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We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a "flattening effect" on the combustion front. [ABSTRACT FROM AUTHOR]

In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results. [ABSTRACT FROM AUTHOR]

The quest for cost-effective and thermal efficient structural materials onto beating the high cost of construction is gaining more attention among researchers. This study focused on the blending of cement and sand with waste paper pulp into cost-effective structural materials. The composites were prepared in four mix groups with each containing a fixed amount of sand at 5, 10, 15, and 20 wt.% (by weight of pulp). Cement was varied at 10, 20, 30, and 40 wt.% in each group, and curing was done for 28 days. Properties evaluated are compressive, bending, and splitting strengths. It was observed that increasing cement and sand contents enhanced strengths; howbeit, the blend of 30 wt.% cement/15 wt.% sand resulted in a reduction in bending strength even as 30 wt.% cement/20 wt.% sand engendered a decrease in bending and splitting strength. The microstructural features showed that inherent fibers of the pulp were well bonded with hydration products and sand content yielding good performance in the composites. The optimization procedure carried out depicted a combination of 35.27% cement and 20% sand as the optimum composition. Experimental outcomes were modelled for the purpose of prediction of responses. The models were confirmed statistically fit showing how varying cement content affected strength responses at fixed sand proportion. ANOVA affirmed the significant contribution of cement and sand on the strength responses. Compliance reliability was observed to be dependent on the interactive pattern between cement and sand. Going by the standard prescription for the strength properties, cement and sand content of 35.27 and sand 20 wt.% satisfied all strength requirements for low-cost construction having a compliance reliability of 1.31. [ABSTRACT FROM AUTHOR]

Industrial progress in papermaking in the early nineteenth century led to the technologies that resulted in more acidic papers, which was caused mainly by the exploitation of alum (KAl(SO4)2) and rosin as sizing agents. The papers prepared by such technologies have degraded more quickly. From the 1930s various deacidification and preservation processes with basic agents have been developed. The most widespread deacidification process is with the aerosol (spray system) consisting of microscale particles MgO and perfluoroheptane (PFH) as a carrier (the so-called Bookkeeper process). The shortcomings of this process are the low dissolution of solid MgO particles and the transport to the interior of acidic paper. We have developed a theoretical two-level model of the Bookkeeper process suitable for prediction of deacidification extent. The model involves both the dissolution/reaction of the solid particles and transport of solvated ions and solid particles inside the bulk of paper. The developed model coincides with the results of the performed deacidification experiment. The model is also in good agreement with the Lucas–Washburn equation, which is usually used for the description of the penetration of a deacidifying agent into the paper. [ABSTRACT FROM AUTHOR]

The assessment of scientific articles regarding their relevance to a research portfolio is becoming increasingly important. The reason is that scientific works have been growing quantitative and qualitatively. Taking this scenario into account, Methodi Ordinatio was proposed, and its major contribution was the 7th phase of the methodology, the InOrdinatio. It is an equation based on the main criteria for selecting a paper related to a theme: year of publication, number of citation and the impact factor (or journal metrics). However, finding the value of these three factors might not be an easy and quick task. Therefore, in order to improve the use of Methodi Ordinatio, two other tools were developed: FInder and RankIn. Thus, the first purpose of this paper is to present these two new tools. Additionally, considering that the impact factor has been a matter of disputes in the academia, the paper also proposes the use of one single indicator for the impact factor in the equation. To achieve this second purpose, a robust mathematical model was elaborated taking into consideration the other journal metrics in order to estimate the alternative impact factor to be used in InOrdinatio in case one or more papers are not indexed to any metrics. After testing with 48 statistical models and tools, the results show that this indicator is robust and trustworthy to be used. Finally, as the third as last purpose, this paper also proposes an alternative version to calculate the InOrdinatio, which can be flexible regarding the weight of its three criteria used in the equation. [ABSTRACT FROM AUTHOR]

Despite artificial intelligence (AI) technology progresses at unprecedented rate, our ability to translate these advancements into clinical value and adoption at the bedside remains comparatively limited. This paper reviews the current use of implementation outcomes in randomized controlled trials evaluating AI-based clinical decision support and found limited adoption. To advance trust and clinical adoption of AI, there is a need to bridge the gap between traditional quantitative metrics and implementation outcomes to better grasp the reasons behind the success or failure of AI systems and improve their translation into clinical value. [ABSTRACT FROM AUTHOR]

Purpose: The mounted stationary sensor on the ring casing has become a widely accepted way to monitor the planetary gear condition and one challenging aspect of this method is the modulation effect caused by the moving planet gears. It is valuable to study the modulation effect caused by the moving planet gears. Method: Different window functions have been proposed to model this modulation phenomenon and there are several drawbacks: the selection of the window function parameters is often arbitrary and subjective instead of basing on the planetary gear physical parameter; the current window function is hard to reflect the impact from the ring gear boundary conditions. Therefore, this paper simulated this modulation phenomenon as moving load dynamic problem to overcome these drawbacks, where the ring casing has been modelled as an axisymmetric flexible structure and the internal meshing forces have been modelled as spatially varying moving loads. Based on the improved hamming window function, this paper related the window function parameters with the planetary gear physical properties and operation conditions and then, quantified the modulation effect with the consideration of moving load speed as well as the ring gear boundary condition. Results: For the planetary gear carrier arm rotation speed, the result suggested that the moving speed mainly affect the parameter β and the corresponding value showed a nonlinear decreasing trend when the moving speed increased. For the ring gear rim thickness, similarly, parameter β increased significantly with the increase of the rim value. For the radial support stiffness, parameter β has also been affected most and it shows a decreasing trend when the support stiffness increased. For the sensor location, both parameter α and β shows a periodical change around the ring casing. Conclusion: The results suggested that both parameters have been impacted by the rotation speed and boundary conditions, among which parameter β has been impacted most. [ABSTRACT FROM AUTHOR]

