World Academy of Science, Engineering and Technology

Authors: Hassan Ibrahim, Moses Anayo Mbah

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The idempotent generators in a finite full transformation and the digraph of full transformation semi group have been an interesting area of research in group theory. In this work, it characterized some idempotent elements in full transformation semigroup T_n by counting the strongly connected and disconnected digraphs, and also the weakly and unilaterally connected digraphs. The order for those digraphs was further obtained in T_n.

Keywords: digraphs, indempotent, semigroup, transformation

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Authors: Hassan Ibrahim

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The prevalence of hyperacusis, an auditory condition characterized by heightened sensitivity to sounds, continues to rise, posing challenges for effective diagnosis and intervention. It is believed that this work deepens will deepens the understanding of hyperacusis etiology by employing graph theory as a novel analytical framework. We constructed a comprehensive graph wherein nodes represent various factors associated with hyperacusis, including aging, head or neck trauma, infection/virus, depression, migraines, ear infection, anxiety, and other potential contributors. Relationships between factors are modeled as edges, allowing us to visualize and quantify the interactions within the etiological landscape of hyperacusis. it employ the concept of the metric dimension of a connected graph to identify key nodes (landmarks) that serve as critical influencers in the interconnected web of hyperacusis causes. This approach offers a unique perspective on the relative importance and centrality of different factors, shedding light on the complex interplay between physiological, psychological, and environmental determinants. Visualization techniques were also employed to enhance the interpretation and facilitate the identification of the central nodes. This research contributes to the growing body of knowledge surrounding hyperacusis by offering a network-centric perspective on its multifaceted causes. The outcomes hold the potential to inform clinical practices, guiding healthcare professionals in prioritizing interventions and personalized treatment plans based on the identified landmarks within the etiological network. Through the integration of graph theory into hyperacusis research, the complexity of this auditory condition was unraveled and pave the way for more effective approaches to its management.

Keywords: auditory condition, connected graph, hyperacusis, metric dimension

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Authors: Alam Ali, Ashok Kumar Pathak

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Path analysis is a statistical technique used to evaluate the direct and indirect effects of variables in path models. One or more structural regression equations are used to estimate a series of parameters in path models to find the better fit of data. However, sometimes the assumptions of classical regression models, such as ordinary least squares (OLS), are violated by the nature of the data, resulting in insignificant direct and indirect effects of exogenous variables. This article aims to explore the effectiveness of a copula-based regression approach as an alternative to classical regression, specifically when variables are linked through an elliptical copula.

Keywords: path analysis, copula-based regression models, direct and indirect effects, k-fold cross validation technique

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Authors: Akash Verma, Sujit Kumar Samanta

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This study examines a discrete-time Geo/G/1 queueing-inventory system attached with (s, Q) inventory policy. Assume that the customers follow the Bernoulli process on arrival. Each customer demands a single item with arbitrarily distributed service time. The inventory is replenished by an outside supplier, and the lead time for the replenishment is determined by a geometric distribution. There is a single server and infinite waiting space in this facility. Demands must wait in the specified waiting area during a stock-out period. The customers are served on a first-come-first-served basis. With the help of the embedded Markov chain technique, we determine the joint probability distributions of the number of customers in the system and the number of items in stock at the post-departure epoch using the Matrix Analytic approach. We relate the system length distribution at post-departure and outside observer's epochs to determine the joint probability distribution at the outside observer's epoch. We use probability distributions at random epochs to determine the waiting time distribution. We obtain the performance measures to construct the cost function. The optimum values of the order quantity and reordering point are found numerically for the variety of model parameters.

