Mathematical Methods Research Articles

Optimal fissioning strategies of social insects with respect to colony dynamics and nest founding probability

AbstractSocial insects demonstrate two fundamentally different modes of reproduction, independent colony foundation (ICF) by single fertilized queens or dependent colony foundation (DCF) by fissioning of existing colonies into two or several new colonies (swarms). In some species, both reproductive modes occur in parallel. The benefits and disadvantages of DCF vs. ICF have been widely discussed and been subject to empirical studies, but a formal theoretical treatment of the topic is still incomplete. Taking honey bees as example, we provide a resource allocation model of colony dynamics to analyze the ecological conditions under which DCF may be favored over ICF. Using mathematical and numerical methods, we show that it critically depends on the survivorship function linking swarm size to the probability of swarm establishment whether ICF or DCF results in a higher output of surviving new colonies. Because building larger swarms requires larger inter-swarm time intervals, DCF can only be a better strategy if this disadvantage is over-compensated for by a strong size-dependent swarm survivorship and survival of single queens is very low. Colony growth rate has no effect on this decision and the impact of maximum possible colony size is negligible. Further, there is a discontinuity in the optimal swarm size, so that either a swarm size of 1 (ICF) is the best strategy, or emitting swarms of considerable size (DCF). Consequently, a direct evolutionary transition from ICF to DCF appears unlikely and may have been triggered by selective pressures promoting movement of complete nests or distributing single colonies over several nests (polydomy).

Mathematical programming tools for randomization purposes in small two-arm clinical trials: A case study with real data.

Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods use mathematical programming to construct attractive clinical trials that balance the group features, such as their sizes and covariate distributions of their subjects. We review some of these methods and compare their performance with common covariate-adaptive randomization methods for small clinical trials. We introduce an energy distance measure that compares the discrepancy between the two groups using the joint distribution of the subjects' covariates. This metric is more appealing than evaluating the discrepancy between the groups using their marginal covariate distributions. Using numerical experiments, we demonstrate the advantages of the mathematical programming methods under the new measure. In the supplementary material, we provide R codes to reproduce our study results and facilitate comparisons of different randomization procedures.

Estimation of gross calorific value of coal: A literature review

ABSTRACT The gross calorific value (GCV), also known as the higher heating value (HHV) of coal is the amount of heat emitted upon complete combustion of coal. The GCV of coal is used to estimate various technoeconomic parameters such as boiler efficiency, combustion values, and production costs. This study seeks to examine the methods that are used to estimate the GCV of coal. These methods can be classified as either mathematical, experimental, or online methods.” It was found that linear and non-linear regression, differential scanning calorimetry (DSC), artificial intelligence (AI) methods have all been frequently used to estimate the GCV. The challenge with these approaches is that they include sophisticated machinery that demand expert operation, and the task is time consuming. Accurate and timely analysis of the GCV coal is a crucial stage in power plants, which can be achieved with online monitoring of the GCV of coal. There is not much literature on the topic of online monitoring of the coal GCV because it hasn’t been studied extensively. In power plant operation, online monitoring of the GCV of coal is a promising technology that hasn’t been studied extensively.

A Discrete Dynamic Conflict Model

Relevance. Conflicts play a significant role in the development of society, the state and all of humanity. They arise in interpersonal relationships, economics, organizational activities, social problems, and world politics. The study of the essence of conflicts, the causes of their emergence and ways to resolve them is carried out by conflictology, which was formed as an interdisciplinary field of knowledge in the middle of the 20th century. Currently, it has become obvious that the conflict itself is not a negative phenomenon, but a competently resolved conflict situation can benefit all parties to the conflict. As a result, it became necessary to consider conflicts not only from a descriptive, philosophical point of view, but also to be able to predict a possible conflict situation, describe its development over time and calculate acceptable ways out of it. This approach to the study of conflicts is mathematical modeling, based on mathematical methods for describing conflict situations, which allow analyzing conflicts and predicting their outcome.The purpose is to describe a general methodology for constructing a conflict scheme of any origin within the framework of the mathematical theory of conflicts. The objectives is to consider and analyze a discrete dynamic model of conflicts using the example of a childparent conflict.Methodology. The work uses algebraic methods and methods of discrete mathematics.Results. Within the framework of the mathematical theory of conflicts, a conflict with a discrete mismatch is considered the example of a child-parent model conflict. A general method for constructing a conflict situation diagram and analyzing it has been developed. Possible ways of influencing the conflicting parties on each other in any conflict situation are discussed. When analyzing possible scenarios for the development of a conflict situation, the possible types of impacts of the conflicting parties on each other are considered.Conclusions. Based on the developed dynamic discrete model, it is shown that the mathematical description of conflicts is reduced to the problem of combinatorial optimization. The developed scheme of mathematical description of conflicts can be applied to a wide class of conflict situations in various subject areas.