In the traditional tobacco drying process, there is often a problem of uneven drying, which is closely related to drying conditions such as air velocity and temperature. To better understand the drying characteristics of tobacco, its drying kinetic performance were experimentally studied and predicted in this paper. In the drying experiment, the range of air temperature and velocity is 20–60℃ and 0.95–4.93 m/s, respectively. The results show that the effective diffusion coefficient increases with the increase of air temperature and decreases with the increase of air velocity. The effective moisture diffusivity( D eff ) ranges from 2.077 × 10–7 to 9.136 × 10–7 m2/s. Additionally, the activation energy (Ea) is between 14.292 and 21.032 kJ/mol according to Arrhenius law. Among the six commonly used empirical correlations, the logarithmic model has higher prediction accuracy, but it has a prediction deviation of more than 20% in the later stage of drying. Based on the logarithmic model and the two models, a new prediction model of tobacco drying characteristics was proposed with a maximum relative deviation error of less than 1%. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the difference between the deterministic and stochastic models of nonlocal diffusion. We use a nonlocal reaction-diffusion equation and a multi-dimensional jump Markov process to analyze these mathematical models. First, we demonstrate that the difference converges to 0 in probability with a supremum norm for a sizeable network. Next, we consider the rescaled difference and show that it converges to a stochastic process in distribution on the Skorokhod space. [ABSTRACT FROM AUTHOR]

In recent years, path dependence has gained increasing scientific attention in many disciplines, leading to various new concepts and notations, such as path creation or path plasticity. However, if mathematical arguments are used, they are based on the early works by Brian W. Arthur and Paul A. David, usually referring to the mathematical concept of ergodicity. We extend their mathematical framework and develop a graphical representation of systems that allows for a metaphorical discussion of system behaviors beyond the original cases, especially in evolving systems, and the inclusion of the recently developed concepts within path dependence. Visualizations are used to explain the definition and characteristics of seven types of path dependence: lock-in, path-breaking, path-furrowing, path plasticity, path formation, path creation, and path selection. Although these visualizations are explained verbally and can be understood without a mathematical expertise, a mathematical model is used to generate them. The deduction of the metaphorical concept from a mathematical model guarantees the completeness of the identified processes and the rigor in their categorization as well as the identification of respective characteristics for their distinction. However, the aim of the paper is to provide an illustrative concept that allows researchers to classify and structure the various path-dependent processes they observe in their application. While five of the identified processes are in line with concepts from the literature and are defined accordingly, we also detect a sixth process that is new to the literature so far: path-furrowing. Moreover, slightly deviating from the literature, we define path selection as the possibility to choose a path intentionally, thereby focusing on the mindful choice of options. [ABSTRACT FROM AUTHOR]

The electronic, magnetic, mechanical, and other properties of crystalline substances are determined by their structure, i.e., by the periodicity and symmetry of the lattice; therefore, the determination of the structure is an important stage in the study of the characteristics of such materials. This paper considers a number of metals having a crystal lattice of the hexagonal closely packed (HCP) structural type: beryllium, cerium, cobalt, dysprosium, erbium, gadolinium, hafnium, holmium, lanthanum, lutetium, magnesium, neodymium, osmium, praseodymium, rhenium, ruthenium, scandium, terbium, titanium, thallium, thulium, yttrium, and zirconium. The application of the annealing simulation algorithm to find the metric parameters of the materials under consideration is shown using the close packing model, which is widely used in crystallographic calculations. The in-house software implementation of the simulated annealing algorithm presented in this paper allows us to determine the coordinates of the atoms included in the unit cell of the crystal lattice, as well as calculate the lattice constants and the packing density of atoms in the crystal cell of the HCP structural type using the given chemical formula and spatial symmetry group. These structural characteristics can be used as the input parameters in modeling the electronic, magnetic, and other properties of the considered materials. This paper compares the values of the crystal lattice constants obtained as a result of the numerical simulation with the published data. [ABSTRACT FROM AUTHOR]

Francine Shapiro, the founder of Eye Movement Desensitization and Reprocessing (EMDR), reported that the therapeutic use of eye movement patterns was discovered by chance while walking in a park. An alternative accounting for the origins of EMDR comes from research that demonstrates individuals are unable to perceive their own eye movements and from historical sources that document Shapiro's acceptance of Neuro-Linguistic Programming theory on eye movement patterns and super-achievers. The present paper brings together this diverse set of findings to provide a more accurate context within which Shapiro's purported discoveries and subsequent claims can best be viewed. [ABSTRACT FROM AUTHOR]

In the mixed-model assembly line balancing and sequencing problem (MALBSP), workstations are assumed to be constantly available. The failure of any workstation will make the entire assembly line stop working. Preventive maintenance (PM) is a way to maintain the workstation before its failure, reduce unexpected downtime, and prolong its useful life. Previous studies have considered PM scenarios (PMS) in the simple and U-shaped assembly line to improve production efficiency and smoothness effectively, but not in the mixed-model assembly line. This paper fills this research gap, and the MALBSP considering PMS (MALBSP_PMS) is studied in this paper. A mixed-integer linear programming model is proposed to minimize makespan and task alteration. A migrating birds optimization algorithm is improved (IMBO) to obtain well-distributed Pareto frontier solutions. This algorithm designs a restart mechanism and an intra-population crossover operator to avoid falling into the local optimal and enhance its searchability. Experimental results demonstrate the effectiveness of two improvements and the IMBO algorithm. In addition, a real-world case study is introduced to illustrate the importance of considering PM scenarios in MALBSP. [ABSTRACT FROM AUTHOR]

This paper studies a mathematical model of the phase transition process as a moving boundary problem (MBP). An equation describing the temperature-dependent thermal conductivity and Robin-type boundary condition at the fixed boundary is used in the model. In order to solve the considered MBP, we propose an iterative-based Keller box method (KBM) for the numerical approximation and boundary immobilization method (BIM) to immobilize the moving boundary. In addition, KBM incorporates nonlinearities in thermal conductivity and boundary conditions. We study the stability and consistency and found out that the scheme is second-order accurate in both time and space. A specific case having a similarity solution has been considered to validate the numerical scheme. Our numerical results show that the KBM is in good agreement with the similarity solution. In addition, the rate of convergence of the KBM scheme is two. Different parameters and temperature-dependent thermal conductivity are studied to determine how these affect the position of the moving boundary. [ABSTRACT FROM AUTHOR]

