Mathematical Operations Research Articles

Cell-nanoparticle stickiness and dose delivery in a multi-model in silico platform: DosiGUI

BackgroundIt is well-known that nanoparticles sediment, diffuse and aggregate when dispersed in a fluid. Once they approach a cell monolayer, depending on the affinity or “stickiness” between cells and nanoparticles, they may adsorb instantaneously, settle slowly – in a time- and concentration-dependent manner - or even encounter steric hindrance and rebound. Therefore, the dose perceived by cells in culture may not necessarily be that initially administered. Methods for quantifying delivered dose are difficult to implement, as they require precise characterization of nanoparticles and exposure scenarios, as well as complex mathematical operations to handle the equations governing the system dynamics. Here we present a pipeline and a graphical user interface, DosiGUI, for application to the accurate nano-dosimetry of engineered nanoparticles on cell monolayers, which also includes methods for determining the parameters characterising nanoparticle-cell stickiness.ResultsWe evaluated the stickiness for 3 industrial nanoparticles (TiO2 – NM-105, CeO2 – NM-212 and BaSO4 – NM-220) administered to 3 cell lines (HepG2, A549 and Caco-2) and subsequently estimated corresponding delivered doses. Our results confirm that stickiness is a function of both nanoparticle and cell type, with the stickiest combination being BaSO4 and Caco-2 cells. The results also underline that accurate estimations of the delivered dose cannot prescind from a rigorous evaluation of the affinity between the cell type and nanoparticle under investigation.ConclusionAccurate nanoparticle dose estimation in vitro is crucial for in vivo extrapolation, allowing for their safe use in medical and other applications. This study provides a computational platform – DosiGUI – for more reliable dose-response characterization. It also highlights the importance of cell-nanoparticle stickiness for better risk assessment of engineered nanomaterials.

Creative and accurate method for optimal hardware implementation of neurons and biological cells: Application in FPGA-based implementation of cardiac pacemaker cell

The sinoatrial (SA) node cells play a vital role as the principal pacemaker in mammalian hearts, generating regular and spontaneous action potentials to regulate the heart’s rhythm. Comprehending the intricate activity of the SA node’s operation necessitates a collection of differential formulas that tackle non-linear functions. The study presents a new technique to improve the digital representation of the SA node cell model, offering benefits such as decreased hardware needs, enhanced processing speed and accuracy, and reduced implementation expenses by transforming the original model’s differential equations into a unified trigonometric function. This transformation significantly simplifies the computational complexity by eliminating the need for multipliers, resulting in a streamlined set of mathematical expressions. The digital implementation of this novel method can be efficiently realized using the Coordinate Rotation Digital Computer (CORDIC) algorithm, which circumvents the necessity for cumbersome mathematical operations. To demonstrate the viability of this approach, the proposed model is successfully synthesized and implemented on a Field-Programmable Gate Array (FPGA). The results of the implementation demonstrate a significant rise in the operating frequency, which is approximately 6.14 times greater than that of the original model. Furthermore, there is a notable 45 percent decrease in power usage. The lowered hardware needs make significant scalability possible, thus allowing for the inclusion of approximately 12 times as many SA node cells on a sole FPGA board in comparison to the original design.

Universal dynamical function behind all genetic codes: [formula omitted]-adic attractor dynamical model

The genetic code is a map which gives the correspondence between codons in DNA and amino acids. In the attractor dynamical model (ADM), genetic codes can be described as the sets of the cyclic attractors of discrete dynamical systems - the iterations of functions acting in the ring of 2-adic integers Z2. This ring arises from representation of nucleotides by binary vectors and hence codons by triples of binary vectors. We construct a Universal Function B such that the dynamical functions for all known genetic codes can be obtained from B by simple transformations on the set of codon cycles - the “Addition” and “Division” operations. ADM can be employed for study of phylogenetic dynamics of genetic codes. One can speculate that the “common ancestor genetic code” was caused by B. We remark that this function has 24 cyclic attractors which distribution coincides with the distribution for the hypothetical pre-LUCA code. This coupling of the Universal Function with the pre-LUCA code assigns the genetic codes evolution perspective to ADM. All genetic codes are generated from B through the special chains of the “Addition” and “Division” operations. The challenging problem is to assign the biological meaning to these mathematical operations.

