Strong Mathematical Basis Research Articles

Role of Mathematics in Data Science - Machine learning

The mathematical concepts help with identifying patterns and algorithmic development. Mathematics is an important part of many modern scientific areas. It is also a field of major significance in data science. Mainly because of the concepts they propose and the tools they allow, statistics and arithmetic have such an essential role in data science. A specific type of mathematical reasoning is needed for analysing data, in addition to the basic concepts of calculus, discrete mathematics, and linear algebra. To understand how to apply such algorithms in data science, one must have a solid understanding of many different statistical and probability theory ideas. Modern data science methods have a strong mathematical basis for almost all of their techniques, including machine learning.

Tool Run-Out in Micro-Milling: Development of an Analytical Model Based on Cutting Force Signal Analysis.

Micro-machining is a widespread finishing process for fabricating accurate parts as biomedical devices. The continuous effort in reducing the gap between the micro- and macro-domains is connected to the transition from conventional to micro-scale machining. This process generates several undesired issues, which complicate the process's optimization, and tool run-out is one of the most difficult phenomena to experimentally investigate. This work focuses on its analytical description; in particular, a new method to calibrate the model parameters based on cutting force signal elaboration is described. Today, run-out prevision requires time-consuming geometrical measurements, and the main aim of our innovative model is to make the analysis completely free from dimensional measurements. The procedure was tested on data extrapolated from the micro-machining of additively manufactured AlSi10Mg specimens. The strategy appears promising because it is built on a strong mathematical basis, and it may be developed in further studies.

Requirement specification extraction and analysis based on propositional projection temporal logic

AbstractAt present, formal methods significantly facilitate the specification and verification of security requirements in requirement engineering, which can reduce requirement errors in the early stage of system development. Extracting formal specifications from security requirements and then evaluating the quality of the requirements are regarded as a promising solution to ensure software quality. Propositional projection temporal logic (PPTL) with a strong mathematical basis and full regular expressiveness is a suitable language for formal specifications. Inspired by natural language processing and text mining techniques, this paper designs and implements a tool, namely, NL2PPTL, to generate formal coarse‐grained and fine‐grained specifications in terms of PPTL formulas automatically. In specific, the grammatical production rules are defined to construct the syntax tree, and then, the formula is obtained by post‐order traversal of the tree. The satisfiability of the PPTL specifications can be checked utilizing PPTLSAT. In addition, the state transformation model is constructed from fine‐grained specifications, so as to discover scope conflicts and verify the security properties of the requirement case.

SISTEM PAKAR DIAGNOSA PENYAKIT DAN HAMA PADA TANAMAN JAGUNG MENGGUNAKAN METODE NAIVE BAYES

Corn is one of the leading agricultural commodities that can be used as a staple plant other than rice. Constraints faced by corn farmers include the lack of information about diseases that attack the corn plants, which causes less productivity. In this study a system was developed that can automatically detect disease that attacks corn plants so that preventive measures can be taken to prevent corn plants from dying. Expert systems are designed to solve certain problems by imitating the work of experts. In addition, this expert system also helps farmers who are experiencing problems regarding diseases and pests and their solutions without relying on an expert. The method used is the Naive Bayes method, Naive Bayes is a method used to predict probabilities and has several characteristics that are istitively in accordance with the way of thinking of an expert and accompanied by a strong mathematical basis. From the tests carried out with diagnoses obtained from the comparison between the results of expert diagnoses and the diagnosis of the system to diagnose diseases and pests in corn plants is 90%.

A Comprehensive Evaluation Model for Wood Companies Websites Based on the AHP/R-TOPSIS Method

Recently, partly as a result of the COVID-19 pandemic, companies are increasingly shifting their activities to the Internet environment, thus accelerating the growth of online shopping. The aim of this study was to develop a comprehensive model for the evaluation of websites of wood companies, as a review of the literature shows that such a model does not yet exist. In developing the model, we used an innovative approach and combined the analytic hierarchy process with R-TOPSIS (technique for order of preference by similarity to ideal solution), which is a novelty in this field. For the final website assessment, the Website Quality Index (WQI) was developed. The main difference to other indexes is that our model has a comprehensive content background (36 criteria and sub-criteria) and a strong mathematical basis, so that it can be used to independently evaluate a single website or to evaluate a larger group of websites from the same industry. We have tested the model on 60 websites of Slovenian wood industry companies with at least ten employees. The results show the low to moderate average quality of the websites, with an average WQI of all evaluated websites of 0.450, indicating only an acceptable website. It has proven to be easy to use, and the results show the reliability of the website rating. Additionally, the designed model is an important tool for industry website developers and the basis for future studies in this field. However, it can also be applied to other areas related to wood and wood products, where the performance of objects should be evaluated with respect to multiple criteria.

