This paper presents a methodology for predictive and prescriptive analytics of complex engineering systems. The methodology is based on a combination of physics-based and data-driven modeling using machine learning techniques. Combining these approaches results in a set of reliable, fast, and continuously updating models for prescriptive analytics. The methodology is demonstrated with a case study of a jet-engine power plant preventive maintenance and diagnostics of its flame tube.

We analyse the light curve in the R-band gathered during the 2015/16 observing season of OJ287. We did a search for QPOs using several methods in wide time domain. No statistically significant periods were found in the high frequency domain both in the ground data and also in K2 observations. In the longer periods domain the Lomb-Scargle periodogram revealed several peaks above the 99\% significance level. The longest one, about 95-day, corresponds to the ISCO period of the more massive SMBH. The 43-day period could be an alias or can be attributed to accretion in the form of two armed spiral wave.

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

This study explores the complexities involved in the extraction and purification of catechins, prominent bioactive compounds found in plant extracts and tea. It addresses challenges arising from the intricate molecular structure of catechins and their inherent variability across botanical sources. Despite these obstacles, catechins present significant potential, particularly in healthcare. Their potent antioxidant properties have been extensively investigated and associated with numerous health benefits, positioning them as promising therapeutic agents for combating chronic diseases. Furthermore, catechins have diverse applications across various industries, including food and beverage, cosmetics, agriculture, and materials science. This abstract emphasizes the importance of continued research and innovation in catechin extraction and utilization, which hold promise for advancing human health and technological progress across multiple domains.

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.

Gamba grass (Andropogon gayanus Kunth) is a tussock-forming forage species adapted to acid soils of Brazilian savannas and cultivated for grazing pastures. Four decades since its releasing, Planaltina prevails as the most commercialized cultivar of the species, even though the new cultivar BRS Sarandi could be a better alternative for Gamba grass-based farms by presenting greater leaf:stem ratio. The objective of this study was to evaluate the average daily live weight gain (ADG) of Nellore bulls (Bos indicus) for two Gamba grass cultivars – Planaltina and Sarandi. The experiment was conducted in Planaltina, Federal District, Brazil, during 3 years, namely 2018, 2018-2019 and 2020. The experimental design was completely randomized block with two treatments and three replicates, each one continuously stocked at three stocking rates (SR) - 1.3, 2.6 and 4 young bulls/ha. Canopy height (CH), forage mass (FM), plant-part proportion (leaf, stem and dead material) and nutritive value were evaluated. In 2018, mean ADG for Sarandi pastures was greater (0.690 kg/bull/d) than Planaltina (0.490 kg/bull/d) (P=0.0839). In the subsequent year (2018-2019), there was no effect of cultivar (P = 0.4089), while in 2020 the ADG was again affected by cultivar (P=0.0412), confirming the advantage of Sarandi (0.790 kg/bull/d) over Planaltina (0.650 kg/bull/d). In 2018 and 2020, the percentage of stems for Sarandi was about 3-6 pp lesser than for Planaltina (P

This article is the fourth part of a scientific project under the general title “Geometrized vacuum physics based on the Algebra of Signatures". In the first three articles [1,2,3], the foundations of the Algebra of Stignatures were laid and the main aspects of the kinematics of vacuum layers were considered. This article continues the development of the mathematical apparatus of the proposed project, in particular, the dynamics of vacuum layers is developed based on the Algebra of Signatures. The development of this direction of research (with simplifications related to Riemann's differential geometry) led to the possibility of a geometrized representation of the electric field strength and magnetic field induction. This geometrized mathematical apparatus allows one to interpret the electromagnetic field as an interweaving of accelerated and rotational flows of the adjacent layers of vacuum. The proposed dynamic models of accelerated movements and rotations of vacuum layers can provide a theoretical basis for the development of “zero” (i.e. vacuum) technologies.