Knowledge Graph Analysis for Chronic Diseases Nursing based on Visualization Technology and Literature Big Data

The use of knowledge graph analysis for chronic disease nursing based on visualization technology and literature big data is an unexplored area of research in this field of study. To uncover research hotspots and developmental trends in the field of chronic disease nursing, and to provide a scholarly reference, we employed mathematical and statistical methods along with CiteSpace literature visualization analysis software for quantitative analysis of extensive literature data from the Web of Science Core Collection. We examined aspects such as publication trends, journals, author collaborations, research institutions, national and regional distributions, keyword co-occurrence, clustering, time zones, emergence, literature co-citations, and more. These analyses identified the current hotspots and future directions for research. Notably, scholars' interest in chronic disease nursing exhibited a consistent upward trajectory. In particular, the field of artificial intelligence technology application in nursing yielded $3,610$ published papers in $141$ journals with more than or equal to $10$ published papers on the topic, accounting for $58.41 \%$ of the total number of published papers in this field of study. Furthermore, the top three publishers were the “Journal of Clinical Nursing,” “Journal of Advanced Nursing,” and “BMC Health Services Research.” Among authors, Hu, Frank B., Willett, Walter C., and Rimm, Eric B., ranked as the top three, and 12 authors had more than 10 publications. The most active research institutions included Harvard University, Harvard Medical School, Brigham & Women’s Hospital, University of California System, University of London, US Department of Veterans Affairs, Veterans Health Administration (VHA), Harvard T. H. Chan School of Public Health, University of Sydney, and the University of Toronto. The United States, Australia, England, China, Canada, Netherlands, Spain, Italy, Sweden, and Germany emerged as the leading countries in terms of research output, while emerging hotspots encompassed topics such as incidence, rheumatoid arthritis, qualitative research, burnout, kidney transplantation, critical illness, COVID-19, Sars-COV-2, public health, and the well-being of medical staff. These findings present valuable insights for prospective research endeavors.

A Systematic Review of Sustainable Supply Chain Network Design: Optimization Approaches and Research Trends

In response to the ever-increasing pursuit of competitiveness among organizations in today’s global business landscape, the subject of supply chain management has become a vital domain encompassing a wide range of sectors and industries across the economy. The growing concern about sustainable development has prompted public and private supply chain players to incorporate the three pillars of sustainability, namely, economic, environmental, and social, into the design of their supply chain networks. This study reviews and examines the content of 102 relevant papers to discuss the mathematical models, modeling approaches, and solutions that have been explored in the existing literature on forward sustainable supply chain network design. This paper also investigates the sustainability elements and supply chain network peculiarities including design factors and decision levels. In this review, several limitations in the current literature on sustainable supply chain network design optimization models are highlighted. According to the analysis, it was found that a better understanding of the industry and its sustainability requirements and priorities is essential for designing sustainable supply chain networks that are tailored to the needs of a specific industry rather than achieving general sustainability objectives. In addition, integrating strategic, tactical, and operational decision levels in the design of supply chain networks is critical for evaluating their impact on each other in terms of sustainability. More sophisticated mathematical solution methods for dealing with real-life scenarios including nonlinearity and uncertainty sources are required. The paper concludes with new prospects of research to promote a better integration of sustainability into supply chain networks.

