We prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron’s method of proving the solvability of the Dirichlet problem for the soft Laplacian.

We present an open-source Star Tracker (ST) for Attitude Determination. Our implementation makes use of open source software of common usage in astronomy running on a Raspberry Pi 2 platform. The developed platform is open and available for parties interested in further development. Evaluation of the system showed that the ST is suitable for Cubesats of 2U or larger. The ST platform is capable of solving the Lost-In-Space (LIS) problem. Currently, the average accuracy reached of the algorithm is close to 5 seconds of arc with an average processing time of 75 seconds. However, a average accuracy of about 3 minutes of arc can be reached with 35 seconds in average processing time. We also describe the evaluation procedure, the found conclusions of this procedure, in particular the section of the algorithm where most of the processing time is spent and other possible source of errors not included in this study.

This paper details the comprehensive activities conducted in a laboratory setting to assess the Structural Health Monitoring (SHM) of prefabricated building envelopes. Aimed at enhancing the structural evaluation of buildings, the focus of this research lies in employing nondestructive sensors for SHM with the objective to advance in the understanding and assessment of facade conditions. The paper outlines the methodologies employed, starting with a modal analysis to define the structural vibration's modal frequency. Subsequently, tests were defined and executed to validate building envelope compliance in case of stress typical of high-rise building. Throughout these tests, continuous monitoring of the façade was conducted using both conventional (accelerometers, extensimeter washers) and non-conventional sensors (Fiber Optic Sensing) The gathered data underwent thorough processing and analysis to provide an overall perspective on the structure's behavior during the stress test. The investigation aimed to identify whether specific physical phenomena correlate with distinct signals and to evaluate if continuous façade monitoring over the building's lifespan aids in preventing potential structural damage. Moreover, two modal analyses were conducted to compare final data and frequencies with earlier data, enabling the detection of any structural alterations. The results from compliance testing and structural analysis yielded noteworthy insights contributing to the evolving field of structural health monitoring, offering valuable findings that advance our ability to proactively manage and maintain the integrity of building structures.

The main purpose of this paper is to present a comprehensive view of the application mathematical models in the designing and implementing SSCM beside to solving problems and making decision. The research questions are: what mathematical models are used for designing and implementing sustainable supply chain management, how to use them, which industries implemented in, what modules of SSCM depth in and finally finding the gaps of researches. The methodology of research is Systematic Literature review through peer review papers which are published in high ranking journals. In this paper, First, we search all papers through scientific data bases like Scopus, science direct, MDPI, Springer, Google Scholar, then, screening papers based on the criteria such as subject of paper, journals impact factor which is published in-should be peer review journal- and relative content of the papers. Finally, we selected 245 papers with three steps screening through 2806 papers that they have enough quality and relative to our research goals for context analysis. Through context analysis, first we categorized the information of the papers and drew the current situation of researches in the framework of our topic. Then, we evaluate and compare the goals of sustainability and current situation and found the gapes, then, offered new suggestions like implementing SSCMs models in pollutant industries like casting industry, Heavy industry, coal Industry and so on. On the other hand, there are gaps in researches in some modules of SSCM such as packaging, designing products, etc.

Every finite simple group P can be generated by two of its elements. Pairs of generators forP are available in the Atlas of finite group representations as (not necessarily minimal) permutation representations P . It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfant D and that a wealth of standard graphs and finite geometries G - such as near polygons and their generalizations - are stabilized by a D. In our paper, tripods P − D − G of rank larger than two,corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurationsdefined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G's have a contextuality parameterclose to its maximal value 1.

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.

Numerical simulations of standard situations in the transition region from gas kinetics to fluid dynamics at small Mach numbers indicate a clear dependence of the simulation results on the underlying kinetic model (here: nonlinear and linearized Boltzmann collision operator vs. BGK relaxation model). We develop an improved mathematical framework (trace theory) to explain these differences. In particular we reveal certain deficiencies for the classical BKG system as well as for the standard Navier Stokes approach.

Compartmental analysis is the mathematical framework for the modelling of tracer kinetics in dynamical Positron Emission Tomography. This paper provides a review of how compartmental models are constructed and numerically optimized. Specific focus is given on the identifiability and sensitivity issues and on the impact of complex physiological conditions on the mathematical properties of the models.

The predictability of wind information in a given location is essential for the evaluation of a wind power project. Predicting wind speed accurately improves the planning of wind power generation, reducing costs and improving the use of resources. This paper seeks to predict the mean hourly wind speed in anemometric towers (at a height of 50 meters) at two locations: a coastal region and one with complex terrain characteristics. To this end, the Holt-Winters (HW), Artificial Neural Networks (ANN) and Hybrid time-series models were used. Observational data evaluated by the Modern-Era Retrospective analysis for Research and Applications-Version 2 (MERRA-2) reanalysis at the same height of the towers. The results show that the hybrid model had a better performance in relation to the others, including when compared to the evaluation with MERRA-2. For example, in terms of statistical residuals, RMSE and MAE were 0.91 and 0.62 m/s, respectively. As such, the hybrid models are a good method to forecast wind speed data for wind generation.

Due to a simple crane limited capacity; there is an urgent need to use high capacity cranes such as tower cranes. However, with regard to their high expense, we have to take into consideration selecting what type of cranes to be utilized which has been discussed by many researchers. In this research, a proposed technique was created to select the suitable type of crane and best place for crane erection, in addition to minimum radius for requested crane in order to minimize cost. To fulfill that target, a computer program is designed to numerate these problems, demonstrating an example explaining how to apply program and the result donated best place.

This paper develops mathematical models examining possible roles of oxytocin and oxytocin receptors in the development of autism. This is done by demonstrating that mathematical operations on normalized data from the Stanford study (K.J. Parker, 2016), which establishes a correspondence between severity of autism in children and their oxytocin blood levels, generates a graph that is the same as the graph of mathematical operations on a normalized theoretical model for the severity of autism. This procedure establishes the validity of the theoretical model and the significance of oxytocin receptors in autism. A steady-state model follows, explaining the constant baseline concentrations of oxytocin observed in the cerebral spinal fluid and blood in terms of the neuromodulation by oxytocin of oxytocin receptors on the magnocellular neurons that produce oxytocin in nuclei in the hypothalamus. The implications of these models for possible roles of oxytocin and oxytocin receptors in autism is considered for several unrelated conditions that may be associated with autism. These are: oxytocin receptor desensitization and down-regulation as factors during labor in offspring autism development; reductions in the oxytocin receptor numbers in the fixed oxytocin receptor expression that occurs before birth; MAST Immune System disease; and the excess number of dendritic spines from lack of pruning observed in brains of autistic people. Research into the feasibility of generating magnocellular neurons and other neurons from adult stem cells is suggested as a way of doing invitro studies of oxytocin and oxytocin receptors to assess the validity of theories presented in this paper.

The current health crisis derived from COVID 19 has become a serious threat to humanity. The collateral effects related to economic aspects are affecting companies, workers and, of course, families in general. The problems of financial insolvency are frequently present in debtors who have contracted a debt with their creditor. Therefore, the objective of the study is focused on modeling a debt restructuring proposal, through three hypothetical scenarios in which the debt is reconvened when some documents have expired and others are yet to expire. In each of the scenarios, the mathematical model is designed and subsequently corroborated in an Excel spreadsheet. The predominant variables in the restructuring are the adjustment rates used to update the past due promissory notes and the discount rates of those promissory notes that have not yet expired, capitalizations, transaction costs and, if applicable, whether the debt is in foreign currency. In this case, it is converted to the local currency, then the spot exchange rate is used.

This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological and psychophysical differences in sensory processing that have been reported in migraine with aura. Reaction-diffusion models have been used to model the hallucinations thought to arise from cortical spreading depolarisation and depression in migraine aura. One aim of this review is to make the underlying principles of these models accessible to a general readership. Cortical spreading depolarisation and depression in these models depends on the balance of the diffusion rate between excitation and inhibition, and the occurrence of a large spike in activity to initiate spontaneous pattern formation. We review experimental evidence, including recordings of brain activity made during the aura and attack phase, self-reported triggers of migraine, and psychophysical studies of visual processing in migraine with aura, and how these might relate to mechanisms of excitability that make some people susceptible to aura. Increased cortical excitability, increased neural noise, and fluctuations in oscillatory activity across the migraine cycle are all factors likely to contribute to the occurrence of migraine aura. There remain many outstanding questions relating to the current limitations of both models and experimental evidence. Nevertheless, reaction-diffusion models, by providing an integrative theoretical framework, support the generation of testable experimental hypotheses to guide future research.