Tropical cyclones have long been known to be powered by turbulent enthalpy fluxes from the ocean surface and retarded by turbulent momentum fluxes into the surface. Here were review evidence that the development and structure of these storms are also partially controlled by turbulence in the outflow near the storm top. Finally, we present new research that shows that tropical cyclone-like, low-aspect-ratio vortices are most likely in systems in which the bottom heat flux is controlled by mechanical turbulence and the top boundary is insulating.

The aim of the article is to develop geometrized physics of a vacuum on the basis of two basic postulates: 1) the constancy of the speed of light (more precisely, the speed of propagation of electromagnetic waves) in the vacuum; 2) the ‘vacuum balance condition’ associated with the statement that only mutually opposite formations are born from the vacuum, so that, on average, they completely compensate of the manifestations of each other. The Algebra of signatures is proposed as a mathematical basis for geometrized physics of a vacuum.

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the mechanical equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

In the past 100 years, quantum theory has achieved remarkable achievements and formed a relatively mature system, but at the same time there are still some incomplete places. For example: What is the origin of quantum? What is the origin of quantum entanglement? What is the origin of quantum mechanical wave-particle duality? This is still a problem that the existing quantum theory has not solved. Therefore, this paper attempts to seek a classic interpretation of quantum mechanics to make up for the shortcomings of existing quantum theory. In the latest research, this paper finds a classic interpretation of blackbody radiation, which can explain the discontinuity of light energy from the perspective of classical mechanics. Based on this discovery, this paper successfully explains the origin of quantum, quantum entanglement and wave-particle duality, and eliminates the confusion of quantum mechanical probability waves.

It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structures organizing the foldings. Then one look at the musical forms employed in the classical and contemporary periods. Finally, one investigates in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.

In the last few decades, the dynamics of tumor cells and their growths are presented via clinical, experimental, and theoretical approaches, which leads to the development of the new idea of multiple cancer therapies to control and reduce the death rate for earlier detection. In this paper, we discussed the dynamics of tumor cell growth and its treatment process. We analyzed some simple mathematical models and generalized the study to understand the growth of tumor cells. The main proposed model is a system of ordinary differential equations which combines interactions among natural killer cells, dendritic cells and cytotoxic CD8+ T cells. The model is solved numerically to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer. It is also studied that how the cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time. Finally, a couple of spatially distributed models are discussed for tumor cell growth.

The swift progress in low-dimensional nanocarbons, specifically in the realm of the authentic one-dimensional carbon chain featuring sp¹ hybridization, has unveiled exciting prospects for integrating them into cutting-edge technologies across diverse industries. To fully harness their potential, precise control over the growth process is necessary to obtain desired nanostructure and functionality. However, optimizing properties through traditional approaches has been challenging due to complex interactions. To address this, we implement a focused data-driven strategy for nanocarbon inverse design by leveraging a state-of-the-art data-driven nanocarbon genome approach (NCGA). By uncovering relationships between growth parameters and resultant traits, this serves as an expedient catalyst in engineering nanostructures with tailored attributes. We introduce an extensive array of technological approaches aimed at precisely controlling the growth process. These methods encompass stimulating and precisely adjusting synergistic effects, coordinating atomic vibrations at a collective level through the implementation of multilayer nano-interfaces, harnessing the potential of active screen plasma surface engineering, utilizing nano-patterning and allotropic phase transformations, incorporating heteroatom doping, and effectively directing self-assembly. These aim to unlock nanomaterials' latent potential and reveal novel neural pathways within the data-driven NCGA, enhancing its predictive capabilities. Specifically, triggering self-organization during growth can potentially unlock previously unexplored neural pathways. The data-driven NCGA offers a paradigm shift, accelerating discovery and design of nanocarbons with optimized, application-specific properties.

