Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string.

The emphasis in the automotive industry towards sustainable mobility has led to a significant interest in hybrid-electric propulsion systems with high energy density batteries. Addressing the needs of this strategy, the battery market is exploring new technologies to improve the safety and lifespan of electric vehicles. To this end, there is a focus on the all-solid-state battery (ASSB) technology for its cycle capabilities. Filling the current void in the literature pertaining to accurate ageing models for ASSBs, in this work, we present an enhanced version of the numerical ageing model, originally developed for liquid electrolyte based batteries, to forecast the development of the solid electrolyte interface layer that is the major cause of battery capacity fading. The model has been tested on prototype batteries and reveals an accuracy of 99%. The capacity fade in ASSBs has been investigated under different conditions, and the enhanced ageing model has been validated using experimental data from these batteries. The findings suggest that there is potential for solid-state batteries to be commercialized, although significant work is needed to match the manufacturing level of lithium-ion batteries with liquid electrolytes.

The blood counts of α thalassemia carriers (α-thal) are similar to those of β thalassemia carriers, except for Hgb A2 that is not elevated. The objective of this study was to determine whether mathematical formulas are effective for detecting suspected α-thal. The data were obtained from the database of the prevention program for detecting couples at risk for having a child with hemoglobinopathy. RBC indices were analyzed using mathematical formulas and the sensitivity and negative predictive value (NPV) calculated. Among 1334 blood counts suspected α-thal analyzed, only the Shine&Lal and the Support Vector Machine formulas revealed high sensitivity and NPV. Sensitivity was 85.54 and 99.33% and NPV 98.93 and 99.93%, respectively. Molecular defects were found in 291, 81 had normal α genes. Molecular analysis was not performed in 962. Based on these results, mathematical formulas incorporating one of these reliable formulas for detecting suspected α or β thalassemia carriers in the program of the automatic analyzers can flag these results and increase the awareness of the primary physicians about the carrier risk and send an alert with a recommendation for further testing.

This manuscript presents a novel approach to estimating the potential within Schrödinger equations, with a particular focus on applications to the Navier-Stokes problem in fluid dynamics. By establishing new theoretical estimates, we delve into the intricate dynamics of fluid flow, aiming to unveil previously obscured aspects of the Navier-Stokes equations. Through a rigorous mathematical framework, we explore how these new potential estimates can provide a fresh perspective on fluid mechanics, contributing to the ongoing quest to solve some of its most persistent challenges.

This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thins films in the cases of the evaporation/condensation and diffusion taken separately. The thermal grooving processes are deeply controlled by the various mass transfer mechanisms of evaporation–condensation, surface diffusion, lattice diffusion, and grain boundary diffusion. This study proposed a new original analytical solution to the mathematical problem governing the grain groove profile in the case of simultaneous effects of evaporation-condensation and diffusion in polycrystalline thin films submitted to thermal and mechanical stress, and fatigue effects; by resolving the corresponding fourth-order partial differential equation ∂y∂t=C∂2y∂x2-B∂4y∂x4 obtained from the approximation y'2≪1. The comparison of the new solution to that of diffusion alone proved an important effect of the coupling of evaporation and diffusion on the geometric characteristics of the groove profile. A second analytical solution based on the series development was also proposed. It was proved that change of the boundary conditions of the grain grooving profile largely affected the different geometric characteristics of the groove profile.

The development of a Digital Track Model (DTM) within Kazakhstan's railway system presents an innovative approach to enhancing efficiency and safety across the network. This paper investigates the economic viability of DTM implementation, offering a comprehensive mathematical model that highlights potential reductions in maintenance costs and improvements in system accuracy and durability. The findings advocate for DTM's potential to significantly elevate railway operations, suggesting a pivotal step towards modernizing Kazakhstan's transit infrastructure.

The present study aims to show on the one hand how easily one can get confused when doing research on the internet. Different platforms, fora and homepages supply the visitor with different - and sometimes contradictory - information. On the other hand, we show how to overcome these contradictions and produce valuable research based on almost all sources. For our study, we use the example of the Feit-Thompson conjecture, which is - in opposite to the well-known Feit-Thompson theorem - not widely known. We try to clarify the scientific literature on this topic and we embed our own result into the present state of art. We prove that pq−1p−1 does not divide qp−1q−1 if p and q are twin primes, i.e. p=q+2. Thus we prove that the Feit-Thompson conjecture is true for twin prime numbers.

The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.

The well-being and sociability of individuals have always been part of modernity. The development of new technologies that meet these aspirations is receiving increasing attention. Thus, strengthening the desired objectives of these tools and minimizing their undesirable side effects is the subject of a growing commitment. The present contribution aims, in this context, to evaluate and analyze the desired and undesirable effects of the interaction of electromagnetic fields with living tissues in general. This involves routines reinforcing expected functions as well as those controlling and protecting against undesirable effects. First, the interactions of electromagnetic fields with tissues are analyzed, involving their thermal biological effects of desired and undesired exposures. The roles of blood and sap fluids in bio-affected tissues are then analyzed. Secondly, the governing electromagnetic, bio-heat equations, and their coupled solution are studied. Third, the thermal behavior of tissues and the exposure adverse effects are examined. Next, monitoring and defending of the effects of exposures are discussed. This contribution illustrates and discusses mathematical modeling routines based on a generalized interaction of electromagnetic fields with living tissues.

The main sources of intrinsic noise in excitable cells at the microcircuit and network levels are the stochastic characteristics of ion channel gating and activation of the synaptic conductance. Studies using in vivo, in vitro, and in silico methods to examine the effects of synaptic background activity were not adequately investigated in non-neuronal excitatory cells, where neurotransmitter-based innervation also occurs. We created a mathematical model to replicate the background synaptic noise dynamics in a non-neuronal cell. We utilized the stochastic Ornstein-Uhlenbeck process to represent excitatory synaptic conductance, which was incorporated into a whole-cell model to produce spontaneous and evoked cellular electrical activities. The single-cell model includes many biophysically detailed ion channels represented by a set of ordinary differential equations in Hodgkin-Huxley and Markov formalisms. This paradigm effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potential (sAP) resembling in vitro-like electrical activity in the cells. The input resistance decreased by multiple factors, and the spontaneous action potential firing rate elevated. The potential to reach the action potential threshold is altered. Background synaptic activity can alter the input/output characteristics of non-neuronal excitatory cells. Suppressing these baseline activities would facilitate the discovery of new pharmaceutical targets for different clinical diseases.

Lactic acid production from lactose by Lactiplantibacillus plantarum AC 11S was studied. The influence of initial substrate concentration was investigated, and optimal pH and temperature were determined. An unstructured mathematical model was developed comprising equations for bacterial growth, substrate consumption, and product formation. The model was solved with different terms for specific growth rates considering substrate and/or product inhibition. The best bacterial growth and lactic acid production were achieved at pH = 6.5 and 30 oC. Production of lactic acid was mainly growth-associated and at substrate concentration over 15 g/L a considerable product inhibition was observed. The parameters of different models were determined and compared. While the modified Gompertz equation gave the best fit for biomass growth, a variant of the logistic equation including a term for product inhibition described in the best way the entire set of equations comprising bacterial growth, substrate consumption, and product formation at different initial substrate concentrations.

: Controlling the distribution of water and wastewater between industrial processes is very vital in rationalizing water and preserving the environment. In this paper, a mathematical technique is proposed to optimize water-wastewater networks; a nonlinear program is introduced to minimize the consumption of freshwater, and consequently, the flowrate of the wastewater dis-charge will be also minimized. A general mathematical model, able to handle industrial plants containing up to eight sources and eight sinks, is developed using LINGO optimization software to facilitate dealing with complex case studies. The introduced model can handle single contam-inant networks as well as multiple contaminants cases. The optimal water network is synthe-sized through two steps; the first step is to introduce the case study data to the developed mathematical model. The second step considers using the optimal solution produced after run-ning the developed LINGO model as feed data for a pre-designed Excel sheet able to deal with these results and simultaneously draw the optimal water-wastewater network. The proposed mathematical model is applied to two case studies; The first case study includes actual data from four fertilizer plants located in Egypt; the water resources and requirements are simultaneously integrated to obtain a sensible cutting in both freshwater consumption (lowered by 52.2%) and wastewater discharge (zero wastewater discharge). The second case study is for a Brazilian pet-rochemical plant; the obtained results showed noticeable reductions in freshwater consumption for the second case study by 12.3 % while the reduction percentage of wastewater discharge is 4.5%.

The objective of this research is to propose a utility function that calculates the possible level of satisfaction that a music consumer would achieve after listening to a song according to the emotional response obtained from a song. Assuming that the consumer's musical preferences are satisfied if the predominant emotions of his current emotional state increase; the probabilistic emotional-musical model (Lugos Abarca, 2023) is used to construct such a utility function. By posing a hypothetical scenario, realistic results were obtained, which guarantee, in principle, its use in theoretical practice. The originality of this research lies in proposing a mathematical tool to study, quantitatively, the decision making of a musical consumer influenced by his emotions. The main conclusion being its importance in the music industry, since the function could predict, theoretically, whether a song will be accepted or rejected by the consumer in comparison with the competition.

This study presents a dynamic modeling approach to investigate the impact of saturation dynamics on HIV/AIDS transmission in the presence of vertical transmission and treatment strategies. The proposed model incorporates disease-free and endemic equilibria, with a focus on analyzing the basic reproduction number and conducting stability analysis. Results indicate that the disease-free equilibrium is locally asymptotically stable under certain conditions. The findings suggest that a combination of treatment interventions and awareness campaigns, along with other control measures, may play a crucial role in curbing the spread of the HIV/AIDS virus. This research contributes to understanding the complex dynamics of HIV/AIDS epidemics and highlights the importance of considering saturation effects in epidemic modeling.

