Mathematical Methodology Research Articles

‘A REMARKABLE ARTIFICE’: LAPLACE, POISSON AND MATHEMATICAL PURITY

Abstract In the early nineteenth century, a series of articles by Laplace and Poisson discussed the importance of ‘directness’ in mathematical methodology. In this thesis, we argue that their conception of a ‘direct’ proof is similar to the more widely contemplated notion of a ‘pure’ proof. More rigorous definitions of mathematical purity were proposed in recent publications by Arana and Detlefsen, as well as by Kahle and Pulcini: we compare Laplace and Poisson’s writings with these modern definitions of purity and show how the modern definitions fail to grasp some more nuanced aspects.

Fuzzy Analytic Network Process with Principal Component Analysis to Establish a Bank Performance Model under the Assumption of Country Risk

In recent years, bank-related decision analysis has reflected a relevant research area due to key factors that affect the operating environment of banks. This study’s aim is to develop a model based on the linkages between the performance of banks and their operating context, determined by country risk. For this aim, we propose a multi-analytic methodology using fuzzy analytic network process (fuzzy-ANP) with principal component analysis (PCA) that extends existing mathematical methodologies and decision-making approaches. This method was examined in two studies. The first study focused on determining a model for country risk assessment based on the data extracted from 172 countries. Considering the first study’s scores, the second study established a bank performance model under the assumption of country risk, based on data from 496 banks. Our findings show the importance of country risk as a relevant bank performance dimension for decision makers in establishing efficient strategies with a positive impact on long-term performance. The study offers various contributions. From a mathematic methodology perspective, this research advances an original approach that integrates fuzzy-ANP with PCA, providing a consistent and unbiased framework that overcomes human judgement. From a business and economic analysis perspective, this research establishes novelty based on the performance evaluation of banks considering the operating country’s risk.

Design and Development of Different Applications of PATB (Porous Aerostatic Thrust Bearing): A Review

In several applications demanding precise and ultra-precision movements, porous aerostatic thrust bearings had been employed as a crucial precision engineering component and enabling technology. By acting as a lubricant between the moving part and the stationary part in aerostatic bearings, pressurized air almost completely eliminates friction. Since air acts as the lubricant, oil-based lubricants leave no debris behind. The air prolongs the life of the substances by preventing them from slipping and wearing. The aerostatic type uses graphite as a porous film to disrupt the air uniformly over the surface, or a tiny hole is drilled through the centre of the bearing to let the air circulate and produce a thin layer between the components. With an increased reliance on computational and mathematical methodologies for design and bearing performance optimization, this review paper aims to present the state-of-the-art in aerostatic bearings advancement and research. It also conducts a critical analysis of their future research directions and development trends in the next ten years and beyond. Air bearings are utilized in the production of tools like lathes, CMM, and grinders because they are highly precise in their operation and decrease mistakes and production time. Air bearings are available in a variety of forms and sizes. The assessment of future trends and obstacles in aerostatic bearings investigation, as well as their prospective applications in the precision engineering sectors, concludes the study.

Capturing COVID-19 spread and interplay with multi-hop contact tracing intervention.

A preemptive multi-hop contact tracing scheme that tracks not only the direct contacts of those who tested positive for COVID-19, but also secondary or tertiary contacts has been proposed and deployed in practice with some success. We propose a mathematical methodology for evaluating this preemptive contact tracing strategy that combines the contact tracing dynamics and the virus transmission mechanism in a single framework using microscopic Markov Chain approach (MMCA). We perform Monte Carlo (MC) simulations to validate our model and show that the output of our model provides a reasonable match with the result of MC simulations. Utilizing the formulation under a human contact network generated from real-world data, we show that the cost-benefit tradeoff can be significantly enhanced through an implementation of the multi-hop contact tracing as compared to traditional contact tracing. We further shed light on the mechanisms behind the effectiveness of the multi-hop testing strategy using the framework. We show that our mathematical framework allows significantly faster computation of key attributes for multi-hop contact tracing as compared to MC simulations. This in turn enables the investigation of these attributes for large contact networks, and constitutes a significant strength of our approach as the contact networks that arise in practice are typically large.