Research on Data Mining and Reinforcement Learning in Recommendation Systems

This paper aims to help students better grasp the required professional knowledge and core concepts. This paper presents a design method for a multi-layer knowledge base based on XML. According to learners' identity characteristics and learning behaviour, using the mathematical statistics method, the feature expression for the learning system is constructed. Multivariable linear regression theory establishes convergence constraints for accurate and deep mining. The average detection results of the collected samples are used for high-quality deep mining of user portraits in the learning system. This project intends to study the method of solving accurate confidence intervals for user portrait data in the education system. Excel and Access are used to complete the data collection of the teaching object and the construction of the database. A multi-mode interactive editing and processing method of user portrait information for education systems is studied in cloud computing. Finally, a learning system based on mathematical loading mode is proposed, and an object-oriented learning recommendation system is designed. The developed teaching software can enable students to get more teaching guidance when they acquire the required knowledge to improve students' learning effect effectively.

Quantitative Structure‐Property Relations for Polyester Materials via Statistical Learning

AbstractWe employ statistical learning to present a principled framework for the establishment of quantitative structure‐property relationships (QSPR). We focus on property predictions of industrial polymers formed by multiple reagents and at varying molecular weights. We develop a theoretical description of QSPR as well as a rigorous mathematical method for the assimilation of experimental data. Results show that our methods can perform exceptionally well at establishing QSPR for glass transition temperature and intrinsic viscosity of polyesters.This article is protected by copyright. All rights reserved

Computational Analysis and Classification of Hernia Repairs

Problems related to ventral hernia repairs (VHR) are very common, and evaluating them using computational methods can assist in selecting the most appropriate treatment. This study is based upon data from 3339 patients from different European countries observed during the last 12 years (2012–2023), which were collected by specialists in hernia surgery. Most patients underwent standard surgical procedures, with a growing trend towards laparoscopic surgery. This paper focuses on statistically evaluating the treatment methods in relation to patient age, body mass index (BMI), and the type of repair. Appropriate mathematical methods are employed to extract and classify the selected features, with emphasis on computational and machine-learning techniques. The paper presents surgical hernia treatment statistics related to patient age, BMI, and repair methods. The main conclusions point to mean groin hernia repair (GHR) complications of 19% for patients in the database. The accuracy of separating GHR mesh surgery with and without postoperative complications reached 74.4% using a two-layer neural network classification. Robotic surgeries represent 22.9% of all the evaluated hernia repairs. The proposed methodology suggests both an interdisciplinary approach and the utilization of computational intelligence in hernia surgery, potentially applicable in a clinical setting.

Non-Invasive Methods for Intracranial Pressure Monitoring in Traumatic Brain Injury Using Transcranial Doppler: A Scoping Review.

Intracranial pressure (ICP) monitoring is necessary for managing patients with traumatic brain injury (TBI). Although gold-standard methods include intraventricular or intraparenchymal transducers, these systems cannot be used in patients with coagulopathies or in those who are at high risk of catheter-related infections, nor can they be used in resource-constrained settings. Therefore, a non-invasive modality that is more widely available, cost effective, and safe would have tremendous impact. Among such non-invasive choices, transcranial Doppler (TCD) provides indirect ICP estimates through waveform analysis of cerebral hemodynamic changes. The objective of this scoping review is to describe the existing evidence for the use of TCD-derived methods in estimating ICP in adult TBI patients as compared with gold-standard invasive methods. This review was conducted in accordance with the Joanna Briggs Institute methodology for scoping reviews, with a main search of PubMed and Embase. The search was limited to studies conducted in adult TBI patients published in any language between 2012 and 2022. Twenty-two studies were included for analysis, with most being prospective studies conducted in high-income countries. TCD-derived non-invasive ICP (nICP) methods are either mathematical or non-mathematical, with the former having slightly better correlation with invasive methods, especially when using time-trending ICP dynamics over one-time estimated values. Nevertheless, mathematical methods are associated with greater cost and complexity in their application. Formula-based methods showed promise in excluding elevated ICP, exhibiting a high negative predictive value. Therefore, TCD-derived methods could be useful in assessing ICP changes instead of absolute ICP values for high-risk patients, especially in low-resource settings.