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.

Dynamic neural networks (DNN) are types of artificial neural networks (ANN) that are designed to work with sequential data where context in time is important. In contrast to traditional static neural networks that process data in a fixed order, dynamic neural networks use information about past inputs, which is important if dynamic of a certain process is emphasized. They are widely used in natural language processing, speech recognition and time series prediction. In industrial processes, their use is interesting for the prediction of difficult-to-measure process variables. In an industrial process of isomerization, it is crucial to measure the quality attributes affecting the octane number of gasoline. Process analyzers that are commonly used for this purpose are expensive and subject to failures, therefore, in order to achieve continuous production in case of malfunction, mathematical models for estimating the product quality attributes are imposed as a solution. In this paper, mathematical models were developed using dynamic recurrent neural networks (RNN), i.e., their subtype of a long short-term memory (LSTM) architecture. The results of the developed models were compared with the results of several types of other data-driven models developed for an isomerization process, such as multilayer perceptron (MLP) artificial neural networks, support vector machines (SVM) and dynamic polynomial models. The obtained results are satisfactory, which suggests a good possibility of application.

Immunotherapy has gained great momentum with chimeric antigen receptor T cell (CAR-T) therapy, in which patient’s T lymphocytes are genetically manipulated to recognize tumor-specific antigens increasing tumor elimination efficiency. In the last years, CAR-T cell immunotherapy for hematological malignancies achieved a great response rate on patients and is a very promising therapy for several other malignancies. Each new CAR design requires a preclinical proof-of-concept experiment using immunodeficient mouse models. The absence of a functional immune system in these mice makes them simple and suitable to be mathematically modeled. In this work, we developed a three population mathematical model to describe tumor response to CAR-T cell immunotherapy in immunodeficient mouse models, encompassing interactions between a non-solid tumor and CAR-T cells (effector and long-term memory). We account for several phenomena, such as tumor-induced immunosuppression, memory pool formation, and conversion of memory into effector CAR-T cells in the presence of new tumor cells. Individual donor and tumor specificities were considered as uncertainties in the model parameters. Our model is able to reproduce several CAR-T cell immunotherapy scenarios, with different CAR receptors and tumor targets reported in the literature. We found that therapy effectiveness mostly depends on some specific parameters such as the differentiation of effector to memory CAR-T cells, CAR-T cytotoxic capacity, tumor growth rate, and tumor-induced immunosuppression. In summary, our model can contribute to reduce and optimize the number of in vivo experiments with in silico tests to select specific scenarios that could be tested in experimental research. Such in silico laboratory was made available in a Shiny R-based platform called CARTmath. It is an open-source, easy to run simulator, available at github.com/tmglncc/CARTmath or directly on the webpage cartmath.lncc.br, containing this manuscript results as examples and documentation. The developed model, together with the CARTmath platform, provides potential use for assessing different CAR-T cell immunotherapy protocols and associated efficacy, becoming an accessory towards in silico trials.

Eddy-driven jets are of importance in the ocean and atmosphere, and to a first approximation are governed by Rossby wave dynamics. This study addresses the time-dependent flux of fluid and potential vorticity between such a jet and an adjacent eddy, with specific regard to determining zonal and meridional wavenumber dependence. The flux amplitude in wavenumber space is obtained, which is easily computable for a given jet geometry, speed and latitude, and which provides instant information on the wavenumbers of the Rossby waves which maximize the flux. This new tool enables the quick determination of which modes are most influential in imparting fluid exchange, which in the long term will homogenize the potential vorticity between the eddy and the jet. The results are validated by computing backward- and forward-time finite-time Lyapunov exponent fields, and also stable and unstable manifolds; the intermingling of these entities defines the region of chaotic transport between the eddy and the jet. The relationship of all of these to the time-varying transport flux between the eddy and the jet is carefully elucidated. The flux quantification presented here works for general time-dependence, whether or not lobes (intersection regions between stable and unstable manifolds) are present in the mixing region, and is therefore also easily computable for wave packets consisting of infinitely many wavenumbers.

Groundwater models serve as support tools to among others: assess water resources, evaluate management strategies, design remediation systems and optimize monitoring networks. Thus, the assimilation of information from observations into models is crucial to improve forecasts and reduce uncertainty of their results. As more information is collected routinely due to the use of automatic sensors, data loggers and real time transmission systems; groundwater modelers are becoming increasingly aware of the importance of using sophisticated tools to perform model calibration in combination with sensitivity and uncertainty analysis. Despite their usefulness, available approaches to perform this kind of analyses still present some challenges such as non-unique solution for the parameter estimation problem, high computational burden and a need of a deep understanding of the theoretical basis for the correct interpretation and use of their results, in particular the ones related to uncertainty analysis. We present a brief derivation of the main equations that serve as basis for this kind of analysis. We demonstrate how to use them to estimate parameters, assess the sensitivity and quantify the uncertainty of the model results using an example inspired by a real world setting. We analyze some of the main pitfalls that can occur when performing such kind of analyses and comment on practical approaches to overcome them. We also demonstrate that including groundwater flow estimations, although helpful in constraining the solution of the inverse problem as shown previously, may be difficult to apply in practice and, in some cases, may not provide enough information to significantly constrain the set of potential solutions.

We extended the usage of the expansion method based on Sine-Gordon equation to the two dimensional Fisher equation. The relation between the trigonometric and hyperbolic functions are derived from the Sine-Gordon equation de ned in two space dimension. The complex-valued traveling wave solutions to the two dimensional Fisher and Nagumo equations are set in forms a nite series of multiplications of powers of sech(.) and tanh(.) functions.

Complex and real valued exact solutions to some reaction-diffusion equations are suggested by using homogeneous balance and Sine-Gordon equation expansion method. The predicted solution of finite series of some hyperbolic functions are determined by using some relations between the hyperbolic functions and trigonometric functions based on Sine-Gordon equation and traveling wave transform. The Newel-Whitehead-Segel and Zeldovich equations are solved explicitly. Some real valued solutions are depicted for some particular choice of parameters.

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.

Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing, and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented as well.

The software industry has adopted component-based software development (CBSD) to rapidly build and deploy large and complex software systems with significant savings at minimal engineering effort, cost, and time. However, CBSD encounters issues on security trust, mainly with respect to dependability attributes. A system is considered dependable when it can produce the outputs for which it was designed with no adverse effect on its intended environment. Dependability consists of several attributes that imply availability, confidentiality, integrity, reliability, safety, and maintainability. Dependability attributes must be embedded in a CBSD model to develop dependable component software. Motivated by the importance of these attributes, this paper pursues two objectives: to design a model for developing a dependable system that mitigates the vulnerabilities of software components, and to evaluate the proposed model. The model proposed in this study is labelled as developing dependable component-based software (2DCBS). To develop this model, the CBSD architectural phases and processes must be framed and the six dependability attributes embedded according to the best practice method. The expert opinion approach was applied to evaluate 2DCBS framing. In addition, the 2DCBS model was applied to the development of an information communication technology (ICT) portal through an empirical study method. Vulnerability assessment tools (VATs) were employed to verify the dependability attributes of the developed ICT portal. Results show that the 2DCBS model can be adopted to develop web application systems and to mitigate the vulnerabilities of the developed systems. This study contributes to CBSD and facilitates the specification and evaluation of dependability attributes throughout model development. Furthermore, the reliability of the dependable model can increase confidence in the use of CBSD for industries.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Considering that cryptocurrencies are now present in practically every financial transaction because they are widely accepted as an alternate means of making payments and exchanging currencies, academics and economists have more opportunities to study cryptocurrency prices. Over the years, investors, traders and investment banks have found it difficult to predict the closing daily price of Ethereum due to its rapid price fluctuation. The daily closing price of cryptocurrency is essential to consider when trading or investing in Ethereum. This report focuses on carrying out a comparative study of the predictive capabilities of deep machine learning algorithms with a stacking ensemble modelling framework using daily historical observations of the price of Ethereum obtained from Coindesk, tweets extracted from Twitter ranging from the 1st of August 2022 to the 8th of August 2022 and other five covariates (closing price lag1, closing price lag2, noltrend, daytype and month) engineered from the closing price of Ethereum. Seven models are used to compute the forecasts for the daily closing price of Ethereum; these are the recurrent neural network, ensemble stacked recurrent neural network, gradient boosting machine, generalized linear model, distributed random forest, deep neural networks and stacked ensemble for gradient boosting machine, generalized linear model, distributed random forest and deep neural networks. The main evaluation metric used is the mean absolute error. According to MAE, RNN forecasts outperform the other model’s forecasts in this study, producing an MAE of 0.0309.