Evolutionary multitasking for bidirectional adaptive codec: A case study on vehicle routing problem with time windows

The vehicle routing problem (VRP), an NP-hard problem of considerable complexity, pertains to the determination of optimal sequences of customer visits in an effort to minimize the total operational cost of vehicles. Conventional approaches to tackling VRP have primarily focused on optimizing each task independently, utilizing mathematical methodologies or evolutionary algorithms. Nevertheless, research exploring the application of the advanced concept of evolutionary multitasking (EMT) to address VRP remains limited. To enrich the body of knowledge in this field, our study presents an innovative EMT algorithm, dubbed EMT-RD. This algorithm employs a bidirectional adaptive codec to facilitate the transfer of information between real and discrete solutions. The EMT-RD algorithm permits the transfer of real and discrete solutions across varying tasks, utilizing an encoding rule that transforms information from real to discrete solutions for each task. Further, a decoding rule from discrete to real solutions generates search experiences, facilitating the transfer of knowledge between real solutions. The mechanism is capped off with an adaptive transfer strategy that instigates transfer operations across different tasks. Each task is tackled using a single-task optimization algorithm that employs an artificial bee colony algorithm. Through comprehensive experimentation, we found that our proposed EMT-RD algorithm outperforms competitors on 168 VRP with time windows multitasking instance pairs and four real-world problem pairs that were developed for this study. These results underscore the efficacy of the adaptive transfer strategy and bidirectional adaptive codec in addressing inter-task correlations when solving the VRP.

Average Impulsive Weight Based Event-Triggered Impulsive Synchronization on Coupled Neural Networks

This article explores the stochastic synchronization for a class of coupled neural networks through a novel event-triggered impulsive control strategy. In view of hybrid impulses in the controller, the desynchronizing and synchronizing impulses are both discussed in consideration of the average impulsive weight. The triggering conditions are presented according to the latest impulsive weight and the overall impulsive weight, respectively and an exponential threshold function is correspondingly proposed to explain the triggering mechanism. Sufficient conditions for the synchronization are successfully obtained with jointly utilizing the mathematical induction methodology and the variation of parameter formula. In addition, the convergence velocity of the coupled neural networks is precisely estimated considering the different delayed impulsive comparison systems. In addition, the Zeno behaviors could be successfully eliminated with the proposed event-triggered function. Finally, one numerical example is presented to validate the results.

P-284 Time-lapse embryo deselection: development of an interpretable numerical prediction algorithm based on 10320 embryos