Lighter-than-air (LTA) aerial vehicles such as airships and aerostats can be found in various strategic and commercial applications, primarily due to their capability to hover and stealth. The mathematical model of these vehicles helps in understanding their complex dynamics and designing and developing proper stabilisation systems for them. Stability derivatives have been used for developing mathematical models for heavier-than-air aerial vehicles since their introduction. This paper presents a methodology to develop a mathematical model of an aerostat based on stability derivatives. One of the major contributions of this study is the estimation of aerostat's added mass terms expressed as longitudinal stability derivatives due to acceleration of the longitudinal motion variables. A longitudinally decoupled linear mathematical model of a single-tethered aerostat using stability derivatives is investigated in this study. A computational fluid dynamics (CFD)-based analysis of the 3D model of the vehicle is used to obtain the stability derivatives. The methodology presented considers the aerostat and tether models separately before coupling them to create the full model. The stability derivative analysis is carried out using ANSYS Fluent, and the coupled tethered aerostat model is investigated using MATLAB 2020. The negative pitch angle of the aerostat is caused by the selection of the pitching centre as the aerostat centre of volume instead of the tether confluence point. The tension force on the tether, which is proportional to the wind velocity, and aerostat velocity components are found to be stabilised within 200–400 s. [ABSTRACT FROM AUTHOR]

Sustainability is an issue of worldwide concern. Twitter is one of the most popular social networks, which makes it particularly interesting for exploring opinions and characteristics related to issues of social preoccupation. This paper aims to gain a better understanding of the activity related to sustainability that takes place on twitter. In addition to building a mathematical model to identify account typologies (bot and human users), different behavioural patterns were detected using clustering analysis mainly in the mechanisms of posting tweets and retweets). The model took as explanatory variables, certain characteristics of the user's profile and her/his activity. A lexicon-based sentiment analysis in the period from 2006 to 2022 was also carried out in conjunction with a keyword study based on centrality metrics. We found that, in both bot and human users, messages showed mostly a positive sentiment. Bots had a higher percentage of neutral messages than human users. With respect to the used keywords certain commonalities but also slight differences between humans and bots were identified. [ABSTRACT FROM AUTHOR]

Recovering three-dimensional structure from images is one of the important researches in computer vision. The quality of feature matching is one of the keys to obtaining more accurate results. However, as different objects or different surfaces of objects have similar images with the same elements and different typography, the camera pose estimation will be wrong and the task will fail. This paper proposes a new mismatch elimination algorithm based on global topology consistency. We first formulate the matching task as a mathematical model based on the global constraints, then convert the feature matching into grid matching, calculate the confidence of the grids according to the changes in the angle and displacement between correspondence grid vectors, and remove the mismatches with low confidence. The experiments have demonstrated that our proposed method performs better than the state-of-the-art feature matching methods to accomplish outlier match rejection in the task of similar image matching and could be helped to obtain the correct camera pose to reconstruct more complete and more accurate object models. [ABSTRACT FROM AUTHOR]

The photovoltaic (PV) cell behavior is characterized by its current–voltage relationship. This relationship is dependent on the PV cell's equivalent circuit parameters. Accurate estimation of such parameters is essential to study and analyze the PV system performance in terms of many aspects such as modeling and control. The main purpose of this paper is to develop mathematical models for the parameters of the single-diode poly and monocrystalline PV cells. The models are formulated using Eureqa software by utilizing training data collected from simulating thousands of PV modules available in Simulink library. The developed models can be easily and instantly executed by only using information available from module datasheet under standard test conditions (STC). The models are then validated using four different assessments by considering testing data, commercial PV modules, and experimental data, in addition to benchmarking with other reported algorithms. As an overall evaluation, the assessments have shown that the developed models are efficient in estimating the PV cell equivalent circuit parameters and can consequently predict the I–V curves for any poly or monocrystalline PV modules, under any weather conditions, with a high degree of accuracy. [ABSTRACT FROM AUTHOR]

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. While current methods can identify such equations, they often require extensive manual hyperparameter tuning, limiting their applicability. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques to smooth the signal, sparse regression to identify the relevant parameters, and bootstrap confidence intervals to quantify the uncertainty of the estimates. We evaluate our method on well-known ordinary differential equations with an ensemble of random initial conditions, time series of increasing length, and varying signal-to-noise ratios. Our algorithm consistently identifies three-dimensional systems, given moderately-sized time series and high levels of signal quality relative to background noise. By accurately discovering dynamical systems automatically, our methodology has the potential to impact the understanding of complex systems, especially in fields where data are abundant, but developing mathematical models demands considerable effort. Discovering nonlinear differential equations from empirical data is a significant challenge, often requiring manual parameter tuning. This paper introduces a machine learning method integrating denoising techniques, sparse regression, and bootstrap confidence intervals, which shows consistent accuracy in identifying 3D dynamical systems with moderate data size and high signal quality. [ABSTRACT FROM AUTHOR]

A non-linear mathematical model of underactuated airship is derived in this paper based on Euler-Newton approach. The model is linearized with small disturbance theory, producing a linear time varying (LTV) model. The LTV model is verified by comparing its output response with the result of the nonlinear model for a given input signal. The verified LTV model is used in designing the LQT controller. The controller is designed to minimize the error between the output and required states response with acceptable control signals using a weighted cost function. Two LQT controllers are presented in this work based on two different costates transformations used in solving the differential Riccati equation (DRE). The first proposed assumption of costates transformation has a good tracking performance, but it is sensitive to the change of trajectory profile, whereas the second one overcomes this problem due to considering the trajectory dynamics. Therefore, the first assumption is performed across the whole trajectory tracking except for parts of trajectory profile changes where the second assumption is applied. The hybrid LQT controller is used and tested on circular, helical, and bowed trajectories. The simulation assured that the introduced hybrid controller results in improving airship performance. [ABSTRACT FROM AUTHOR]