Оценка Индекса Инклюзивного Развития на Основе Нейросетевой Модели REL-PCANet

В 2018 году на Всемирном экономическом форуме в Давосе была представлена новая метрика экономической эффективности стран под названием Индекс инклюзивного развития (IDI), состоящий из 12 показателей. Новая метрика подразумевает, что странам может потребоваться проведение структурных реформ для улучшения как экономического роста, так и эффективности социальной инклюзивности. Именно поэтому важно, чтобы метод расчета IDI имел сильную статистическую и математическую основу для точности и прозрачности результатов и их дальнейшего использования в общественных целях.В данной работе мы предлагаем новый подход к оценке IDI — нейросетевую модель REL-PCANet, которая основана на принципах RELARM и RankNet и объединяет элементы PCA, методы, применяемые в распознавании изображений и механизмах обучения ранжированию. Кроме того, мы определяем новый подход к оценке матрицы целевых вероятностей TRnet для отражения динамических изменений в инклюзивном развитии стран. Эмпирическое исследование показало, что REL-PCANet обеспечивает надежные оценки и результаты ранжирования, что позволяет рекомендовать ее для использования в практической деятельности.

An improved variational mode decomposition method and its application in diesel engine fault diagnosis

The diesel engine is a complex mechanical device, with the characteristics of multi-source, multi moving parts, complex work. For the complex multi-component signal, it is usually necessary to decompose it into a number of single-component AM-FM signals, and each component is analyzed to extract amplitude and frequency information. VMD is essentially composed of a plurality of adaptive Wiener filter and has good noise robustness. Compared with EMD, EEMD, CEEMDAN, LMD and ITD, VMD has strong mathematical theory basis. At the same time, VMD rejects the method of recursive screening stripping. So VMD can effectively alleviate or avoid a series of problems which appear in other methods. However, it is a problem how to determine the number of decomposition layers and the penalty factor, because human factors will affect the decomposition results. In order to solve the problem, an improved adaptive genetic algorithm (IAGA) is proposed to optimize the parameters of VMD. Genetic algorithms mainly include 3 genetic operators: selection, crossover and mutation. The cross probability and mutation probability will directly affect the optimization results. In the traditional genetic algorithm, the probability of cross and mutation are fixed, and the genetic algorithm is easy to fall into the local optimal. According to the regulation of hormone regulation, the cross probability and mutation probability in evolution were improved. The permutation entropy is a new method of mutation detection, which mainly aims at the spatial characteristics of the time series itself. Therefore, the entropy of the components obtained by the VMD decomposition is used as the fitness function of the IAGA. The modal number K and penalty factor α of VMD were iteratively optimized by IAGA, and the optimal combination of parameters was obtained. Based on the proposed method, the vibration signals of the crankshaft bearing fault simulation experiment were decomposed into several components. According to the value of the permutation entropy, the fault components were selected and the energy was extracted. The fault pattern is identified by the support vector machine (SVM) successfully. The simulation analysis and the simulation experiment of the crankshaft bearing fault show that the proposed method is effective. For the diagnosis of other engines, a large number of validation experiments are needed for further research.

Convolutional Noise PDF at the Convergence State of a Blind Adaptive Equalizer

In the literature, the convolutional noise obtained at the output of a blind adaptive equalizer, is often modeled as a Gaussian process during the latter stages of the deconvolution process where the process is close to optimality. However, up to now, no strong mathematical basis was given supporting this phenomenon. Furthermore, no closed-form or closed-form approximated expression is given that shows what are the constraints on the system’s parameters (equalizer’s tap-length, input signal statistics, channel power, chosen equalization method and step-size parameter) for which the assumption of a Gaussian model for the convolutional noise holds. In this paper, we consider the two independent quadrature carrier input case and type of blind adaptive equalizers where the error that is fed into the adaptive mechanism which updates the equalizer’s taps can be expressed as a polynomial function of the equalized output up to order three. We show based on strong mathematical basis that the convolutional noise pdf at the latter stages of the deconvolution process where the process is close to optimality, is approximately Gaussian if complying on some constraints depending on the step-size parameter, input constellation statistics, channel power, chosen equalization method and equalizer’s tap-length. Simulation results confirm our findings.