Abstract Study question Is it possible to build a numerical Day 3 prediction model based on calculated weightings of time-lapse deselection measures? Summary answer A numerical Day 3 prediction model was developed incorporating computed weightings for a range of contributing factors, showing satisfactory performance. What is known already The transferability issue of time-lapse embryo selection algorithms is gaining wider attention, with growing evidence revealing altered embryo morphokinetics in response to different culture conditions and patients’ profiles. In fact embryo deselection using abnormal cleavage patterns, such as direct cleavage or reverse cleavage, have been shown to produce superior inter-laboratory reproducibility. However data is limited in the literature on the weightings between individual measures for prognosis prediction, where disagreement often exist amongst embryologists. In this study, we aimed to build a mathematical blastocyst prediction model for improved transferability and robustness, by incorporating computed weightings for a range of contributing factors. Study design, size, duration Time-lapse annotation data were retrospectively extracted from 10320 Day 3 embryos created at Fertility North between January 2017 and June 2022. A subset of 3432 embryos were excluded due to poor quality according to standard Day 3 criteria. Data training and model development were based on 6019 embryos with subsequent blastulation outcomes up to Day 6. Further validation was conducted using another 969 embryos with known implantation outcomes following single fresh Day 3 transfers. Participants/materials, setting, methods Embryos were assessed using both static morphology criteria and time-lapse annotation. Time-lapse deselection parameters included direct cleavage (DC), reverse cleavage (RC) and <4 intercellular contact points at 4-cell stage (<4ICCP). For DC and RC, the number of affected blastomeres was also recorded for the 1st (1-cell), 2nd (2-3-cell), and 3rd cleavage cycles (4-8-cell), respectively. Fivefold cross validation (n = 6019) was used to develop the numerical model, followed by additional validation (n = 969) via receiver operating characteristics (ROC). Main results and the role of chance Multivariate logistic regression identified 11 variables that were independently associated with blastulation, including insemination methods (IVF or ICSI, odds ratio or OR = 0.757, 95% confidence interval or CI 0.676-0.847, P < 0.001), maternal age (OR = 0.937, 95% CI 0.926-0.949, P < 0.001), <4ICCP (OR = 0.733, 95% CI 0.599-0.895, P = 0.002), number of DC blastomeres at the 1st (OR = 0.036, 95% CI 0.022-0.058, P < 0.001), 2nd (OR = 0.139, 95% CI 0.109-0.176, P < 0.001) or 3rd cleavage cycle (OR = 0.375, 95% CI 0.270-0.521, P < 0.001), number of RC blastomeres at the 1st (OR = 0.082, 95% CI 0.028-0.238, P < 0.001), 2nd (OR = 0.304, 95% CI 0.231-0.400, P < 0.001), or 3rd cleavage cycle (OR = 0.482, 95% CI 0.411-0.567, P < 0.001), cell number (OR = 0.890, 95% CI 0.849-0.934, P < 0.001) and degree of fragmentation (OR = 0.675, 95% CI 0.598-0.763, P < 0.001) on Day 3. A mathematical model was constructed using coefficients of 11 variables via fivefold cross validation (AUCs ranged from 0.765 to 0.777 in 5 development subsets and 0.757 to 0.782 in 5 testing subsets), giving rise to a blastulation prediction score (range 0-10). Blastulation rates rose (5%, 11%, 28%, 47%, 70% to 84%) along score increments (<4, 4-4.9, 5-5.9, 6-6.9, 7-7.9, 8+, respectively). Further validation of the proposed model using a separate dataset with known implantation outcomes also showed satisfactory performance (AUC = 0.626, 95% CI 0.590-0.662, P < 0.001). Limitations, reasons for caution Our model was developed using a clinic-specific dataset so might not generalize to other clinics with different laboratory setups and patient profiles. Prospective validation, ideally using randomized controlled design, is required to validate its effectiveness in clinic practice. Wider implications of the findings In comparison to most machine learning or black box-based embryo selection algorithms, the development of our model only engaged mathematical methodologies with complete interpretability. We acknowledge the transferability issue of embryo selection algorithms and would invite external validation of our algorithm by sharing the full details of our mathematical formula. Trial registration number N/A

NEW CONTINUUM OF OPTIONS VOLATILITY SMILE; Modification, Verification and Its Application

This functional exploration inspects the instability smile patters and its determinants for file choices. To survey the determinants that cause the grin design, we utilized Dumas et al. (1998) equation which gave us the best fitted suggested instability. So, it tends to be utilized in three distinct models, for example, Black et al. (1973), Heston (1993) and the MSV model to concentrate on the grin shape. This paper means to summing up the various methodologies in deciding the suggested unpredictability for the choices. Considering point-by-point writing on the guess strategies, a mathematical methodology is made sense of. This paper gives a survey of: (1) the improvement of the choice estimating model by Black et al. (1973), and the resulting changes of this model after 1987 (2) the experimental confirmation of each of the three models; and (3) uses of these models to really look at the examples of grin among various business sectors. We infer that there exists a positive connection between suggested instability and cash ness and the unpredictability grin is less lopsided for call choices. Likewise, the chance to termination for a choice and authentic unpredictability are the significant determinant.

Application of TOPSIS method for flood susceptibility mapping using Excel and GIS

This study elaborately manifests a simplified Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) multicriteria decision-making (MCDM) approach that goals to determine the disparity among the distances between the positive and negative ideal solutions. MCDM methods evaluate options based on a variety of criteria by using mathematical and analytical methodologies. This promotes a more transparent and objective decision-making process by removing human biases and subjective judgements. By considering the comparative proximity to the optimal situation, TOPSIS considers the distances between the ideal and the negative-ideal alternatives. This study has concentrated on the normalization process, the appropriate determination of the ideal and the anti-ideal solution, and the metric utilized to compute the euclidean distances from the ideal best and the ideal worst.•This study expresses the simplified TOPSIS methodology as stated by Hwang and Yoon (1981). The categorization and weight assignments of the criteria have been executed from the expert's opinion and based on existing literatures.•Integration of the TOPSIS technique with GIS has been properly performed for the production of a flood susceptibility map of a highly vulnerable region and visual interpretation of the TOPSIS algorithm.•This kind of investigation saved time by sufficiently skilled specialized personnel in this field.