Keywords: discrete-time queueing inventory model, matrix analytic method, waiting-time analysis, cost optimization

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Authors: Adji Achmad Rinaldo Fernandes

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SEM analysis is a complex multivariate analysis because it involves a number of exogenous and endogenous variables that are interconnected to form a model. The measurement model is divided into two, namely, the reflective model (reflecting) and the formative model (forming). Before carrying out further tests on SEM, there are assumptions that must be met, namely the linearity assumption, to determine the form of the relationship. There are three modeling approaches to path analysis, including parametric, nonparametric and semiparametric approaches. The aim of this research is to develop semiparametric SEM and obtain the best model. The data used in the research is secondary data as the basis for the process of obtaining simulation data. Simulation data was generated with various sample sizes of 100, 300, and 500. In the semiparametric SEM analysis, the form of the relationship studied was determined, namely linear and quadratic and determined one and two knot points with various levels of error variance (EV=0.5; 1; 5). There are three levels of closeness of relationship for the analysis process in the measurement model consisting of low (0.1-0.3), medium (0.4-0.6) and high (0.7-0.9) levels of closeness. The best model lies in the form of the relationship X1Y1 linear, and. In the measurement model, a characteristic of the reflective model is obtained, namely that the higher the closeness of the relationship, the better the model obtained. The originality of this research is the development of semiparametric SEM, which has not been widely studied by researchers.

Keywords: semiparametric SEM, measurement model, structural model, reflective model, formative model

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Authors: Chad Brown

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This paper establishes general conditions for the convergence rates of nonparametric sieve estimators with dependent data. We present two key results: one for nonstationary data and another for stationary mixing data. Previous theoretical results often lack practical applicability to deep neural networks (DNNs). Using these conditions, we derive convergence rates for DNN sieve estimators in nonparametric regression settings with both nonstationary and stationary mixing data. The DNN architectures considered adhere to current industry standards, featuring fully connected feedforward networks with rectified linear unit activation functions, unbounded weights, and a width and depth that grows with sample size.

Keywords: sieve extremum estimates, nonparametric estimation, deep learning, neural networks, rectified linear unit, nonstationary processes

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Authors: Othmane Zarhali, Cécilia Aubrun, Emmanuel Bacry, Jean-Philippe Bouchaud, Jean-François Muzy

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The Nested factor model was introduced by Bouchaud and al., where the asset return fluctuations are explained by common factors representing the market economic sectors and residuals (noises) sharing with the factors a common dominant volatility mode in addition to the idiosyncratic mode proper to each residual. This construction infers that the factors-residuals log volatilities are correlated. Here, we consider the case of a single factor where the only dominant common mode is a S-fbm process (introduced by Peng, Bacry and Muzy) with Hurst exponent H around 0.11 and the residuals having in addition to the previous common mode idiosyncratic components with Hurst exponents H around 0. The reason for considering this configuration is twofold: preserve the Nested factor model’s characteristics introduced by Bouchaud and al. and propose a framework through which the stylized fact reported by Peng and al. is reproduced, where it has been observed that the Hurst exponents of stock indices are large as compared to those of individual stocks. In this work, we show that the Log S-fbm Nested factor model’s construction leads to a Hurst exponent of single stocks being the ones of the idiosyncratic volatility modes and the Hurst exponent of the index being the one of the common volatility modes. Furthermore, we propose a statistical procedure to estimate the Hurst factor exponent from the stock returns dynamics together with theoretical guarantees, with good results in the limit where the number of stocks N goes to infinity. Last but not least, we show that the factor can be seen as an index constructed from the single stocks weighted by specific coefficients.

Keywords: hurst exponent, log S-fbm model, nested factor model, small intermittency approximation

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Authors: Usriatur Rohma, Adji Achmad Rinaldo Fernandes

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Nonparametric path analysis is a statistical method that does not rely on the assumption that the curve is known. The purpose of this study is to determine the best nonparametric truncated spline path function between linear and quadratic polynomial degrees with 1, 2, and 3-knot points and to determine the significance of estimating the best nonparametric truncated spline path function in the model of the effect of population migration and agricultural economic growth on rural poverty through the variable unemployment rate using the t-test statistic at the jackknife resampling stage. The data used in this study are secondary data obtained from statistical publications. The results showed that the best model of nonparametric truncated spline path analysis is quadratic polynomial degree with 3-knot points. In addition, the significance of the best-truncated spline nonparametric path function estimation using jackknife resampling shows that all exogenous variables have a significant influence on the endogenous variables.