PERBANDINGAN METODE BACKPROPAGATION DENGAN MONTE CARLO DALAM MEMPREDIKSI JUMLAH PENDERITA DEMAM BERDARAH DENGUE DI KOTA PEKANBARU

Pekanbaru city is one of the cities that have high dengue fever cases. in 2012 recorded 202 cases, 2013 426 cases, 2014 recorded 113 cases and in 2015 recorded as many as 272 cases. The number of each year is always changing, due to various factors that are erratic and other weather changes, it proves that Departmenet of Health of Pekanbaru City has not been able to control the rate of increase in dengue fever patients. The Backpropagation method is a systematic forecasting method for multilayer training, has a strong mathematical basis and is trained by guided methods. With 3 layers, the input layer, the hidden layer and the output layer. Monte Carlo simulation is a probabilistic type of simulation where to obtain the problem solving used sampling method from random process. Monte Carlo experiments on probabilistic elements through random sampling with the aid of generating random numbers.By comparing the two can be known which method is better in predicting the number of patients with dengue fever. The results of data testing with both methods found that Backpropagation method has a low standard deviation compared to Monte Carlo method, so the method of backpropagation is said to be better in predicting the number of dengue hemorrhagic fever patients in Pekanbaru City

Analytic Hierarchy Process (AHP) as a Decision-Making Tool for Spouse Selection

Decision-making can be considered a choice, on some basis or criteria, of one alternative among set of alternatives. A decision may need to be taken on the basis of multiple criteria. When the criteria to be considered for taking a decision involves subjectivity, the decision maker would be at confusion. This is true as far as decision-making in personal life is concerned, where feelings, intuition and other biased judgements play a vital role. Here comes analytical hierarchy process (AHP) which considers subjective judgments and converts them into suitable values so that decision maker can opt for a right choice. In the present paper, an attempt has been made to apply AHP technique, which has strong mathematical basis to quantify subjective factors into numerical values, to select a suitable bridegroom. A hypothetical case has been considered which involves ten criteria and three alternatives.

IMPLEMENTATION OF ANALYTIC HIERARCHY PROCESS (AHP) AS A DECISION SUPPORT TOOL FOR SELECTION OF ROBOT FOR SPOT WELDING OPERATION

Flexible production lines are most essential for any lean manufacturing system for cost effectiveness. Automobile industry is extensively making use of lean manufacturing philosophy where reduction of waste is paramount importance without sacrificing the quality. Production of an automobile consists of number of phases in which fabrication of body by portable spot welding guns using robots is a significant stage. Robotic Spot welding operation is accomplished to manufacture the body of the automobile, because of its inherent accuracy and repeatability. Robot is a programmable machine which offers flexibility to switch over from one type of model of automobile to another type of model swiftly. But selection of an appropriate robot for the desired task to be accomplished is a crucial decision to be taken. Many factors are to be considered before arriving at an apt decision. Thescenario of this sort may be considered as multi-criteria decisionmaking (MCDM) problem. Though many techniques are available to solve problems of this type, Analytic Hierarchy Process (AHP) has been selected, because of its strong mathematical basis. In the present paper AHP is implemented to address this MCDM problem which acts as a decision support tool to select an appropriate robot for spot welding operation.

Towards a workable model of final unification

Even though ‘String theory’ models and “quantum gravity’ models are having a strong mathematical back ground and sound physical basis, they are failing in implementing the Newtonian gravitational constant in atomic and nuclear physics and thus seem to fail in developing a ‘workable’ model of final unification. In this context, extending Abdus Salam’s old concept of ‘nuclear strong gravitational coupling’ we consider two very large pseudo gravitational constants assumed to be associated with electromagnetic and strong interactions. By combining the two microscopic pseudo gravitational constants with the Newtonian gravitational constant, we make an attempt to combine the old ‘strong gravity’ concept with ‘Newtonian gravity’ and try to understand and re-interpret the constructional features of nuclei, atoms and neutron stars in a unified approach. Finally we make a heuristic attempt to estimate the Newtonian gravitational constant from the known elementary atomic and nuclear physical constants. By exploring the possibility of incorporating the proposed two pseudo microscopic gravitational constants in current unified models, in near future, complete back ground physics can be understood and observable low energy predictions can be made.