In this study, we present comprehensive climatologies of effective ultraviolet (UV) quantities and photosynthetically active radiation (PAR) over Cyprus for the period 2004 to 2023, leveraging the synergy of earth observation (EO) data and radiative transfer model simulations. The EO dataset, encompassing satellite and re-analysis data for aerosols, total ozone column, and water vapor, alongside cloud modification factors, to capture the nuanced dynamics of Cyprus's atmospheric conditions. With a temporal resolution of 15 minutes and a spatial of 0.05°x0.05°, these climatologies undergo rigorous validation against established satellite datasets and are further evaluated through comparisons with ground-based global horizontal irradiance measurements provided by the Meteorological Office of Cyprus. This dual-method validation approach not only underscores the models' accuracy but also highlights their proficiency in capturing intra-daily cloud coverage variations. Our analysis extends to investigating the long-term trends of these solar radiation quantities, examining their interplay with changes in cloud attenuation, aerosol optical depth (AOD), and total ozone column (TOC). Significant decreasing trends in the noon ultraviolet index (UVI), of -2 to -4% per decade have been found in Autumn, especially marked on the island’s Northeastern part, mainly originating from the (significant) positive trends in TOC. The significant decreasing trends in TOC, of -2 to -3% per decade that were found in Spring do not result in correspondingly significant positive trends in the noon UVI since variations in cloudiness and aerosols also have a strong impact on the UVI in this season. The seasonal trends in the Daylight Integral (DLI) were generally not significant. These insights provide a valuable foundation for further studies aimed at developing public health strategies and enhancing agricultural productivity, highlighting the critical importance of accurate and high-resolution climatological data.

The aim of this research work is to study the influence of temperature, solar irradiation and wind dust on the production of solar energy. In addition, it aims to study the assessment of water quality, in particular groundwater used for cooling and cleaning photovoltaic panels (quality analysis). it's an important source, stable and sustainable can be used entirely for cooling and cleaning PV modules from the sales dust, in order to improve their performance. To date, all research studies carried out in this context of cooling and cleaning using water have not taken account of the nature of this water. We have taken a sample of water from a well in a rural area in the Darra Tafilalet region of Morocco. This region has an arid and semi-arid climate, with very high temperatures and dust-laden winds, particularly in summer. These meteorological characteristics influence the efficiency of cells, particularly photovoltaic (PV) panels, reducing their performance. Next, the water sample was analysed in the laboratory. The results obtained show that the groundwater in this area is very sensitive to cooling and cleaning photovoltaic panels. Moreover, these results indicate that the temperature, solar irradiation and wind-blown dust have a significant influence on energy production.

According to the fact that the low convergence level on the complete elliptic integral of the first kind for the modulus which having values approach to one. In this paper we propose novelty of the complete elliptic integral consists of the new infinite series. We apply the scheme of iteration by substituting the common modulus with own modulus function into the new infinite series. We obtained so many new exact formulas of the complete elliptic integral derived from this method correspond to the number of iteration order. On the other hand, it has been also obtained a lot of new modulus functions rather than common used previously. The calculation results show that the number of significant figures of the new infinite series of the complete elliptic integral of the first kind is increased more and more. It means more fastly convergent would be obtained comparison values with the previous infinite series.

In the present time, the biggest problem of the world is the outbreak of novel coronavirus. Novel coronavirus (COVID-19), this one name has become a part of our daily lives over the past few months. Beyond the boundaries of medical science, coronavirus is now the main subject of research in all fields like Applied Mathematics, Economy, Philosophy, Sociology, Politics upto living room. The epidemic has brought unimaginable changes in our traditional habits and daily routines. Thousands of people in our country are fighting with the rest of the world to survive in various new situations. There are different kinds of coronavirus appeared in different times. In this time, Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) is responsible for the coronavirus disease of 2019 (COVID-19). This virus was first identified towards the end of 2019 in the city of Wuhan in the province of Hubei in China. Within very short duration of time and very fast, it has spread throughout a large part of the world. In this study, the main aim is to investigate the spreading rate, death rate, recovery rate due to corona virus infection and to study the future of the coronavirus in India by using mathematical modeling based on the previous data. Mathematical models, in this situation, are the important tools in recruiting effective strategies to fight this epidemic. India is at high risk of spreading the disease and is facing many losses in socio-economic aspects. With current infection rates and existing levels of personal alertness, the number of infected people in India will increase at least in the next three months. Proper social awareness, maintain of social distance, large rate of testing and separation may break the chain of the Coronavirus-2.