Keywords: nonparametric path analysis, truncated spline, linear, quadratic, rural poverty, jackknife resampling

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Authors: Zohreh Moghaddas, Morteza Yazdani, Farhad Hosseinzadeh

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Nowadays, data envelopment analysis (DEA) models featuring network structures have gained widespread usage for evaluating the performance of production systems and activities (Decision-Making Units (DMUs)) across diverse fields. By examining the relationships between the internal stages of the network, these models offer valuable insights to managers and decision-makers regarding the performance of each stage and its impact on the overall network. To further empower system decision-makers, the inverse data envelopment analysis (IDEA) model has been introduced. This model allows the estimation of crucial information for estimating parameters while keeping the efficiency score unchanged or improved, enabling analysis of the sensitivity of system inputs or outputs according to managers' preferences. This empowers managers to apply their preferences and policies on resources, such as inputs and outputs, and analyze various aspects like production, resource allocation processes, and resource efficiency enhancement within the system. The results obtained can be instrumental in making informed decisions in the future. The top result of this study is an analysis of infeasibility and incorrect estimation that may arise in the theory and application of the inverse model of data envelopment analysis with network structures. By addressing these pitfalls, novel protocols are proposed to circumvent these shortcomings effectively. Subsequently, several theoretical and applied problems are examined and resolved through insightful case studies.

Keywords: inverse models of data envelopment analysis, series network, estimation of inputs and outputs, efficiency, resource allocation, sensitivity analysis, infeasibility

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Authors: Yu Lu

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Fixed point theory is a basic tool for the study of the existence of Nash equilibria in game theory. This paper presents a significant generalization of the Veinott-Zhou fixed point theorem for increasing correspondences, which serves as an essential framework for investigating the existence of Nash equilibria in supermodular and quasisupermodular games. To establish our proofs, we explore different conceptions of multivalued increasingness and provide comprehensive results concerning the existence of the largest/least fixed point. We provide two distinct approaches to the proof, each offering unique insights and advantages. These advancements not only extend the applicability of the Veinott-Zhou theorem to a broader range of economic scenarios but also enhance the theoretical framework for analyzing equilibrium behavior in complex game-theoretic models. Our findings pave the way for future research in the development of more sophisticated models of economic behavior and strategic interaction.

Keywords: fixed-point, Tarski’s fixed-point theorem, Nash equilibrium, supermodular game

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Authors: Rizwan Rizwan

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Differentially private ({DP}) training preserves the data privacy but often leads to slower convergence and lower accuracy, along with notable mis-calibration compared to non-private training. Analyzing {DP} training through a continuous-time approach with the neural tangent kernel ({NTK}). The {NTK} helps characterize per sample {(PS)} gradient clipping and the incorporation of noise during {DP} training across arbitrary network architectures as well as loss functions. Our analysis reveals that noise addition impacts privacy risk exclusively, leaving convergence and calibration unaffected. In contrast, {PS} gradient clipping (flat styles, layerwise styles) influences convergence as well as calibration but not privacy risk. Models with a small clipping norm generally achieve optimal accuracy but exhibit poor calibration, making them less reliable. Conversely, {DP} models that are trained with a large clipping norm maintain the similar accuracy and same privacy guarantee, yet they demonstrate notably improved calibration.

Keywords: deep learning, convergence, differential privacy, calibration

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Authors: Henok Metaferia Gebremariam

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Worldwide, considerable resources are spent implementing public health interventions that are interrupted soon after the initial funding ends. However, ambiguity remains as to how health programs can be effectively sustained over time because of the diversity of perspectives, definitions, study methods, outcomes measures and timeframes. From all the above-mentioned research challenges, standardized measures of sustainability should ultimately become a key research issue. To resolve this key challenge, the objective of the study was to adapt a tool for measuring the program’s capacity for sustainability and evaluating its reliability and validity. To adapt and validate the tool, a cross-sectional and cohort study design was conducted at 26 programs in Addis Ababa between September 2014 and May 2015. An adapted version of the tool after the pilot test was administered to 220 staff. The tool was analyzed for reliability and validity. Results show that a 40-item PSAT tool had been adapted into the Amharic version with good internal consistency (Cronbach’s alpha= 0.80), test-retest reliability(r=0.916) and construct validity. Factor analysis resulted in 7 components explaining 56.67 % of the variance. In conclusion, it was found that the Amharic version of PAST was a reliable and valid tool for measuring the program’s capacity for sustainability.