Generating immunogenomic data-guided virtual patients using a QSP model to predict response of advanced NSCLC to PD-L1 inhibition

Generating realistic virtual patients from a limited amount of patient data is one of the major challenges for quantitative systems pharmacology modeling in immuno-oncology. Quantitative systems pharmacology (QSP) is a mathematical modeling methodology that integrates mechanistic knowledge of biological systems to investigate dynamics in a whole system during disease progression and drug treatment. In the present analysis, we parameterized our previously published QSP model of the cancer-immunity cycle to non-small cell lung cancer (NSCLC) and generated a virtual patient cohort to predict clinical response to PD-L1 inhibition in NSCLC. The virtual patient generation was guided by immunogenomic data from iAtlas portal and population pharmacokinetic data of durvalumab, a PD-L1 inhibitor. With virtual patients generated following the immunogenomic data distribution, our model predicted a response rate of 18.6% (95% bootstrap confidence interval: 13.3-24.2%) and identified CD8/Treg ratio as a potential predictive biomarker in addition to PD-L1 expression and tumor mutational burden. We demonstrated that omics data served as a reliable resource for virtual patient generation techniques in immuno-oncology using QSP models.

Study of the passengers average waiting time at public transport stops

When predicting public transport routes in cities, important indicators should be considered: the duration of stay on the bus route, passenger flow on the bus route, points of attraction and the passenger’s average waiting time at stops. These indicators are the basis for planning the operation of city transport. In particular, predicting the duration of traffic by studying the average passenger’s waiting time at stops is an important planning tool for transport companies. Therefore, this study can improve the quality of scheduled services by reducing the gap between actual and scheduled travel time. This article discusses this relevance and, based on experimental evidence, points to the benefit of using studies of average passenger waiting times, especially considering population groups. In fact, most of the factors which affect public transport operation, as had been proven by previous studies, follow a definite mathematical methodology. The analysis was performed using the data from field studies of passenger flow at bus stops (Lviv, Ukraine). The study of passengers at stopping points makes it possible to improve the quality of public transport services (calculate travel duration between stops and the duration of stay at them more accurately). The duration of stay at selected objects depending on a number of passengers was studied. Also, there are given the results of a study of the waiting time of public transport passengers at bus stops are given. A comparison of the dependence of the bus waiting time on population groups was obtained. After receiving this information, system operators can design and adjust the data according to the estimated trip duration. Nevertheless, it is necessary to carry out research at different types of stops in different parts of cities to clarify these data and for a more detailed analysis.

Representational change is integral to reasoning.

Reasoning is the derivation of new knowledge from old. The reasoner must represent both the old and new knowledge. This representation will change as reasoning proceeds. This change will not just be the addition of the new knowledge. We claim that the representation of the old knowledge will also often change as a side effect of the reasoning process. For instance, the old knowledge may contain errors, be insufficiently detailed or require new concepts to be introduced. Representational change triggered by reasoning is a common feature of human reasoning but it has been neglected both in Cognitive Science and Artificial Intelligence. We aim to put that right. We exemplify this claim by analysing Imre Lakatos's rational reconstruction of the evolution of mathematical methodology. We then describe the abduction, belief revision and conceptual change (ABC) theory repair system, which can automate such representational change. We further claim that the ABC system has a diverse range of applications to successfully repair faulty representations. This article is part of a discussion meeting issue 'Cognitive artificial intelligence'.

Synthetic Data Generation for Deep Learning-Based Inversion for Velocity Model Building

Recent years have seen deep learning (DL) architectures being leveraged for learning the nonlinear relationships across the parameters in seismic inversion problems in order to better analyse the subsurface, such as improved velocity model building (VMB). In this study, we focus on deep-learning-based inversion (DLI) for velocity model building, leveraging on a conditional generative adversarial network (PIX2PIX) with ResNet-9 as generator, as well as a comprehensive mathematical methodology for generating samples of multi-stratified heterogeneous velocity models for training the DLI architecture. We demonstrate that the proposed architecture can achieve state-of-the-art performance in reconstructing velocity models using only one seismic shot, thus reducing cost and computational complexity. We also demonstrate that the proposed solution is generalisable across linear multi-layer models, curved or folded structures, structures with salt bodies as well as higher-resolution structures built from geological images through quantitative and qualitative evaluation.