This study examines Einstein's field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated. [ABSTRACT FROM AUTHOR]

Photoacoustic (PA) medical imaging is a crossbred technique relying on light-induced ultrasonic waves due to the PA effect phenomenon recorded primarily in 1880 by A. G. Bell. Numerical simulation, also known as in-silico, studies assist scientists in minimizing incorrect PA experiments in both in-vitro and in-vivo. Numerical modeling techniques help to achieve a fast simulation process in contrast to pure mathematics alone. However, if a suitable facilitated mathematical model can be established prior to applying numerical modeling, it will be of great interest to the whole numeric model. Numerous mathematical equations, theorems, and propositions have been proposed to model the whole PA signal generation and propagation process in biological media. However, most of them are complicated and difficult to be understood by researchers, especially beginners. That's why this paper was introduced. Our paper aims to simplify the understanding of the generation and propagation process of biomedical PA waves. We have developed a facilitated mathematical model for the entire process. The introduced developed mathematical model is based on three steps: (1) pulsed laser stimulation, (2) light diffusion, and (3) PA stress wave generation and propagation. The developed mathematical model has been implemented utilizing COMSOL Multiphysics, which relies on the finite element method (FEM) numerical modeling principle. The in-silico time-dependent study's results confirmed that the proposed mathematical model is a simple, efficient, accurate, and quick starting point for researchers to simulate biomedical PA signals' generation and propagation process utilizing any suitable software such as COMSOL multiphysics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a qualitative approach to the theory of conceptual spaces, in contrast to the usual metric framework. This requires qualitative notions of similarity, simple concepts, prototypes and conceptual categorisation. For this purpose, I will introduce three mathematical models for conceptual spaces. The first one is topological and has been proposed by Mormann. The other two are new and are based on atomistic orders and similarity relations. I will discuss how each of them deals with the Design Principles proposed by Douven and Gärdenfors and with further Adequacy Conditions. Despite being apparently different, I will show that these three models are mathematically equivalent. Finally, I will address three objections to the present approach. The first one says that the qualitative notion of a prototype is a bad analogue of the metric one. The second one suggests that, in contrast to the Voronoi construction, the function qualitatively representing the conceptual categorisation process is arbitrary. The last one appeals to Goodman's companionship and imperfect community problems to show that there is a flaw in defining simple concepts from similarity relations. [ABSTRACT FROM AUTHOR]

The paper presents a brief analytical review of the current state of research in the field of recovery and its modeling in order to predict the structure and properties, as well as a review of experimental research methods and mathematical models of the processes of structure formation during annealing of cold-rolled steels. The paper also presents the results of an experimental study of the recovery process in cold-rolled automotive steels using various techniques and describes a mathematical model for calculating the kinetics of this process depending on the temperature and chemical composition of steels. [ABSTRACT FROM AUTHOR]

The paper proposes a methodology for mathematical modeling of the phased development of nodes and transport routes in a hierarchical network with multicommodity discrete flows of correspondences based on solving the problems of optimizing its structure and distribution of flows. As a rule, such networks consist of a decentralized mainline network and networks in the internal service areas of mainline nodes. In a multicommodity network, each node can exchange correspondence (products, goods, cargo, messages) with the other nodes. Correspondence is characterized by a source node, a sink node, and a quantity, which for data transmission networks is given by the number of bytes, kilobytes, etc., and for transport networks by the number of cargo units in a package of uniform size. In the mainline network, all correspondences are transmitted via communication channels or transported by vehicles in transport units of a given size (capacity, volume). The authors considered the main postulates of generating a mathematical model of the perspective development of mainline network. They presented a method of mathematical modeling of the phased development of nodes and transport routes, which includes, for each stage of development, the forecasting of data and network parameters, solving the problem of packing correspondence and choosing the structure of the network, and solving the problem of distribution and routing of transport unit flows. [ABSTRACT FROM AUTHOR]

This article discusses current problems of the synthesis of new materials in modern conditions. Today this is the most important strategic task for the innovative development of Russian industry. The factors determining the relevance of this task are formulated. A brief analysis of the state of Russian microelectronics is given. The importance of mathematical modeling methods and the need to develop innovative approaches in the field of the synthesis of new materials are shown. The main directions of scientific research related to the development of new model concepts, methods, and algorithms used in the field of mathematical modeling of the structures and properties of nanomaterials, as well as systems based on them, discussed at the IV International Conference "Mathematical Modeling in Materials Science of Electronic Components" (ICM3SEC-2022), are highlighted. This paper shows that for the further development of methods and means of mathematical modeling, a domestic high-performance environment for scientific research is required, with a comfortable user interface, flexibility in setting up resources, high performance, and reliability. [ABSTRACT FROM AUTHOR]

This paper presents results of computational and experimental studies of the evolution of turbulent mixing in three-layer gas systems with the development of hydrodynamic instabilities, in particular, the Richtmyer–Meshkov and Kelvin–Helmholtz instabilities, under the action of shock waves. One of the contact boundaries between gases is flat, while the other one has the form of a chevron. The numerical simulations are carried out both with and without initial perturbations of contact boundaries. It is shown that the roughness of the contact boundary significantly affects the width of the mixing zone. [ABSTRACT FROM AUTHOR]

Deblurring is a challenging problem in image restoration. It's important to use both local details and global information of the image for deblurring. Therefore, this paper proposes a deblurring model that integrates Convolution and Transformer in a parallel manner. Unlike existing methods that use single operators or serial combinations, the convolution operation and self-attention mechanism in this model are learned in parallel and extract features separately, and then the features are fused in the frequency domain. The convolution operation is beneficial in extracting local information while the self-attention mechanism focuses more on global information. The parallel structure enables the model to capture both local and global information simultaneously. Additionally, the frequency domain fusion module is proposed based on the analysis of the mathematical model of image blur, and the results indicate that the proposed model is reasonable. Experiments on multiple deblurring datasets verify that the proposed parallel structure of Convolution-Transformer and frequency domain fusion method are effective. [ABSTRACT FROM AUTHOR]