Due to their high specificity, monoclonal antibodies (mAbs) have garnered significant attention in recent decades, with advancements in production processes, such as high seeding density (HSD) strategies, contributing to improved titers. This study provides a thorough investigation of high seeding processes for mAb production in Chinese hamster ovary (CHO) cells. Using a metabolic network and flux balance analysis, we compared standard fed-batch (STD FB) with HSD cultivations, exploring supplementary lactate and cysteine, and a bolus medium enriched in amino acids. We observed high glycolytic fluxes and depletion of asparagine simultaneously with the lactate shift building kinetic models around this and other observations. An ensemble of kinetic models assessed the impact of a feeding medium enriched with additional asparagine, revealing a missing lactate shift without enhancing mAb productivity in the experiments. This research provides valuable model-based insights into cellular metabolism during HSD processes, laying the foundation for refined CHO cell-based mAb production. The proposed hypothesis on the regulations guides future experimental validation and bioprocess optimization for enhanced mAb production efficiency.

The agronomic characteristics of Cenchrus purpureus were assessed through a randomized block experimental design with seven accessions (Taiwan grass, King grass, Elephant grass, Merkeron, CT-115, Purpule grass and Maralfalfa) as treatments and four replications research was carried out at the Instituto Tecnológico Superior de Tantoyuca, in 2019 and 2020, under rainfed conditions. Sowing density was established at 36 tillers in 25 m2. Green and dry matter yield, daily rates of dry matter accumulation in leaves, leaf/stem ratio, height, leaf area index and cutting frequency were assessed. Rainfall amount, temperature, relative humidity and global radiation levels were recorded to assess their effect on the evaluated variables. One-way ANOVA and multivariate analysis techniques, such as multiple linear regression (MLR), Clustering, and Principal component analysis (PCA) with the Statistica V7 software, were used. The leaf area index was greatest (p < 0.05) on the dry season. Green and dry matter yield were greatest in Maralfalfa (p < 0.05). Variation in the results is attributed to weather phenomena; nonetheless, Elephant grass and Maralfalfa showed the highest yields. Quality parameters must be evaluated to identify those grasses with the best attributes.

We present detailed models at the hydrodynamics and decoherence phenomena observed in ideal quantum gases. The model is expressed in terms of a quantum field theory, where the action involves both hydrodynamic and decoherence terms. The density-current relation is derived, and the current Green function is introduced. The effective action for two fields is presented, and the physical field is defined in terms of the bare action. Identities such as CTP symmetry, transposition, and the Ward identity are discussed. The Green function and its inverse for different components are also explored. These notes provide a comprehensive understanding of the theoretical framework for studying the hydrodynamics and decoherence of ideal quantum gases.

Oscillons, fundamental to various physical domains, are examined in-depth in this paper. From Josephson junctions in superconducting circuits to classical and quantum field theories, oscillators reveal profound insights into diverse phenomena. The study primarily focuses on oscillons, distinctive field configurations with enduring localization, establishing intriguing connections with well-known models like the Sine-Gordon breather. Surprising parallels in the weak coupling limit illuminate the rich dynamics of oscillators. A semi-classical quantization method, discretizing the field into spatially homogeneous regions, exposes stability angles, providing insights into the quantum nature of oscillons. The application of this quantization framework to specific cases, including the Sine-Gordon breather, showcases its versatility. The results offer a comprehensive perspective on the quantization of oscillons, unraveling the intricate interplay between classical and quantum dynamics. In conclusion, this paper provides a profound exploration of quantum oscillators, unveiling novel connections and presenting a rigorous quantization framework. The gained insights contribute significantly to the broader understanding of oscillatory systems and their pivotal role in diverse physical phenomena.

This paper proposes an electric vehicle routing problem with considering states of charging stations and suggests solution strategies. Charging of electric vehicles is a main issue in the field of electric vehicle routing problem. There are many studies to find locations of charging stations, recharging functions for batteries of vehicles, and so on. However, states of charging stations significantly affect the routes of electric vehicles, which is not much explored. The states may include open or close of charging stations, occupied or empty of charging slots, and so on. This paper investigates how the states of charging stations are estimated and routing strategies are determined. We formulate a mixed integer programming model and suggest how to solve the problem with exact method. Numerical examples provide the optimal routing strategies of electric vehicles in the changing environments of the states of charging stations.

Mathematical modelling is widely used for describing infection transmission and evaluating interventions. The lack of reliable social parameters in the literature has been mentioned by many modelling studies, leading to limitations in the validity and interpretation of the results. Using data from the European MSM Internet survey 2017, we developed a network model to describe sex acts among MSM in Belgium. The model simulates daily sex acts among steady, persistent casual and one-off partners in a population of 10,000 MSM, grouped as low- or high-activity by using three different definitions. Model calibration was used to estimate partnership duration and homophily rates to match the distribution of cumulative sex partners over 12 months. We estimated an average duration between 1065 and 1409 days for steady partnerships, 4-6 and 251-299 days for assortative high- and low-activity individuals and 8-13 days for disassortative persistent casual partnerships, respectively, varying across the three definitions. High quality data on social network and behavioral parameters are scarce in literature. Our study addresses this lack of information by providing a method to estimate crucial parameters for network specification.

This paper offers an integrated approach for correlated storage assignment strategy (CSAS) to optimize travel distance by considering item correlation, picking frequency, zoning, and slot constraints to improve operational efficiency in distribution centers. We simplify the mixed integer non-linear programming (MINLP) model and incorporate integrated heuristic procedures for faster convergence. We introduce positive and negative centroid deviations as techniques to guide the model convergence and explore different scenarios. In the second stage of item assignment, we prioritize items within zones using a ranking formula that is optimal for both single-item and multiple-item orders. By analyzing the distribution of correlated item across zones and the impact of their picking frequency on optimizing travel distance, we propose an improved CSAS that minimize travel distance by strategically placing items based on their proximity to the depot. Our model reduces trips in distant zones by prioritizing larger average order sizes, while maximizing trips for frequently ordered smaller lists in closer zones. This method significantly reduces travel distance by minimizing the need for pickers in distant zones to frequently travel to the depot. Simulation results show reductions of up to 36.75% for fitted data and 33.59% for recent data.

We extend the concept of metallic ratios to the real argument n considered as a dimension by analytic continuation showing that they are defined by an argument of a normalized complex number, and for rational n ≠ {0, ±2}, they are defined by Pythagorean triples. We further extend the concept of metallic ratios to metallic angles.

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprised of fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed wing aircraft systems. Here the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity techniquesto recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models will enable us to avoid common control design methods, such as gain scheduling, where stability issues can be extremely challenging.

In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained by the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion.

In the evolving landscape of vibration analysis, the integration of machine learning technologies for semi-automated analytical processes presents challenges in establishing clear cause-and-effect relationships in decision-making formulas. This research addresses this gap by exploring analytical diagnosis through residual signals, enabling the identification of anomalies and underperformance in machinery. Vibration signature analysis, focusing on distinctive vibration patterns, proves instrumental in detecting bearing defects and optimizing maintenance for enhanced operational efficiency and safety. Mathematical modeling, particularly worst-case analysis, provides a structured framework for decision-making under uncertainty. The research employs descriptive methods to analyze bearing wear data, transforming it into quantitative data for multiple regression equations. The derived equations reveal the dominance of harmonics in determining bearing wear stages, with PeakVue and overall vibration further indicating damage progression. The findings emphasize the significance of harmonic detection and high-frequency vibration analysis in predicting bearing health, offering a comprehensive approach to enhance machinery reliability. The study concludes with practical recommendations for bearing damage diagnosis based on the developed mathematical models, providing valuable insights for predictive maintenance strategies.

Abdominal aortic aneurysm (AAA) is a chronic disease in which the abdominal aorta expands until it ruptures. AAA incidence: 10 million/year (India), deaths: 40%-90% (13th leading cause of death in the USA). Current treatment methods make diagnosis difficult due to the lack of noticeable symptoms and inaccurately planned operations. Rupture Scope is a mathematical model to dramatically reduce AAA deaths and improve treatment efficiency. Using a case-specific replica/simulation of real-time abdominal aortic blood flow for monitoring without frequent imaging scans and a novel derived mathematical linear regression model to predict rupture date and expansion rate with an overall accuracy of 95.64%.

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

We assume that the current mathematical knowledge K is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any theorem of any mathematician from past or present belongs to K. The set K exists only theoretically. Ignoring K and its subsets, sets exist formally in ZFC theory although their properties can be time-dependent (when they depend on K) or informal. In every branch of mathematics, the set of all knowable truths is the set of all theorems. This set exists independently of K. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivial statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. This and the next sentence justify the article title. For any empirical science, we can identify the current knowledge with that science because truths from the empirical sciences are not necessary truths but working models of truth about particular real phenomena.

On February 24, 2022 Russia started the full-scale invasion of Ukraine, which created an unprecedented number of refugees. To estimate the influence of this humanitarian disaster on the COVID-19 pandemic dynamics, the averaged daily numbers of cases and reproduction numbers in Ukraine, the UK, Poland, Germany, the Republic of Moldova, and in the whole world were calculated for the period February-April 2022. The registered numbers of cases were compared with ones calculated with the use of the generalized SIR-model and corresponding parameter identification procedure for the previous epidemic waves in Ukraine, Poland, Germany, and the world. Since before February 24, 2022 the estimation of the number of infectious persons per capita in Ukraine 3.6 times exceeded the global figure, the increase of the number the new cases and the pandemic duration was expected. In March 2022 the increase of the averaged number of new cases in the UK, Germany, and worldwide was visible. A simple formula to estimate the effective reproduction number based on the smoothed accumulated numbers of cases is proposed. The results of calculations agree with the figures presented by John Hopkins University and demonstrate a short-term growth of the reproduction number in the UK, Poland, Germany, Moldova, and worldwide in March 2022.