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

The development of plant-based meat analogues has become a significant challenge for the food industry in recent years due to the increasing demand for sustainable and healthier proteins in the context of a global protein transition. Plant-based meat analogues imitate the visual, textural, and chemical properties of traditional meat products and are required to closely resemble meat to appeal to consumers. In addition, consumers demand natural, clean-label, and nutritional and healthy products. To address these challenges, the food industry must develop highly healthy, nutritious, and E-number-free meat analogue products. Understanding the functionality of each ingredient and its role in the food matrix is crucial to being a key player in the innovation of the meat analogues market. This review provides updated information on the primary ingredients utilized for the development of plant-based burger meat alternatives and their functionality. The key components of meat analogue burgers are outlined, including plant proteins, binding agents, fats and oils, flavorings, colorings, preservatives, fortificants, and clean-label considerations.

The philosophy of testing statistical hypothesis is a natural consequence and functional extension of mathematical analysis of Probability. Along with the concept of recurrence when applied to random sequences and functions, it leads to the analysis of a priori and posterior which implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic, functional and dimensional considerations, which are found in the works of Laplace. Aspects of mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy, Information, and various functional dependencies are the main factors explained in the five properties that lead to implication of testing statistical hypothesis. Various interesting examples with modern scientific significance from genetics, astrophysics, and other areas give methodological access to answers of different problems and phenomena which are involved in the logic of testing statistical hypothesis.

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.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

Managing a portfolio whose value closely tracks an index by trading only in a subset of the index constituents involves an NP-hard optimisation problem. In the prior literature, it has been suggested to solve this problem using sequential Monte Carlo (SMC, a.k.a. particle filter) methods. However, this literature does not take transaction costs into account, although transaction costs are the primary motivation for attempting to replicate the index by trading in a subset, rather than the full set of index constituents. This paper extends the SMC approach to index tracking to allow for proportional transaction costs and implements this extended method on empirical data for a variety stock indices. In addition to providing a more practically useful tracking strategy by allowing for transaction costs, we find that including a penalty for transaction costs in the optimisation objective can actually lead to better tracking performance.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

High-precision conical threads are widely used in responsible joints in the drilling of oil and gas wells. Difficult underground drilling conditions due to the occurrence of significant mechanical loads and an aggressive environment in wells require the use of workable materials that are often difficult to machine. The huge need for such connections dictates the use of high-performance cutting tools, which means that high demands are placed on their effective geometric performance. The study describes the theoretical dependence of the profile precision of the tapered drill-string tool-joint threads of all standard sizes on the complex of a cutting tool geometric parameters and cutting tool setting accuracy. The experiments include an assessment of the geometric accuracy of the profile of the obtained NC23 thread connector, depending on the values of the installation angles and the declared tangential displacement of the standard threaded carbide insert.

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.

Biowaste generated in the process of Oxytree cultivation and logging represents a potential source of energy. Torrefaction (a.k.a. low-temperature pyrolysis) is one of the methods proposed for the valorization of woody biomass. Still, energy is required for the torrefaction process during which the raw biomass becomes biochar with fuel properties similar to lignite coal. In this work, models describing the influence of torrefaction temperature and residence time on the resulting fuel properties (mass and energy yields, energy densification ratio, organic matter and ash content, combustible parts, lower and higher heating values, CHONS content, H:C and O:C ratios) were proposed according to the Akaike criterion. The degree of the models’ parameters matching the raw data expressed as the determination coefficient (R²) ranged from 0.52 to 0.92. Each model parameter was statistically significant (p<0.05). Estimations of the value and quantity of the produced biochar from 1 Mg of biomass residues were made based on two models and a set of simple assumptions. The value of torrefied biochar (€123.4·Mg^-1) was estimated based on the price of commercially available coal fuel and its lower heating value (LHV) for biomass moisture content of 50%, torrefaction for 20 min at 200 °C. This research could be useful to inform techno-economic analyses and decision-making process pertaining to the valorization of pruned biomass residues.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

The manuscript studies the release kinetic of fluorescein from colloidal liquid crystals made up from monoglyceride and different non-ionic surfactants. The release experiments were carried out under sink conditions, and mathematical models were described as extrapolations from solutions of diffusion equation in different initial and boundary conditions imposed by pharmaceutical formulations. The diffusion equation was solved, using Laplace and Fourier transformed functions for the release kinetic from infinite reservoirs in a semi-infinite medium. Solutions represents a general square root law and can be applied for the release kinetic of fluorescein from monoglyceride colloidal liquid crystals. Akaike, Schwartz and Imbimbo criteria were used to establish the appropriate mathematical model and the hierarchy of performances of different models applied to the release experiments. The Fisher statistic test was applied to perform significance of differences among mathematical models. Differences evaluated by mathematical criteria demonstrated that small or no significant statistic differences were carried out between various applied models and colloidal formulations. Phenomenological models were preferred over to empirical and semi-empirical ones. The general square root model shows that the diffusion-controlled release of fluorescein is the mathematical models extrapolated for monoglyceride colloidal liquids, in the first part of the process.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S₅³ (∆_mn⁽²⁾). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibres. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualisation such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilise finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.

The abilities of quantitative description of noise are restricted due to its origin and only the statistical and spectral analysis methods can be applied while an exact time evolution cannot be defined or predicted. It emphasizes the challenges faced in many applications including communication systems where noise can play, on one hand, a vital role impacting signal-to-noise ratio but possessing, on the other hand, unique properties such as infinite entropy (infinite information capacity), exponentially decaying correlation function and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criteria, on which the main idea of the study is based on, is the Central Limit Theorem which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. The study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.) whose output signals are analyzed according to criteria that encompass the probability density functions of a chaotic signal itself and its envelope and phase, statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. The analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates Gaussian distribution. It allows generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

The conformity assessment of products or a measured value with the given standards is carried out based on the global risk of producers and consumers calculation. A product may conform to specifications but be falsely rejected as non-conforming. This is about the producer's risk. If a product doesn't meet the requirements but is falsely accepted as conforming, that poses a risk to the consumer. The conventional approach to risk assessment, which yields only a single numerical value for the global risk of producers and consumers, is naturally extended, and utilized for assessing risk in measurement models with linear regression. The outcomes of the two-dimensional extension, along a moderate scale, are the parabolas with an opening upwards. Risk surfaces were obtained through three-dimensional extension over the area limited by the moderate scale and guard band axes. Four models with different ranges of tolerance intervals were used to test this innovative method of risk assessment in linear regression. The corresponding standard measurement uncertainties are determined by applying a simplified measurement model with the use of comprehensive data on the measurement performance and by determining measurement uncertainty derived from consideration of the functional relationship obtained by linear regression analysis. Models that utilize information from linear regression analysis to determine measurement uncertainty are biased towards risks at the edges of the moderate scale. Testing the model's performances with metrics related to the confusion matrix, such as the F1 score, further substantiated this assertion. The diagnostic odds ratio has been proven to be extremely effective in identifying the curve along the guard band axis, along which the global risks of producers and consumers are at their lowest.

With the development of organizational biology and forced from the EU Cosmetic Regulation (EU/1223/2009) with the complete ban of animal testing for cosmetic purposes, 3D skin models have been widely developed due to their similar physiological structure and metabolic function to native human tissue. 3D skin models for in vitro cosmetic evaluation are still promising alternative methods for evaluating phototoxicity, corrosivity and irritation. These models have been used for early screening and later validation of toxicity and efficacy evaluation by many well-known cosmetic companies. 3D skin models have become an important tool in cosmetic evaluation research. This article reviews the development of 3D skin models and their application in cosmetic evaluation. An outlook on the current application and future technological development directions in the cosmetic field is also presented.

Keywords: Marine Coasts; Protected Areas; Defense and Conservation; Asbestos Cement Materials; Wastes; Contamination; Human Health Risk; Medical Geology.