Soft super-continuity and soft delta-closed graphs.

Introducing a strong form of soft continuity between soft topological spaces is significant because it can contribute to our growing understanding of soft topological spaces and their features, provide a basis for creating new mathematical tools and methods, and have significant applications in various fields. In this paper, we define soft super-continuity as a new form of soft mapping. We present various characterizations of this soft concept. Also, we show that soft super-continuity lies strictly between soft continuity and soft complete continuity and that soft super-continuity is a strong form of soft δ-continuity. In addition, we give some sufficient conditions for the equivalence between soft super-continuity and other related concepts. Moreover, we characterize soft semi-regularity in terms of super-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and products by soft super-continuity. In addition to these, we study the relationship between soft super-continuity and soft δ-continuity with their analogous notions in general topology. Finally, we give several sufficient conditions on a soft mapping to have a soft δ-closed graph.

PALEOCLIMATIC AND PALEOGEOGRAPHIC RECONSTRUCTIONS OF SEDIMENTATION CONDITIONS IN THE FUXIN BASIN USING METHODS OF MATHEMATICAL STATISTICS

In the paper, the relationship between climatic changes and sedimentation conditions for 4 accumulation stages of the Fuxin and Shahai coal-bearing formations of the Fuxin coal basin in the Aptian-Albian time was established using mathematical statistical methods. As a result, it was observed that the increase in climate humidity coincided with the widespread anoxic oceanic Paquie event (Paquie, OAE1b) during the early Albian time. In addition, a significant influence of facies conditions on the intensity of peat and coal accumulation processes of the Fuxin and Shakhai coal-bearing formations was revealed.

Oil-source correlation in the Yangjiang Uplift, South China Sea: A comparative analysis of mathematical and fingerprint methods

In recent years, significant exploration breakthroughs have been achieved in the Yangjiang Uplift. However, the source of crude oil is ambiguous, and the prevailing view suggests a remote hydrocarbon supply. To clarify the source of the crude oil in the Yangjiang Uplift, 30 source rocks and 15 crude oil samples collected from the Wenchang A Sag and Yangjiang Uplift were subjected to Rock-Eval pyrolysis, maceral analysis, vitrinite reflectance, biomarker analysis, among other experiments. Principal component analysis (PCA) and hierarchical cluster analyses (HCA) were performed. The results indicate that source rocks in the Yangjiang Uplift exhibit robust hydrocarbon-generating potential, with S1 + S2 values ranging between 0.04–140.5 mg/g (averaging: 13.54 mg/g), indicative of reaching the oil generation period. Using 13 biomarker compounds, two types of biomarkers were selected to compare the sources of the crude oils: Pristane/Phytane (Pr/Ph), representing the depositional environment, and tricyclic terpanes, representing the source input. The crude oil in the Yangjiang Uplift can be divided into two types: one with high values of bicadinane-T (T)/C30 hopane and ΣC30-4 methyl sterane/ΣC29 regular sterane and another with a low ratio of (C19tricyclic terpane + C20tricyclic terpane)/C23tricyclic terpane according to the charting method. The investigated crude oil was mixed with the source rocks of the Wenchang A Sag and the Yangjiang Uplift. Furthermore, owing to differences in the mixing ratios, the crude oil in the study area exhibited two distinct characteristics. Type A is characterized by a higher proportion of Wenchang A sag crude oil in the mixture, whereas type B is characterized by a higher proportion of local crude oil. This study established that the Yangjiang Uplift boasts large petroleum resources.