Open Systems, Quantum Probability, and Logic for Quantum-like Modeling in Biology, Cognition, and Decision-Making.

The aim of this review is to highlight the possibility of applying the mathematical formalism and methodology of quantum theory to model behavior of complex biosystems, from genomes and proteins to animals, humans, and ecological and social systems. Such models are known as quantum-like, and they should be distinguished from genuine quantum physical modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems or, to be more precise, to information processing in them. Quantum-like modeling has its basis in quantum information theory, and it can be considered one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on the theory of open systems in its most general form-the theory of open quantum systems. In this review, we explain its applications to biology and cognition, especially theory of quantum instruments and the quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest given to QBism, as it may be the most useful interpretation.

Developing Teaching Material of Research Methodology and Learning with 4D Model in Facilitating Learning During the Covid-19 Pandemic to Improve Critical Thinking Skill

This research and development aimed to produce teaching materials for research and teaching methodology courses using the 4D model. Teaching materials were arranged based on a 4-D procedure: Define, Design, Develop and Disseminate. The validated teaching materials were tested through small groups of 30 students and large groups of 90 students. It collected data using observation, interviews, documentation, and questionnaires. The data were analyzed qualitatively by data reduction, data presentation, and drawing conclusions and verification. The quantitative analysis was done by processing data from expert reviews and responses from lecturers and students using percentages. The development results were teaching materials validated by four expert validators: content-focused material, curriculum-focused material, learning design, and language. The research and development resulted in a defined stage obtained material elaboration from the point of view of the research methodology of language, mathematics, and geography. The design stage was based on the design validator's suggestion regarding an attractive appearance on the cover, chapter titles, and the format of the content of the Deepublish textbook. In the development stage, the validation results obtained an average of 76.37% with good qualifications, and the average test decision was feasible with revisions in certain parts. The test results of small group students obtained 75.19% or good qualifications. The results of the large group trial got 76.83% or good qualifications. The research concludes that teaching materials have been compiled based on 4D steps. Based on the findings, the implications of this study show that the teaching materials resulting from the development can be used as material for consideration for teachers in delivering related material under the conditions during the Covid-19 pandemic.

Investigating the compressibility and flowability of cocoa powders: A solution for chocolate industry

AbstractThe flowability and compressibility properties were determined for two types of cocoa powders, which are used commercially in chocolate industries; alkalized and natural cocoa powders. Physical and flow properties have a very significant role in the flow behavior, which relates to the handling, transportation, and storage of bulk powders. Throughout the research, it was observed that the properties of both cocoa powders are similar. The objectives of this work are to compare the compressibility and flowability between alkalized and natural cocoa powders and to design the minimum opening size of hopper for mass flow based on their flow properties. Jenike's mathematical methodology is applied during the research for the design of conical hoppers for mass flow. Besides, powder flow analysis using powder flow analyzer is one of the testing methodologies in this research. In addition, direct shear box tests were performed with three different normal stresses. The alkalized cocoa powder needs 1.366 m in diameter for the opening of the hopper, while the natural cocoa powder needs 1.531 m. From the results of the study conducted, it was concluded that both cocoa powders are very cohesive and have poor flow properties. This research reveals that the physical and flow properties of two main types of cocoa powder contributed a lot to the process of hopper design, enhance process understanding, and also applicable for analyzing the powder behavior at any stage in industry.Practical applicationsCocoa powder is the essential ingredient of chocolate manufacturing and other food industry having a chocolate‐like flavor including beverages, biscuits, desserts, and so forth. In chocolate industry, the flow behavior of cocoa powders can affect manufacturing efficiency, which directly affects the production capacity and product quality in terms of its weight and content uniformity. In this study, the critical design parameters such as hopper angle and size of opening were determined to improve the flowability of cocoa powders when passes through hopper. The findings of the present study make it possible for an accurate estimation of a correct intersection with the hopper flow factor line and effective angle of internal friction (δ), extrapolating the powder flow function ff curve to obtain hopper opening size for each cocoa powder for better flowability.