The assortment of low-cost 3D printers for “in-practice” use, e.g., for clear aligner therapies, is ever increasing. To address concerns about the accuracy of orthodontic models produced on such printers when cost efficient modes of 3D printing are employed, this study examined the effect of print model body type and print angulation on accuracy. Six printing-configuration groups were included: 2 model types (solid or hollow shell) combined with 3 print angles (0°, 70°, or 90°) with 10 models/group; all models were printed with 100-µm layer thickness using a digital light processing-based 3-dimensional printer. Eleven selected structures and distances were measured on the printed models with a digital microscope and compared to the same measures on a digitized master model. The clinically-acceptability range was set at ±0.25 mm difference from the master model for single tooth measurements (intra-tooth) and ±0.5 mm for cross-arch measurements (inter-tooth). For individual measurements across all models, 98% fell within clinical acceptability. For mean measurements within each model group, only canine height for the shell-0° model had a mean difference (0.26 mm ± 0.03) outside the clinically acceptable range for intra-tooth measurements. Standard deviations for all intra-tooth measurements were within 0.07 mm. While none of the mean inter-tooth measurements exceeded the acceptability range, the standard deviations were larger (0.04 to 0.30 mm). Accuracy of orthodontic models for clear aligner therapies was not impacted beyond the clinically acceptable range when altering model body type and print angulation to improve efficiency of 3D printing. These findings suggest greater flexibility of the practitioner to alter print settings to address time and cost efficiency in various clinical scenarios and still maintain clinically acceptable model accuracy.

As Artificial Intelligence (AI) technology, particularly Machine Learning algorithms, becomes increasingly ubiquitous, our abilities to understand and interpret AI and machine learning algorithms are becoming increasingly desirable. Visualization has been used as a common tool to view and understand complex machine learning processes. In this paper, we will focus on developing a general framework for the visualization of machine learning models as a scalar valued multi-dimensional function to help users understand how the models behave over different viewing spaces. We first give a formal definition of the visualization problem. Interpolation-based morphing and subspace sampling techniques are applied to generate various renderings through projections and cross-sections of the model space as 3D surfaces or heatmap images. This method will be applied to two real-world datasets and applications: the diagnosis of Alzheimer's Disease (AD) using a human brain networks dataset and a real-world benchmark dataset for predicting home credit default risks. The visualizations show that different machine learning algorithms can behave quite differently under different conditions.

The massive amount of human biological, imaging and clinical data produced by multiple and diverse sources, necessitates integrative modeling approaches able to summarize all this information into answers to specific clinical questions. In this paper, we present a hypermodeling scheme able to combine models of diverse cancer aspects regardless of their underlying method or scale. Describing tissue-scale cancer cell proliferation, biomechanical tumor growth, nutrient transport, genomic-scale aberrant cancer cell metabolism, and cell signaling pathways that regulate the cellular response to therapy, the hypermodel integrates mutation, miRNA expression, imaging, and clinical data. The constituting hypomodels as well as their orchestration and links are described. Two specific cancer types, Wilms tumor (nephroblastoma) and non-small cell lung cancer, are addressed as proof of concept study cases. Personalized simulations over the actual anatomy of a patient have been carried out. The hypermodel has also applied to predict tumor control after radiotherapy and the relationship between tumor proliferative activity and response to neoadjuvant chemotherapy. Our innovative hypermodel holds promise as a digital twin based clinical decision support system and the core of future in silico trial platforms, although additional retrospective adaptation and validation is necessary.

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author’s earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

Driven by mounting environmental apprehensions stemming from the over dependence on fossil fuels in energy and transportation sectors, extensive exploration into alternative energy sources, particularly biomass, has stimulated profound research on harnessing the potential of computational and mathematical techniques. This comprehensive survey delves into optimal models and strategies, unveiling their pivotal role in the design of biomass gasification processes.of hydrogen through biomass gasification. In this study, we aim to provide a comprehensive overview of the computational and mathematical techniques employed in optimizing biomass gasification processes, with a specific focus on enhancing hydrogen yield. Through an extensive literature review, various models and strategies will be examined, including thermodynamic analysis, kinetic modeling, reactor design, and process optimization. By uncovering the power of these techniques, we aim to contribute to the advancement of sustainable and efficient biomass utilization for the hydrogen-based future economy.This paper aims to provide an updated and comprehensive coverage of the investigations conducted on the potential of producing hydrogen from biomass through gasification. To achieve this, we incorporate the latest works that have utilized numerical modeling, simulation, optimization techniques, process heat integration, and co-generation in their studies. By encompassing these aspects, we aim to offer a broader and more in-depth re-appraisal of the subject matter. This will ensure that readers gain a holistic understanding of the advances made in the field and the potential for sustainable hydrogen production of biomass gasification.Through a meticulous re-appraisal and analysis of each subject, we can identify their respective strengths and areas that require further research effort. By thoroughly examining numerical modeling, simulation, optimization techniques, process heat integration, and co-generation, we can assess their effectiveness and applicability in the context of biomass gasification for hydrogen production. This analysis shed light on the areas where these techniques excel, as well as pinpoint limitations or gaps in current understanding. By identifying these areas, we can highlight the need for further research and development, enabling us to make significant advancements in biomass gasification processes and pave the way for a sustainable and efficient hydrogen-based future economy..

Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly actual field of research, which has evolved over the last decades into a specialized part of mathematical physics. The applications of the mathematical models for rogue events is directly relevant to technology development for prediction of rogue ocean waves, and for signal processing in quantum units. In this survey, a comprehensive perspective of the most recent developments in methods for representing rogue waves is given, along with discussion of the devised and forms and solutions. The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and further to other models are discussed, and their properties highlighted. This survey shows that the most recent advancement in modeling rogue waves give models which can be used to establish methods for prediction of rogue waves at open seas, which is important for the safety and activity of marine vessels and installations. The study further puts emphasis on the difference between the methods, and how the resulting models form a basis for representing rogue waves in various forms, solitary or with a wave-background. This review has also a pedagogic component directed towards students and interested non-experts, and forms a complete survey of the most conventional and emerging methods published until recently

Predicting human trajectories poses a significant challenge due to the complex interplay of pedestrian behavior, which is influenced by environmental layout and interpersonal dynamics. This complexity is further compounded by variations in scene density. To address this, we introduce a novel dataset from the Festival of Lights in Lyon 2022, characterized by a wide range of densities (0.2-2.2 ped/m2). Our analysis demonstrates that density-based classification of data can significantly enhance the accuracy of predictive algorithms. We propose an innovative two-stage processing approach, surpassing current state-of-the-art methods in performance. Additionally, we utilize a collision-based error metric to better account for collisions in trajectory predictions. Our findings indicate that the effectiveness of this error metric is density-dependent, offering prediction insights. This study not only advances our understanding of human trajectory prediction in dense environments but also presents a methodological framework for integrating density considerations into predictive modeling, thereby improving algorithmic performance and collision avoidance.

The multiphase motors due to their reliability find new areas of application in the industry and transportation. Developing of any system with multiphase motors at first requires elaborate model of the system, define control mode and controllers. The model of control system for the six-phase drive is based on its conventional d-q mathematical model and indirect field-oriented control. Simulink model of six-phase drive with indirect field-oriented control and simulated with two types PID and PID fuzzy controllers. The simulation results, reflecting step response and provided speed reference law as well as load application at constant speed, are presented and analyzed. Fuzzy controller with 49 rules is considered and applied. Six-phase electric drive with field-oriented control at well-tuned PID controller has good step response specifications: settling time 0.13 s at starting without load, step response has no overshoot, small about 1 % short time decrease of speed at load of 5 Nm application. The system employing PID fuzzy controller shows slightly better results in response to torque application: the decrease in speed 1 % is eliminated in shorter time. Simulation results indicate the robustness of both systems with six-phase drive to disturbance and provide high quality transient specifications at determined reference speed.

The impacts of inflation on international finance are generally reflected in the decline of buying power, risks of investment and deposit loss from currency devaluation. For the purpose of optimized allocation and management of asset values, i.e., annual income or research grants, a framework of a three-level model for static financial management is presented to maximize banking interests, bonuses, and the remaining balance after spending necessary expenditures. Meanwhile, in retrospect to higher-level financial inflation, strategies of dynamic investment, i.e., posing regular tests of flipping coins, exploiting variations of the currency exchange rate, as well as applying the theory of broad money, are presented to increase the appreciation rate of net assets in and post the era of COVID-19. Quantitative evaluations in case studies verify the feasibility of improving the financial situation, indicating broader applications for budgeting and investing when US inflation rate is below 3.0%. Besides, combining approaches of static and dynamic strategies, the expected annual growth rate of individual zero-risk asset investment is predicted as within the range of 8.30~9.62% according to budgeted appreciation on net assets in 12 months, which is capable of overcoming negative impacts from higher level annual inflation, i.e., those as highest as 8.01% in the Year 2022.