Keywords: program sustainability, public health interventions, reliability, validity

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Authors: Yakin Hajlaoui, Richard Labib, Jean-François Plante, Michel Gamache

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This study introduces the Multi-Layer Inverse Distance Weighting Model (ML-IDW), inspired by the mathematical formulation of both multi-layer neural networks (ML-NNs) and Inverse Distance Weighting model (IDW). ML-IDW leverages ML-NNs' processing capabilities, characterized by compositions of learnable non-linear functions applied to input features, and incorporates IDW's ability to learn anisotropic spatial dependencies, presenting a promising solution for nonlinear spatial interpolation and learning from complex spatial data. it employ gradient descent and backpropagation to train ML-IDW, comparing its performance against conventional spatial interpolation models such as Kriging and standard IDW on regression and classification tasks using simulated spatial datasets of varying complexity. the results highlight the efficacy of ML-IDW, particularly in handling complex spatial datasets, exhibiting lower mean square error in regression and higher F1 score in classification.

Keywords: deep learning, multi-layer neural networks, gradient descent, spatial interpolation, inverse distance weighting

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Authors: Khaled M. Alqahtani

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Copy number alterations (CNA) are variations in the structure of the genome, where certain regions deviate from the typical two chromosomal copies. These alterations are pivotal in understanding tumor progression and are indicative of patients' survival outcomes. However, effectively modeling patients' survival based on their genomic CNA profiles while identifying relevant genomic regions remains a statistical challenge. Various methods, such as the Cox proportional hazard (PH) model with ridge, lasso, or elastic net penalties, have been proposed but often overlook the inherent dependencies between genomic regions, leading to results that are hard to interpret. In this study, we enhance the elastic net penalty by incorporating an additional penalty that accounts for these dependencies. This approach yields smooth parameter estimates and facilitates variable selection, resulting in a sparse solution. Our findings demonstrate that this method outperforms other models in predicting survival outcomes, as evidenced by our simulation study. Moreover, it allows for a more meaningful interpretation of genomic regions associated with patients' survival. We demonstrate the efficacy of our approach using both real data from a lung cancer cohort and simulated datasets.

Keywords: copy number alterations, cox proportional hazard, lung cancer, regression, sparse solution

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Authors: Mohammed Abdullah Alshahrani

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The research focuses on investigating the use of partial least squares (PLS) methodology for addressing challenges associated with high-dimensional correlated data. Recent technological advancements have led to experiments producing data characterized by a large number of variables compared to observations, with substantial inter-variable correlations. Such data patterns are common in chemometrics, where near-infrared (NIR) spectrometer calibrations record chemical absorbance levels across hundreds of wavelengths, and in genomics, where thousands of genomic regions' copy number alterations (CNA) are recorded from cancer patients. PLS serves as a widely used method for analyzing high-dimensional data, functioning as a regression tool in chemometrics and a classification method in genomics. It handles data complexity by creating latent variables (components) from original variables. However, applying PLS can present challenges. The study investigates key areas to address these challenges, including unifying interpretations across three main PLS algorithms and exploring unusual negative shrinkage factors encountered during model fitting. The research presents an alternative approach to addressing the interpretation challenge of predictor weights associated with PLS. Sparse estimation of predictor weights is employed using a penalty function combining a lasso penalty for sparsity and a Cauchy distribution-based penalty to account for variable dependencies. The results demonstrate sparse and grouped weight estimates, aiding interpretation and prediction tasks in genomic data analysis. High-dimensional data scenarios, where predictors outnumber observations, are common in regression analysis applications. Ordinary least squares regression (OLS), the standard method, performs inadequately with high-dimensional and highly correlated data. Copy number alterations (CNA) in key genes have been linked to disease phenotypes, highlighting the importance of accurate classification of gene expression data in bioinformatics and biology using regularized methods like PLS for regression and classification.