Unlocking the complexity of phrasal composition: An interplay between semantic features and linguistic relations

Understanding the computational operations involved in conceptual composition is fundamental for theories of language. However, the existing literature on this topic remains fragmented, comprising disconnected theories from various fields. For instance, while formal semantic theories in Linguistics rely on type-driven interpretation without explicitly representing the conceptual content of lexical items, neurolinguistic research suggests that the brain is sensitive to conceptual factors during word composition. What is the relationship between these two types of theories? Do they describe two distinct aspects of composition, operating independently, or do they connect in some way during interpretation by our brain? To probe this, we explored how the mathematical operations explaining the combination of two words into a phrase are affected by the semantic content of items and the formal linguistic relations between the combining items. For six phrase types that varied properties relevant to type-driven interpretation such as modification vs. argument-saturation and modifier context sensitivity, we collected human ratings of experiential semantic features both for the phrases and for all the individual words within the phrases. We then compared the ability of different computational combination rules to explain the phrase ratings based on the individual word ratings. Our results indicate that composition operations are not one-size-fits-all but rather depend on both feature type and linguistic relation. For example, in intersective Adjective-Noun phrases, addition is used to merge attention-related features, while color features are predominantly determined by the first word's ratings. In the case of social features, the verb chiefly guides interpretation in Verb-Noun phrases, whereas in Noun-Noun phrases, the model employs multiplication to combine the social features of the nouns.

VISION - an open-source software for automated multi-dimensional image analysis of cellular biophysics.

Environment-sensitive probes are frequently used in spectral and multi-channel microscopy to study alterations in cell homeostasis. However, the few open-source packages available for processing of spectral images are limited in scope. Here, we present VISION, a stand-alone software based on Python for spectral analysis with improved applicability. In addition to classical intensity-based analysis, our software can batch-process multidimensional images with an advanced single-cell segmentation capability and apply user-defined mathematical operations on spectra to calculate biophysical and metabolic parameters of single cells. VISION allows for 3D and temporal mapping of properties such as membrane fluidity and mitochondrial potential. We demonstrate the broad applicability of VISION by applying it to study the effect of various drugs on cellular biophysical properties. the correlation between membrane fluidity and mitochondrial potential, protein distribution in cell-cell contacts and properties of nanodomains in cell-derived vesicles. Together with the code, we provide a graphical user interface for easy adoption.

A New Hybrid Improved Arithmetic Optimization Algorithm for Solving Global and Engineering Optimization Problems

The Arithmetic Optimization Algorithm (AOA) is a novel metaheuristic inspired by mathematical arithmetic operators. Due to its simple structure and flexible parameter adjustment, the AOA has been applied to solve various engineering problems. However, the AOA still faces challenges such as poor exploitation ability and a tendency to fall into local optima, especially in complex, high-dimensional problems. In this paper, we propose a Hybrid Improved Arithmetic Optimization Algorithm (HIAOA) to address the issues of susceptibility to local optima in AOAs. First, grey wolf optimization is incorporated into the AOAs, where the group hunting behavior of GWO allows multiple individuals to perform local searches at the same time, enabling the solution to be more finely tuned and avoiding over-concentration in a particular region, which can improve the exploitation capability of the AOA. Second, at the end of each AOA run, the follower mechanism and the Cauchy mutation operation of the Sparrow Search Algorithm are selected with the same probability and perturbed to enhance the ability of the AOA to escape from the local optimum. The overall performance of the improved algorithm is assessed by selecting 23 benchmark functions and using the Wilcoxon rank-sum test. The results of the HIAOA are compared with other intelligent optimization algorithms. Furthermore, the HIAOA can also solve three engineering design problems successfully, demonstrating its competitiveness. According to the experimental results, the HIAOA has better test results than the comparator.

Task Characteristics Associated with Mathematical Word Problem-Solving Performance Among Elementary School-Aged Children: A Systematic Review and Meta-Analysis

Mathematical word problem-solving skills are crucial for students across their lives, yet solving such tasks poses challenges for many. Therefore, understanding the characteristics of mathematical word problems that are associated with students’ performance is important. The objective of this systematic review and meta-analysis was to evaluate the effects of linguistic and numerical task characteristics associated with mathematical word problem-solving performance among elementary school-aged children (Grades 1 to 6). The systematic review was based on five electronic databases and citation searching. Reporting was conducted following The Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA). The findings (K = 69) showed that five of the six investigated linguistic task characteristics (i.e., the position of the unknown, schematic structure, irrelevant information, realistic considerations, and lexical consistency) and one of the two numerical task characteristics (i.e., number of operations) were related (g = 0.39 to 4.26) with elementary school-aged children’s mathematical word problem-solving. However, the findings did not provide support for a general association between a familiar situational narrative or the required operation with mathematical word problem-solving. The findings highlight that elementary school-aged children especially struggle with mathematical word problems requiring realistic considerations or multiple mathematical operations, containing lexical inconsistency, and problems in which the position of the unknown is the first value. This further understanding of elementary schoolers’ word problem-solving performance may guide the design of appropriate and progressive instruction and assessment tools and steer research into the interactions within task characteristics and with individual characteristics.