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

As global warming intensifies, the development of offshore wind farms is swiftly progressing, especially deep-water floating offshore wind turbines (FOWTs) capable of energy capture in deep-sea regions, which have emerged as a focal point of both academic and industrial interest. Although numerous researchers have conducted comprehensive and multifaceted studies on various components of wind turbines, less attention has been paid to the operational stage response of FOWTs to wind, waves, and currents, and the reliability of structural components. This study primarily employs theoretical analysis to establish mathematical models under a series of reasonable assumptions, examining the possibility of collisions between FOWT transport fleets and other vessels in the passage area during the towing process. Using the model, this paper takes the Wanning Offshore Floating Wind Farm (FOWF) project, which is scheduled to be deployed in the South China Sea, as the research object and calculates the probability of collisions between FOWTs and other vessels in three time periods from the total assembly pier in Hainan Wanning to the predetermined position 22 km away. The findings of the analysis suggest that the mathematical model has the capability to efficiently determine the frequency of collisions between vessels within the domain and the transport team during the transportation process. This holds substantial relevance for future risk assessment and disaster prevention and mitigation measures in the context of FOWT transportation.

As most of the current dynamic positioning systems are based on model ships, they cannot accu-rately reflect the motion state, position changes, and mutual influence of each part of the dynamic positioning system of actual ships in complex environments. Other actual ships such as cargo ships cannot add various sensors and auxiliary equipment to verify and analyze the positioning system. This article takes the intelligent research and training dual-use ship of Dalian Maritime University, which integrates scientific research and training, as the object of study. This ship will not be affected by the voyage period and route and can choose a suitable sea area for research. Therefore, in order to improve the accuracy and reliability of the dynamic positioning system, research on the ship’s dynamic positioning system was carried out. Firstly, an accurate mathematical model of ship motion was established, and the hydrodynamic derivatives of ship model motion were obtained by nu-merical calculation, and applied to the three-degree-of-freedom model of the intelligent research and training dual-use ship. Then, the model was used as part of the closed-loop simulation model of the ship’s dynamic positioning system, and the terminal sliding mode controller was used for sim-ulation and emulation, thereby obtaining ideal simulation test results. This research helps to im-prove the accuracy and reliability of the dynamic positioning system and provides new ideas and methods for ship motion control.

To achieve a micro-destructive and rapid measurement of the wood density of standing trees, this study investigated the feasibility of using the micro-drilling resistance method, formulated a mathematical model, explored the potential for a unified model across multiple tree species, and analyzed the influence of moisture content on measurement accuracy. First, 231 tree cores and drill resistance data were sampled from Pinus massoniana, Cunninghamia lanceolate, and Cryptomeria fortunei. The basic density and moisture content of each core were measured, and the average value of each resistance data record was calculated. Second, the average drill resistance, the natural logarithm of average drill resistance, and absolute moisture content were used as independent variables, while the wood basic density was used as the dependent variable. Third, the total model of the three tree species and sub-model for each tree species were established through a stepwise regression method. Finally, the accuracy of each model was compared and analyzed with that of using the average basic density of each tree species as an estimated density. The results revealed that the estimation accuracy of the sub-model for each tree species was 1.670 percentage points higher than the average value of each tree species used as the density estimation value for these tree species. Additionally, except for Cryptomeria fortunei, the natural logarithm of drill resistance significantly influenced the wood density model at a significance level of 0.05. Moreover, moisture content significantly affected the total model and sub-models of Pinus massoniana at a significance level of 0.05. The estimation accuracy of the total mathematical model was 2.125 percentage points lower than that achieved using the average basic density of each tree species to predict their density. The results indicated the feasibility of using the micro-drilling resistance method to measure the wood density of standing trees. Moreover, the relationship between wood density and drill resistance did not follow a linear pattern, and moisture content slightly influenced the drill needle resistance. Furthermore, the establishment of a mathematical model for each tree species was deemed essential. This study provides valuable guidance for measuring the wood density of standing trees through the micro-drilling resistance method.

In this paper, we propose to explore a nonlinear fractional mathematical model of HFMD- Hand Foot Mouth Disease with vaccinated compartment. Firstly, we prove the non negativity and boundedness for the fractional order dynamical model. The system’s existence and uniqueness are studied using the formulation of the Caputo derivative operator. The fixed-point approach was used to get results indicating the presence of at least one solution. In numerical simulation, we obtained the approximate solution by using fractional Euler method.

Antiangiogenic therapy (AAT) is an indirect oncological modality which is aimed at disruption of cancer cells nutrient supply. Invasive tumors have been shown to possess inherent resistant to this treatment, while compactly growing benign tumors react to it by shrinkage. It is generally accepted that AAT by itself is not curative. This study presents a mathematical model of non-invasive tumor growth with physiologically justified account of alteration of microvasculature and biomechanical aspects during tumor growth and AAT. In untreated setting the model reproduces tumor growth with saturation, where the maximum tumor volume depends on the level of angiogenesis. The outcomes of simulations of AAT depend on the tumor size at the moment of treatment initiation. If it is close to the stable size of avascular tumor grown in absence of angiogenesis, then the tumor is rapidly stabilized by AAT. Treatment of large tumors is accompanied by displacement of normal tissue due to the tumor shrinkage. During it, microvasculature undergoes distortion which degree depends on the displacement distance. As it affects tumor nutrient supply, the stable size of a tumor that undergoes AAT negatively correlates with its size at the beginning of treatment. For sufficiently large initial tumors, the long-term survival of tumor cells is compromised by competition with normal cells for severely limited inflow of nutrients, which makes AAT effectively curative.

Higher traffic density in Russian cities and less uniform traffic due to congestions are reasons for increased emissions of pollutants contained in exhaust gases of vehicles. The paper presents the modeling results of pollutant dispersion in Magnitogorsk. The analysis of these results shows that now many blocks of flats and social infrastructure of the city are in a zone with an excess of maximum allowable concentration of pollutants. Having summarized the methodological framework formulated by Russian and foreign researchers, the authors systemized the existing methods used to decrease pollutants produced by vehicles. It is proposed to choose an optimal combination of such methods applying a developed mathematical model. By adopting an optimal combination of the methods, it is possible to ensure minimum air pollutant emissions from vehicles, allocating limited financial resources. The mathematical modeling of the solutions on changing traffic density and structure and implementing methods used to decrease pollutants on one of the Magnitogorsk crossroads with the heaviest traffic is used to draw a conclusion about efficiency of the designed model used as a tool for strategic planning of development and transformation of street networks.

The mathematical structure underlying a sentence is made of two independent processing units in series. The conditional probability density function of sentence length (measured in words) recordable in the extended short–term memory (E–STM) buffer made of CF cells is Gaussian. The number of sentences that authors of Italian and English Literatures have written is compared to that theoretically available to them. The multiplicity factor α describes this comparison. α>1 is more likely than α<1 and often α≫1, therefore the same sentence pattern is reused many times. These texts are easier to read. Very few novels show α<1. In these cases, there are enough diverse sentence patters to convey meaning, but most of them are not used. Texts are more difficult to read, as measured by a universal readability index GU. A mismatch index IM synthetically describes the process. α, GU. and IM increase with year of publication. Future work will concern other literatures – including ancient ones as Greek and Latin – to confirm what, in our opinion, is general feature of human mind.

The continuous casting tundish is non-isothermal due to heat losses and temperature variation from the inlet stream generating relevant convection forces. This condition is commonly avoided through qualitative fluid dynamic analysis only. This work searches to establish the conditions for which non-isothermal simulations are mandatory or for which isothermal simulations are enough to accurately describe the fluid dynamics inside the tundish by quantifying the buoyant and inertial forces. The mathematical model, simulated by CFD software, considers the Navier-Stokes equations, the realizable k- model for solving the turbulence, and the Lagrangian discrete face to track the inclusion trajectories. The results show that temperature does not significantly impact the volume fraction percentages or the mean residence time results, nevertheless, bigger velocity magnitudes under non-isothermal conditions than in isothermal conditions and noticeable changes in the fluid dynamics between isothermal and non-isothermal cases in all the zones where buoyancy force dominates over inertial forces were observed. Because of the results, it is concluded that isothermal simulations can accurately describe the flow behavior in tundishes when the flow control devices control the fluid dynamic, but the simulation without control devices or with a weak fluid dynamic dependence on the control devices requires non-isothermal simulations.

This paper shows the development of a numerical analysis model, which enables the calculation of the cargo transport capacity of a vehicle that circulates through a vacuum tube at high speed, whose effectiveness in transport is analyzed. The simulated transportation system is based on vehicles moving in vacuum tubes at high speed, a concept commonly known as Hyperloop, but assuming the vehicles for cargo containers. For the specific vehicle proposed, which does not include a compressor and levitates on magnets, the system formed by the vehicle and the vacuum tube has been conceptually developed, establishing the corresponding mathematical relationships that define its behavior. To properly model the performance of this transport system, it has been necessary to establish the relationships between the design variables and the associated constraints, such as the Kantrowitz limit, aerodynamics, transport, energy consumption, etc. Once the model was built and validated, it was used to analyze the effects of the variation of the number of containers, the operating speed and the tube length, considering the total and specific consumption of energy. Once the most efficient configuration was found regarding energy consumption and transport effectiveness, the complete system was calculated. The results obtained constitute a first approximation for the pre-design of this transport system and the built model allows different alternatives to be compared according to the design variables.

Hund's rule of maximum multiplicity is a powerful empirical tool for determining the electron population of electronic shells. It was recently discovered that it is also the rule of minimum Shannon entropy. This study extends these findings to the Aufbau rule and discusses them from the perspective of emergent dimensionality, providing a monotonically increasing entropy function. We observed that some elements that violate the Aufbau rule have the same entropies in the actual and Aufbau electron configurations. On the other hand, lower entropies of all actual elements' configurations are associated with higher or equal numbers of unpaired electrons in these configurations compared to the Aufbau configurations. The only exception to this rule is palladium.