Keywords: partial least square regression, genetics data, negative filter factors, high dimensional data, high correlated data

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Authors: Nacera Yassa, Abdelmalek Saidoune, Ghania Ouadfel, Hamza Houassine

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The rapid advancement in electrical technologies has underscored the increasing importance of multiphase machines across various industrial sectors. These machines offer significant advantages in terms of efficiency, compactness, and reliability compared to their single-phase counterparts. However, early detection and diagnosis of electrical faults remain critical challenges to ensure the durability and safety of these complex systems. This paper presents an advanced analytical model for multiphase machines, with a particular focus on dual stator asynchronous machines. The primary objective is to develop a robust diagnostic tool capable of effectively detecting and locating electrical faults in these machines, including short circuits, winding faults, and voltage imbalances. The proposed methodology relies on an analytical approach combining electrical machine theory, modeling of magnetic and electrical circuits, and advanced signal analysis techniques. By employing detailed analytical equations, the developed model accurately simulates the behavior of multiphase machines in the presence of electrical faults. The effectiveness of the proposed model is demonstrated through a series of case studies and numerical simulations. In particular, special attention is given to analyzing the dynamic behavior of machines under different types of faults, as well as optimizing diagnostic and recovery strategies. The obtained results pave the way for new advancements in the field of multiphase machine diagnostics, with potential applications in various sectors such as automotive, aerospace, and renewable energies. By providing precise and reliable tools for early fault detection, this research contributes to improving the reliability and durability of complex electrical systems while reducing maintenance and operation costs.

Keywords: faults, diagnosis, modelling, multiphase machine

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Tan Zhang, Zhongjian Wang, Jack Xin, Zhiwen Zhang

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We aim to efficiently compute the spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence-free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We study a stochastic interacting particle method (IPM) for the reduced principal eigenvalue (Lyapunov exponent) problem of an associated linear advection-diffusion operator with spatially random coefficients. The Fourier representation of the random advection field and the Feynman-Kac (FK) formula of the principal eigenvalue (Lyapunov exponent) form the foundation of our method implemented as a genetic evolution algorithm. The particles undergo advection-diffusion and mutation/selection through a fitness function originated in the FK semigroup. We analyze the convergence of the algorithm based on operator splitting and present numerical results on representative flows such as 2D cellular flow and 3D Arnold-Beltrami-Childress (ABC) flow under random perturbations. The 2D examples serve as a consistency check with semi-Lagrangian computation. The 3D results demonstrate that IPM, being mesh-free and self-adaptive, is simple to implement and efficient for computing front spreading speeds in the advection-dominated regime for high-dimensional random flows on unbounded domains where no truncation is needed.

Keywords: KPP front speeds, random flows, Feynman-Kac semigroups, interacting particle method, convergence analysis

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Authors: Ali Kazemi

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The digital evolution of financial services, while offering unprecedented convenience and accessibility, has also escalated the vulnerabilities to fraudulent activities. In this study, we introduce a distinct approach to real-time anomaly detection in financial transactions, aiming to fortify the defenses of banking and financial institutions against such threats. Utilizing unsupervised machine learning algorithms, specifically autoencoders and isolation forests, our research focuses on identifying irregular patterns indicative of fraud within transactional data, thus enabling immediate action to prevent financial loss. The data we used in this study included the monetary value of each transaction. This is a crucial feature as fraudulent transactions may have distributions of different amounts than legitimate ones, such as timestamps indicating when transactions occurred. Analyzing transactions' temporal patterns can reveal anomalies (e.g., unusual activity in the middle of the night). Also, the sector or category of the merchant where the transaction occurred, such as retail, groceries, online services, etc. Specific categories may be more prone to fraud. Moreover, the type of payment used (e.g., credit, debit, online payment systems). Different payment methods have varying risk levels associated with fraud. This dataset, anonymized to ensure privacy, reflects a wide array of transactions typical of a global banking institution, ranging from small-scale retail purchases to large wire transfers, embodying the diverse nature of potentially fraudulent activities. By engineering features that capture the essence of transactions, including normalized amounts and encoded categorical variables, we tailor our data to enhance model sensitivity to anomalies. The autoencoder model leverages its reconstruction error mechanism to flag transactions that deviate significantly from the learned normal pattern, while the isolation forest identifies anomalies based on their susceptibility to isolation from the dataset's majority. Our experimental results, validated through techniques such as k-fold cross-validation, are evaluated using precision, recall, and the F1 score alongside the area under the receiver operating characteristic (ROC) curve. Our models achieved an F1 score of 0.85 and a ROC AUC of 0.93, indicating high accuracy in detecting fraudulent transactions without excessive false positives. This study contributes to the academic discourse on financial fraud detection and provides a practical framework for banking institutions seeking to implement real-time anomaly detection systems. By demonstrating the effectiveness of unsupervised learning techniques in a real-world context, our research offers a pathway to significantly reduce the incidence of financial fraud, thereby enhancing the security and trustworthiness of digital financial services.