Modelagem de conceitos e processos matemáticos por redes de petri coloridas: o caso da integrabilidade de funções reais

As redes de Petri (RPs) constituem-se em uma ferramenta matemática e gráfica de uso geral. Sugere-se, neste trabalho, o uso de RPs como uma ferramenta de modelagem voltada para o ensino de noções matemáticas. A modelagem apoia-se no fato de as RPs terem como característica a representação de sistemas que utilizam forte base matemática. Como estudo de caso, apresenta-se uma modelagem para a organização do conteúdo de ensino sobre integrabilidade de funções reais baseada na evolução do conceito de integral. Para isto, considera-se uma função limitada, definida em um intervalo fechado e limitado da reta, que é analisada relativamente a condições que garantam ou excluam a sua integrabilidade por Cauchy, por Riemann, por Lebesgue ou por nenhum destes. A ideia de se modelar este conceito por RPs originou-se no contexto da sala de aula, por ocasião de seu ensino a alunos de primeiro ano de engenharia.

MatCarloRe: An integrated FT and Monte Carlo Simulink tool for the reliability assessment of dynamic fault tree

With the aim of a more effective representation of reliability assessment for real industry, in the last years concepts like dynamic fault trees (DFT) have gained the interest of many researchers and engineers (dealing with problems concerning safety management, design and development of new products, decision analysis and project management, maintenance of industrial plant, etc.). With the increased computational power of modern calculators is possible to achieve results with low modeling efforts and calculating time. Supported by the strong mathematical basis of state space models, the DFT technique has increased its popularity. Nevertheless, DFT analysis of real application has been more likely based on a specific case to case resolution procedure that often requires a great effort in terms of modeling by the human operator. Moreover, limitations like the state space explosion for increasing number of components, the constrain of using exponential distribution for all kind of basic events constituting any analyzed system and the ineffectiveness of modularization for DFT which exhibit dynamic gates at top levels without incurring in calculation and methodological errors are faces of these methodologies. In this paper we present a high level modeling framework that exceeds all these limitations, based on Monte Carlo simulation. It makes use of traditional DFT systemic modeling procedure and by replicating the true casual nature of the system can produce relevant results with low effort in term of modeling and computational time. A Simulink library that integrates Monte Carlo and FT methodologies for the calculation of DFT reliability has been developed, revealing new insights about the meaning of spare gates.

DESIGN UNDER UNCERTAINTY EMPLOYING STOCHASTIC EXPANSION METHODS

Non-intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification (UQ) due to their strong mathematical basis and ability to produce functional representations of stochastic variability. PCE estimates coefficients for known orthogonal polynomial basis functions based on a set of response function evaluations, using sampling, linear regression, tensor-product quadrature, or Smolyak sparse grid approaches. SC, on the other hand, forms interpolation functions for known coefficients, and requires the use of structured collocation point sets derived from tensor product or sparse grids. When tailoring the basis functions or interpolation grids to match the forms of the input uncertainties, exponential convergence rates can be achieved with both techniques for general probabilistic analysis problems. Once PCE or SC representations have been obtained for a response metric of interest, analytic expressions can be derived for the moments of the expansion and for the design derivatives of these moments, allowing for efficient design under uncertainty formulations involving moment control (e.g., robust design). This paper presents two approaches for moment design sensitivities, one involving response function expansions over both design and uncertain variables and one involving response derivative expansions over only the uncertain variables. These approaches present a trade-off between increased dimensionality in the expansions (and therefore increased simulation runs required to construct them) with global expansion validity versus increased data requirements per simulation with local expansion validity. Given this capability for analytic moments and their sensitivities, we explore bilevel, sequential, and multifidelity formulations for OUU. Initial experiences with these approaches is presented for a number of benchmark test problems.

Model interoperability via Model Driven Development

Among the factors that contribute to the inherent complexity of the software development process is the gap between the design and the formal analysis domains. Software design is often considered a human oriented task while the analysis phase draws on formal representation and mathematical foundations. An example of this dichotomy is the use of UML for the software design phase and Petri Nets for the analysis; a separation of concerns that leads to the creation of heterogeneous models. Although UML is widely accepted as a language that can be used to model the structural and behavioural aspects of a system, its lack of mathematical foundations is seen as a serious impediment to rigorous analysis. Petri Nets on the other hand have a strong mathematical basis that are well suited for formal analysis; they lack however the appeal and the ease-of-use of UML. A pressing concern for software developers is how to bridge the gap between these domains and allow for model interoperability and the integration of different toolsets across them, and thus reduce the complexity of the software development process. The aim of this paper is to present a Model Driven Development (MDD) model transformation which supports a seamless transition between UML and Petri Nets. This is achieved by model interoperability from UML Sequence Diagrams to Petri Nets and supported by tool integration. The model transformation framework allows a software system to be designed in terms of UML Sequence Diagrams and subjected to formal analysis by taking advantage of the strong mathematical framework of Petri Nets. The behaviour of a Personal Area Network will be used to illustrate the proposed approach and to highlight model interoperability and tool integration through the design, the transformation and the analysis phases.