Electricity price forecasting has become a crucial element for both private and public decision-making. This importance has been growing since the wave of deregulation and liberalization of energy sector worldwide late 1990s. Given these facts, this paper tries to come up with a precise and flexible forecasting model for the wholesale electricity price for the Italian power market on an hourly basis. We utilize artificial intelligence models such as neural networks and bagged regression trees that are rarely used to forecast electricity prices. After model calibration, our final model is bagged regression trees with exogenous variables. The selected model outperformed neural network and bagged regression with single price used in this paper, it also outperformed other statistical and non-statistical models used in other studies. We also confirm some theoretical specifications of the model. As a policy implication, this model might be used by energy traders, transmission system operators and energy regulators for an enhanced decision-making process.

In this study, we investigated the features of co-infection with SARS-CoV-2 and nonpathogenic strain LEV8 of coxsackievirus A7 or enterovirus A71 for Vero E6 cells and Syrian hamsters. The investigation of co-infection with SARS-СoV-2 and LEV-8 or EV-A71 in the cell model was shown that a competitive inhibitory effect for these viruses were especially significant against SARS-CoV-2. Pre-infection with enteroviruses in animals caused more than a 100-fold decrease in the levels of SARS-CoV-2 virus replication in the respiratory tracts and more rapid clearance of the lower respiratory tract from infectious SARS-CoV-2. Co-infection with SARS-CoV-2 and LEV-8 or EV-A71 also reduced the severity of clinical manifestations of the SARS-CoV-2 infection for animals. Additionally, the histological data illustrated that co-infection with nonpathogenic coxsackievirus decreased the level of pathological changes by SARS-CoV-2 in the lungs. Research into the chemokine/cytokine profile demonstrated that the studied enteroviruses efficiently triggered this part of antiviral immune response, which can be associated with significant inhibition of SARS-CoV-2 infection. These results demonstrate that there exists a strong viral interference between the studied nonpathogenic strain of coxsackievirus A7 or enteroviruses A71 and SARS-CoV-2 pathogenic for humans in vitro and in vivo.

Molnupiravir, a prodrug known for its broad antiviral activity, demonstrated efficacy in animal models of Covid-19, prompting clinical trials where initial results indicated a significant effect against the disease. However, subsequent clinical studies did not confirm these findings, leading to the rejection of molnupiravir for permanent market authorization in many countries. This report critically assessed 19 studies published in 17 reports that investigated the efficacy of molnupiravir in animal models of Covid-19 with the purpose of determining how well the design of these models informed human studies. We found that the administered doses of molnupiravir in most studies involving animal Covid-19 models were disproportionately higher than the dose rec-ommended for human use. Specifically, when adjusted for body surface area, half of the doses of molnupiravir used in the animal studies were more than twice as high as the human dose. Addi-tionally, the drug was frequently given prophylactically or shortly after SARS-CoV-2 inoculation in these models, in contrast to clinical trials where such timing is not consistently achieved. Furthermore, the recommended five-day treatment duration for humans was exceeded in several animal studies. Collectively, we suggest that these design elements in the reported animal studies contributed to a bias favoring molnupiravir, and thus inflated expectations for its efficacy against Covid-19. Addressing these elements may offer avenues to enhance the clinical efficacy of mol-nupiravir for treatment of Covid-19 that include dose increment, early treatment, and admin-istration by inhalation along with use of molnupiravir in antiviral combination therapy.

This work promotes new methods in Mathematical Modeling, consisting in the use of the methods of Non-standard Analysis in Topoi, having as its main purpose, the mathematical definitions of the pseudoparticles from the title, with arguments from Biology/Physiology (Mathematical Neuroscience), Physics (String Theory and Emergent Quantum Mechanics), and Cybernetics (Global Brain, including Natural and Artificial Intelligence). The connections between brain and mind will be scketched via the genetic/epigenetic interplay. The topoi model the intuitionistic logic (multi-valued) and have been used in Quantum Physics while Non-Standard Analysis in SET (= the Category of sets) has been applied in Mathematical Economics; topics from Theory of Categories were also used in the study of Consciousness; however, the combination topoi - non-standard analysis was never used until now in Applied Mathematics. Another important objective is to produce progress in this aria of Pure Mathematics also - the build of non-standard analysis in classes of topoi, already used in Physics. We propose the logic of non-standard extensions in topoi as a model of the human thinking (based on infons/receptons), these theories representing new top and very difficult results in Abstract Mathematics either.

This study considers an application of the first-order Grey Markov Model to foresee the values of Italian power generation in relation to the available energy sources. The model is used to fit data from the Italian energy system from 2000 to 2022. The integration of Markovian error introduces a random element to the model, which is able now to capture inherent uncertainties and misalignments between the Grey model predictions and the real data. This application provides valuable insights for strategic planning in the energy sector and future developments. The results show good accuracy of the predictions, which provides powerful information for the effective implementation of energy policies concerning the evolution of energy demand in the country. Despite advancements, Italy’s 2032 energy mix will still significantly rely on fossil fuels, emphasizing the need for sustained efforts beyond 2032 to enhance sustainability.

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.

In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.

The pursuit of Artificial Intelligence (AI) that emulates human cognitive processes is a cornerstone of ethical AI development, ensuring that emerging technologies can integrate seamlessly into societal frameworks requiring nuanced understanding and decision-making. Zero-Shot Instance Retrieval (ZSIR) stands at the forefront of this endeavour, potentially providing a robust platform for AI systems, particularly large visual language models, to demonstrate and refine cognition-aligned learning without the need for direct experience. In this paper, we critically evaluate current cognition alignment methodologies within traditional zero-shot learning paradigms, using visual attributes and word embedding generated by large AI models. We propose a unified similarity function that quantifies the cognitive alignment level, bridging the gap between AI processes and human-like understanding. Through extensive experimentation, our findings illustrate that this similarity function can effectively mirror the visual-semantic gap, steering the model towards enhanced performance in zero-shot instance retrieval. This work not only benchmarks the cognition alignment of AI, but also sets a new precedent for the development of visual language models attuned to the complexities of human cognition.}

The speed-density or flow-density relationship is a fundamental aspect of traffic flow theory. Single-regime models often face challenges in consistently fitting empirical data under diverse traffic conditions. This paper addresses the inaccuracies of single-regime models, attributing them not only to their functional forms but also to data dispersion and sample selection bias. To mitigate these issues, the data is segmented into day and night periods, leading to the creation of separate models for each. Calibration results, conducted on data from two freeways, Tehran-Karaj and Tehran-Qom, reveal distinct challenges, with the former exhibiting high dispersion and the latter showing low dispersion. Surprisingly, single-regime models demonstrate notable effectiveness when applied to distinct day and night data. Further analysis, categorizing data into day and night, results in reduced errors (20-60% improvement in R-Square), emphasizing the potential for enhanced accuracy by considering distinct regimes. Overall, the study underscores the significance of regime-specific considerations for accurate traffic flow modeling. Upon thorough evaluation, the study highlights the superiority of the neural network Multi-layer Perceptron (MLP) over traditional models. The research discusses the implications of incorporating day and night parameters into the models, emphasizing their potential for accuracy enhancement.

In this note we introduce the notion of polynions and discuss their mathematical relevance. We note that the well-known mathematical structures like quaternions, octonions and sedenions etc. are special cases of polynions.

This paper presents a study about the integration of Piezoelectric Energy Harvesting Systems (PE-EHS) in building envelopes for powering Fiber Bragg Grating (FBG) sensors, enabling efficient and low-consumption monitoring with the objective to leverage Structural Health Monitoring (SHM). The research includes preliminary tests conducted in a real environment to validate the PE-EHS when fully integrated into the façade, capturing mechanical vibrations generated mainly by wind loads. Based on these activities, the final configuration of PE-EHS is defined to provide a complete system for façade monitoring. This integrated system includes the Piezoelectric Generator (PEG), Supercapacitor (SC), Power Conditioner Circuit (PCC), Fibre Optic Sensing (FOS) Interrogator, and the IoT Gateway trans-mitting measurement data within an Internet of Things (IoT) monitoring platform. This configuration is tailored to address the challenges related to the structural integrity of building envelopes. Results demonstrate a potential for a stand-alone solution in the façade sector, but, raising issues for certain limitations, requiring further investigation. In particular, the study emphasizes constraints related to the energy production of PE-EHS for façade integration. It highlights the necessity to carefully consider these limitations within the broader context of their applicability, providing insights for the informed deployment of Piezoelectric Energy Harvesting technology in building envelope monitoring.