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the Kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the Kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously-emitted thermal fluctuations and the background turbulence leads to the formation of non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the Kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

Drilling operation is the major cost factor for the industry. Appropriately designed operations are essential for successful drilling. Optimized drilling operations also allow enhanced drilling performance and reduce the drilling cost. This is achieved by increasing the bit life (minimizing premature bit wear), drilling faster that allows reducing drilling time, and also reducing tripping operations. The paper presents two parts. The first part compares the parametric physic-based swab and surge simulation results obtained from Bingham Plastic, Power Law, and Robertson and Stiff models. The aim is to show how the model predictions deviate from each other. Two 80-20 Oil Water ratios (OWR) and two 90-10 OWR oil-based drilling fluids with 1.96 sg and 2.0 sg were considered in vertical- and deviated wells. Simulation results analysis revealed that the deviations depend on the drilling fluid’s physical and rheological parameters as well as the well trajectory. Moreover, the model’s predictions were inconsistent. Data-driven machine learning (ML) modeling makes up the second section. Data-driven modeling was done using both software-generated datasets and field datasets. Results show that the Random Forest Regressor (RF), Artificial Neural Network (ANN), Long Short-Term Memory (LSTM), LightGBM, XGboost, and Multivariate regression models predict the training and test datasets with higher R-squared and minimum root means square values. Deploying the ML model in real-time applications and the planning phase would have the potential application of artificial intelligence for well planning and optimization processes.

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

In a recent paper, we calculate spectral energy distributions (SEDs) for 1425 Fermi blazars, classifications of low synchrotron peak sources (LSPs) if log $\nu_{\rm p} (\rm Hz) \leq $ 14.0, intermediate synchrotron peak sources (ISPs) if $14.0 < \,\log\, \nu_{\rm p} (\rm Hz) \leq 15.3 $, and high synchrotron peak sources (HSPs) if $ \log\, \nu_{\rm p} (\rm Hz) > 15.3$ are made based on 999 logarithms of synchrotron peak frequencies with known redshift, and we obtain an empirical relation to estimate the synchrotron peak frequency, $\nu_{\rm p}^{\rm Eq.}$ from effective spectral indexes $\alpha_{ox}\, {\rm and}\, \alpha_{ro}$ as $\log \nu_{\rm p}^{\rm Eq.} = 16+4.238X $ if $X < 0$, and $\log \nu_{\rm p}^{\rm Eq.} = 16+4.005Y $ if $X > 0$, where $X = 1.0 - 1.262 \alpha_{ro} - 0.623 \alpha_{ox}$, and $Y = 1.0 + 0.034 \alpha_{ro} - 0.978 \alpha_{ox}$ \cite{Fan16}. In the present work, we investigate the correlation between the peak frequency and the radio to X-ray spectral index, that between peak luminosity (integrated luminosity) and $\gamma$-ray/optical luminosity, and that between peak luminosity and integrated luminosity. Some discussions are presented.

With reference to Planck scale Hubble parameter, super luminal expansion speeds, super luminal rotation speeds, Mach’s principle and Holographic principle, we review the current cosmological observations with eight simple assumptions. By understanding Yuri N. Obukhov and V.A. Korotky proposed cosmic rotational effects of polarization of radiation due to massive bodies, to some extent cosmic rotation can be deep-rooted in an observational approach and the ratio of current angular velocity and Hubble parameter can be estimated. It is possible to show that, at H₀ =70 km/sec/Mpc, current cosmic temperature, age, radius, mass, mass density are 2.721 K, 4.41x10¹⁷ sec, 90 billion light years, 1.14654x10⁵⁴ kg, 0.0482 times the current critical density respectively. Clearly speaking, current universe seems to constitute 267 Hubble spheres. Important point to be noted is that, current rotational kinetic energy is 0.6667 times the current critical energy. Based on the estimated current mass density and current rotational kinetic energy, current cosmic dark matter density can be shown to be 0.2851 times the current critical density. These numerical coincidences cast serious doubt on the on the real existence of currently believed ‘dark energy’. Initial and current expansion speeds are 3x10⁸ m/sec and 3.56x10⁹ m/sec respectively. With increasing cosmic age and increasing cosmic expansion speed, current universe is expanding with a speed of 11.885c. By knowing the time to time future cosmic temperatures, future Hubble parameters and corresponding future cosmic expansion speeds can be estimated and thus future expansion speed can be understood. Starting from ‘speed of light’, our model assumes a continuous increase in expansion speed and attains a current radius of 90 billion light years (without inflationary concepts) and casts a serious doubt on the actuality of currently believed ‘inflation’.