Keywords: anomaly detection, financial fraud, machine learning, autoencoders, isolation forest, transactional data analysis

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Authors: Ali Kazemi

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Those within the volatile and interconnected international economic markets, appropriately predicting market trends, hold substantial fees for traders and financial establishments. Traditional device mastering strategies have made full-size strides in forecasting marketplace movements; however, monetary data's complicated and networked nature calls for extra sophisticated processes. This observation offers a groundbreaking method for monetary marketplace prediction that leverages the synergistic capability of Graph Convolutional Networks (GCNs) and Long Short-Term Memory (LSTM) networks. Our suggested algorithm is meticulously designed to forecast the traits of inventory market indices and cryptocurrency costs, utilizing a comprehensive dataset spanning from January 1, 2015, to December 31, 2023. This era, marked by sizable volatility and transformation in financial markets, affords a solid basis for schooling and checking out our predictive version. Our algorithm integrates diverse facts to construct a dynamic economic graph that correctly reflects market intricacies. We meticulously collect opening, closing, and high and low costs daily for key inventory marketplace indices (e.g., S&P 500, NASDAQ) and widespread cryptocurrencies (e.g., Bitcoin, Ethereum), ensuring a holistic view of marketplace traits. Daily trading volumes are also incorporated to seize marketplace pastime and liquidity, providing critical insights into the market's shopping for and selling dynamics. Furthermore, recognizing the profound influence of the monetary surroundings on financial markets, we integrate critical macroeconomic signs with hobby fees, inflation rates, GDP increase, and unemployment costs into our model. Our GCN algorithm is adept at learning the relational patterns amongst specific financial devices represented as nodes in a comprehensive market graph. Edges in this graph encapsulate the relationships based totally on co-movement styles and sentiment correlations, enabling our version to grasp the complicated community of influences governing marketplace moves. Complementing this, our LSTM algorithm is trained on sequences of the spatial-temporal illustration discovered through the GCN, enriched with historic fee and extent records. This lets the LSTM seize and expect temporal marketplace developments accurately. Inside the complete assessment of our GCN-LSTM algorithm across the inventory marketplace and cryptocurrency datasets, the version confirmed advanced predictive accuracy and profitability compared to conventional and opportunity machine learning to know benchmarks. Specifically, the model performed a Mean Absolute Error (MAE) of 0.85%, indicating high precision in predicting day-by-day charge movements. The RMSE was recorded at 1.2%, underscoring the model's effectiveness in minimizing tremendous prediction mistakes, which is vital in volatile markets. Furthermore, when assessing the model's predictive performance on directional market movements, it achieved an accuracy rate of 78%, significantly outperforming the benchmark models, averaging an accuracy of 65%. This high degree of accuracy is instrumental for techniques that predict the course of price moves. This study showcases the efficacy of mixing graph-based totally and sequential deep learning knowledge in economic marketplace prediction and highlights the fee of a comprehensive, records-pushed evaluation framework. Our findings promise to revolutionize investment techniques and hazard management practices, offering investors and economic analysts a powerful device to navigate the complexities of cutting-edge economic markets.

Keywords: financial market prediction, graph convolutional networks (GCNs), long short-term memory (LSTM), cryptocurrency forecasting

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Authors: Ranjit Biswas

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The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.