Particle-mediated elasticity/viscoelasticity imaging has potential to expand the elasticity imaging field, as it can provide accurate and local tissue elastic properties as well as density, Poisson’s ratio, and viscosity. Here, we investigated elasticity imaging based on the use of small particles located within the tissue and at the tissue interface exposed to a static and dynamic external load. First, we discuss elasticity/viscoelasticity imaging methods based on the use of particles (bubbles and rigid spheres) located within the tissue. Elasticity/viscoelasticity imaging techniques based on the use of particles (bubbles, rigid and soft spheres) located at the tissue interface are then presented. Based on new advances, we updated some of the models for the responses of the particles located within the tissue and at the tissue interface available in the literature. Finally, we compared the mathematical models for the particles located within the tissue and at the tissue interface and evaluated the elasticity/viscoelasticity imaging methods based on the use of small particles. Therefore, instead of the use of the term elasticity imaging, we suggest the use of the term viscoelasticity imaging.

Descriptive geometry has indispensable applications in many engineering activities, some of which are presented in the first chapter of this paper in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the search for the right projection direction. A special method of enumerating the possible infinite viewpoints for the representation of the surface edge curves is presented in another part of the paper. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. The analysis and some of the results of the Monge mapping, which is suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, are also presented.

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

Calcium and magnesium are important not only for human health, but also for reducing problems related to the corrosive and aggressive effects of soft water on drinking water distribution materials. Experimental and mathematical modeling of the recarbonization process aimed at increasing the content of these biogenic elements in water was carried out using the novelty of a continuous laboratory and pilot scale fluidized bed reactors. Water remineralization using half-calcined dolomite (HCD) and carbon dioxide was used. The influence of operating conditions Q(CO2), freshwater inflow and HCD dose on quality indicators of treated drinking water (c(Ca2+), c(Mg2+), c(Ca2++Mg2+) and Ca/Mg) was studied. The results show that the concentration of Mg2+ is more significantly affected by the amount of HCD in the system and the flow of CO2. The influence of freshwater inflow on the Mg2+content is to a lesser extent. At a constant CO2 flow, therefore, as the tap water inflow increases, the Ca2+ content decreases and the Mg2+ content increases, which has results in a decrease in the Ca/Mg molar ratio. However, the Ca/Mg ratio can be effectively controlled by adding an appropriate amount of HCD at certain time intervals. Overproduction of ions is easily controlled by CO2 flow.

Mathematical models of non-small cell lung cancer are powerful tools that use clinical and experimental data to describe various aspects of tumorigenesis. The developed algorithms capture phenotypic changes in the tumor and predict changes in tumor behavior, drug resistance, and clinical outcomes of anti-cancer therapy. The aim of this study was to propose a mathematical model that predicts the changes in the cellular composition of patient-derived tumor organoids over time with a perspective of translation of these results to the parental tumor, and therefore to possible clinical course and outcomes for the patient. Using the data on specific biomarkers of cancer cells (PD-L1), tumor-associated macrophages (CD206), natural killer cells (CD8), and fibroblasts (αSMA) as input, we proposed a model that accurately predicts the cellular composition of patient-derived tumor organoids at a desired time point. Combining the obtained results with “omics” approaches will improve our understanding of the nature of NSCLC. Moreover, their implementation into clinical practice will facilitate a decision-making process on treatment strategy and develop a new personalized approach in anti-cancer therapy.

Covid-19 pandemic has greatly affected the whole world since the beginning and it continues to affect it. The main aim of this study is to show how Covid-19 affect other mortal diseases; cancer, heart diseases, and diabetes in near future. With this purpose two mathematical models are proposed via Ordinary Differential Equations (ODEs); one for the relationship between Covid-19 and cancer and one for the relationship between Covid-19, diabetes and heart diseases. Afterwards, stability analyses of these models are demonstrated. In order to see the effect of parameters on the disease compartments, sensitivity analysis is applied. Results of sensitivity analysis revealed that huge percentage of people are still scared of visiting doctors and this may lead a massive increase in the diagnosis of other diseases for upcoming years. Moreover, figures displayed that there exists a relationship between diabetes and heart diseases. Especially, diabetes patients should be careful about their health situations and take care of their heart. In order to provide these, awareness of people should be developed.

This paper presents an original method of additive manufacturing of cylindrical parts with variable circumference thickness, which allows the control of the deposition of molten material using an algorithm for decomposing the part geometry into volumetric elements with known dimensional configuration. In the absence of a post-processor capable of controlling additive manufacturing on a 5-axis numerical control machine, control of the deposition of molten material is done using parameterized programs, which can control both the feed speeds of the machine tool axes and the specific functions of the printing equipment. Additive manufacturing can make a positive contribution to sustainable development compared to traditional manufacturing technologies, thus making a positive contribution for a sustainable future. The aim of the work is to make it possible to 3D print parts with variable wall thickness using a CNC machining centre. To obtain the variable thickness layer we have implemented an original method of deposition with molten material (FDM), the coordination of the system composed of physical elements respectively programmable elements, is realized through control functions materialized in parameterized part programs, the generated outputs being the variable speed of the machine axes on a circular trajectory, the angular positioning, the filament advance.

Pacing strategy refers to the distribution of effort and speed throughout the race to achieve optimal performance. The study aims to understand whether the choice of pacing strategy in swimming depends on the length of competitions and how sex, age, and performance level influence this strategy. Participants were the finalists of the 800-meter and 1500-meter freestyle events at the elite and junior world championships in 2022-2023. Race outcomes and pacing parameters were compared between the two distances and across different groups of swimmers. Swimmers in both distances did not break world records. Pacing strategy generally followed a U-shape with significant differences in the frequency and duration of speed changes between the two distances. The 800-meter exhibited more frequent changes in acceleration while the 1500-meter events generally followed a more consistent time series pattern. There were differences in pacing strategies between males and females and between junior and elite swimmers. Swimmers closer to world records showed more consistent pacing patterns compared to those farther from records. The study suggests that pacing strategies are influenced by race distance, sex, age, and performance level. The research highlights the complex interplay between physiological and psychological factors that shape a swimmer's decision-making during a race.

Ensuring fire safety is an important condition for the successful operation of industrial enterprises. It is necessary to detect the threat of fire before ignition. An indicator of danger is the appearance of gas, which occurs as a result of unauthorized heating of equipment. Gas sensors make it possible to detect the appearance of gases characteristic of the decomposition of materials at the stage of smouldering and pyrolysis, which cause a change in the composition of the atmosphere. This paper presents a mathematical method for the rational placement of gas analyzers for premises of potentially hazardous industries. It is the rational placement of gas sensors, which ensures safety, taking into account economic feasibility that determines the effectiveness of their use. For the first time, the analysis of gas accumulation during the movement of the flow from the source to the ceil-ing, then propagation to the location of the sensors, is used for the first time to select the placement of gas sensors. Depending on the permissible values of the gas volume, the placement and number of gas sensors are selected. The calculation of the conditions for the rational placement of gas sen-sors for the most common indicators, such as carbon monoxide and hydrogen at different sizes and heights of rooms, is carried out. The method of calculating the location of gas analyzers makes it possible to diagnose and predict fire hazard at technological facilities on the basis of gas control, and compare the obtained values with the maximum permissible values. This method provides cal-culation of the coordinates of the gas source from the coordinates of the triggered sensors. Knowing the coordinates of all sensors, the coordinates of the sensors that gave the alarm, and the formula for determining the volume of the gas cloud under these sensors, it is possible to assess the localization of the source of dangerous gas in the protected room. This increases the efficiency of the fire safety system. The method makes it possible to control the layout of sensors depending on the volume of protected premises, types of production, the creation of new sensors, changes in the composition of hazardous gas in different technological conditions.

Debris flows have generated major disasters worldwide due to their great destructive capacity, which is associated with their high energy levels and short response times. To achieve an adequate risk management of these events, it is necessary to define as accurately as possible the different hazard levels to which the territory is exposed. This article develops a new methodology to estimate this hazard based on the hydrodynamic characteristics of the flow and the granulometry of the sediments that can be mobilized by the flow. The hydrodynamic characteristics of the flow are determined through a mathematical modeling that considers the rheology of non-Newtonian flows and the different volumes of sediments that could be transported during events corresponding to different return periods. The proposed methodology was implemented in the Jamundí River basin (Colombia). The results obtained indicate that in the upper part of this basin there is a low hazard level, while in the lower part of the basin approximately 15% of the affected territory has a medium hazard level and the remaining 85% has a low hazard level. The methodology developed is simple to implement but technically rigorous since it considers all relevant aspects in the generation of debris flows.

Concrete cracks have a detrimental effect on the strength properties and durability of the structures. So, repairing of concrete cracks to recover their strength parameters is more important task in civil engineering. To repair concrete cracks, MICP has been widely analysed in recent times; but, zero research is conducted to deeply investigate the repair effects of MICP on concrete cracks with rough surface by using the theoretic model. In current research, MICP with a novel mathematical model was attained by taking the precipitation of calcium carbonate (CaCO3), ureolysis, suspended biomass, geochemistry, transport of solute and biofilm growth. Furthermore, crack repair experiments were performed to check the workability of the new mathematical method. The outcomes revealed that the designed suspended biomass concentrations in cracks diminished step by step. The comparison in between the experimental results and calculated results verified the precision of migration behaviour of the suspended biomass. At the inlet, the solute concentrations and biofilm volume fractions was higher, causing in rise of yield amounts for calcium carbonate. The consumed solutes concentrations were higher for cracks of less rough surface, ultimately causing in smaller sonic time; and the values of sonic time for upper portions of cracks was smaller, showing good repair impacts. The recommended mathematical model provides a better tool that controls repair time and microbial metabolism process to report a new adjustive, bioremediation and biomineralization to concrete, which could provide a firm base for remediation of material in civil engineering field.