Machine Learning and the Digital Measurement of Psychological Health

Since its inception, the discipline of psychology has utilized empirical epistemology and mathematical methodologies to infer psychological functioning from direct observation. As new challenges and technological opportunities emerge, scientists are once again challenged to define measurement paradigms for psychological health and illness that solve novel problems and capitalize on new technological opportunities. In this review, we discuss the theoretical foundations of and scientific advances in remote sensor technology and machine learning models as they are applied to quantify psychological functioning, draw clinical inferences, and chart new directions in treatment.

MATHEMATICAL MODELLING OF THE PROCESS OF QUALITY CONTROL OF CONSTRUCTION PRODUCTS

The study's abstract summarizes the findings of years of research in the area of quality management of industrial production and construction production, which were based on mathematical modeling techniques, process, and outcomes of implementing the developed program of monitoring and quality control in the enterprise's production process. The objective of this work is to show to the scientific community the useful outcomes of mathematical modeling in software applications. Quality control and safety represent increasingly important concerns for project managers. Defects or failures in constructed facilities can result in very large costs. Even with minor defects, re-construction may be required and facility operations impaired. Increased costs and delays are the result. In the worst case, failures may cause personal injuries or fatalities. Accidents during the construction process can similarly result in personal injuries and large costs. Indirect costs of insurance, inspection and regulation are increasing rapidly due to these increased direct costs. Good project managers try to ensure that the job is done right the first time and that no major accidents occur on the project. The research focused on describing applicable mathematical models, viewpoints, and practical outcomes of their use in the applied sector to evaluate quality control. This mathematical model was applied by the authors. The outcomes of using this approach are presented in the article. By utilizing mathematical modeling techniques, the authors created an experimental software management and quality assessment system. The authors continue their study in this area to enhance prognostic and diagnostic processes based on mathematical modeling methodologies for diagnostic systems and quality management systems.. The independent quality control, which was based on some traditional inspection techniques and used mathematical modeling techniques, revealed a negligible partial discrepancy in the results of the estimation, proving both the efficacy of the product and the suitability of the mathematical modeling concept. Keywords: Quality control, mathematical modeling, construction quality.

Feedback control laws to ensure generalized mutual exclusion constraints in a network of partially observable timed event graphs

This paper deals with the control problem of partially-observable Discrete Event Systems (DESs) which are modelled by Networks of Timed Event Graphs (NTEGs) and subject to Generalized Mutual Exclusion Constraints (GMECs). A new mathematical methodology based on the use of Min-Plus formalisms to synthesize control laws that guarantee the concerned constraints is suggested. For this, the dynamic behavior of the NTEGs is described by linear equations in Min-Plus algebra and the GMECs are represented by weighted inequalities in Min-Plus algebra too. Sufficient conditions are supplied to verify the existence of feedback gains guaranteeing the satisfaction of GMECs. Eventually, to verify the analytical results, it is important to examine a real case study of manufacturing systems.

Why Corporate Sustainability Is Not Yet Measured

Measuring Corporate Sustainability (CS) has been identified as an important enabler for integrating sustainability into corporate practices. Different methodologies and frameworks for measuring CS have been developed in the literature with limited success, as reflected by the lack of application in the real world. Among practitioners, the effort has been on developing frameworks that provide useful indicators of the different items that need to be considered for integrating sustainability. Notwithstanding the increasing attention and progress on the subject, a cohesive and applicable measure of CS across firms, industries and geographies is still missing. This paper provides an examination of the different methodologies for measuring CS, with an analysis of their merits and limitations, as well as guidance for future research focus. The findings show a failure to coherently link the mathematical measurement and data aggregation methodologies to a well-constructed concept where the linkage between the defining features and causal relations are appropriately identified. The proposed models and mathematical techniques are not able to inform on the extent to which a corporation acts sustainably because sustainability is not being measured in its highest extension, making the results narrow, non-referential and non-comparable. Furthermore, there is confusion between developing the indicators of CS, providing their measurement and enabling their integration.