Background: Music evokes positive emotions and reduces stress and anxiety. Operating Room (OR) staff face various challenges which can lead to high levels of stress. The aim of the study is to assess whether listening to music during intraoperative phases improves the work environment by reducing anxiety and stress in the entire surgical team. Methods. A prospective observational study was conducted from February to September 2023, involving medical personnel, nursing staff, and nursing students. They were divided into two groups: Group 1 with music during surgical procedures, and Group 2 without music. Participants were administered two validated instruments: the Zung Anxiety Self-Assessment Scale (SAS) to measure anxiety, and the Positive and Negative Affect Schedule to assess emotions generating stress. Additional items were included for demographics, job satisfaction, and the organization method. Results. Music did not impact anxiety but increased positive emotions while reducing negative ones. Music had an ancillary effect, highlighting the need for significant organizational interventions aimed at increasing operator satisfaction, including voluntary rather than mandatory assignments for nursing staff. Conclusions. Music appears to reduce stress in the intraoperative team when supported by a positive work environment in which assigned operators have chosen to work in the OR.

We present a novel approach to quantum theory construction that involves maximizing the Shannon entropy of quantum measurements relative to their initial preparation. By constraining the maximization problem with a phase that vanish under measurements, we obtain quantum mechanics (vanishing U(1)-valued phase), relativistic quantum mechanics (vanishing Spin^c(3,1)-valued phase), and quantum gravity (also a vanishing Spin^c(3,1)-valued phase, but with a dilation constraint replacing the normalization constraint). The first two cases are equivalent to established theory, whereas the later case yields a quantum theory of accelerated reference frames, in which a quantized version of the Einstein field equation lives. Specifically, the spacetime interval is promoted to an observable, effectively building the metric tensor from the underlying quantum structure. Moreover, the SU(3)xSU(2)xU(1) gauge symmetries of the Standard Model arise naturally without additional assumptions. Finally, the solution is consistent only with 3+1 spacetime dimensions, as it encounters obstructions in all other dimensional configurations. This framework integrates quantum mechanics, relativistic quantum mechanics, quantum gravity, spacetime dimensionality, and particle physics gauge symmetries from a simple entropy maximization problem constrained by a vanishing phase.

Partial differential equations (PDEs) are used to describe a wide range of phenomena, such as heat transfer, fluid dynamics, and quantum mechanics. By solving PDEs, we can ob- tain insights into the behavior of the system and make predictions about its future evolution. Conventional numerical methods for obtaining the approximate solutions of PDEs may re- quire extensive computational resources and time, especially for complex PDEs and large- scale problems. The recently developed physics-informed neural network (PINN) has shown promise in a variety of scientific and engineering fields by incorporating physical laws into the loss functions of the neural network (NN). In addition, the training of PINN does not require ground truth data, but it has poor generalization ability to unseen domains. On the other hand, a convolutional neural network (CNN) has fast inference and better generalization ability, but it requires a large amount of training data. Taking the advantages of PINN and CNN by using Legendre multiwavelets (LMWs) as basis functions, we introduce a new method to approach the PDEs in this paper, namely Physics-Informed Legendre Multiwavelets CNN (PiLMWs-CNN), in order to continuously approximate a grid-based state representation that can be handled by a CNN. PiLMWs-CNN enable us to train our models using only physics-informed loss functions without any pre- computed training data, simultaneously providing fast and continuous solutions that gener- alize to previously unknown domains. In particular, the LMWs can simultaneously possess compact support, orthogonality, symmetry, high smoothness, and high approximation order. Compared to orthonormal polynomial (OP) bases, the approximation accuracy can be greatly increased and computation costs can be significantly reduced by using LMWs. We applied PiLMWs-CNN to approximate the damped wave equation, incompressible Navier-Stokes (N- S) equation, and two-dimensional heat conduction equation. The experimental results show that this method provides more accurate, efficient, and fast convergence with better stability when approximating the solution of PDEs.