To assess the impact of tourism on the incidence of HIV and AIDS using Malaysian epidemiological data over the period of 1986-2011 with additional consideration for newborns infected with HIV. A population-level mathematical model was used to investigate: i) the role of tourism in the spread of HIV and measures used to reduce HIV spread in Malaysia; ii) whether the stability of infectious disease transmission is dependent on the flow of visiting tourists. We first derived an equation for the reproduction number (R0) threshold to quantify the contagiousness of HIV in Malaysia. Sensitivity analyses were used to determine the effect of various parameters on HIV transmission with respect to the increase in tourism. Our findings suggest that a stable disease-free state is sustainable based on the low value of R0 was 0.0017. This result is encouraging from a public health perspective. Approximately 14% of outbound tourists who leave the country return infected with HIV and the difference between the rate at which tourists move to the susceptible category and the rate at which tourists leave the susceptible is category is 12%. Estimated parameters for the influx of tourist rates, δ=1.1540x10-3[1.1477x10-3 - 1.15954x10-3], δ1=7.7901x10-4[7.7867x10-4 - 7.79418x10-4], and δ2=1.4030x10-8[-7.2287x10-7-7.5096x10-7], significantly impacted the spread of HIV in Malaysia. Some significant adjustments were made to the expected parameters. The methods used are helpful to public health analyses and provide a framework for epidemiological modeling of HIV spread among tourists. The trend and magnitude of tourist inflows may be determinants in the incidence of HIV and AIDS in Malaysia.

This study proposes a nonlinear mathematical model of virus transmission based on the SEIR model. In this study, the interaction between viruses and immune cells is investigated using phase-space analysis of a mathematical model. Specifically, it is focused on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune systems cells. The endemic equilibrium points are found and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis either, at disease-free equilibria, or in endemic equilibria is discussed by constructing the Lyapunov function which shows the validity of the concern model exists. Finally, a simulated solution is achieved and the relationship between viruses and immune cells is highlighted.

In this paper, we study the black hole solution of self-similar gravitational collapse in the Einstein-axion-dilaton system for the elliptic class in four dimensions. The solution is invariant under space-time dilation, which is combined with internal SL(2,R) transformations. Due to the complex and highly nonlinear pattern of the equations of motion in the physics of black holes, researchers typically have to use various numerical techniques to make the equations tractable to estimate the parameters and the critical solutions. To this end, they have to ignore the numerical measurement errors in estimating the parameters. To our knowledge, for the first time in the literature on axion-dilation systems, we propose to estimate the critical collapse functions in a Bayesian framework. We develop a novel methodology to translate the modelling of the complexity of the elliptic black hole to a sampling problem using Hamiltonian Monte Carlo with stacked neural networks. Unlike methods in the literature, this probabilistic approach enables us not only to recover the available deterministic solution but also to explore possibly all physically distinguishable self-similar solutions that may occur due to numerical measurement errors.

Relative contribution of different repair pathways to the radiation-induced DNA damage responses remains a challenging issue of studying the radiation injury endpoints. Comparative manifestation of homologous recombination (HR) after application of different radiation doses greatly determines an overall effectiveness of recovery in dividing cell after irradiation, since HR is an error-free mechanism intended for repair of DNA double strand breaks (DSB) during S/G2 phases of cell cycle. In this article, we present an experimentally observed evidence of dose-dependent shift in relative contribution of HR in human fibroblasts after X-ray exposure at doses 20-1000 mGy, which is also supported by quantitative modeling of DNA DSB repair. Our findings indicate that the radiation dose increase leads to dose-dependent decrease in relative contribution of HR into the entire repair process.

This paper discusses the mathematical modelling of exothermic explosions in a slab. This model is based on a nonlinear equation containing a nonlinear term related to Arrhenius, bimolecular, and sensitised laws of reaction kinetics. The absolute temperature can be obtained by solving the nonlinear equation using Akbari-Ganji’s method. The influence of the parameters Frank-Kamenetskii, activation energy and numerical exponent on temperature is discussed. The analytical results are compared with previous available analytical and numerical results ( Matlab). A satisfactory agreement is noted.

Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease that has afiected millions of people worldwide. Initially, basic public health measures were implemented to control specially the spread of such virus. However, vaccination has emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent spread of the disease. In this study, a modeling approach is used to analyze the impact of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical method, the model is solved based on reported cases in Pakistan. A spectral method is employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known as R0, which indicates the potential for disease transmission. The study also includes a detailed stability analysis, examining the invariance properties of the model solution and discussing equilibrium points and their stability in disease-free and endemic states. Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.

A mathematical model is proposed to analyze the spreading dynamics of COVID-19. By using the parameters of the model, namely the basic reproduction number (R0) and the attenuation constant (k), the daily number of infections (DNI) and the cumulative number of infections (CNI) are deduced and shown to be in good agreement with experimental data. This model effectively addresses three key issues: explaining the waveform pattern of DNI, predicting the occurrence of the second wave of infection, and understanding the competitive spread of two viruses in a region. The findings demonstrate that these significant challenges can be comprehensively tackled using a simple mathematical framework. The theoretical insights derived from this model hold potential in guiding the estimation of the severity of an infection wave and formulating effective strategies for the control and mitigation of epidemic outbreaks.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

In this paper, Akbari-Ganji's and Taylor series methods are applied to find analytical solutions to nonlinear differential equations that arise in an immobilized-cell photobioreactor. Approximate analytical expressions for substrate and product concentrations and both liquid and gas phases for various parameter values are derived using both methods. Efficiency, accuracy, and convergence of the two methods relative to highly accurate numerical methods are investigated to establish reliable profiles of these two methods for solving general nonlinear equations that model various physical phenomena. Numerical simulations are presented to validate the theoretical investigations.

The Oxford English Dictionary includes 17 definitions for the word “model” as a noun and other 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For in-stance, “model railways” refer to replicas of railways and trains at a smaller scale and a “model student” refers to an exemplar individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning of a model. Even if the context is narrowed, specifically to the research related to the tumour microenvironment, a “model” can be understood in a wide variety of ways, from an animal model, to a mathematical expression. This paper presents a review of the different “models” of the tumour microenvironment grouped by the different def-initions of the word into four categories: model organisms, in vitro models, mathematical models, and computational models. Then, the frequency of different meanings of the word “model” related to the tumour microenvironment is measured from the number of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequency of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, in particular xenografts and mouse models are the most common used “models”, the number of entries have been slowly de-creasing. Mathematical models, prognostic and risk models follow in frequency and these have been growing in use.

To effectively estimate airport terminal area capacity and assess the maximum throughput the sector can achieve when the capacity is given, this research proposes an approach to assess the terminal area capacity from the viewpoint of service provision resources. Terminal area capacity is optimized based on the equilibrium of air traffic service resource supply and demand. The supply-demand nexus is examined in consideration of terminal area route structure, traffic flow characteristics, and safety regulations. A flight service probability matrix and a terminal area demand and supply service time model are constructed to quantify resource expenditure at varied capacity levels. A optimization model is then developed to apportion maximal capacity under resource limitations. Model computation and computation results demonstrate the deviation between estimated and amended capacities is under 0.3 flight sorties per hour. The outcomes are congruent with historical statistics, thereby validating the accuracy and reliability of the model proposed in this study. Given capacity parameters, the model can deduce the maximal aircraft quantity served concurrently in terminal areas during peak periods. These revelations indicate the submitted model furnishes theoretical foundation and reference for terminal area sector partition and traffic alerting.

Mathematical modeling is the most important tool for constructing the theory of different kinds of two-phase flows. The review is devoted to the analysis of the advent of the approach of mathematical modeling of two-phase flows, where solid particles act mainly as the dispersed phase. The main problems and features of the study of gas-solid two-phase flows are excluded. The main characteristics of gas flows with solid particles are given and the classification of two-phase flows is developed on their basis. The Lagrangian and Euler approaches to modeling the motion of a dispersed phase (particles) are described. Much attention is paid to the consideration of numerical simulation methods that describe descriptions of turbulent gas flow at different hierarchical levels (RANS, LES, DNS), different levels of description of interphase interactions (one-way coupling (OWC), two-way coupling (TWC) and four-way coupling (FWC)), as well as at different levels of interface resolution (partial-point (PP) and particle-resolved (PR)). Excluded are examples of some studies carried out on the basis of the identified approaches, as well as their exclusion for mathematical modeling of various classes of gas-solid two-phase flows.

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

The paper presents the results of modeling the problem of injecting liquid sulfur dioxide into a porous reservoir initially saturated with methane and ice. The model presented in the paper assumes the formation of three different regions, namely, the near one, saturated with liquid SO2 and its hydrate; the far one, containing methane and ice, and the intermediate one, saturated with methane and water. The effects of various parameters of the porous medium and injected SO2 on the nature of the course of the hydrate formation process have been studied. It is shown that with a decrease in reservoir permeability or injection pressure, the length of the intermediate region decreases, which in the limiting case means the formation of SO2 hydrate in the mode without the formation of an extended region saturated with methane and water. It is shown that such a regime is also typical for the case of high initial injection pressures, as well as low values of the initial reservoir temperature and injection temperature.