During the construction of a metro system, it is inevitable that deviations will occur between the excavated tunnel and the original designed scheme. As such, it is necessary to adjust the designed scheme to accommodate these discrepancies. Specifically, the adjustment of the designed scheme involves a rigorous process of repeatedly selecting and verifying the feasibility of the proposed modifications using point-cloud data obtained from the tunnel. However, this process can be considerably time-consuming due to the large-scale and potentially redundant nature of the point-cloud data. This paper proposes a mathematical model for point-cloud data acquired in measuring a mined tunnel, which may deviate from the originally designed one. The modeling, which mainly includes determining its normal plane, and building the equation of tunnel point-cloud data, is to quickly extract several key locations in the tunnel surface for modifying the original design in order to achieve a minimum error between the modified design and the mined tunnel. In comparison with the conventional processing of extracting several key locations directly from point-cloud data, our model shows a significant promotion of extraction efficiency under an acceptable error bound. The model is tested in a real tunnel point-cloud data and the testing results confirm the increase of fitting accuracy and the decrease of computational load. [ABSTRACT FROM AUTHOR]

The electric vehicle battery state prediction in real time is an important issue to avoid the risks of burning the battery due to over-charging or dead batteries that are caused by aging. Based on the past works, it is found that the State of Charge (SOC) can be predicted, while predicting the State of Health (SOH) is a difficult challenge. Usually, the SOH is predicted after the end of the driving or the charging cycle under constant conditions; this method is practically impossible because the battery can reach the end of the battery life before achieving the prediction process. In this paper, a SOH prediction method is proposed based on SOC prediction because there is a relation between the SOC and the SOH as indicated by deriving a mathematical model. The prediction process of battery age is achieved during the beginning of the battery charging process under constant conditions of charging, in which a SOC estimation has been implemented by the nonlinear auto-regressive with exogenous input neural network (NARX) with two initial values of SOC, the default value (0%) and practical value (10%) and two charging current rates (0.5C and 1C). The proposed method has been simulated by MATLAB, which several scenarios have been achieved to validate the proposed method. The root-mean-square error (RMSE) values are very promising for both predicting SOC and SOH that are 0.5% and 0.018%, respectively. [ABSTRACT FROM AUTHOR]

Steelmaking-refining-Continuous Casting (SCC) is a bottleneck in the iron and steel production operation. In order to enhance production efficiency, SCC scheduling is employed to find an optimal schedule. Unfortunately, dynamic events such as charge start-time delay may occur in a real-world SCC process, which will invalidate the optimal SCC schedule, i.e., making the schedule not optimal or inexecutable. To cope with such a situation, SCC rescheduling is significant for generating a new optimal schedule. This paper proposes a mathematical model of the SCC rescheduling problem considering charge start-time delay, and further presents an Elite solutions and Tabu assisted Variable Neighbourhood Descent (ETVND) method to tackle the problem. The main framework of the ETVND method is Variable Neighbourhood Descent (VND). In the ETVND method, three Tabu based neighbourhood structures are elaborately designed. Moreover, three distinguished features are incorporated, i.e., an elite solutions based exploration strategy, two-layer local search based on the Fruit fly Optimization Algorithm, and multi-type perturbation. The first two features are devised to enhance the intensification abilities while the third is devised to improve the diversification abilities. Experimental results have demonstrated the effectiveness of the ETVND method by comparing with several algorithms in the literature. Further comparison experiments have validated the efficiency of the Tabu based neighbourhood structures and specially devised strategies. [ABSTRACT FROM AUTHOR]

Predicting and understanding the behavior of dynamic systems have driven advancements in various approaches, including physics-based models and data-driven techniques like deep neural networks. Chaotic systems, with their stochastic nature and unpredictable behavior, pose challenges for accurate modeling and forecasting, especially during extreme events. In this paper, we propose a novel deep learning framework called Attractor-Inspired Deep Learning (AiDL), which seamlessly integrates actual statistics and mathematical models of system kinetics. AiDL combines the strengths of physics-informed machine learning and data-driven methods, offering a promising solution for modeling nonlinear systems. By leveraging the intricate dynamics of attractors, AiDL bridges the gap between physics-based models and deep neural networks. We demonstrate the effectiveness of AiDL using real-world data from various domains, including catastrophic weather mechanics, El Niño cycles, and disease transmission. Our empirical results showcase AiDL's ability to substantially enhance the modeling of extreme events. The proposed AiDL paradigm holds promise for advancing research in Time Series Prediction of Extreme Events and has applications in real-world chaotic system transformations. [ABSTRACT FROM AUTHOR]

In the literature, fuzzy arithmetic approach has been used for solving fuzzy data envelopment analysis (DEA) model in the presence of undesirable outputs by use of ideal and anti-ideal decision-making units (DMUs). In order to obtain the best and the worst fuzzy efficiencies, such an approach allows each DMU to choose the most favorable weights via optimizing its own evaluation that needs to solve various mathematical models. On the one hand, solving one mathematical model to find the best fuzzy efficiency and solving another mathematical model to find the worst fuzzy efficiency for each DMU increase the computational complexity significantly. On the other hand, the fully flexibility of weights leads to the different set of weights that may not be desirable. This paper proposes a common-weight method from two optimistic and pessimistic perspectives in fuzzy environment to determine the common sets of weights (CWS) to compute the best and the worst fuzzy efficiencies of all DMUs. The advantages of using common-weight DEA method based upon fuzzy arithmetic approach are reduction of the computational complexities and evaluation of equitably the best and the worst fuzzy efficiencies on the same base. The proposed approach first solves one linear programming model to compute each of the best and the worst fuzzy efficiencies of all DMUS, and then combines them to find a relative closeness index for the overall assessment. The developed approach is illustrated by a numerical example form the literature and the obtained results are compared with those from the existing ones. [ABSTRACT FROM AUTHOR]