Simulation of radiative nonlinear heat dynamism on Buongiorno-modeled nanoliquid through porous inclined plate with adjustable chemical response

Nanofluids are the fluid suspensions in nanoparticles. A considerable enhancement in their features is less nanoparticle concentrations. Various studies on nanofluids focused on representing their performance with respect to the functions — here enhancing straight heat transfer was critical, like that in nuclear reactors, transportation, different industrial settings, biology, food and electronics. Hence, this consideration analyzes the utilization of the novel mathematical method, called the bvp4c method by viscous heat energy research in Buongiorno-modeled nanoliquid confined by the apt permeable plate along with slip mechanism. The thermophoresis and Brownian dispersion affects are again assumed. This transfer of solutal and thermal energy was dependent on the appreciable effect on heat source, variable chemical reactions and nonlinear thermal radiation. The dimensional model of partial differential equations (PDEs), applied to precise related applications, had been adapted into ordinary differential equations (ODEs). This modified Nusselt number decreases with increasing viscous heating, thermal radiation, thermophoresis parameter and Brownian motion, always it rises due to increasing temperature ratio parameter. The validation of the outcomes was attained with past solutions by free convectional flow and non-magnetic research. There are many functions in petroleum industries and engineering like electroplating, chemical processing of substantial metals and solar water heaters.

Novel solitary waves solutions of the extended cubic(3+1)-dimensional Schr$$\ddot{o}$$dinger equation via applications of three mathematical methods

Novel solitary waves solutions of the extended cubic(3+1)-dimensional Schr$$\ddot{o}$$dinger equation via applications of three mathematical methods

Study of the Dependence of the Friction Force and Coefficient of the Abrasive in the Metal Contact Zone on Various Factors

In the article, the interaction of the coefficient of friction for friction pairs operating under conditions of abrasive wear is considered, depending on a number of factors. Thus, the friction coefficient is one of the main indicators characterizing the performance of friction nodes. Analytical expressions obtained based on the calculation of the results of the conducted tests using mathematical statistical and mathematical methods allow to determine the coefficient of friction and allow the designer to effectively choose the material and oils before designing.

SOFTWARE FOR SOLVING THE TWO-STAGE LOCATION-ALLOCATION PROBLEMS

This article explores the construction of the mathematical model, method, and algorithm for solving the two-stage optimal location-allocation problem, along with the software implementation for algorithm execution. The developed algorithm enables the resolution of resource management and transportation problems from supply centers to consumer spaces. Considering that in the contemporary world where all resources and goods are transported over considerable distances in substantial volumes, the task of optimizing delivery routes and minimizing delivery costs remains relevant. The created algorithm can be integrated into a logistics system comprising two layers of resource delivery: initially to an intermediate supply center and subsequently to the ultimate consumer.

Abstract LB396: The power of NetraAI: Precision medicine in oncology through sub-insight learning from small data sets

Abstract The capabilities of artificial intelligence (AI) and machine learning (ML) are pivotal for refining patient stratification and subtype discrimination in clinical trials. Conventional ML methods often rely on large data sets for meaningful discoveries. NetraAI is a novel ML approach designed and trained to work with smaller data sets. The challenge with smaller data sets is that they do not reflect the totality of the disease that they represent. NetraAI employs a novel approach termed “Sub-Insight Learning”, utilizing validated mathematical methods to analyze even small patient data sets. This allows the system to decompose the data sets into high and low confidence patient subpopulations, enhancing predictive model accuracy and reducing overfitting. Further, the system explains what variables are driving the etiology defining the subpopulations of patients. Using two non-small cell lung cancer (NSCLC) data sets (GSE18842 and GSE10245) consisting of only 104 samples from adenocarcinoma (ADC) and squamous cell carcinoma (SCC), NetraAI distinguished the two subtypes through unique genetic signatures. Notably, nine of the ten variables identified correlate with known NSCLC markers, with PIGX emerging as a novel target. Leveraging protein-protein interaction networks (PPI) revealed connections between PIGX and BACE1. BACE1 has been implicated as a driver of NSCLC brain metastasis. These findings shed light on the biology of membrane proteins and their post-translational modifications, a factor implicated in various diseases, prompting further exploration. NetraAI demonstrates a significant breakthrough in precision medicine for oncology, capable of generating meaningful insights from small data sets. The discovery of novel biomarkers and their implications in cancer and other diseases underline the potential of this AI-driven approach in advancing current research paradigms and patient-specific treatments. Citation Format: Bessi Qorri, Mike J. Tsay, Paul Leonchyk, Larry Alphs, Luca Pani, Joseph Geraci. The power of NetraAI: Precision medicine in oncology through sub-insight learning from small data sets [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 2 (Late-Breaking, Clinical Trial, and Invited Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(7_Suppl):Abstract nr LB396.

