Mathematical Approach Research Articles

Simulation and application assessment of the efficacy of fosthiazate-loaded microcapsules against root-knot nematode.

Although microencapsulation technology is an effective pesticide formulation method, the correlation between the release properties of microcapsules and pesticide concentrations in soil and their efficacy has not been thoroughly investigated. Here, the effects of the release properties of the nematicide Fosthiazate (FTZ) from microcapsules on their efficacy against the nematode Meloidogyne incognita were examined using experimental and mathematical approaches. Gradual release of FTZ from both polyurea microcapsules (PU-MC) and melamine-formaldehyde microcapsules (MF-MC) was observed over 30 days in the release test, and each release curve was completely distinct. In the biological test, the efficacy of both microcapsules against M. incognita 42 days after the application was 8-15% higher than that of the non-encapsulated FTZ at a concentration of 2.0 mg FTZ kg-1 soil. Soil degradation experiments suggested that the microcapsules worked effectively to protect the FTZ from degradation, which resulted in higher efficacy at a later stage. A simulation study to predict the concentration of FTZ outside the microcapsule found that the timing of supplying FTZ was important and suggested that the mixture of non-encapsulated FTZ (non-MC) and MF-MC showed enhanced efficiency for the entire cultivation period in the biological test; the efficacy against nematodes was also confirmed by the measurement of nematode density using the Bearman funnel method. The release properties of FTZ from microcapsules are critical for their effective application against M. incognita, and the established simulation study is a useful step in designing suitable release properties under complex soil conditions. © 2024 Society of Chemical Industry.

Formalising the role of behaviour in neuroscience.

We develop a mathematical approach to formally proving that certain neural computations and representations exist based on patterns observed in an organism's behaviour. To illustrate, we provide a simple set of conditions under which an ant's ability to determine how far it is from its nest would logically imply neural structures isomorphic to the natural numbers . We generalise these results to arbitrary behaviours and representations and show what mathematical characterisation of neural computation and representation is simplest while being maximally predictive of behaviour. We develop this framework in detail using a path integration example, where an organism's ability to search for its nest in the correct location implies representational structures isomorphic to two-dimensional coordinates under addition. We also study a system for processing strings common in comparative work. Our approach provides an objective way to determine what theory of a physical system is best, addressing a fundamental challenge in neuroscientific inference. These results motivate considering which neurobiological structures have the requisite formal structure and are otherwise physically plausible given relevant physical considerations such as generalisability, information density, thermodynamic stability and energetic cost.

Application of X-ray principles to quantify sulfur oxidation states in concrete

This study introduces a novel mathematical approach rooted in X-ray spectroscopy principles to evaluate the oxidation state of sulfur, which is then applied in concrete and cementitious materials. Unlike previous studies that relied on an empirical quadratic relationship based on the ratios of characteristic X-ray lines (SKα, SKβ, and SKβ') for sulfur oxidation state determination, unique linear relationships between the intensities of the three X-ray lines for each oxidation state and total sulfur were utilized. Rational equations are then derived by combining these linear relationships for each species. Two independent rational calibration curves are constructed using the SKβ/SKα and SKβ'/SKβ ratios for samples containing sulfide-sulfate mixtures, irrespective of total sulfur concentration within the range of 0.3% to 2.0% by weight of concrete. These equations demonstrated interchangeability across three simulated matrices (Portland cement, concrete, and silica) and two sulfide species (pyrrhotite and pyrite). Absolute quantification of sulfide and sulfate species in concrete is achieved by independently measuring total sulfur. Compared to previous quadratic and linear equations, this approach is shown to minimize the difference between the experimental and calculated ratios of the calibration samples. Agreement was also observed between the sulfate ratio calculated through the rational approach and gravimetric analysis for concrete samples.