The therapeutic alliance has a robust association with positive outcome in psychotherapy. It is considered a common factor of change independent of the diagnosis and type of therapy. The alliance is commonly defined phenomenologically as a relationship between a client and a therapist characterized by such attributes as agreement on the goals of the treatment, agreement on the tasks, and a personal bond made up of reciprocal positive feelings. There is no commonly accepted mechanistic model of the alliance. In this paper, we present the alliance in active inference terms as an affiliative behavioral strategy meant to decrease the free energy of the participants' generative models of each other and of their social exchange. In this view, the initial apprehension of affiliation with a stranger is a normative reaction in the therapeutic (or any social) encounter. We identify trust and self-efficacy as processes central to the development of the alliance and suggest an active inference model of the alliance based on their interaction and dynamics. The paper concludes with suggestions for the model's practical application. [ABSTRACT FROM AUTHOR]

This manuscript delves into the examination of the stochastic fractional derivative of Drinfel'd-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. In our study, the proposed equation is through examined through various viewpoints, encompassing soliton dynamics, bifurcation analysis, chaotic behaviors, and sensitivity analysis. A few dark and bright shaped soliton solutions, including the unperturbed term, are also examined, and the various 2D and 3D solitonic structures are computed using the Tanh-method. It is found that a saddle point bifurcation causes the transition from periodic behavior to quasi-periodic behavior in a sensitive area. Further analysis reveals favorable conditions for the multidimensional bifurcation of dynamic behavioral solutions. Different types of wave solutions are identified in certain solutions by entering numerous values for the parameters, demonstrating the effectiveness and precision of Tanh-methods. A planar dynamical system is then created using the Galilean transformation, with the actual model serving as a starting point. It is observed that a few physical criteria in the discussed equation exhibit more multi-stable properties, as many multi-stability structures are employed by some individuals. Moreover, sensitivity behavior is employed to examine perturbed dynamical systems across diverse initial conditions. The techniques and findings presented in this paper can be extended to investigate a broader spectrum of nonlinear wave phenomena. [ABSTRACT FROM AUTHOR]

The Electronic Personal Health Record (EPHR) provides an innovative service for citizens and professionals to manage health data, promoting patient-centred care. It enhances communication between patients and physicians and improves accessibility to documents for remote medical information management. The study aims to assess the prevalence of awareness and acceptance of the EPHR in northern Italy and define determinants and barriers to its implementation. In 2022, a region-wide cross-sectional study was carried out through a paper-based and online survey shared among adult citizens. Univariable and multivariable regression models analysed the association between the outcome variables (knowledge and attitudes toward the EPHR) and selected independent variables. Overall, 1634 people were surveyed, and two-thirds were aware of the EPHR. Among those unaware of the EPHR, a high prevalence of specific socio-demographic groups, such as foreign-born individuals and those with lower educational levels, was highlighted. Multivariable regression models showed a positive association between being aware of the EPHR and educational level, health literacy, and perceived poor health status, whereas age was negatively associated. A higher knowledge of the EPHR was associated with a higher attitude towards the EPHR. The current analysis confirms a lack of awareness regarding the existence of the EPHR, especially among certain disadvantaged demographic groups. This should serve as a driving force for a powerful campaign tailored to specific categories of citizens for enhancing knowledge and usage of the EPHR. Involving professionals in promoting this tool is crucial for helping patients and managing health data. [ABSTRACT FROM AUTHOR]

Since the discovery and the development of many technological instruments such as modern communication and communication technologies, digital media has served widely from the technology, and thus intersected quasi all life's domains, by providing news, information, and also discussions of quasi all subjects. In social sciences, for example, a major part of digital media sites discusses the well-being of both individuals, and societies, especially with the presence of many challenging phenomena like pandemics, wars, and financial crises. A major concern for QoL index for example resides in whether it is a uniform stable index or on the contrary a non-uniform index depending strongly and point-wisely on the time scale. This motivates the consideration of a non-uniform QoL index based on non-uniform wavelets to take into account the influence of many factors issued from political, social, environmental, economic effects according to the time scale. The model developed is tested on Saudi Arabia QoL index case. Recall that the Kingdom of Saudi Arabia has fixed many aims in its 2030-vision plan including the quality of life as a major goal. For example, the KSA worldwide NEOM project necessitates surely a supportive environment to be realized. The second purpose of our paper is also to study the impact of digital media such as social one on the QoL. Therefore, the data collected is basically issued from a set of conversations on social media platforms. To obtain a suitable time series, we developed a backward-forward non-uniform wavelet forecasting model to extend the data sample suitably. The whole time series is by the next applied for the QoL index dynamics and interpretations. The findings showed that effectively, the QoL index is never a stable single index on the whole year, but on the contrary, the dependence on the time scale is non-uniform. Moreover, to interpret suitably and for a correct policy, the non-uniform behavior should be considered adequately. [ABSTRACT FROM AUTHOR]

The aerospace industry is pivotal for global transportation and is a cornerstone of high-tech industry growth in both developed and developing nations. Ensuring the integrity of aircraft products and components, maintenance, repair, and overhaul (MRO) operations is critical to the sector's success. This paper presents a linear programming model for scheduling aircraft C-check and D-check maintenance operations with multiple component treatment options: replacement, repair, and remanufacturing. Risk of component failure before the next maintenance is integrated into the model. The objective is to minimize maintenance cost while adhering to safety standards. The model also incorporates allocation of maintenance resources including labor and machinery capacities. Scenario analyses are conducted to assess varying parameters such as resource availability, unplanned maintenance costs, and penalty on the model solutions. The potential for remanufacturing to reduce maintenance expenses in MRO operations is evaluated. The main contribution of this work lies in its novel approach to integrating risk assessment with resource optimization in MRO scheduling with remanufacturing and in providing a comprehensive framework to enhance decision-making for MRO maintenance operations. [ABSTRACT FROM AUTHOR]

