Language Processing has been extensively used in different organizations to categorize sentiments, perform recommendation, summarizing information and topic modelling. This research aims to understand the non-medical impact of COVID-19 on global economy by leveraging the natural language processing methodology. This methodology comprises of text classification which includes topic modelling on unstructured COVID-19 media articles dataset provided by Anacode. Like other Natural Language Processing algorithms, Latent Dirichlet allocation (LDA) and Non-negative matrix factorization (NMF) has been proposed to classify the media articles dataset in order to analyze COVID-19 pandemic impacts in the different sectors of global economy. Model Accuracy was examined based on the coherence and perplexity score which came out to be 0.51 and -10.90 using LDA algorithm. Both the LDA and NMF algorithm identified similar prevalent topics that was impacted by COVID-19 pandemic in multiple sectors of economy. Through intertopic distance map visualization produced by LDA algorithm, it can be reciprocated that general industries which includes children schooling, parental care, and family gatherings had the major impact followed by business sector and the financial industry.

The main goal of the present paper is to construct some families of the Carlitz’s q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and investigate their some explicit properties and identities arising from the bosonic q-Volkenborn integral on ℤ_p. We then define the modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate Carlitz’s q-Bernoulli polynomials with weight (α, β), the Stirling numbers of the first kind and second kind.

In this paper, we study the symmetry between the supersingular prime number according to smallest sphenic number. With this symmetry, we show that the elements of sporadic group generates all prime numbers with the order by a simple application.

Abstract: Insecure and portable devices in the smart city’s Internet of Things (IoT) network are increasing at an incredible rate. Various distributed and centralized platforms against cyber-attacks have been implemented in recent years, but these platforms are inefficient due to their constrained levels of storage, high energy consumption, the central point of failure, underutilized resources, high latency, and etc. In addition, the current architecture confronts the problems of scalability, flexibility, complexity, monitoring, managing & collecting of IoT data, and defend against cyber-threats. To address these issues, the author presents distributed and decentralized Blockchain-Software Defined Networking (SDN) based energy-optimized architecture for IoT in smart cities. Thus, SDN continuous observing, controlling, managing IoT devices activities and detect possible attacks in the network; Blockchain provides adequate security & privacy against cyber-attacks, reduces the central point of failure issues; Network Function Virtualization (NFV) are used to saving energy, load balancing, as well as increasing the lifetime of the entire network. Also, we introduce a Cluster Head Selection (CHS) algorithm to reduce the energy consumption in the presented model. Finally, we analyze the performance using various parameters (e.g. throughput, response time, gas consumption, communication overhead) and demonstrating the result that provides higher throughput, lower response time, lower gas consumption than existing works for smart cities.

The current paper explores the tenuous interlink between names of individuals in a society and its collective social consciousness, particularly with reference to the pervasive occurrence of the ‘mathematical names’ in the current Hindu society in the Indian subcontinent and beyond. Initially, an attempt is made to put things into mathematical perspective by drawing a quick sketch of the mathematical achievements of the Indian mathematicians. Then, under the six broad categories of geometry, trigonometry, numeration, arithmetic, algebra and mathematics in the Vedic tradition, a concise layman description of these subdivisions are presented, underlining the names of the concepts and terms, sometimes by producing the textual references. Next, upon identification of such mathematical terms, these names are juxtaposed with the names current in the Indian Hindu setting. By employing an extensive dataset of university student names in India and the databases of Facebook and LinkedIn, we produce both qualitative and quantitative evidence of the presence of such names in the Indian subcontinent. Evidently, these names reflect impressions of the rich mathematical heritage left by the Hindu stalwart mathematicians. This hypothesis has also been examined by taking surveys of people bearing these mathematical names, as well as by documenting the ‘conscious procedures’ that go behind the naming of a Hindu Indian child. In trying to investigate if such a phenomenon is unique to the Indian tradition, a stark contrast with the ‘names in mathematics’ as prevalent in the European mathematical traditions is presented, as cultural roots of mathematics are explored. Further, we ascribe the presence of these names as the extant remains of the colossal impact of multifarious mathematical traditions existing in India. In fact, the present research also brings to the fore, certain unseen facets of the Indian Hindu society as regards the education of mathematics to women – through an indirect exploration of their names. We then show that the pervasive occurrence of these names are not merely the result of semantic chance events, but denote the richness of the Indian mathematical legacy. We also present cross-cultural comparisons to show the uniqueness of Indian mathematical and scientific traditions that led to the pervasiveness of ‘mathematical names’ in India. Finally, an attempt is made to clarify some subtle points on the associations between mathematics and religion in India and other cultures of the world. It is a sincere hope that the present study may shed light on the cultural roots of mathematics and may provide a different dimension in the study of mathematics and society, across other civilizations.