Water resource pollution, particularly in river channels, presents a grave environmental challenge that necessitates a comprehensive and systematic approach encompassing assessment, forecasting, and effective management. This article provides a comprehensive exploration of the methodology and modeling tools employed to scrutinize the process of river channel pollution due to silting, rooted in the fundamental principles of hydrodynamics and pollutant transport dynamics. The study's methodology seamlessly integrates numerical simulations with state-of-the-art neural network techniques, with a specific focus on the Physics-informed neural networks (PINN) method. This innovative approach represents a groundbreaking fusion of artificial neural networks (ANN) and physical equations, offering a more efficient and precise means of modeling a wide array of complex processes and phenomena. The proposed mathematical model, grounded in the Euler equation, has been meticulously implemented using the Ansys Fluent software package, ensuring accuracy and reliability in the computations. In a pivotal phase of the research, a thorough comparative analysis was conducted between the results derived from the PINN method and those obtained through conventional numerical approaches using the Ansys Fluent software package. The outcomes of this analysis revealed the superior performance of the PINN method, characterized by the generation of smoother pressure fluctuation profiles and significantly reduced computation time, underscoring its potential as a transformative modeling tool. The calculated data originating from this study assumes paramount significance in the ongoing battle against river sedimentation. Beyond this immediate application, these findings also serve as a valuable resource for creating predictive materials pertaining to river channel silting, thereby empowering decision-makers and environmental stakeholders with essential information. The utilization of modeling techniques to address pollution concerns in river channels holds the potential to revolutionize risk management and safeguard the integrity of our vital water resources. However, it is imperative to underscore that the effectiveness of such models hinges on ongoing monitoring and frequent data updates, ensuring that they remain aligned with real-world conditions. This research not only contributes to the enhanced understanding and proactive management of river channel pollution due to silting but also underscores the pivotal role of advanced modeling methodologies in the preservation of our invaluable water resources for present and future generations.

The adoption of Machine Learning (ML) for building emulators for complex physical processes has seen an exponential rise in the recent years. While neural networks are good function approximators, optimizing the hyper-parameters of the network to reach a global minimum is not trivial, and often needs human knowl- edge and expertise. In this light, automatic ML or autoML methods have gained large interest as they automate the process of network hyper-parameter tuning. In addition, Neural Architecture Search (NAS) has shown promising outcomes for improving model performance. While autoML methods have grown in popularity for image, text and other applications, their effectiveness for high-dimensional, complex scientific datasets remains to be investigated. In this work, a data driven emulator for turbulence closure terms in the context of Large Eddy Simulation (LES) models is trained using Artificial Neural Networks and an autoML frame- work based on Bayesian Optimization, incorporating priors to jointly optimize the hyper-parameters as well as conduct a full neural network architecture search to converge to a global minima, is proposed. Additionally, we compare the effect of using different network weight initializations and optimizers such as ADAM, SGDM and RMSProp, to explore the best performing setting. Weight and function space similarities during the optimization trajectory are investigated, and critical differences in the learning process evolution are noted and compared to theory. We observe ADAM optimizer and Glorot initialization consistently performs better, while RMSProp outperforms SGDM as the latter appears to have been stuck at a local minima. Therefore, this autoML BayesOpt framework provides a means to choose the best hyper-parameter settings for a given dataset.