Many drylands around the world have seen both soil and vegetation degradation around watering points. It can be seen in spaceborne imagery as radial brightness belts that fade with distance from the water areas. The study's primary goal was to characterize spatio-temporal land degradation/rehabilitation in the drylands of the southeast Iberian Peninsula. The brightness index of Tasseled Cap was discovered to be the best spectral transformation for enhancing the contrast between the bright-degraded areas near the points and the darker surrounding areas far from and in-between these areas. To comprehend the spatial structure present in spaceborne imagery of two desert sites and three key time periods, semi-variograms were created (mid-late 2000s, around 2015, and 2020). In order to assess spatio-temporal land-cover patterns, a geostatistical model (kriging) was used to smooth brightness index values extracted from 30 m spatial resolution images. To assess the direction and intensity of changes between study periods, a change detection analysis based on kriging prediction maps was performed. These findings were linked to the socioeconomic situation prior to and following the EU economic crisis. The study discovered that degradation occurred in some areas as a result of the region's agricultural activities being exploited.

The dynamics of the main photosynthetic structures is studied by mathematical modeling methods in this article. Chlorophyll portion variability in phytoplankton and the formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their participation in the growth of specific biomass. Computational experiments are presented that simulate various degrees of environmental friendliness. The corresponding functions are built in accordance with seasonal fluctuations throughout the year in the Far East region of Russia. The stability of model solutions in long-term dynamics is also investigated. The models were tested for biological adequacy and their effectiveness was compared. For the model selected as a result of the comparison, the optimal control problem has been formulated and solved. It is shown that in this way it is possible to reduce the space of the initial components of the model system.

The main objective of this study is to find out the influence of cooperation and intra-specific competition in escaping predation through refuge of the prey population and the effect of the two intra-specific interactions on the dynamics of prey-predator systems. For this purposes, two mathematical models with Holling type-II functional response function have been proposed and analyzed. The first model includes cooperation among prey populations whereas the second one incorporates intra-specific competition. Existence conditions and stability of different equilibrium points of both models have been carried out for the qualitative behaviour of the systems. Refuge through intra-specific competition has a stabilizing role, whereas cooperation has a destabilizing role on the system dynamics. Periodic oscillations are observed in both the systems through Hopf bifurcation. From the analytical and numerical findings, we conclude that intra-specific competition affects the prey population and continuously checks the refuge class under a critical value, and thus it never becomes too large to cause predator extinction due to food scarcity. Conversely, cooperation leads maximum individuals to escape predation through the refuge so that predators will suffer from low predation success.

The use of mathematical models of physiological systems in medicine has allowed the development of diagnostic, treatment, and medical educational tools, but their application for predictive, preventive, and personalized purposes is restricted by their complexity. Although there are strategies that reduce the complexity of applying models by fitting techniques, they focus on a single instant of time, neglecting the effect of the system's temporal evolution. The aim of this work is to propose a dynamic fitting strategy of physiological models with large number of parameters and a constrained amount of experimental data, focused on obtaining better predictions based on the system's temporal trend and useful to predict future states. It was applied in a cardiorespiratory model as a case study. Experimental data from a longitudinal study of healthy adult subjects under aerobic exercise were used for fitting and validation. The model predictions obtained at steady-state using the proposed strategy and the nominal values of the parameters were compared. The best results corresponded mostly to the proposed strategy, mainly regarding the overall prediction error. The results evidenced the usefulness of the dynamic fitting strategy, highlighting its use for predictive, preventive, and personalized applications.

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solu-tions. At the same time, depending on parameter values, different dynamic regimes - stationary, oscillatory, established as a result of transient modes of various types - can be implemented in the system. Predicting changes in the solution dynamics type depending on changes of model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computa-tional experiments, i.e. solving a series of direct problems with various sets of parameters fol-lowed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allow-ing to obtain and analyze information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for visualization and classification of various dy-namic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method allows to obtain a qualitative visualisation of the results of the set of solutions of a mathematical model and to carry out the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka-Volterra model and artificial sets of var-ious dynamics

The article proposes a method for determining the p-value of correlations in compositional data, i.e., those data that arise as a result of dividing the original values by their sum. Data organized in this way are typical for many fields of knowledge, but there is still no consensus on methods for interpreting correlations in such data. In a space closed by normalizing quantity, correlation coefficients behave differently than under normal conditions: their probabilities of occurrence do not coincide with those inherent in the standard scale of estimates. In the tens of the new millennium, almost all newly emerging methods for estimating correlation in compositional data began to require mandatory log-transformation of the variable values. In the method proposed here there are no log-transformations. We return to the early stages of attempting to solve the problem and rely on negative shifts in correlations in the multinomial distribution. In modeling the data, we use a hybrid method that combines the hypergeometric distribution with the distribution of any other law. During our work on the calculation method, we found that the number of degrees of freedom in compositional data measures discretely only when all the normalizing sums are equal and that it decreases when the sums are not equal, becoming a continuously varying quantity. Estimation of the number of degrees of freedom and the strength of its influence on the magnitude of the shift in the distribution of correlation coefficients is the basis of the proposed method.

The bridge crane is often used in a complex environment, often subject to interference of all loads. Some uncertainties factors often have an inevitable impact on its swing. So the force situation of the bridge crane during a working cycle is analyzed, and a three-dimensional dynamic mathematical model of the bridge crane is built. Through the simulation analysis of the model under the action of driving force and wind load, the change law of the swing angle of the bridge crane is studied. Then, the fuzzy control theory is used to determine the control parameter in the anti sway control process. The position, swing angle deviation and deviation rate of the bridge crane are taken as the input, and the parameter correction is obtained after the fuzzification by using the center of gravity method, the anti sway fuzzy control system of the bridge crane is designed and simulated. The research results show that the fuzzy PID anti sway controller can not only improve the adaptability of the control system, but also overcome the large overshoot, quickly restrain the swing, and effectively realize the anti sway function of the bridge crane.

A mathematical model of energy metabolism in erythrocyte-bioreactors loaded with alcohol dehydrogenase and acetaldehyde dehydrogenase was constructed and analyzed. Such erythrocytes can convert ethanol to acetate using intracellular NAD and, thus, can be used to treat an alcohol intoxication. Analysis of the model reveals that the rate of ethanol consumption by the erythrocyte-bioreactors increases proportionally to activity of incorporated ethanol-consuming enzymes until their activity reaches a specific threshold level. When the ethanol-consuming enzyme activity exceeds this threshold, the steady state in the model becomes unstable and the model switches to an oscillation mode caused by a competition of glyceraldehyde phosphate dehydrogenase and ethanol-consuming enzymes for NAD. An amplitude and period of metabolite oscillations first increase with the increase in the activity of e encapsulated enzymes. A further increase in these activities leads to a loss of the glycolysis steady state, and a permanent accumulation of glycolytic intermediates. The oscillation mode and the loss of the steady state can lead to osmotic destruction of erythrocyte-bioreactors due to an accumulation of intracellular metabolites. Our results demonstrate that the interaction of enzymes encapsulated into erythrocyte-bioreactors with erythrocyte metabolism should be taken into account in order to obtain an optimal efficacy of these bioreactors.

This paper presents some aspects of command and control of the new generation of machines-tools with numerical control. A problem faced by numerical control programmers is related to the length (relatively long) of the programs, with implications in the costs and duration of the manufacturing preparation. A method of reducing the main program and other redundant expenses is the introduction and use of processing cycles and subroutines for automatic calculation of the cutting tool trajectory, a fact that also allows the optimization and simplification of numerical control programming on flexible order manufacturing systems numeric. The method involves the use of predefined cycles and appropriate subroutines in order to improve the efficiency of the programming activity in a balanced way. It is a new and rapid method for optimize the structure of program using the numerical subroutine for command the movement of tool, in our case, with application for turning and milling.

Infectious diseases continue to be a significant threat to human health and civilization, and finding effective methods to combat them is crucial. In this research, we investigate the impact of awareness campaigns and optimal control techniques on infectious diseases without proper vaccines. Specifically, we develop an SIRS type mathematical model that incorporates awareness campaigns through media and treatment for disease transmission dynamics and control. The model displays two equilibria, a disease-free equilibrium and an endemic equilibrium, and exhibits Hopf bifurcation when the bifurcation parameter exceeds its critical value, causing a switch in the stability of the system. We also propose an optimal control problem that minimizes the cost of control measures while achieving a desired level of disease control. By applying the minimum principle to the optimal control problem, we obtain analytical and numerical results that show how the infection rate of the disease affects the stability of the system and how awareness campaigns and treatment can maintain system stability. This study highlights the importance of awareness campaigns in controlling infectious diseases and demonstrates the effectiveness of optimal control theory in achieving disease control with minimal cost.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

Rapid in vitro assessment of antimicrobial drug efficacy under clinically relevant pharmacokinetic conditions is an essential element of both drug development and clinical use. Here we present an overview of a novel integrated methodology for rapid assessment of such efficacy, particularly against emergence of resistant bacterial strains, as jointly researched by the authors in recent years. This methodology enables rapid in vitro assessment of antimicrobial efficacy of a single or multiple drugs in combination, following clinically relevant pharmacokinetics. The proposed methodology entails (a) automated collection of longitudinal time-kill data in an optical-density instrument; (b) processing of collected time-kill data with the aid of a mathematical model to de-termine optimal dosing regimens under clinically relevant pharmacokinetics for a single or mul-tiple drugs; and (c) in vitro validation of promising dosing regimens in a hollow fiber system. Proof-of-concept of this methodology through a number of in vitro studies is discussed. Future directions for refinement of optimal data collection and processing are discussed.