Analysis of fibrin networks using topological data analysis – a feasibility study

Blood clot formation, a crucial process in hemostasis and thrombosis, has garnered substantial attention for its implications in various medical conditions. Microscopic examination of blood clots provides vital insights into their composition and structure, aiding in the understanding of clot pathophysiology and the development of targeted therapeutic strategies. This study explores the use of topological data analysis (TDA) to assess plasma clot characteristics microscopically, focusing on the identification of the elements components, holes and Wasserstein distances. This approach should enable researchers to objectively classify fibrin networks based on their topologic architecture. We tested this mathematical characterization approach on plasma clots formed in static conditions from porcine and human citrated plasma samples, where the effect of dilution and direct thrombin inhibition was explored. Confocal microscopy images showing fluorescence labeled fibrin networks were analyzed. Both treatments resulted in visual differences in plasma clot architecture, which could be quantified using TDA. Significant differences between baseline and diluted samples, as well as blood anticoagulated with argatroban, were detected mathematically. Therefore, TDA could be indicative of clots with compromised stability, providing a valuable tool for thrombosis risk assessment. In conclusion, microscopic examination of plasma clots, coupled with Topological Data Analysis, offers a promising avenue for comprehensive characterization of clot microstructure. This method could contribute to a deeper understanding of clot pathophysiology and thereby refine our ability to assess clot characteristics.

An instructional approach in mathematics learning for fourth-grade students based on collaborative learning and inquiry-based learning

An instructional approach in mathematics learning for fourth-grade students based on collaborative learning and inquiry-based learning

Application of dominance-based rough set approach in vaginal dosage forms optimization

The objective of this study was to identify cause-effect relationships between various data related to vaginal dosage forms, such as composition, process parameters (condition attributes), and quality (decision attribute), by employing a mathematical data mining approach that utilizes Rough Set Theory. The analyzed data were organized in a tabular format known as an information system. Objects were labeled as rows, and attributes as columns, with attribute-values serving as entries. Each formulation was described by its condition attributes (composition, manufacturing process, quality parameters), while the decision attribute indicated the quality of the formulation (expressed as pH after vaginal tablet or pessary application) and enabled classification as correct/incorrect or good/bad. The decision rules generated by the study provide insights into relationships between the condition attributes and the decision attribute. They highlight the importance of LA content and LA:polymer ratios in maintaining physiological pH. Additionally, the findings confirm the favorable impact of chitosan on pH regulation while indicating that the type of formulation (pessaries or tablets) does not significantly affect the classification of objects. Decision rules with high confirmation coefficients of condition attributes can help developing optimal formulations. These decision rules contain essential information that describes the cause-and-effect relationships and are free of redundant information. They form the basis for understanding and optimizing processes, and establishing a design space.

THE IMPACT OF DIGITAL DISINFORMATION ON QUALITY OF LIFE: A FUZZY MODEL ASSESSMENT

Quality of Life (QoL) is a multifaceted concept encompassing economic, social, environmental, psychological, and physical dimensions of an individual’s life, including personal living conditions, happiness, well-being, and life satisfaction. As a vital criterion for sustainable development and active social policy in countries, QoL has been significantly influenced by the dynamic technological evolution of social media. However, the comprehensive impact of social media, including its role in disseminating disinformation – a major social and socio-economic concern – on QoL remains underexplored. This research aims to develop a novel fuzzy model to assess the level of disinformation on digital platforms and its correlation with the population’s QoL. Employing a mathematical approach rooted in expert evaluation, this study leverages intellectual knowledge analysis and fuzzy set theory. Grounded in data from real respondents and knowledge-based models, this study pioneers an information model to evaluate inhabitants’ QoL, incorporating factors such as financial concerns, perception of disinformation, and its influence on digital platforms. The fuzzy estimation model, verified with data from 3,036 respondents, quantitatively assesses citizens’ QoL. An illustrative application of the model demonstrates its effectiveness. The findings are particularly valuable for policymakers, experts in economic and innovative development, aiding the creation of regulatory and monitoring mechanisms to foster sustainable economic growth and devise effective development strategies.

Ten simple rules to make computable knowledge shareable and reusable.

Computable biomedical knowledge (CBK) is: "the result of an analytic and/or deliberative process about human health, or affecting human health, that is explicit, and therefore can be represented and reasned upon using logic, formal standards, and mathematical approaches." Representing biomedical knowledge in a machine-interpretable, computable form increases its ability to be discovered, accessed, understood, and deployed. Computable knowledge artifacts can greatly advance the potential for implementation, reproducibility, or extension of the knowledge by users, who may include practitioners, researchers, and learners. Enriching computable knowledge artifacts may help facilitate reuse and translation into practice. Following the examples of 10 Simple Rules papers for scientific code, software, and applications, we present 10 Simple Rules intended to make shared computable knowledge artifacts more useful and reusable. These rules are mainly for researchers and their teams who have decided that sharing their computable knowledge is important, who wish to go beyond simply describing results, algorithms, or models via traditional publication pathways, and who want to both make their research findings more accessible, and to help others use their computable knowledge. These rules are roughly organized into 3 categories: planning, engineering, and documentation. Finally, while many of the following examples are of computable knowledge in biomedical domains, these rules are generalizable to computable knowledge in any research domain.