Brief summaries on symmetries in the history of physics–mathematics: James Clerk Maxwell (1865–1873), Emmy Noether (1915–1918) and Albert Einstein (1905–1926)

Abstract The physical phenomenon of symmetries and their physical–mathematical conceptualisation traverse the history of science, particularly in geometry, physics and mathematics. In order to understand and describe the laws of nature (in certain situations, e.g. status, relationships, applicability, fields etc.), scientists, historians and philosophers persistently worked on these subjects, particularly on the significance of gauge symmetry and its correlated mathematical operations (theorems, transformations, conserved quantities, violation, breaking, etc.). One of the main purposes is to understand when and how a violation - a breaking of symmetry - is performed. For the sake of brevity and taking into account the physics–mathematics relationship between Physics and Mathematics in the history of physics/mathematics, this paper concisely discusses the intellectual role played by the Physics and Mathematics relationships in the work by James Clerk Maxwell, Emmy Noether and Albert Einstein.

Framework for LLM applications in manufacturing

In the era of Industry 4.0, the proliferation of data within manufacturing environments has presented both unprecedented opportunities and challenges. This paper introduces a framework that capitalizes on the capabilities of Large Language Models (LLMs) to revolutionize data integration and decision-making processes in manufacturing systems. Addressing the critical need for efficient data management, our framework streamlines the consolidation, processing, and generation of responses to essential inquiries, thus enhancing manufacturers’ capabilities to extract valuable insights. The focus of this paper is twofold. First to establish a framework for the use of LLM applications in manufacturing settings. Secondly, to provide an overview of the manufacturing connection between data, AI, and chat-bots, while also addressing a few pain points identified from the manufacturing literature. The paper then introduces FILLIS (Factory Integrated Logic and Language Interface System), a Large Language Model assistant, through a compelling case study. FILLIS showcases remarkable versatility, excelling in tasks ranging from elucidating machine operations to language translation. The study underscores FILLIS’s proficiency in handling specific contexts, answering questions from uploaded documents with precision. However, inherent limitations surface in tasks involving mathematical operations, emphasizing the need for external agents in specific scenarios. This pivotal opportunity is explored in the proposed framework as it advocates for integrating external agents alongside LLMs, creating a more versatile and comprehensive assistant tool. The findings of this paper and proposed framework position LLMs as transformative tools for intelligent data processing.

Development of the Combined Operations Method to Improve the Efficiency of Block Encryption

Real-time information protection requires the implementation of special methods aimed at providing reliable and fast encryption algorithms to protect personal and corporate information from unauthorized access. With the growth of data volumes and the speed of their processing, the importance of effective encryption methods increases significantly. One of the common, reliable and well-known encryption algorithms is AES (Advanced Encryption Standard), also known as Rijndael, which is a symmetric block cipher. AES has high efficiency and cryptoresistance and is suitable for processing large volumes of data. The reliability and speed of encryption and decryption using the AES algorithm depends on the size of the key and the data. This paper proposes to improve algorithm of symmetric block encryption AES to provide faster data processing. The possibility of combining mathematical operations that have a similar principle of processing elements is shown. This approach made it possible to reduce the processing time for data encryption and decryption compared to known implementations. A comparative analysis of the practical implementation of the standard and optimized AES cryptoalgorithms has been carried out. The general principles of the proposed method are to transform all two-dimensional arrays into one-dimensional arrays, add auxiliary tables for ShiftRows and MixColumns operations, and combine operations with similar element processing principles. The simulation results showed that the modified implementation of the AES algorithm demonstrates a reduction in processing time of up to 50% when encrypting and up to 75% when decrypting data compared to known results

An exploration of physics envy with implications for desiderata of psychology theories.