Keywords: region, ROR, RORR, region algebra

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Authors: Samir K. Safi

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The purpose of this study was to compare the performance of two types of models, namely MIDAS and MIDAS-GARCH, in predicting the volatility of crude oil returns based on gold price returns and the COVID-19 pandemic. The study aimed to identify which model would provide more accurate short-term and long-term predictions and which model would perform better in handling the increased volatility caused by the pandemic. The findings of the study revealed that the MIDAS model performed better in predicting short-term and long-term volatility before the pandemic, while the MIDAS-GARCH model performed significantly better in handling the increased volatility caused by the pandemic. The study highlights the importance of selecting appropriate models to handle the complexities of real-world data and shows that the choice of model can significantly impact the accuracy of predictions. The practical implications of model selection and exploring potential methodological adjustments for future research will be highlighted and discussed.

Keywords: GARCH-MIDAS, MIDAS, crude oil, gold, COVID-19, volatility

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Authors: Lukas Vierus, Thomas Schuster

Abstract:

A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.

Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions

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Authors: Francis O. Nwawuru, Jeremiah N. Ezeora

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In this paper, a new algorithm for solving the system of split equilibrium and fixed point problems in real Hilbert spaces is considered. The equilibrium bifunction involves a nite family of pseudo-monotone mappings, which is an improvement over monotone operators. More so, it turns out that the solution of the finite family of nonexpansive mappings. The regularized parameters do not depend on Lipschitz constants. Also, the computations of the stepsize, which plays a crucial role in the convergence analysis of the proposed method, do require prior knowledge of the norm of the involved bounded linear map. Furthermore, to speed up the rate of convergence, an inertial term technique is introduced in the proposed method. Under standard assumptions on the operators and the control sequences, using a modified Halpern iteration method, we establish strong convergence, a desired result in applications. Finally, the proposed scheme is applied to solve some optimization problems. The result obtained improves numerous results announced earlier in this direction.

Keywords: equilibrium, Hilbert spaces, fixed point, nonexpansive mapping, extragradient method, regularized equilibrium

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Authors: Andrey Egorov

Abstract:

A product of the specific Lagrangian and the entropy factor is defined. Its positive definiteness is stated for the proper coupling constant. The passage from statistical mechanics to quantum field theory is performed by Wick rotation. The Green function (a convolution of the spectral amplitude and the propagator) is positive. Masses of quasiparticles are computed as residues. The role of the zeta derivative at zeta zeros is then highlighted, and the correspondent low bound is obtained.

Keywords: mass gap, positive definite kernels, quantum fields, Riemann zeta zeros

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Authors: Francis O. Nwawuru

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The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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Authors: Shunpu Zhang

Abstract:

We propose a new multiple test called the minPOP test for testing multiple hypotheses simultaneously. Under the assumption that the test statistics are independent, we show that the minPOP test has higher global power than the existing multiple testing methods. We further propose a stepwise multiple-testing procedure based on the minPOP test and two of its modified versions (the Double Truncated and Left Truncated minPOP tests). We show that these multiple tests have strong control of the family-wise error rate (FWER). A method for finding the p-values of the proposed tests after adjusting for multiplicity is also developed. Simulation results show that the Double Truncated and Left Truncated minPOP tests, in general, have a higher number of rejections than the existing multiple testing procedures.

Keywords: multiple test, single-step procedure, stepwise procedure, p-value for multiple testing

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Authors: Arum Kingsley Chinedu, Ugwuowo Fidelis Ifeanyi, Oranye Henrietta Ebele

Abstract:

The Poisson regression model (PRM) is a nonlinear model that belongs to the exponential family of distribution. PRM is suitable for studying count variables using appropriate covariates and sometimes experiences the problem of multicollinearity in the explanatory variables and outliers on the response variable. This study aims to address the problem of multicollinearity and outliers jointly in a Poisson regression model. We developed an estimator called the robust modified jackknife PCKL parameter estimator by combining the principal component estimator, modified jackknife KL and transformed M-estimator estimator to address both problems in a PRM. The superiority conditions for this estimator were established, and the properties of the estimator were also derived. The estimator inherits the characteristics of the combined estimators, thereby making it efficient in addressing both problems. And will also be of immediate interest to the research community and advance this study in terms of novelty compared to other studies undertaken in this area. The performance of the estimator (robust modified jackknife PCKL) with other existing estimators was compared using mean squared error (MSE) as a performance evaluation criterion through a Monte Carlo simulation study and the use of real-life data. The results of the analytical study show that the estimator outperformed other existing estimators compared with by having the smallest MSE across all sample sizes, different levels of correlation, percentages of outliers and different numbers of explanatory variables.