The quadratic MITC plate and MITC shell elements in plate bending

The analysis of plates can be achieved using the quadratic MITC plate or MITC shell elements. The plate elements have a strong mathematical basis and have been shown to be optimal in their convergence behavior, theoretically and numerically. The shell elements have not (yet) been analyzed mathematically in depth for their rates of convergence, with the plate/shell thickness varying, but have been shown numerically to perform well. Since the shell elements are general and can be used for linear and nonlinear analyses of plates and shells, it is important to identify the differences in the performance of these elements when compared to the plate elements. We briefly review the quadratic quadrilateral and triangular MITC plate and shell elements and study their performances in linear plate analyses.

Revisiting the Myths of Protein Interior: Studying Proteins with Mass-Fractal Hydrophobicity-Fractal and Polarizability-Fractal Dimensions

A robust marker to describe mass, hydrophobicity and polarizability distribution holds the key to deciphering structural and folding constraints within proteins. Since each of these distributions is inhomogeneous in nature, the construct should be sensitive in describing the patterns therein. We show, for the first time, that the hydrophobicity and polarizability distributions in protein interior follow fractal scaling. It is found that (barring ‘all-α’) all the major structural classes of proteins have an amount of unused hydrophobicity left in them. This amount of untapped hydrophobicity is observed to be greater in thermophilic proteins, than that in their (structurally aligned) mesophilic counterparts. ‘All-β’(thermophilic, mesophilic alike) proteins are found to have maximum amount of unused hydrophobicity, while ‘all-α’ proteins have been found to have minimum polarizability. A non-trivial dependency is observed between dielectric constant and hydrophobicity distributions within (α+β) and ‘all-α’ proteins, whereas absolutely no dependency is found between them in the ‘all-β’ class. This study proves that proteins are not as optimally packed as they are supposed to be. It is also proved that origin of α-helices are possibly not hydrophobic but electrostatic; whereas β-sheets are predominantly hydrophobic in nature. Significance of this study lies in protein engineering studies; because it quantifies the extent of packing that ensures protein functionality. It shows that myths regarding protein interior organization might obfuscate our knowledge of actual reality. However, if the later is studied with a robust marker of strong mathematical basis, unknown correlations can still be unearthed; which help us to understand the nature of hydrophobicity, causality behind protein folding, and the importance of anisotropic electrostatics in stabilizing a highly complex structure named ‘proteins’.

Transfer of algebraic and graphical thinking between mathematics and chemistry

AbstractStudents in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the investigation we exposed a group of students to a chemistry instrument based on the Nernst equation in electrochemistry, and an equivalent group of students to a similar mathematics instrument in which the questions were stripped of all chemistry context. Both tests contained items requiring algebraic as well as graphical skills. Students experienced few problems with the algebraic questions in both the chemistry and mathematics tests. Their graphical construction and interpretation skills, on the other hand, are inadequate, as can be seen from the poor performance in both the mathematics and the chemistry results of the graphical question. Our conclusion is that the problem seems to lie at the mathematics side and is not due to the transfer of mathematics to an application. © Wiley Periodicals, Inc. J Res Sci Teach 45: 197–218, 2008.

Contact of Planar Flexible Multibody Systems Using a Linear Complementarity Formulation

AbstractDescriptions leading to Linear Complementarity Problems (LCPs) are well established in the contact modeling of rigid multibody systems and have a very strong mathematical basis. These approaches yield exact solutions for contact problems consisting of contact (force/acceleration level) and impact (impulse/velocity level). By utilizing these methods, also frictional contact can be handled appropriately, see [1] and [2].In this paper a formulation for extending these methods for consideration of planar deformable bodies is given. In the case of deformable bodies, a finite wave propagation speed is inherent and, thus, impact computations on impulse/velocity level which lead to jumps in velocity are no longer required. In this paper only the case of continual contact is taken into account. For this purpose, the complementarity relations are reformulated in such a way that contact modeling of constrained and non‐constrained planar deformable bodies is possible, too. In this formulation, deformable bodies are modeled based on the moving frame of reference approach with modal coordinates which is frequently used for the simulation of deformable multibody systems [3]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)