There is a trepidation, anxiety, or intuition, which has persisted for more than a century, that psychology theories are less anchored in fundamental laws than physics theories. Rather than attempt to refute the concern, the present work accepts it and tries out candidate explanations. These pertain to empirical laws, parsimony, scope, reductionism, falsifiability, mathematical operations (multiplication vs. addition), internal coherence, ceteris paribus stipulations, and purposeful omission of relevant factors (idealization). The conceptions underlying these explanations are not strictly independent, but they point to different distinctive features that might account for the unequal status of physics and psychological science and to different means of improving contemporary psychology. Although the available evidence for or against these candidate explanations is scarce and relies mainly on a few telling examples, we conclude that the last of our candidate explanations-reliance on idealized universes-works best and leads to the most insights about what psychology might learn from physics and what research strategies might foster the ideal of theory-driven psychological science in the future. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Advancing Pharmaceutical Science with Artificial Neural Networks: A Review on Optimizing Drug Delivery Systems Formulation.

Drug Delivery Systems (DDS) have been developed to address the challenges associated with traditional drug delivery methods. These DDS aim to improve drug administration, enhance patient compliance, reduce side effects, and optimize target therapy. To achieve these goals, it is crucial to design DDS with optimal performance characteristics. The final properties of a DDS are determined by several factors that go into formulating a pharmaceutical preparation. Thus, optimizing these factors can lead to the ideal DDS formulation. Artificial Neural Networks (ANN) are computational models that mimic the function of biological neurons and neural networks and perform mathematical operations on inputs to generate outputs. ANN is widely used in medical sciences for modeling disease diagnosis and treatment, dose adjustment in combination therapy, medical education, and other fields. In the pharmaceutical sciences, ANN has gained significant attention for designing and optimizing pharmaceutical formulations. This article reviews the use of ANN in the design and optimization of pharmaceutical formulations, specifically DDS. Since DDS is highly diverse, different factors are examined for each type of DDS. These factors are considered independent and dependent parameters for each ANN model, and various examples are provided. By utilizing ANN, it is possible to establish the relationship between the formulation factors and the resulting DDS characteristics, ultimately leading to the development of optimized DDS.

Analysis of Students' Difficulties in Solving Physics Problems Using Polya's Theory

The ability of students in solving physics problems used Polya's theory is still at a low level, in general students have difficulty in solving physics problems at the stages of planning and implementing problem solving. This study aims to determine the level of difficulty of students in solving physics problems used Polya's theory and find out what are the difficulties of students in solving physics problems used Polya's theory. The research approach used is mixed method, with the explanatory sequential design. Data collection techniques used tests and interviews. The results of data analysis show that the very high level of difficulty of students in solving equilibrium problems of rigid bodies is at the stage of seeing / checking back, but the difficulties experienced by students at this stage are very dependent on the other three stages of Polya, namely understanding the problem, planning problem solving and implementing problem solving. Students' difficulties in solving physics problems used Polya's theory, among others, students had difficulty in translating or changing the problem in physics symbols, students had difficulty in making plans because they did not know the formula that should be used, students had difficulty in completing mathematical operations and students did not re-examine the solution steps and answers that had been obtained so that some answers were still not correct.

Security, QoS and energy aware optimization of cloud-edge data centers using game theory and homomorphic encryption: Modeling and formal verification

Privacy and efficient data processing are crucial research areas in the field of outsourcing computing. Thus, the contribution of the paper is twofold. First of all, we develop a secure offloading technique that can process data while preserving privacy. Although RSA and Paillier cryptosystems are highly beneficial for mathematical operations on basic encrypted data due to their homomorphic properties, images are processed using permutation-ordered binary (POB) and Shamir's secret sharing (SSS). Second, a non-cooperative game theory model was formulated to examine the interactions between service providers, characterizing each edge as an M/M/1 system with an infinite queue. Through formal verification using rigorous mathematical reasoning, the suggested strategies for task offloading and resource allocation are shown to be effective in terms of security, quality of service (QoS), and energy consumption. The best-response dynamics approach is used to calculate the final strategy for each participant and assess how fairly resources are allocated. Finally, the potential of our approach is demonstrated numerically, revealing a faster convergence towards attaining Nash equilibrium in a duopoly cloud-edge data center market, granted that the necessary and sufficient conditions are met.