This article describes an algorithm for estimation the variance of Gaussian noise. The data is smoothed using the Savitsky-Golay polynomial filter. Absolute differences between original and smoothed data are sorted in ascending order. The initial part of this sequence is selected for analysis. The result of calculation mean value of differences can be used to estimate the variance of the noise. By selecting points for analysis, the impact of cosmic ray noise and other artifacts can be reduced. The use of the proposed method for artificial and real spectra shows the ability to effectively estimate the noise variance. The algorithm contains no user-defined parameters.

Recent neuroscience research results show that the nerve information in the brain is not only encoded by the spatial information. Spiking neural network based on pulse frequency coding plays a very important role in dealing with the problem of brain signal, especially complicated space-time information. In this paper, an unsupervised learning algorithm for bilayer feedforward spiking neural networks based on spike-timing dependent plasticity (STDP) competitiveness is proposed and applied to SAR image classification on MSTAR for the first time. The SNN learns autonomously from the input value without any labeled signal and the overall classification accuracy of SAR targets reached 80.8%. The experimental results show that the algorithm adopts the synaptic neurons and network structure with stronger biological rationality, and has the ability to classify targets on SAR image. Meanwhile, the feature map extraction ability of neurons is visualized by the generative property of SNN, which is a beneficial attempt to apply the brain-like neural network into SAR image interpretation.

In this paper, we introduce a new class of Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Hermite-Fubini numbers and polynomials by using generating functions.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

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

The Kummer surface was constructed in 1864. It corresponds to the desingularisation of the quotient of a 4-torus by 16 complex double points. Kummer surface is kwown to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)≅Z5⋊2O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)≅Z6⋊2O and G7:=(336,118)≅Z7⋊2O can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups G6 and G7 are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested.

The COVID-19 pandemic starting in the first half of 2020 has changed the lives of everyone across the world. Reduced mobility was essential due to it being the largest impact possible against the spread of the little understood SARS-CoV-2 virus. To understand the spread, a comprehension of human mobility patterns is needed. The use of mobility data in modelling is thus essential to capture the intrinsic spread through the population. It is necessary to determine to what extent mobility data convey the same message of mobility within a region. This paper compares different mobility data sources by constructing spatial weight matrices and further compares the results through hierarchical clustering. This provides insight for the user into which data provides what type of information and in what situations a particular source is most useful.

Researchers are concerned about the impact of fake news on democracy, while it could also escalate to life-threatening problems. Fake news continues to spread, so does people's behaviour and emotions about fake news via social media. This opens up the back door for cyber-criminals to entice people (i.e. taking advantage of victims' emotional and behavioural aspects) to click on fraudulent links (e.g. phishing links) associated with fake news when reading. Therefore, we investigate how people's emotional and behavioural features influence reading and diffusing fake news on social media. We proposed a classification model incorporating people's behavioural features and their emotions to better detect fake news in social media. Our results reveal that fake news has more negative emotions than legitimate ones and both title and the content of the news/posts are equally important. Furthermore, we have identified that there exist strong correlations between some of the behavioural and emotional features. Finally, we concluded that emotional and behavioural features are important for fake news classifications as they improve the accuracy of detecting fake news, and the findings of our study can ultimately be used to develop a risk score prediction model for fake news in social media.

In this paper defines the consecutive sum of the digits of a natural number, so far as it becomes less than ten, as an arithmetic function called and then introduces some important properties of this function by proving a few theorems in a way that they can be used as a powerful tool in many cases. As an instance, by introducing a test called test, it has been shown that we are able to examine many algebraic equalities in the form of in which and are arithmetic functions and to easily study many of the algebraic and diophantine equations in the domain of whole numbers. The importance of test for algebraic equalities can be considered equivalent to dimensional equation in physics relations and formulas. Additionally, this arithmetic function can also be useful in factorizing the composite odd numbers.

This is an article or technical note which is intended to provides an insight journey of Machine Learning Systems (MLS) testing, its evolution, current paradigm and future work. Machine Learning Models, used in critical applications such as healthcare industry[1], Automobile [2], [3] and Air Traffic control, Share Trading etc., and failure of ML Model can lead to severe consequences in terms of loss of life or property. To remediate this, developers, scientists, and ML community around the world, must build a highly reliable test architecture for critical ML application. At the very foundation layer, any test model must satisfy the core testing attributes such as test properties and its components. This attribute comes from the software engineering [5], [6], but the same cannot be applied in as-is form to the ML testing and we will tell you “why”.

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

The hybrid numbers are a generalization of complex, hyperbolic and dual numbers. In this paper, we introduce the Horadam hybrid polynomials called Horadam hybrinomials. We also give some special cases and algebraic properties of the Horadam hybrinomials. Finally we obtain some applications related to the Horadam hybrinomials in matrices.