University course scheduling (UCS) is one of the most important and time-consuming issues that all educational institutions face yearly. Most of the existing techniques to model and solve UCS problems have applied approximate methods, which are different in terms of efficiency, performance, and optimization speed. Accordingly, this research aims to apply an exact optimization method to provide an optimal solution to the course scheduling problem. In other words, in this research, an integer programming model is presented to solve the USC problem. In this model, hard and soft constraints include the facilities of classrooms, courses of different levels and compression of students' curriculum, courses outside the faculty and planning for them, and the limited time allocated to the professors. The objective is to maximize the weighted sum of allocating available times to professors based on their preferences in all periods. To evaluate the presented model's feasibility, it is implemented using the GAMS software. Finally, the presented model is solved in a larger dimension using a real data set from a college in China and compared with the current program in the same college. The obtained results show that considering the mathematical model's constraints and objective function, the faculty courses' timetable is reduced from 4 days a week to 3 working days. Moreover, master courses are planned in two days, and the courses in the educational groups do not interfere with each other. Furthermore, by implementing the proposed model for the real case study, the maximum teaching hours of the professors are significantly reduced. The results demonstrate the efficiency of the proposed model and solution method in terms of optimization speed and solution accuracy.

Malaria is a critical fevered illness caused by Plasmodium parasites transmitted among people through the bites of infected female Anopheles mosquitoes. Public awareness about the disease is important for the control of disease. This article proposes a mathematical model to study the dynamics of malaria disease transmission with the influence of awareness-based control interventions. We found two equilibria of the model, namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable globally if basic reproduction number (R0) is less than unity (R0&lt;1). Some basic mathematical properties of the proposed model, such as nonnegativity and boundedness of solutions, the feasibility of the equilibrium points and their stability properties, have been studied. Finally, we adopted optimal control to minimize the cost of disease control and solve the problem by formulating Hamiltonian functional. The optimal use of insecticides for controlling the mosquito population is determined. Numerical simulations have been provided for the confirmation of the analytical results. We conclude that media awareness with optimal control approach is best for cost-effective malaria disease management.

The study shows that the volumes and surfaces of $n$-balls, $n$-simplices, and $n$-orthoplices are holomorphic functions of $n$, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about $n$-balls reveal previously unknown properties of these geometric objects. In particular, for $0 < n < 1$, the volumes of the omnidimensional polytopes are larger than those of circumscribing $n$-balls, and both their volumes and surfaces are smaller than those of inscribed $n$-balls. The surface of an $n$-simplex circumscribing unit diameter $n$-ball is spirally convergent to zero with real $n$ approaching negative infinity but first has a local maximum at $n=-3.5$. The surface of an $n$-orthoplex circumscribing unit diameter $n$-ball is spirally divergent with real $n$ approaching negative infinity but first has a local minimum at $n=-1.5$, where its real and imaginary parts are equal to each other; similarly, as its volume, where the similar local minimum occurs at $n=-3.5$. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about $n$-balls are proposed. symmetries of products and quotients of volumes in complex dimensions $n$ and $-n$ and of surfaces in complex dimensions $n$ and $2-n$ are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between volumes and surfaces in dimensions $n = -1/2$ and $n = 1/2$.

A model is proposed that describes the transfer of ions and the process of water dissociation in a system with a bipolar membrane and adjacent diffusion layers. The model considers the transfer of four types of ions: the cation and anion of salt and the products of water dissociation – hydrogen and hydroxyl ions. To describe the process of water dissociation, a model for accelerating the dissociation reaction with the participation of ionogenic groups of the membrane is adopted. The boundary value problem is solved numerically using COMSOL® Multiphysics 5.5 software. An analysis of the results of a numerical experiment shows that, at least in a symmetric electromembrane system, there is a kinetic limitation of the water dissociation process, apparently associated with the occurrence of water recombination reaction at the of the bipolar region. An interpretation of the entropy factor (β) is given as a characteristic length which shows the possibility of an ion that appeared as a result of the water dissociation reaction to be removed from the reaction zone without participating in recombination reactions.

In sub-Saharan Africa, malaria is a leading cause of mortality and morbidity. As a result of the interplay between many factors, the control of this disease can be challenging. However, few studies have demonstrated malaria's complexity, control, and modeling although this perspective could lead to effective policy recommendations. This paper aims to be a didactic material providing the reader with an overview of malaria. More importantly, using a system approach lens, we intend to highlight the debated topics and the multifaceted thematic aspects of malaria transmission mechanisms, while showing the control approaches used as well as the model supporting the dynamics of malaria. As there is a large amount of information on each subject, we have attempted to provide a basic understanding of malaria that needs to be further developed. Nevertheless, this study illustrates the importance of using a multidisciplinary approach to designing next-generation malaria control policies.

Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave, had subsequent waves of the COVID-19 infections and it remains to be seen whether there will be more waves. In this paper, we formulate a deterministic model for COVID-19 incorporating dynamic non-pharmaceutical interventions, dubbed social dynamics. The model steady states are determined and their stability analysed. Numerical simulations are carried out to determine the pack of various parameters that influence the social dynamics. In South Africa, the first wave was the only wave in which the only interventions rested solely on human behavior. The model is thus fitted to COVID-19 data on the first wave in South Africa. The results presented in this paper have implications on the trajectory of the pandemic in the presence of changing social processes.

In this paper mathematical analysis of the HIV/AIDS deterministic model exposed in [Espitia, C. et. al. Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia, Journal of Computational Biology 29 (2022) 483–493] is made. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness, calculus of basic reproduction number, stationary points such as disease free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE) are calculated, local stability (LAS) of disease free equilibrium. It research allow to conclude that the best way to reduce contagion and consequently to reach a DFE is thought to be the reduction of homosexual partners rate as they are the most affected population by the virus, and are therefore the most likely to become infected and to spread the infection. Increasing the departure rate of infected individuals, leads to a decrease in untreated infected heterosexual men and untreated infected women.

In the present paper, we investigate the impact of the timescale factor on the quality of life index behavior on specific time intervals characterized by the presence of socio-economic, political, and/or health severe movements such as pandemics and crises. We essentially aim to show that effectively the quality of life measuring based on a single index in the existing studies may be described more adequately by a variable index due to the social, political, economic, and also healthy environment. The variability discovered is expressed by the existence and the estimation of a multi-index instead of a single one relatively to many factors. Our focus is mainly on the effect of the COVID-19 pandemic on the quality of life. Our model is applied empirically to a sample corresponding to Saudi Arabia as a case of study during the period from January 1990 to December 2021 as the main period affected by the COVID-19 pandemic. The sample is based on social media conversations and texts discussing and describing the satisfaction with the quality of life. The study confirms effectively that the role of the timescale factor is more described when considering a multi-index rather than measurement on the whole time interval.

This research investigates a model for the COVID-19 outbreak in Indonesia by analyzing comorbid diseases, self-quarantine, government-provided quarantine, and immunization regimens. Some model parameters are derived from academic journals, others are extrapolated from data collected by the Indonesian Ministry of Health in 2020, and others are assumed. Evaluation of the model reveals non-endemic equilibrium points, endemic equilibrium points, and the basic reproduction number (BRN). The contact rate and infected probability factors impact the increase in the number of COVID-19-infected individuals with comorbid disease within a group. According to the sensitivity analysis of the BRN, the key parameters impacting the spread of COVID-19 are the rate of susceptible recruitment, the rate of contact, the COVID-19 infection death rate, and the likelihood of infection. In addition, sensitivity analyses are provided to examine the effect of parameter changes on subpopulations. We discovered that the natural death rate is the most sensitive parameter based on the sensitivity index after reaching equilibrium. Symmetry aspects appear in some of the visualization of the model’s solution and the BRN and parameters’ sensitivity.

Introduction. Musculoskeletal disorders related to work might follow with a cumulative effect during working life. We aimed to develop a new model to allow to compare the accuracy of duration of work and intensity/frequency associations in application to severe knee pain. Methods. The CONSTANCES cohort is used with data from n=66553 subjects who were working at inclusion and coded. From a biomechanical job exposure matrix “JEM Constances”, intensity/frequency of heavy lifting and kneeling/squatting were used and applied to the work history in comparison to severe knee pain. An innovative model was developed and evaluated, allowing to compare the accuracy of duration of work and intensity/frequency associations. Results. The mean age is 49 years at inception with 46 percent of women. The G model developed was slightly better than regular models. In men, odds ratios of the highest quartile for the duration and low intensity were not significant for both exposures, whereas intensity/duration were for every duration. Results in women were less interpretable. Conclusion. Though increased duration increased strength of association with severe knee pain, intensity/frequency were important predictors among men. Exposure estimation along working history should have emphasis on such parameters, though other outcomes should be studied such as women.

Pancreatic cancer represents one of the difficult problems of contemporary medicine. The development illness evolves very slowly, takes place in special sake (stroma) and manifests clinically close to a final stage. Another feature of this pathology is a coexistence (symbiotic) effect between cancer cells and normal cells inside stroma. All these aspects make it difficult to understand the pathogenesis of pancreatic cancer and develop a proper therapy. The emergence of pancreatic pre-cancer and cancer cells represents a branching stochastic process engaging populations of 64 cells differing in the number of acquired mutations. In this study we formulate and calibrate the mathematical model of pancreatic cancer using the quasispecies framework. The mathematical model incorporates the mutation matrix, fineness landscape matrix and the death rates. Each element of the mutation matrix presents the probability of appearing a specific mutation in the branching sequence of cells representing the accumulation of mutations. The model incorporates the cancer cell elimination by effect CD8 T cells (CTL). The down-regulation of the effector function of CTLs and exhaustion are parameterized. The symbiotic effect of coexistence of normal and cancer cells is considered. The computational predictions obtained with the model are consistent with empirical data. The modelling approach can be used to investigate other types of cancers and examine various treatment procedures.

Globally, zoonotic diseases have been on the rise in recent years. Predictive modelling approaches have been successfully used in the literature to identify the underlying causes of these zoonotic diseases. We examine the latest research in the field of predictive modeling that verifies the growth of zoonotic pathogens and assesses the factors associated with their spread. The results of our survey indicate that popular mathematical models can successfully be used in modeling the growth rate of these pathogens under varying storage temperatures. Additionally, some of them are used for the assessment of the inactivation of these pathogens based on various conditions. Based on the results of our study, machine learning models and deep learning are commonly used to detect pathogens within food items and to predict the factors associated with the presence of the pathogens.