The penetration coefficient can represent the relationship between force and depth in the rock drilling process, but its understanding is limited. Therefore, based on the rock drilling theory with a hydraulic breaking hammer, a mathematical model of the penetration coefficient is established in this paper, and the main influencing factors of the penetration coefficient are determined. The discrete element method is used to establish a rock simulation model that can represent the real characteristics, and the variation law of the penetration coefficient under cyclic impact is studied. In addition, the drilling processes of drill bits with different impact velocities, shapes, and angles are simulated to evaluate the effects of operational parameters on the penetration coefficient. The results show that cyclic impact will change the rock cohesion and affect the change in the penetration coefficient. With an increase in impact times by the same drill bit, the penetration coefficient first increases and tends to be stable, and then decreases. Regarding operational parameters, the impact velocity has little effect on the penetration coefficient, while the shape and angle of the drill bit have a significant effect on the penetration coefficient, and a drill bit with a smaller angle is accompanied by more rock debris. Highlights: A theoretical model of the penetration coefficient is established. DEM simulation reveals the rock drilling mechanism under cyclic impact. The effect law and significance of operation parameters are obtained. [ABSTRACT FROM AUTHOR]

Hybrid ion exchange (IX) and biological processes have been developed for various water and wastewater treatment applications. These hybrid systems integrate multiple physical, chemical, biological, hydrodynamics, and substrate transport processes to improve the treatment efficiencies and system stability. The mathematical description of the individual process has been well established previously; however, there is a lack of a holistic review and guidelines to develop hybrid models for different treatment systems. In this paper, we summarize the applications of hybrid IX and biological systems, critically review the representative individual process models, and propose the framework to integrate these models for the hybrid process. Additionally, we provide a comprehensive review of the equilibrium, kinetic, and thermodynamic models for the IX process and the key biological process models, along with their applied scenarios. Advanced data-driven modelling and its combination with mechanistic models are also discussed to overcome the drawbacks in conventional modeling approach. We highlight emerging techniques that would lead to higher fidelity models. This review provides a comprehensive guideline for the model development of hybrid systems and presents future research directions to build robust systems. [ABSTRACT FROM AUTHOR]

In this paper, the structural vibration control of short-period systems by a sliding model of a tuned liquid column damper (herein referred to as STLCD) is investigated from both theoretical and experimental points of view. The proposed STLCD is essentially composed of a U-tube container with liquid inside, which can slide on a linear guide rail and is connected to the structure by a spring-dashpot system. Unlike traditional fixed TLCDs, this type of arrangement allows the proposed STLCD to be tuned to short-period structural systems since the spring can be used for tuning while the dashpot provides additional damping. Details on the selection of the optimal design parameters of the STLCD are provided, and the validity of the introduced mathematical model is verified both in time and frequency domains through experimental tests conducted at the Laboratory of Experimental Dynamics at the University of Palermo, Italy. For the experimental tests, a scale model of an STLCD-controlled structure is considered, focusing on the reduction of the roof accelerations. Finally, for comparison purposes, the control performance of the proposed control strategy for the vibration suppression of stiff structures is evaluated by analyzing its structural responses in contrast with the corresponding uncontrolled structure under harmonic excitations. [ABSTRACT FROM AUTHOR]

Elite sports contexts are highly pressurised and frequently enforce a win-at-all-costs approach. This narrow focus on performance outcomes can potentially contribute in negative ways to the mental health of those within these environments. In this Current Opinion paper, we propose a model that outlines how key elements contributing to psychologically safe or unsafe environments may contribute to better or worse mental health outcomes, respectively. In an environment in which individuals feel safe to show their authentic selves rather than 'wear a mask', different experiences of mental health are likely to be normalised, help-seeking behaviour increased, and thus, mental health outcomes enhanced. We outline how sports teams and organisations can contribute to this through the creation of appropriate policies and procedures, in addition to leaders modelling and reinforcing positive cultural norms. It is intended that the theoretical model can inform stakeholders in elite sport as well as future research directions. [ABSTRACT FROM AUTHOR]

The social identity of a researcher can affect their position in a community, as well as the uptake of their ideas. In many fields, members of underrepresented or minority groups are less likely to be cited, leading to citation gaps. Though this empirical phenomenon has been well-studied, empirical work generally does not provide insight into the causes of citation gaps. I will argue, using mathematical models, that citation gaps are likely due in part to the structure of academic communities. The existence of these 'structural causes' has implications for attempts to lessen citation gaps, and for proposals to make academic communities more efficient (e.g. by eliminating pre-publication peer review). These proposals have the potential to create feedback loops, amplifying current structural inequities. [ABSTRACT FROM AUTHOR]

There is a trend to deploy neural network on edge devices in recent years. While the mainstream of research often concerns with single edge device processing and edge-cloud two-layer neural network collaborative computing, in this paper, we propose partitioning multi-layer edge network for neural network collaborative computing. With the proposed method, sub-models of neural network are deployed on multi-layer edge devices along the communication path from end users to cloud. Firstly, we propose an optimal path selection method to form a neural network collaborative computing path with lowest communication overhead. Secondly, we establish a time-delay optimization mathematical model to evaluate the effects of different partitioning solutions. To find the optimal partition solution, an ordered elitist genetic algorithm (OEGA) is proposed. The experimental results show that, compared with traditional cloud computing, single-device edge computing and edge-cloud collaborative computing, the proposed multi-layer edge network collaborative computing has a smaller runtime delay with limited bandwidth resources, and because of the pipeline computing characteristics, the proposed method has a better response speed when processing large number of requests. Meanwhile, the OEGA algorithm has better performance than conventional methods, and the optimized partitioning method outperforms other methods like random and evenly partition. [ABSTRACT FROM AUTHOR]