When dealing with limited sample sizes or missing values in time series data, achieving high accuracy in forecasting becomes challenging. This challenge is particularly common in wind energy forecasting, where many wind farms lack complete data. In this paper, we employ the widely-used ARIMA (Autoregressive Integrated Moving Average) model for time series forecasting. To address the difficulties posed by limited sample sizes and missing values, we adopt a unique approach by utilizing multiple ARIMA models for different datasets. A key distinction from other multiple models methods for time series forecasting lies in each model within our approach using its own dataset, making the fusion process more intricate. To overcome this, we incorporate neural networks and two techniques for model fusion: direct fusion with a learning mechanism and compensation for missing data through training. For each ARIMA model, we introduce a noise estimation method to circumvent the white noise assumptions inherent in ARIMA models. Finally, we apply these methods to wind energy prediction, and our experimental results showcase a significant enhancement in forecasting accuracy.

Previously, we described a 19-base pair double-stranded RNA with 3'-trinucleotide overhangs, acting as immunostimulatory RNA (isRNA). This molecule demonstrated notable antiproliferative effects on cancer cells, inhibited tumor growth, and elicited immunostimulatory and antiviral responses by inducing cytokine and interferon production. Within this study, we compared the efficiency of lung fibrosis development, initiated in mice by BLM or LPS using different schemes of induction. Then we compared the effect of isRNA used in a preventive or therapeutic regimen on the development of fibrosis in selected BLM- and LPS-induced mouse models and showed that isRNA can be used in pathological conditions accompanied by the development of inflammation and the risk of fibrosis formation, without adverse side effects. Prophylactic regimen of isRNA application is beneficial for prevention of the development of pulmonary fibrosis.

Count data analysis presents unique challenges due to its discrete nature, often exhibiting excessive zeros and overdispersion. To address these complexities, count models, such as Poisson regression and Negative Binomial regression, have been developed, enabling modeling and prediction of count-based phenomena. Additionally, it’s important to notice that zero inflation, a phenomenon commonly observed in count data, requires specialized techniques for robust analysis. This article provides an overview of count data and count models, explores zero inflation, introduces Likelihood Ratio Tests, and explains how the Vuong Test can be used as a model selection criteria. Furthermore, we created a Vuong Test implementation from scratch using the Python programming language. This implementation enhances the accessibility and applicability of the Vuong Test in real-world scenarios, providing a valuable contribution to the academic community, since Python didn’t have an implementation of this statistical test.

This paper is aimed at studying the temporal evolution of the surface displacements occurred over the past few years in the ocean-reclaimed platforms of the Shanghai megacity (China), which are mainly ascribable to consolidation processes of large dredger fills and alluvial deposits. With respect to previous analyses carried out over the same area, this work provides a joint multi-platform differential interferometry synthetic aperture radar (DInSAR) analysis, based on the application of the advanced Small BAseline Subset (SBAS) algorithm. This led us to retrieve long-term deformation time-series that are helpful for a better understanding of the on-going deformation phenomena. To this aim, we have exploited two sequences of SAR data collected by the ASAR/ENVISAT and by the COSMO-SkyMed (CSK) sensors, respectively, spanning the whole time period from 2007 to 2016. Unfortunately, the large time gap (of about three years) existing between the available ASAR/ENVISAT and CSK datasets gave rise to additional difficulties for their combination. Nevertheless, this problem has been faced by benefiting from the knowledge of a time-dependent model describing the temporal evolution of the expected deformations affecting the Shanghai ocean-reclaimed platforms.

A review of quantitative risk assessment (QRA) models of L. monocytogenes in produce was carried out, with the objective of appraising and contrasting the effectiveness of the control strategies placed along the food chains. Despite nine of the thirteen QRA models recovered focused on fresh or RTE leafy greens, none of them represented important factors or sources of contamination in the primary production, such as type of cultivation, water, fertilisers or irrigation method/practices. Cross-contamination at processing and during consumer’s handling was modelled using transfer rates, which were shown to moderately drive the final risk of listeriosis; highlighting therefore the importance of accurately representing the transfer coefficient parameters. Many QRA models coincided in the fact that temperature fluctuations at retail or temperature abuse at home were key factors contributing to increasing the risk of listeriosis. In addition to a primary module that could help assess current on-farm practices and potential control measures, future QRA models for minimally-processed produce should also contain a refined sanitisation module able to estimate the effectiveness of various sanitisers as a function of type, concentration and exposure time. Finally, L. monocytogenes growth in the products down the supply chain should be estimated by using realistic time-temperature trajectories, and validated microbial kinetic parameters, both of them currently available in the literature.

The identification of fetal cells in the blood and tissues of healthy mothers raised questions about the potential alloreactive origins of various diseases, such as autoimmunity, diabetes, arteriosclerosis, and cancer. However, the extent to which alloreactivity contributes to these diseases remains unverified. This study presents a basic mathematical disease model based on the genes’ origin and immunological interactions. This model, grounded in set theory, classifies these immunological interactions based on their intrinsic, extrinsic, and allogeneic nature. Therefore, this model offers an unexpected common theoretical foundation for understanding alloreactivity, genetic diseases, and infections. Furthermore, this model provides a valuable framework for scrutinizing the role of alloreactivity in health and disease.

The generation and maintenance of membrane potential is considered a fundamental element of the cellular machinery. They are based on elements of physics and chemistry. Mathematics is used to validate the equations and evaluate the results. However, this computation process can lead to a misunderstanding of the phenomena involved or to the masking of crucial events. It is even possible that the calculation no longer corresponds to the hypothesis considered. Membrane theory is no exception to these trivial considerations, which are essential for normal theory validation.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

Natural language Processing (NLP) has significantly transformed in the last decade, especially in the field of Language Modeling. Large Language Models (LLMs) have achieved SOTA performances on Natural Language Understanding (NLU) and Natural Language Generation (NLG) tasks by learning language representation in self-supervised ways. This paper provides a comprehensive survey to capture the progression of advances in Language Models. In this paper, we examine the different aspects of Language Models, which started with a few million parameters but have reached the size of a trillion in a very short time. We also look at how these LLMs transitioned from task-specific to task-independent to task-and-language-independent architectures. This paper extensively discusses different pre-training objectives, benchmarks, and transfer learning methods used in LLMs. It also examines different fine-tuning and In-Context learning techniques used in downstream tasks. It also explores how LLMs can perform well across many domains and datasets if sufficiently trained on a large and diverse dataset. Next, it discusses how, over time, the availability of cheap computational power and large datasets have improved LLM’s capabilities and raised new challenges. As part of our study, we also inspect LLMs from the lens of scalability to see how their performance is affected by the model’s depth, width, and data size. Lastly, we provide an empirical comparison of existing trends and techniques and a comprehensive analysis of where the field of LLM currently stand.

Responding to changing value creation processes in the sheet metal working sec-tor, where the complexity and interchangeability of products challenge traditional dif-ferentiation strategies, this empirical analysis explores integrating service-oriented and data-driven business models as new paths to ensure competitiveness, especially for small and medium-sized enterprises (SMEs). This study aims to capture the current state and challenges associated with the implementation of these business models in this sector. The research was conducted through semi-structured interviews with SMEs in the industry. The findings indicate that service-oriented and data-driven business models are not yet widely adopted and that manufacturing companies re-quire support in their implementation. Fields of action were identified for the industry. These are "Creating awareness and understanding", "Recognizing added value", "In-creasing company maturity" and "Understanding the change process". Cooperation between science and industry is essential in tackling these fields of action to ensure the successful integration of such business models in manufacturing companies. This pa-per identifies challenges in the fields of action that companies must address through a structured approach promoting awareness, recognizing value, improving organiza-tional maturity, and understanding the change process to successfully implement ser-vice-oriented and data-driven business models.

Differential equation models to understand interaction between plant and nutrient solution are presented. The root cells selectively emit H+ ions with active transport consuming ATPs to establish electrical gradient along the cell membrane. It establishes electrical field with Nernst potential to make positively charged ions outside the cell membrane flow into the root cell. Anion influx is also modulated by H+ ion concentration because plant root cell absorbs negatively charged particles with symport. If an anion collides with H+ cell to make net charge as neutral, at symport channel, it can flow through. In this paper, mathematical models for cation and anion absorption are introduced. Cation absorption model was induced from Ohm's law combined with Goldman's equation. Anion absorption model is similar to chemical reaction rate model. Both models have physiological terms influenced by gene expression pattern, species or phenotypes. Cation model also includes terms for ion's kinetic and electrical properties, growth of plant and interaction between the root and the surroundings. Simulation for 20 different sets of coefficients showed that the physiology-related coefficient has important role on nutrition absorption tendencies of plants.