From light polarization to quantum physics: Supporting lower secondary school students’ transition from gestalt to functional thinking

In this paper, we present a new minimal mathematical conceptual approach to quantum mechanics using light polarization for lower secondary school students with the aim of bringing students closer to the so-called quantum mechanical way of thinking. We investigated how students think about some of the basic concepts and fundamental laws and we found that certain concepts are quite well-understandable in younger grades too. We studied the introduction of the so-called state circle, which can faithfully represent quantum mechanical formalism without involving students in abstract algebraic calculations. We then categorized and analyzed students’ thoughts on the superposition principle and the lack of trajectory, finding that the concept of measurement and the lack of trajectory were problematic. We explored that younger students tend to hold gestalt-like mental models of quantum concepts, while at the same time being able to use visualizations correctly for reasoning in the quantum realm. Overall, this paper provides evidence in favor of introducing basic features of quantum mechanics as early as in lower secondary school.

Developing RME-based module in statistics to improve problem-solving skills for higher education students

In university learning, it is important to use learning resources that can facilitate students' thinking skills. So it is necessary to develop teaching materials for learning material in class, So it is necessary to develop teaching materials that can help students understand the concepts of the material. This research aims to develop a statistics teaching module based on a realistic mathematical approach to foster student problem-solving. This research and development uses a 4-D model in four stages, namely: definition, design, development, and dissemination. Product trials are carried out in three stages, namely: a validity test, a limited test, and a wide-scale test. The test subjects in this research were students from the mathematics education study program at three universities in Bengkulu. The research instruments were questionnaire sheets and problem-solving tests on basic statistical material. The research results show that the RME statistics teaching module meets the criteria of being valid, practical, and effective in terms of students' problem-solving abilities. The suggestion from the research results is that it is important to present a context that is relevant to the student's environment in the use of RME teaching materials.

Magnetic Nanoparticles in Cancer Thermotherapy: A Mathematical Approach to Optimal Treatment Design

Thermotherapy, often called Hyperthermia treatment is a cancer treatment modality that involves raising the temperature of the tumor mass to over 315 K (42°C) for a specific duration, which leads to cell death through apoptosis or necrosis. Magnetic Particle Hyperthermia (MPH) is a non-invasive technique where magnetic nanoparticles are introduced into the tumor and then exposed to a magnetic field which convert magnetic energy into heat. Due to their high acidity, tumor cells are more sensitive to heat than healthy cells, meaning that heating the tumor to 315-319 K (42°C–46°C) can destroy it with minimal damage to the surrounding healthy tissues. During hyperthermia treatment, blood perfusion helps protect the healthy tissues around the tumor by dissipating excess heat. This paper presents a study where the temperature profiles within a spherical hepatic tumor mass are estimated by solving Pennes’ Bio-heat Equation, incorporating a power term. The study uses analytical methods to examine the effects of magnetic fluid hyperthermia treatment. Numerical illustrations are carried out using magnetite (Fe3O4) nanoparticles having an average diameter of 10.9 nm with mineral oil as a carrier liquid, subjected to magnetic fields of varying intensities. By analysing the model, the present work helps in designing an optimal treatment protocol by identify the time threshold of the therapy for varying magnetic field strengths.