A calibrated mathematical model of antiviral immune response to SARS-CoV-2 infection is developed. The model considers the innate and antigen-specific responses to SARS-CoV-2 infection. Recently published data sets from human challenge studies with SARS-CoV-2 were used for parameter estimation. Understanding the regulation of multiple intertwined reaction components of the immune system is necessary for linking the clinical phenotypes of COVID-19 with the kinetics of immune responses. Consideration of multiple immune reaction components in a single calibrated mathematical model allowed us to address some fundamental issues related to pathogenesis of COVID-19, i.e. sensitivity of the peak viral load to parameters characterizing the specific response components, the kinetic coordination of the individual responses, and the factors favoring a prolonged viral persistence. The model provides a tool for predicting the infectivity of patients, i.e. the amount of virus which is transmitted via droplets from the person infected with SARS-CoV-2, depending on the time of infection. The thresholds in the relative unbalance between innate and adaptive response parameters which lead to a prolonged persistence of SARS-CoV-2 due to the loss of a kinetic response synchrony/coordination were identified.

In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.

The development of synthetic biology has enabled us to make massive progress on biotechnology and to approach research questions from a brand new perspective. In particular, the design and study of gene regulatory networks in vitro, in vivo and in silico, have played an increasingly indispensable role in understanding and controlling biological phenomena. Among them, it is of great interest to understand how associative learning is formed at the molecular circuit level. Noticeably, mathematical models have been increasingly used to predict the behaviors of molecular circuits. The Fernando’s model, which is thought to be one of the first works in this line of research using the Hill equation, attempted to design a synthetic circuit that mimics Hebbian learning in the neural network architecture. In this article, we carry out in-depth computational analysis of the model and demonstrate that the reinforcement effect can be achieved by choosing the proper parameter values. We also construct a novel circuit that can demonstrate forced dissociation, which was not observed in the Fernando’s model. Our work can be readily used as reference for synthetic biologists who consider implementing the circuits of this kind in biological systems.

To verify the authors’ mathematical model for water jet cooling of steel sheet, the previously performed experimental studies of temperature of the test plate in the roller quenching machine (RQM) were used. The calculated data of steel temperature evolution along the RQM length were compared with the readings of thermocouples inserted in the center of the test plate and at its surfaces. The core of the model is the dependence of the temperatures of film, transition and nucleate boiling regimes on the thickness of the oxide scale layer on the cooled surface. It was found that the model correctly takes into account the oxide scale on the sheet surface, flow rates and combinations of the RQM banks used, water temperature and other factors. For all experiments the calculated metal temperature corresponds well to the measured one. In the experiments with interrupted cooling, the calculated temperature plots repeat the characteristic changes in the experimental curves. The main uncertainty in the modeling of cooling in a wide temperature range can be contributed by the random nature of changes in the oxide scale thickness during water cooling. In this regard, the estimated thickness of the oxide scale layer should be considered as the main parameter for adapting the sheet temperature control process. The obtained data confirm the possibility of effective application of the model in the ACS of industrial TMCP (Thermo-Mechanical Controlled Process) systems.

Immune checkpoint blockade (ICB)-based therapy is revolutionizing cancer treatment by fostering successful immune surveillance and effector cell responses against various types of cancers. However, patients with HER2+ cancers are yet to benefit from this therapeutic strategy. Precisely, several questions regarding the right combination of drugs, drug modality, and effective dose recommendations pertaining to the use of ICB-based therapy for HER2+ patients remain unanswered. In this study, we use a mathematical modeling-based approach to quantify the growth inhibition of HER2+ breast cancer (BC) cell colonies (ZR75) when treated with anti-HER2; trastuzumab (TZ) and anti-PD-1/PD-L1 (BMS-202) agents. Our data show that a combination therapy of TZ and BMS-202 can significantly reduce the viability of ZR75 cells and trigger several morphological changes. The combination decreased the cell’s invasiveness along with altering several key pathways, such as Akt/mTor and ErbB2 compared to monotherapy. In addition, BMS-202 causes dose-dependent growth inhibition of HER2+ BC cell colonies alone, while this effect is significantly improved when used in combination with TZ. Based on the in-vitro monoculture experiments conducted, we argue that BMS-202 can cause tumor growth suppression not only by mediating immune response but also by interfering with the growth signaling pathways of HER2+ BC. Nevertheless, further studies are imperative to substantiate this argument and to uncover the potential crosstalk between PD-1/PD-L1 inhibitors and HER2 growth signaling pathways in breast cancer.

Marketing is the manner of how to make our sales the best in the market, our prices the most accessible, our clients satisfactory, and thus our brand is the largest distributed. This needs sophisticated and advanced understanding of the total network related. Indeed, marketing data may be seen in different forms such as qualitative and quantitative. However, in the literature, it is easily noticed that large bibliography may be collected about qualitative studies, against few studies on the quantitative point of view. This is a major drawback that makes the marketing science still focusing on the design, although the market is strongly depending on quantities such as money and time. Indeed, marketing data may be a time series such as brand sales per specified periods, brand related-prices over specified periods, market shares, ..., etc. The purpose of the present work is to investigate some marketing models based on time series due to brands. We will precisely study the effect of the time scale on the persistence of brands sales in the market and on the forecasting of such a persistence according to the characteristics of the brand and the related market competition or competitors. Our study is acted on a sample of Saudi brands during the period November 22, 2017 to December 30, 2021.

Patients with COVID-19 may develop pneumonia, severe symptoms of acute respiratory distress syndrome, and multiple organ failure. Nevertheless, the variety of forms of this disease, requires further research on the pathogenesis of this disease. Based on the analysis of published data on the concentrations of SARS-CoV-2 in biological fluids of the nasopharynx, lungs and intestines and using a developed modular model of the virus distribution in human tissue and organs, an assessment of the SARS-CoV-2 reproduction in various compartments of the body is presented. Most of viral particles can enter into the esophagus from nasopharynx. Entering viral particles into the gastrointestinal tract will obviously be accompanied by infection of the intestinal epithelium and accumulation of the virus in the intestinal lumen in an amount proportional their secretory and protein-synthetic activities. The relatively low concentration of SARS-CoV-2 in tissues implies an essential role of transport processes and redistribution of the virus from nasopharynx and intestines to lungs. The model simulations also supposes that sanitation of the nasopharynx mucosa at the initial stage of the infectious process considering inhibition of the virus accumulation by means of cellular and humoral responses has prospects for the use in medicine practice.

The present paper is concerned with the study of the quality of life index. Such an index has become an important index for measuring the well-being of individuals. However, the quality of life index is always a subjective, intangible, and often hard to quantify with precision due to the lack of quantitative models dealing with. The main goal of the present paper is thus to propose a mathematical, quantitative model for the measurement of a quality of life index. The main novelty is firstly the construction of a wavelet dynamic multiscale model to quantify and investigate the effect of time scale on the quality of life index measuring. The proposed procedure is acted empirically on a sample corresponding to Saudi Arabia as a case of study during the period from 2003 to 2020 as part of the 2030-vision plan. Saudi Arabia has implemented the so-called 2030-vision plan where the quality of life improvement is one of the main goals to be attempted. The findings show that wavelets are capable to localize the time-wise behavior of the index contrarily to classical studies which estimate a global view of the index. Moreover, the study shows the link between the quality of life behavior and many other indices.

This article describes the methodology used to identify the mathematical model that describes the correlations between the input parameters of an experiment and the parameters being followed. As a technological process, the aerodynamic separation was chosen, respectively, the behavior of a solid particle within an ascending vertical airflow. The experimental data obtained were used to identify two parameters, the average linear velocity, and the angular velocity, and through the Table Curve 3D program was developed a mathematical model which describes the dependence between the input parameters (the shape and size of the solid particle and the velocity of the airflow) and the monitored parameters. In order to determine a single mathematical equation that describes as accurately as possible the correlation between the input variables and those obtained, a pyramid-type analysis was designed. The determination of the mathematical equation started from the number of equations generated by the Table Curve 3D program, then the equations with a correlation coefficient greater than 0.85 were chosen, and finally, the common equations were identified. Respecting the working methodology was identified one equation which has for the average linear velocity a correlation coefficient r2 between 0.88-0.99 and 0.86-0.99 for the angular velocity.

Schistosomiasis is a parasitic disease acquired through contact with contaminated freshwater. The definitive hosts are terrestrial mammals, including humans, with some Schistosoma species crossing the animal-human boundary through zoonotic transmission. An estimated 12 million people live at risk of zoonotic schistosomiasis caused by Schistosoma japonicum and Schistosoma mekongi, largely in the World Health Organization’s Western Pacific Region and in Indonesia. Mathematical models have played a vital role in our understanding of the biology, transmission, and impact of intervention strategies, however, these have mostly focused on non-zoonotic Schistosoma species. Whilst these non-zoonotic-based models capture some aspects of zoonotic schistosomiasis transmission dynamics, the commonly-used frameworks are yet to adequately capture the complex epi-ecology of multi-host zoonotic transmission. However, overcoming these knowledge gaps goes beyond transmission dynamics modelling. To improve model utility and enhance zoonotic schistosomiasis control programmes, we highlight three pillars that we believe are vital to sustainable interventions at the implementation (community) and policy-level, and discuss the pillars in the context of a One-Health approach, recognising the interconnection between humans, animals and their shared environment. These pillars are: (1) human and animal epi-ecological understanding; (2) economic considerations (such as treatment costs and animal losses); and (3) sociological understanding, including inter- and intra-human and animal interactions. These pillars must be built on a strong foundation of trust, support and commitment of stakeholders and involved institutions.

ATP Synthase is an essential molecule in cell and molecular biology. It is responsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase’s rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total linear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.