Comprehensive evaluation of rural regional integrated clean energy systems considering multi-subject interest coordination with pythagorean fuzzy information

In the development of a comprehensive clean energy system in rural areas, how to evaluate it scientifically and effectively is an urgent problem to be solved. Artificial intelligence has already been widely applied in the field of energy technology, but its application in the comprehensive benefit evaluation is still insufficient. The purpose of this study is to conduct a comprehensive evaluation of the rural, regional integrated clean energy system with coordinated multi-subject interests. Firstly, the interest relationship between the subjects of the participating rural regional comprehensive clean energy system is analyzed. And, the comprehensive benefit evaluation index system is established based on farmers, rural grid, new energy investment operators, government and interest subject reciprocity partners. Secondly, Sugeno-Weber aggregation operators are more flexible and used to acquire smooth aggregated outcomes from a group of information in a single set. Moreover, an algorithm of the multi-attribute decision-making process also reveals the supremacy and reliability of the research work. A case study is established to evaluate the rural integrated clean energy system with coordinated multi-subject interests. The results are as follows. The index system reflects the characteristics of the comprehensive clean energy system in rural areas, such as environmental characteristics, economic characteristics, safety characteristics and clean energy characteristics. The advantages and validity of developed research work are proved by comparing the findings of pioneered approaches with existing mathematical operators. The ranking of suitable energy sources is Solar power > Biomass energy > Geothermal energy > Wind and hydropower based integrated clean energy system.

An Improved MOEA/D with an Auction-Based Matching Mechanism

Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm.

A discrete element solution method embedded within a Neural Network

This paper introduces a novel methodology, the Neural Network framework for the Discrete Element Method (NN4DEM), as part of a broader initiative to harness specialised AI hardware and software environments, marking a transition from traditional computational physics programming approaches. NN4DEM enables GPU-parallelised computations by mapping particle data (coordinates and velocities) onto uniform grids as solution fields and computing contact forces by applying mathematical operations that can be found in convolutional neural networks (CNN). Essentially, this framework transforms a DEM problem into a series of layered “images” composed of pixels, using stencil operations to compute the DEM physics, which is inherently local. The method revolves around custom kernels, with operations prescribed by the laws of physics for contact detection and interaction. Therefore, unlike conventional AI methods, it eliminates the need for training data to determine network weights. NN4DEM utilises libraries such as PyTorch for relatively easier programmability and platform interoperability. This paper presents the theoretical foundations, implementation and validation of NN4DEM through hopper test benchmarks. An analysis of the results from random packing cases highlights the ability of NN4DEM to scale to 3D models with millions of particles. The paper concludes with potential research directions, including further integration with other physics-based models and applications across various multidisciplinary fields.

ViCE: An automated and quantitative program to assess intestinal tissue morphology

Background and objectiveThe tissue morphology of the intestinal surface is architecturally complex with finger-like projections called villi, and glandular structures called crypts. The ratio of villus height-to-crypt depth ratio (Vh:Cd) is used to quantitatively assess disease severity and response to therapy for intestinal enteropathies, such as celiac disease and is currently quantified manually. Given the time required, manual Vh:Cd measurements have largely been limited to clinical trials and are not used widely in clinical practice. We developed ViCE (Villus Crypt Evaluator), a user-friendly software that automatically quantifies histological parameters in standard hematoxylin and eosin-stained intestinal biopsies. MethodsViCE is based on mathematical morphology operations and is scale and staining agnostic. It evaluates tissue orientation, identifies geometrical structure, and outputs key tissue measurements. ResultsThe output measurements of Vh:Cd are concordant with manual quantifications across multiple datasets. ConclusionsThe underlying mathematical morphological approach for ViCE is robust, and reproducible and easily adaptable for measurement of morphological features in other tissues.

A NEW ALGORITHM FOR GENERATING POWER SERIES SOLUTIONS FOR A BROAD CLASS OF FRACTIONAL PDES: APPLICATIONS TO INTERESTING PROBLEMS

This research offers a precise analytical solution for initial value problems of both linear and nonlinear fractional order partial differential equations. A new approach called the limit residual function method is developed and utilized to generate a series solution for the equations. The key tools of this method are the concepts of power series, residual function, and the limit at zero. The new method is characterized by the speed of determining the series solution coefficients and the limited mathematical operations used. The study examines five significant applications of fractional partial differential equations using this new method. To validate the accuracy of the results, they are compared with exact solutions in the classical case for the discussed applications. We conclude that the proposed approach is straightforward, effective, and successful in solving linear and nonlinear fractional differential equations.

Mathematical Operations Research for Deep Learning-Based Beamforming in WCS

Mathematical Operations Research for Deep Learning-Based Beamforming in WCS