Keywords: jackknife modified KL, outliers, multicollinearity, principal component, transformed M-estimator.

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Authors: Liudmyla Vesper

Abstract:

The problems of modern education are large-scale and diverse. The aspirations of parents, teachers, and experts converge - everyone interested in growing up a generation of whole, well-educated persons. Both the family and society are expected in the future generation to be self-sufficient, desirable in the labor market, and capable of lifelong learning. Today's children have a powerful potential that is difficult to realize in the conditions of traditional school approaches. Focusing on STEM education in practice often ends with the simple use of computers and gadgets during class. "Science", "technology", "engineering" and "mathematics" are difficult to combine within school and university curricula, which have not changed much during the last 10 years. Solving the problems of modern education largely depends on teachers - innovators, teachers - practitioners who develop and implement effective educational methods and programs. Teachers who propose innovative pedagogical practices that allow students to master large-scale knowledge and apply it to the practical plane. Effective education considers the creation of stable neural structures during the learning process, which allow to preserve and increase knowledge throughout life. The author proposed a method of integrated lessons – cases based on the maths patterns for forming a holistic perception of the world. This method and program are scientifically substantiated and have more than 15 years of practical application experience in school and student classrooms. The first results of the practical application of the author's methodology and curriculum were announced at the International Conference "Teaching and Learning Strategies to Promote Elementary School Success", 2006, April 22-23, Yerevan, Armenia, IREX-administered 2004-2006 Multiple Component Education Project. This program is based on the concept of interdisciplinary connections and its implementation in the process of continuous learning. This allows students to save and increase knowledge throughout life according to a single pattern. The pattern principle stores information on different subjects according to one scheme (pattern), using long-term memory. This is how neural structures are created. The author also admits that a similar method can be successfully applied to the training of artificial intelligence neural networks. However, this assumption requires further research and verification. The educational method and program proposed by the author meet the modern requirements for education, which involves mastering various areas of knowledge, starting from an early age. This approach makes it possible to involve the child's cognitive potential as much as possible and direct it to the preservation and development of individual talents. According to the methodology, at the early stages of learning students understand the connection between school subjects (so-called "sciences" and "humanities") and in real life, apply the knowledge gained in practice. This approach allows students to realize their natural creative abilities and talents, which makes it easier to navigate professional choices and find their place in life.

Keywords: science education, maths education, AI, neuroplasticity, innovative education problem, creativity development, modern education problem

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Authors: Hiba El Assibi

Abstract:

This study aims to weakly solve Kalah, a two-player board game, by developing a start-to-finish winning strategy using an optimized Minimax algorithm with Alpha-Beta Pruning. In weakly solving Kalah, our focus is on creating an optimal strategy from the game's beginning rather than analyzing every possible position. The project will explore additional enhancements like symmetry checking and code optimizations to speed up the decision-making process. This approach is expected to give insights into efficient strategy formulation in board games and potentially help create games with a fair distribution of outcomes. Furthermore, this research provides a unique perspective on human versus Artificial Intelligence decision-making in strategic games. By comparing the AI-generated optimal moves with human choices, we can explore how seemingly advantageous moves can, in the long run, be harmful, thereby offering a deeper understanding of strategic thinking and foresight in games. Moreover, this paper discusses the evaluation of our strategy against existing methods, providing insights on performance and computational efficiency. We also discuss the scalability of our approach to the game, considering different board sizes (number of pits and stones) and rules (different variations) and studying how that affects performance and complexity. The findings have potential implications for the development of AI applications in strategic game planning, enhancing our understanding of human cognitive processes in game settings, and offer insights into creating balanced and engaging game experiences.

Keywords: minimax, alpha beta pruning, transposition tables, weakly solving, game theory

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