De-identification and anonymization: legal and technical approaches

"This study analyzes legal and technical approaches to data de-identification and anonymization, motivated by the need to develop balanced standards that preserve privacy without stifling beneficial data uses. Doctrinal and technical literature review methods examine provisions in major data protection laws worldwide, including the EU's GDPR, US HIPAA, and emerging frameworks in China, India, and Uzbekistan, alongside mathematical models like differential privacy and k-anonymity. The legal analysis reveals common themes like flexible research exemptions for anonymized data and calibrating standards based on sensitivity, but also gaps such as ambiguities around pseudonymization. The technical review highlights the strengths and weaknesses of encryption, perturbation, generalization, and federation techniques, emphasizing the need to complement mathematical methods with governance controls. Key findings include the importance of allowing contextual optimization, providing detailed regulatory guidance, and addressing re-identification incentives. Recommendations are provided for advancing Uzbekistan's data protection laws and practices based on international experiences, such as enabling public oversight, conducting localized impact assessments, and promoting privacy-enhancing technologies. The study concludes that to anonymize data in a way that enables research while also protecting people's rights, we need a comprehensive approach that includes laws, organizational rules, technical safeguards, ethical decision-making, and public input. All of these parts working together is important for successful data anonymization."

Abstract LB395: NetraAI-driven discovery of novel biomarkers in MSI-high colon cancer for precision immunotherapy

Abstract By leveraging NetraAI, a novel machine learning (ML) approach, we identify potential biomarkers in microsatellite instability-high (MSI-H) colon cancer. MSI, marked by DNA mismatch repair (MMR) defects characterizes 5-20% of colorectal cancers (CRCs). MSI-H tumors harbor higher mutational burdens, produce neoantigens, and enhance immune recognition and responsiveness to immunotherapy. The innovative Sub-Insight Learning approach of NetraAI, allows us to overcome challenges associated with smaller data sets not reflecting the totality of the disease they represent. This approach utilizes a set of validated mathematical methods to identify sub-insights about patients even from small data sets. This allows the system to decompose the data sets into high and low confidence patient subpopulations, enhancing predictive model accuracy and reducing overfitting. Further, the system explains what variables are driving the etiology defining the subpopulations of patients. Utilizing a small data set consisting of 141 RNA expression profiles of CRC samples (E-GEOD-41258) with MSI-H and MSI-low colon cancer, we were able to derive several unique insights into patients’ molecular profiles. NetraAI analysis identified several unique variables, including CATSPERB, FUT8, PLLP, DUSP4, and MLPH that may play significant roles in MSI-H colon cancer pathology. These markers hold potential for personalizing clinical trials as well as potential therapeutic targets. Furthermore, protein-protein interaction (PPI) networks revealed co-expression and co-localizations that exist amongst these genes, suggesting a complex interplay among these genes, particularly in the context of spermatogenesis. The application of NetraAI and its Sub-Insight Learning paradigm has revealed novel insights into the molecular profile of MSI-H colon cancer. These findings pave the way for more targeted and effective precision immunotherapy strategies, demonstrating the power of AI in advancing the understanding and treatment of complex cancers. Citation Format: Bessi Qorri, Mike J. Tsay, Paul Leonchyk, Larry Alphs, Luca Pani, Joseph Geraci. NetraAI-driven discovery of novel biomarkers in MSI-high colon cancer for precision immunotherapy [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 2 (Late-Breaking, Clinical Trial, and Invited Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(7_Suppl):Abstract nr LB395.