Herein, we examined the effects of weather parameters and individual clinicodemographic risk factors on hemorrhagic stroke (HS) incidence, severity on admission, and disability at discharge in a harsh desert climate. In a retrospective design we studied patients admitted to a stroke unit in Arab Emirates in 2016-2019. With a distributed lag nonlinear model we explored immediate and delayed effects of weather on stroke incidence. Supervised machine learning was used to build models predictive of scores in NIHSS and mRS scales. We assessed model performance by calculating ROC AUC, F1 scores, specificity, and sensitivity. HS risk increased after a significant change in any weather parameter. The risk was reduced below baseline after 1-week adjustment to environmental changes. Climate input from the previous 3 days yielded reliable classification models. Humidex was a better predictor of severity than air temperature, whereas body mass index, age, and time of day at stroke onset were the strongest clinical predictors. Weather parameters before admission were stronger predictors of disease severity than individual clinical factors. We addressed limitations of previous studies by analyzing a full set of climate parameters: ambient temperature, relative humidity, humidex, atmospheric pressure, and wind speed. Predictive models may help to optimize patient management and develop preventative strategies.

Crash prediction of the sharp horizontal curve segment (SHCS) of a freeway is an important tool in analyzing safety of SHCSs and in building a crash prediction model (CPM). The design and crash report data of 88 SHCSs from different institutions were surveyed and three negative binomial (NB) regression models and three generalized negative binomial (GNB) regression models were built to prove that the interactive influence of explanatory variables plays an important role in fitting goodness. The study demonstrates the effective use of the GNB model in analyzing the interactive influence of explanatory variables and in predicting freeway basic segments. Traffic volume, highway horizontal radius, and curve length have been formulated as explanatory variables. Subsequently, we performed statistical analysis to determine the model parameters and conducted sensitivity analysis. Among the six models, the result of model 6, which considered interactive influence, is much better than those of the other models by fitting rules. We also compared the actual results from crashes of 88 SHCSs with those predicted by models 1, 3, and 6. Results demonstrate that model 6 is much more reasonable than models 1 and 3.

Effective agricultural management in maize production operations starts with the early quantification of seedlings. Accurately determining plant presence allows growers to optimize planting density, allocate resources, and detect potential growth issues early on. This study presents an in-depth analysis of multiple object detection models used by drones to count maize seedlings, while concurrently investigating the influence of planting density, flight altitude, and plant growth stage. The findings of this study demonstrate that one-stage models are able to more accurately detect maize seedlings than two-stage models. In particular, YOLOv8n exhibits outstanding performance, achieving an F1-score of over 0.92 under various density conditions and maintaining a stable performance, especially under densities below 105,000 plants/ha. Additionally, planting density and growth stage were observed to significantly affect detection accuracy, with performance declining as density and growth stage increased. Image resolution and detection were impacted by flight altitude, with lower flights producing higher-quality results. Ultimately, YOLOv8n displays optimal performance under various conditions, providing crucial data to support intelligent decision-making. This research offers valuable insights into the application of object detection technology and provides a basis for the future development of precision agriculture.

Although researchers have proposed various indentation size effect (ISE) models, these models often involve different form and number of parameters that can make our wonder which is the best in existed ISE models. Three types of ISE test data, namely, normal ISE, reverse ISE and transition of normal to reverse ISE, are used to evaluate the sixteen ISE models. The comparatively study indicates that H-J, N-G-Fs, N-G-H, N-G-A and N-G-Qs models can accurately predict the normal ISE. The reason for this is that the friction stress that is not related to dislocation activities or the indentation size effect of plastic zone has been introduced into these models. Therefore, these two factors should be considered in future ISE models. The sixteen ISE models are originally proposed to describe the normal ISE of different materials. However, to our surprise, some of these models are able to capture the reverse ISE and the transition of normal to reverse ISE of different materials. The determination coefficients (DC) of the sixteen ISE models are also determined for different materials. For reverse ISE, the highest DC value for NiCSi, TC4 and PED Ni are given by the EXP, N-G-Fs and N-G-A models, respectively. For the transition of normal to reverse ISE, the N-G-YC, N-G-Fs, and N-G-H models produce the maximum DC for ZrO2, Cu and Y2O3-ZrO2, respectively. Moreover, the mean DC of the N-G-Fs model is the maximum among the sixteen ISE models, followed by the N-G-H model, but they cannot accurately predict the reverse ISE. Therefore, the N-G-Fs and N-G-H models should be further modified to accurately predict the reverse ISE.

This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.

The advent of deep learning (DL) has revolutionized medical imaging, offering unprecedented avenues for accurate disease classification and diagnosis. DL models have shown remarkable promise for classifying brain tumor from Magnetic Resonance Imaging (MRI) scans. However, despite their impressive performance, the opaque nature of DL models poses challenges in understanding their decision-making processes, particularly crucial in medical contexts where interpretability is essential. This paper explores the intersection of medical image analysis and DL interpretability, aiming to elucidate the decision-making rationale of DL models in brain tumor classification. Leveraging state-of-the-art DL frameworks with transfer learning, we conduct a comprehensive evaluation encompassing both classification accuracy and interpretability. Using state-of-the-art DL frameworks with transfer learning, we conduct a thorough evaluation covering both classification accuracy and interpretability. We employ adaptive path-based techniques to understand the underlying decision-making mechanisms of these models. Grad-CAM and Grad-CAM++ highlight critical image regions where the tumors are located.

A hallmark of Alzheimer’s disease (AD) are the proteinaceous aggregates formed by the amyloid-beta peptide (Aβ) that is deposited inside the brain as amyloid plaques. The accumulation of aggregated Aβ may initiate or enhance pathologic processes in AD. According to the amyloid hypothesis any agent that has the capability to inhibit Aβ aggregation and/or destroy amyloid plaques represents a potential disease modifying drug. In 2023, a humanized IgG1 monoclonal antibody (lecanemab) against the Aβ soluble protofibrils was approved by US FDA for AD therapy thus providing compelling support to the amyloid hypothesis. To acquire a deeper insight on the in vivo Aβ aggregation, various animal models, including aged herbivores and carnivores, non-human primates, transgenic rodents, fish and worms are widely exploited. This review is based on the recent data obtained using transgenic animal AD models and presents experimental verification of the critical role in Aβ aggregation seeding of the interactions between zinc ions, Aβ with the isomerized Asp7 (isoD7- Aβ) and the α4β2 nicotinic acetylcholine receptor.

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.

Creative thinking is increasingly recognised as an essential ability that should be part of school curricula. Given the move towards online learning and assessment, we investigate whether mathematical creativity can be assessed at-scale in the Numbers game, an arithmetic game in Math Garden, a popular online math practice platform. In the Numbers game, a generalisation of the 24 Game, children are asked to figure out how to compute a target number using basic arithmetic operations and a given set of numbers. We argue that creative thinking is required when the search space is complex, and propose that the base-pattern, i.e., the sequence of the operations needed to solve a Numbers game item, indicates search space complexity. We then demonstrate that items with disordered base-patterns are more likely to require mathematical creativity to figure out. Specifically, our analysis shows that for items with only one solution sequence, those with disordered base-patterns are more difficult and take longer to solve compared to items with ordered base-patterns. For items where multiple solution sequences are possible, nine times out of ten children choose ordered over disordered base-patterns. We conclude that the Numbers game has potential for assessing mathematical creativity at-scale.

This paper emphasises on the analogous modelling of hardwood (Acacia) pyrolysis. The effect of physical characteristics of hardwood chips on the pyrolysis is examined through the conservation of solid mass fraction of biomass. The chip size of G30 and G50 are used in the pyrolysis reactor. In the analogous situation, the fixed bed is assumed to be a wooden slab with a porosity equivalent to the voidage of bed. The bulk density, the length of the bed and the porosity are some of the physical attributes of a fixed bed used to determine the variation of solid mass of the hardwood across the fixed bed. The four-temperature sensors separated from each other by 80 mm are used to determine the temperature along the length of the pyrolysis unit. The heating element of 2 kWe is used to initiate the pyrolysis of biomass. The experiments are conducted in three different stages. The ONORM standard chips, G30 and G50, and the combination of them are separately pyrolysis to determine the validity of a model for different sizes of chips. The proposed model is also used to establish the relationship between the kinetics of pyrolysis and decomposition of the hardwood.