The performance growth in processors has been continuing toward increasing the number of processing cores on the chip and scaling the feature size of transistors. However, in the nanoera, side effects of the scaling, such as induced heterogeneities in the performance, power, and soft error rate of identically designed cores, prevent the potential performance from being fully utilized. In this paper, we harness the mentioned side effects in shared-memory multicore processors with unknown workloads by a dynamic heuristic scheduling algorithm called HDSAP. HDSAP aims to maximize performance, i.e., the average response time, under power and reliability constraints in presence of induced heterogeneities. In this regard, we use a mathematical model to quantify task to core assignments based on performance variation. We also consider the variation in power to change selected cores when the power constraint is missed. To meet the reliability constraint, we use N-modular redundancy while being aware of the variation in the soft error rate of cores to prevent under/over reliability estimation. To evaluate HDSAP, we run SPLASH benchmark suite on Sniper and MACPat simulators. As a result, the response time of HDSAP reduces by 6%, 8%, and 25% in comparison with similar algorithms under the same power and reliability constraints. [ABSTRACT FROM AUTHOR]

This paper proposes a method to deform a continuum robot into a complex shape with distributed curvature using a single motor drive. This continuum robot can be deformed to a desired shape by placing tendon guides at appropriate intervals. We used several target shapes, including clothoid and sin curves, as well as a circular curve of constant curvature and confirmed that the deformed shapes match them both in the simulation and prototype. This paper proposes two models of continuum robots. One is the Plain Model in which the tendons are parallel to the rod and the Penetration Model in which the tendon penetrates to the rod. By placing the penetrating position(s), this continuum robot can be deformed into a shape with inflection point(s). We designed a mathematical model to simulate the deformed shape of the prototype to obtain the proper placement of the guides and penetration point(s). Through the optimization, it was able to find the parameters that, in most cases, result in the error of less than 4 % between the target and deformed shapes on simulation. We applied these conditions to the prototype and evaluated the errors, which were approximately 10 % , the same as the related works that use a conventional constant curvature model. We think that the results of this paper can be applied to reduce the number of actuators required and the size and weight of continuum or biomimetic robots. [ABSTRACT FROM AUTHOR]

This paper proposes a method to deform a continuum robot into a complex shape with distributed curvature using a single motor drive. This continuum robot can be deformed to a desired shape by placing tendon guides at appropriate intervals. We used several target shapes, including clothoid and sin curves, as well as a circular curve of constant curvature and confirmed that the deformed shapes match them both in the simulation and prototype. This paper proposes two models of continuum robots. One is the Plain Model in which the tendons are parallel to the rod and the Penetration Model in which the tendon penetrates to the rod. By placing the penetrating position(s), this continuum robot can be deformed into a shape with inflection point(s). We designed a mathematical model to simulate the deformed shape of the prototype to obtain the proper placement of the guides and penetration point(s). Through the optimization, it was able to find the parameters that, in most cases, result in the error of less than 4 % between the target and deformed shapes on simulation. We applied these conditions to the prototype and evaluated the errors, which were approximately 10 % , the same as the related works that use a conventional constant curvature model. We think that the results of this paper can be applied to reduce the number of actuators required and the size and weight of continuum or biomimetic robots. [ABSTRACT FROM AUTHOR]

In this paper, we study a free boundary problem modeling spherically symmetric tumor growth with angiogenesis and a periodic supply of nutrients. The mathematical model is a free boundary problem since the external radius of the tumor denoted by R (t) changes with time. The characteristic of this model is the consideration of both angiogenesis and periodic external nutrient supply. The cells inside the tumor absorb nutrient u (r , t) through blood vessels and attracts blood vessels at a rate proportional to α. Thus on the boundary, we have u r (r , t) + α (u (r , t) − ψ (t)) = 0 , r = R (t) , t > 0 , where ψ (t) is the nutrient concentration provided externally. Considering that the nutrient provided externally to the tumor are generally provided periodically, in this paper, we assume that ψ (t) is a periodic function. Sufficient conditions for a tumor to disappear are given. We investigate the existence, uniqueness, and stability of solutions. The results show that when the nutrient concentration exceeds a certain value and c is sufficiently small, the solutions of the model can be arbitrarily close to the unique periodic function as t → ∞ . [ABSTRACT FROM AUTHOR]

In this paper, we study a free boundary problem modeling spherically symmetric tumor growth with angiogenesis and a periodic supply of nutrients. The mathematical model is a free boundary problem since the external radius of the tumor denoted by R (t) changes with time. The characteristic of this model is the consideration of both angiogenesis and periodic external nutrient supply. The cells inside the tumor absorb nutrient u (r , t) through blood vessels and attracts blood vessels at a rate proportional to α. Thus on the boundary, we have u r (r , t) + α (u (r , t) − ψ (t)) = 0 , r = R (t) , t > 0 , where ψ (t) is the nutrient concentration provided externally. Considering that the nutrient provided externally to the tumor are generally provided periodically, in this paper, we assume that ψ (t) is a periodic function. Sufficient conditions for a tumor to disappear are given. We investigate the existence, uniqueness, and stability of solutions. The results show that when the nutrient concentration exceeds a certain value and c is sufficiently small, the solutions of the model can be arbitrarily close to the unique periodic function as t → ∞ . [ABSTRACT FROM AUTHOR]

This paper aims to construct a general framework of coupling tumor–bone remodeling processes in order to produce plausible outcomes of the effects of tumors on the number of osteoclasts, osteoblasts, and the frequency of the bone turnover cycle. In this document, Komarova's model has been extended to include the effect of tumors on the bone remodeling processes. Thus, we explored three alternatives for coupling tumor presence into Komarova's model: first, using a "damage" parameter that depends on the tumor cell concentration. A second model follows the original structure of Komarova, including the tumor presence in those equations powered up to a new parameter, called the paracrine effect of the tumor on osteoclasts and osteoblasts; the last model is replicated from Ayati and collaborators in which the impact of the tumor is included into the paracrine parameters. Through the models, we studied their stability and considered some examples that can reproduce the tumor effects seen in clinic and experimentally. Therefore, this paper has three parts: the exposition of the three models, the results and discussion (where we explore some aspects and examples of the solution of the models), and the conclusion. [ABSTRACT FROM AUTHOR]