The accurate wellbore pressure control not only prevents from lost circulation/blowout and fracturing formation by managing density of drilling fluid, but also improves productivity by mitigating reservoir damage. The geothermal pressure calculated by constant parameters for geothermal well would bring big error easily, as the changes of physical, rheological and thermal properties of drilling fluids with temperature were neglected. This paper researches the wellbore pressure coupling by calculating the temperature distribution with existed model, fitting the rule of density of drilling fluid with temperature and establishing mathematical models to stimulate the wellbore pressures, which is expressed as the variation of Equivalent Circulating Density (ECD) under different conditions. With this method, temperature and ECDs in the wellbore of the first medium-deep geothermal well ZK212 Yangyi Geothermal Field in Tibet were determined, and the sensitivity analysis was simulated by assumed parameters, i.e. circulating time, flow rate, geothermal gradient, diameters of wellbore, rheological models and regimes, the results indicated the geothermal gradient and flow rate were the most influence parameters on the temperature and ECD distribution, and additives added in drilling fluid should be careful which would change the properties of drilling fluid and induce the temperature redistribution. To make sure the safe drilling, velocity of pipes tripping into the hole, depth and diameter of wellbore are considered to control the surge pressure.

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

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

Synthetic Aperture Radar (SAR) is an active type of microwave remote sensing. Using the microwave imaging system, remote sensing monitoring of the land and global ocean can be done in any weather conditions around the clock. Detection of SAR image targets is one of the main needs of radar image interpretation applications. In this paper, an improved two-parameter CFAR algorithm based on Rayleigh distribution and morphological processing is proposed to perform ship detection and recognition in high resolution SAR images. Through simulation experiments, comprehensive study of the two algorithms for high resolution SAR image target detection is achieved. Finally, the results of ship detection experiments are compared and analyzed, and the effects of detection are evaluated according to the Rayleigh distribution model and algorithms.

Synergy of radiation and immune system is currently receiving significant attention in oncology as numerous studies have shown that cancer irradiation can induce strong antitumor immune responses. It remains unclear, however, what are the best radiation fractionation protocols to maximize the therapeutic benefits of this synergy. Here, we present a novel mathematical model that can be used to predict and dissect the complexity of the immune-mediated response at multiple tumor sites after applying focal irradiation and systemic immunotherapy. We successfully calibrate the proposed framework with published experimental data, in which two tumors were grown in mice at two spatially separated sites from which only one was irradiated using various radiation fractionation protocols with and without concurrent systemic immunotherapy. The proposed model is calibrated to fit the temporal dynamics of tumor volume at both sites and can predict changes in immune infiltration in the non-irradiated tumors. The model was then used to investigate additional radiation fractionation protocols. Model simulations suggest that the optimal radiation doses per fraction to maximize antitumor immunity are between 10-13 Gy, at least for the experimental setting used for model calibration. This work provides the framework for evaluating radiation fractionation protocols for radiation-induced immune-mediated systemic antitumor responses.

Arc sensors have been used in seam tracking and widely studied since the 80s; commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and swing or rotate speed.

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

In this research, we present the Combined Theoretical Signal (CTS) model, which integrates influences from dark matter, quantum fluctuations, and higher-dimensional effects. Our goal is to provide a potential framework for unifying gravity and quantum physics. We validate the CTS model against observational gravitational wave data and perform residual analysis to assess its accuracy. The results suggest that CTS aligns well with the observational data and provides a robust theoretical model that may contribute significantly to the quest for a universal theory. This model has the potential to enhance our understanding of the fundamental forces and the structure of the universe, supporting a hierarchical tree structure rather than parallel universes.

It is shown that gravity and quantum physics can be unified upon the basis of a quark description in terms of a gravitational Dirac particle. It requires the awareness of a second elementary dipole moment (isospin) next to the angular moment (spin) of Dirac particles and the awareness of an (unbroken) omnipresent energetic cosmological background field. The unification has been made explicit by an expression that relates the two major gravitational constants of nature (the gravitational constant and Milgrom’s acceleration constant) with the two major nuclear constants of nature (the weak interaction boson and the Higgs boson).