Nuclear Magnetic Resonance (NMR) and its various forms are extensively utilized in both research and clinical settings to analyse molecules. NMR data pre-processing, while essential to NMR data analysis, can be uniquely complex. Despite the availability of software tools, understanding these processes can be challenging, complicating the selection of appropriate pre-processing steps. In this review, we elucidate pre-processing steps in the time domain from a mathematical and statistical perspective, explaining direct current offset removal, eddy current correction, shift and linear prediction, weighting, zero filling, and domain transformation using plain language and fundamental mathematical formulas. Our objective is to clarify these processes in simple terms and provide general guidance.

Magnetic Resonance Imaging (MRI) is widely used in clinics and research due to its accurate disease identification and non-invasive nature. MRI is based on Nuclear Magnetic Resonance (NMR), which is also extensively employed in various fields. NMR and its modern versions involve intricate pre-processing steps before data analysis. These steps are initially processed in the time domain and subsequently in the frequency domain. While our previous review focused on time domain pre-processing (https://www.preprints.org/manuscript/202310.2032/v1), this review delves into the mathematical and statistical aspects of frequency domain pre-processing. We discuss essential pre-processing steps like phase error correction, baseline correction, solvent filtering, calibration and alignment, reference deconvolution, binning/bucketing and peak picking, peak fitting/deconvolution and compound identification, integration and quantification, normalization and transformation. Furthermore, we offer practical recommendations for each step.

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.

A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data in China and Austria. Prediction of the total number of the COVID-19 cases is discussed and examples are presented using the measured data in Austria, France and Poland.

The managers’ strategic behavior of commercial real estate in a competitive environment is discussed. The means of this research are methods of mathematical and experimental game theory. Illustrates an example of a decision-theoretic game problem with two players engaged in the management of competing shopping centers. The strategies of these players are determined by the costs of the development. Since the number of visitors is constantly and changing the quality of shopping centers, managers actually pull visitors from each other, the game-theoretical formulation of the problem of management of shopping centers corresponds to the zero-sum game. The model example shows that with the help of mathematical modeling it is possible to determine the theoretical expected behavior of agents. The model of the software module created specifically for experimental research is described. The experiments are designed to compare the theoretically predicted behavior with the real actions of people. The novelty is that at significant costs of the Manager for the development and promotion of shopping and entertainment centers, the strategies of managers are resistant to each other's actions, in contrast to changes in the external environment is shown.

Background: Health insurance (HI) run by government is providing health care service to large population. Due to poor accountability, participation and sustainability, cooperative health insurance is becoming more popular and effective in low and middle income and some high-income countries too. In Nepal, there are public and cooperative HI is in practice. The aim of this study is to compare the effectiveness of public (government) and cooperative HI in relation to benefit packages, population coverage, inclusiveness, health care utilization, and promptness for treatment in these two health insurance models in Nepal. Method: This is an institution based concurrent mixed study consists of qualitative and quantitative variables from public and cooperative groups. We included all public HI operated by government hospitals and cooperatives groups those purchased hospital service in contract. Two separate study tools were applied to access the effectiveness of insurance models. The key questions were asked for the representatives of government and private health insurance. The numeric information consisted of in quantitative data and subjective response was included in qualitative approach. Descriptive statistics and Mean Whitney U test was applied in numeric data and qualitative information were analyzed by inductive approach Results: The study revealed that new enrolment was not increased, health care utilization rate was increased and the benefit package was almost same in both groups. The overall inclusiveness was higher for the government HI, but enrolment from the religious minority, proportion of negotiated amount during treatment were significantly higher (p<0.05). During illness, the response time to reach hospital was significantly faster in cooperative health insurance than government health insurance. Qualitative findings showed that level of participation, accountability, transparency and recording system was better in cooperative health insurance than public. Conclusion: Cooperative HI could be more sustainable and accountable to the community for all; low, middle and high-income countries.

This paper studies the duration patterns of unemployment spells for immigrants and the determinants of unemployment’s completion into one of a number of studied labour market states in Finland. We estimate a duration model for unemployment with competing risks of its terminating into employment, labour market training or economic inactivity. Taking into account the wide period of observation and opportunities to analyse processes of labour market integration during various periods of economic development in Finland, in combination with the individualistic character of the labour careers of immigrants, this research is beneficial owing to the many various findings concerning labour market integration of immigrants. The approach undertaken in this research has a dualistic “descriptive-dynamic” character under which integration is understood as a never-ending process, which is conditioned by a time period of long-term existence and a context of solitary action. We find that transitions out of unemployment spells have a cyclical character; after every new “cycle” in unemployment, the probability of terminating unemployment decreases further. We also find that ascriptive factors make sense in the process of job-placement of immigrants from unemployment. Therefore, the gender, education and age of immigrants, as well as the effect of the period in which first unemployment occurred, potentially predict transitions out of unemployment and further labour market integration of immigrants.

Knowledge is a property that measures the degree of awareness of an agent about a target in an environment. The goal in conventional intelligent and cognitive agent development is to build agents that can be trained to gain knowledge about a target. The definition and operations of this knowledge associated to the agent is not clear, whereas these are required for developing a reliable, scalable and flexible agent. In this paper, we provide a concise theoretical framework for the description and quantification of the knowledge property needed for an efficient design of cognitive and rational intelligent agents. We relate the quantification scheme to the epistemological description of knowledge and present many illustrative examples on the usefulness of the quantification scheme.

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.

The method propose in this study for stock market multi-objective mathematical model was linear programming using simplex algorithms to optimize the portfolio in the Nigerian Stock Market. The study selected five banks from the list of operators in the market and data were gathered from the banks to have individual market performances over a period of 5years. The data collected contains: Geometric Mean of Monthly Capital Gain Yields and Annual Capital Gain Yields from which Dividend Yields (%) were deducted to arrive Actual rate of return for the banks and the expected rate of return. Furthermore, the risk of semi-absolute deviation below the expected return is reduced. The data was analysed using Python programming because of some clauses in the data gathered. At first, the data assumes integer (-or +) and random in nature. As such, Python programming is one of the software suitable for such solution since the barrier for additivity is broken. Based on the analysis, the study therefore conclude that the potential investor(s) should invest in 13 units of investment x(GTbank Plc), 3 units of First Bank Plc`s Investment (y), 450 units of Zenith bank`s investment (z), and 8 units of Wema bank`s investment (m), and no units of investment of (n) Access bank. These investment quantities will result in the Optimal profit of p= 12797.902 billion naira.

Cell migration is essential for physiological, pathological and biomedical processes such as, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion and inflammation. In light of this, quantifying mechanical properties during the process of cell migration is of great interest in experimental sciences, yet few theoretical approaches in this direction have been studied. In this work, we propose a theoretical and computational approach based on the optimal control of geometric partial differential equations to estimate cell membrane forces associated with cell polarisation during migration. Specifically, cell membrane forces are inferred or estimated by fitting a mathematical model to a sequence of images, allowing us to capture dynamics of the cell migration. Our approach offers a robust and potentially accurate framework to compute geometric mechanical membrane forces associated with cell polarisation during migration and also yields geometric information of independent interest, we illustrate one such example that involves quantifying cell proliferation levels which are associated with cell division, cell fusion or cell death.

So called Higuchi’s method of fractal dimension estimation is widely used and the term Higuchi’s fractal dimension even occurs in many publications. This paper deals with this method from mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. Definition of Higuchi’s dimension was comparated with mathematical definition of the distance and dimension. It is showed, that the definition of the Higuchi’s dimension does not satisfy axioms of distance and dimension. So called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

Identifying the correct dosage and time are key factors to successful implementation of anthelmintic. Comparing differential evolution of infection between anthelmintic treated animals against untreated ones, we present a mathematical model that first calibrates data collected and analyzed over an extended period of 10 years (2011-2019), and then predicts the dynamical evolution of gastrointestinal parasites in livestock, focusing specifically on Stronglye \& Coccidia oocysts, the two prime negative contributors to cattle health, measured using the standard Eggs-Per-Gram (EPG) index. The model incorporates information about all three critical regimes of infection - low infection regime ($< 50$ EPG), medium infection regime ($50-100$ EPG) and high infection regime ($>100$ EPG), including fatally large doses of infection ($> 500$), and probabilistically estimates the variation in animal weight due to infection propagation. A key success of our model is its ability to accurately predict the appropriate anthelmintic treatment times for cattle from a numerical solution of the model presented. The generic model can be applied to other agroclimatic conditions and can serve as a major diagnostic tool for anthelmintic strategizing.