Exploring optical solitary wave solutions in the (2+1)-dimensional equation with in-depth of dynamical assessment

The current study explores the (2+1)-dimensional Chaffee-Infante equation, which holds significant importance in theoretical physics renowned reaction-diffusion equation with widespread applications across multiple disciplines, for example, ion-acoustic waves in optical fibres, fluid dynamics, electromagnetic wave fields, high-energy physics, coastal engineering, fluid mechanics, plasma physics, and various other fields. Furthermore, the Chaffee-Infante equation serves as a model that elucidates the physical processes of mass transport and particle diffusion. We employ an innovative new extended direct algebraic method to enhance the accuracy of the derived exact travelling wave solutions. The obtained soliton solutions span a wide range of travelling waves like bright-bell shape, combined bright-dark, multiple bright-dark, bright, flat-kink, periodic, and singular. These solutions offer valuable insights into wave behaviour in nonlinear media and find applications in diverse fields such as optical fibres, fluid dynamics, electromagnetic wave fields, high-energy physics, coastal engineering, fluid mechanics, and plasma physics. Soliton solutions are visually present by manipulating parameters using Wolfram Mathematica software, graphical representations allow us to study solitary waves as parameters change. Observing the dynamics of the model, this study presents sensitivity in a nonlinear dynamical system. The applied mathematical approaches demonstrate its ability to identify reliable and efficient travelling wave solitary solutions for various nonlinear evolution equations.

Measuring absorbed energy in the human auditory system using finite element models: A comparison with experimental results.

There are different ways to analyze energy absorbance (EA) in the human auditory system. In previous research, we developed a complete finite element model (FEM) of the human auditory system. In this current work, the external auditory canal (EAC), middle ear, and inner ear (spiral cochlea, vestibule, and semi-circular canals) were modelled based on human temporal bone histological sections. Multiple acoustic, structure, and fluid-coupled analyses were conducted using the FEM to perform harmonic analyses in the 0.1-10 kHz range. Once the FEM had been validated with published experimental data, its numerical results were used to calculate the EA or energy reflected (ER) by the tympanic membrane. This EA was also measured in clinical audiology tests which were used as a diagnostic parameter. A mathematical approach was developed to calculate the EA and ER, with numerical and experimental results showing adequate correlation up to 1 kHz. Another published FEM had adapted its boundary conditions to replicate experimental results. Here, we recalculated those numerical results by applying the natural boundary conditions of human hearing and found that the results almost totally agreed with our FEM. This boundary problem is frequent and problematic in experimental hearing test protocols: the more invasive they are, the more the results are affected. One of the main objectives of using FEMs is to explore how the experimental test conditions influence the results. Further work will still be required to uncover the relationship between middle ear structures and EA to clarify how to best use FEMs. Moreover, the FEM boundary conditions must be more representative in future work to ensure their adequate interpretation.

Predictive Wireless Received Signal Strength Using Friis Transmission Technique

A good WLAN performance is crucial in determining the quality of experience (QoE) among the campus community. Proper WLAN planning and design should be done beforehand to ensure good WLAN performance. Various studies have discussed different methods of conducting WLAN planning to predict WLAN's best performance, including using artificial intelligence and mathematical approaches. One of the processes involved in performing WLAN planning is measuring performance parameters. Signal strength is one of the vital parameters to be measured in determining the excellent performance of WLAN in a particular area. When deploying a WLAN design in two different environments, the signal strength outcomes can differ due to various factors, including obstacles and path loss propagation issues within the deployment area. Higher Learning Institutions (HLIs) present a unique challenge as their building designs vary to accommodate student needs. As a result, the selection of materials used will also be different, affecting the WLAN performance. A detailed study should investigate the effect of path loss propagation and the type of obstacle that affects WLAN performance in HLI. Thus, this study focuses on predicting received signal strength using Friis Transmission and studying the effect of path loss propagation on WLAN performance. The simulated model significantly affects signal strength when the signal passes through different types of building material (non-LOS) and line-of-sight (NLOS), where concrete walls substantially affect the received signal strength between transmitters. The proposed model can assist network planners in designing robust WLAN infrastructure by improving signal strength, particularly in the HLI WLAN environment.Â

Optimizing heat transfer with nano additives: A mathematical approach

This study is carried out to investigate heat transfer of hybrid nanofluid between two concentric cylinders using the fractional Maxwell model. The fractional model is solved numerically; fractional derivatives are integrated using the L1 algorithm of Caputo derivative and the integer order derivatives are discretized using the Crank–Nicolson numerical method. The findings show that skin friction decreases when the relaxation time parameter increases. The thermal performance of the working fluid increased up to 5% when hybrid nanoparticles were suspended to it.

Simulation of Chemical Reactions on a Quantum Computer.

Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum computing algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Møller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Møller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the colinear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.

Squaring Circuit Using 14nmFinFET Technology with Vedic Mathematics Approach

FinFET technology is an alternative to CMOS technology as in this technology device has higher drive current, speed, and low-power consumption. FinFET has better mobility and scaling than CMOS technology. A dedicated Squaring circuit is needed by many digital signal processors (DSP) and arithmetic and logical units (ALU). So fast, power-efficient, and compact squaring circuits can be designed with Vedic sutras. Vedic mathematics has 16 sutras and 13 sub-sutras that touch almost all different chapters of mathematics. Out of these sutras, Dwandwayoga has a duplex property that is used to find a square of an N-bit number. Also, Yavadunam is a special case for finding the square of a number that is closer to the base. This work targets a comparative analysis of these two square circuits having a Vedic approach with a conventional array multiplier. The proposed designs are implemented in micro-wind 3.9 electronic design automation tool (EDA) with 14 nm deep submicron technology post-layout. The values of model parameters are used from the current Berkeley 4 short channel model (BSIM4). It is observed that the proposed square architecture design using the Dwandwayog sutra and Yavadunam sutra achieves 185%, 272.45% delay depletion and a 122.22%, and 46.52% reduction in transistor requirements compared to the conventional array multiplier, respectively.

Emergence failure of early epidemics: A mathematical modeling approach.

Epidemic or pathogen emergence is the phenomenon by which a poorly transmissible pathogen finds its evolutionary pathway to become a mutant that can cause an epidemic. Many mathematical models of pathogen emergence rely on branching processes. Here, we discuss pathogen emergence using Markov chains, for a more tractable analysis, generalizing previous work by Kendall and Bartlett about disease invasion. We discuss the probability of emergence failure for early epidemics, when the number of infected individuals is small and the number of the susceptible individuals is virtually unlimited. Our formalism addresses both directly transmitted and vector-borne diseases, in the cases where the original pathogen is 1) one step-mutation away from the epidemic strain, and 2) undergoing a long chain of neutral mutations that do not change the epidemiology. We obtain analytic results for the probabilities of emergence failure and two features transcending the transmission mechanism. First, the reproduction number of the original pathogen is determinant for the probability of pathogen emergence, more important than the mutation rate or the transmissibility of the emerged pathogen. Second, the probability of mutation within infected individuals must be sufficiently high for the pathogen undergoing neutral mutations to start an epidemic, the mutation threshold depending again on the basic reproduction number of the original pathogen. Finally, we discuss the parameterization of models of pathogen emergence, using SARS-CoV1 as an example of zoonotic emergence and HIV as an example for the emergence of drug resistance. We also discuss assumptions of our models and implications for epidemiology.

Simulation of Orbital Fractures Using Experimental and Mathematical Approaches: A Pilot Study.

This contribution gives basic information about the mechanical behavior of the facial part of the human skull cranium, i.e., the splanchnocranium, associated with external loads and injuries caused mainly by brachial violence. The main areas suffering from such violence include the orbit, frontal, and zygomatic bones. In this paper, as a first approach, brachial violence was simulated via quasi-static compression laboratory tests, in which cadaveric skulls were subjected to a load in a testing machine, increasing till fractures occurred. The test skulls were also used for research into the dynamic behavior, in which experimental and numerical analyses were performed. A relatively high variability in forces inducing the fractures has been observed (143-1403 N). The results lay the basis for applications mainly in forensic science, surgery, and ophthalmology.

Failing to Hash Into Supersingular Isogeny Graphs

Abstract An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of ‘hard supersingular curves’ that is equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular $\ell $-isogeny graph, which does not reveal the endomorphism ring, or a path to a curve of known endomorphism ring. Such a hash function would open up interesting cryptographic applications. In this paper, we document a number of (thus far) failed attempts to solve this problem, in the hope that we may spur further research, and shed light on the challenges and obstacles to this endeavour. The mathematical approaches contained in this article include: (i) iterative root-finding for the supersingular polynomial; (ii) gcd’s of specialized modular polynomials; (iii) using division polynomials to create small systems of equations; (iv) taking random walks in the isogeny graph of abelian surfaces, and applying Kummer surfaces and (v) using quantum random walks.