Deformation of the surface of diamagnetic liquid by magnetic field is called the “Moses Effect”. Physics and applications of the direct and inverse Moses effects are reviewed. Experimental techniques enabling visualization of the effects are surveyed. Impact of magnetic field on micro- and macroscopic properties of liquids is addressed. Influence of the surface tension on the shape of the near-surface dip formed in a diamagnetic liquid by magnetic field is reported. Floating of diamagnetic bodies driven by the Moses effect is treated. The effect of the “magnetic memory of water” in its relation to the Moses Effect is discussed. The dynamics of self-healing of near-surface dips due to the Moses Effect is considered.

The current paper explores the potential interlink between names of individuals in a society and its collective social consciousness, particularly with reference to the pervasive occurrence of the ‘mathematical names’ in the current Hindu society in the Indian subcontinent and beyond. Initially, an attempt is made to put things into mathematical perspective by drawing a quick sketch of some of the stellar achievements of the Indian mathematicians. Under the six broad categories of geometry, trigonometry, numeration, arithmetic, algebra, and mathematics in the Vedic tradition, a concise simple description of these subdivisions is presented, underlining the names of the concepts and terms, sometimes by producing the textual references. Then, upon identification of such mathematical terms, an attempt is made to juxtapose these with the names current in the Indian Hindu society. By employing an extensive dataset of university student names in India and the directories of Facebook and LinkedIn, we produce both qualitative and quantitative evidence of the presence of such names in the Indian subcontinent. Evidently, these names reflect the impressions of the tremendously rich mathematical heritage left by the Hindu stalwart mathematicians. This hypothesis has also been examined by taking surveys of people bearing these mathematical names, as well as by documenting the ‘conscious procedures’ that go behind the naming of a Hindu Indian child. In trying to investigate if such a phenomenon is unique to the Indian tradition, a stark contrast with the ‘names in mathematics’ as prevalent in the European mathematical traditions is presented, as cultural roots of mathematics are explored. Further, we ascribe the presence of these names as the extant remains of the colossal impact of multifarious mathematical traditions existing in India. Interestingly, the present research also brings to the fore, certain unseen facets of the Indian Hindu society as regards the education of mathematics to women – through an indirect exploration of their names. We also show that the pervasive occurrence of these names is not merely the result of semantic chance events, but denotes the richness of the Indian mathematical legacy. Next, we also present cross-cultural comparisons to show the uniqueness of Indian mathematical and scientific traditions that led to the pervasiveness of ‘mathematical names’ in India. Finally, an attempt is made to clarify some subtle points on the associations between mathematics and religion in India and other cultures of the world. It is sincerely hoped that the present study may shed light on the cultural roots of mathematics and may furnish a new dimension in the study of mathematics, culture and civilizations across the world.

The quantified residence time distribution (RTD) provides a numerical characterization of mixing in the continue casting tundish, thus allowing the engineer to better understand the metallurgical performance of the reactor. This paper describes a computational fluid dynamic (CFD) modelling study for analyzing the flow pattern and the residence time distribution in a five-strand tundish. Two passive scalar transport equations are applied to separately calculate the E-curve and F-curve in the tundish. The numerical modelling results are compared to the water modelling results for the validation of the mathematical model. The volume fraction of different flow regions (plug, mixed and dead) and the intermixing time during the ladle changeover are calculated to study the effects of the flow control device (FCD) on the tundish performance. The result shows that a combination of the U-baffle with deflector holes and the turbulence inhibitor has three major effects on the flow characteristics in the tundish: i) reduce the extent of the dead volume; ii) evenly distribute the liquid streams to each strand and iii) shorten the intermixing time during the ladle changeover operation.

The paper highlights the performance of the seismic isolation devices, installed on retrofitted buildings in reducing the seismic response when subjected to earthquakes. Two buildings from the beginning of the XX-th century in Bucharest are chosen from many more, monitored over the city area. We discuss the response of these base-seismic isolated structures, relying on good quality data acquired from the recent strong earthquake (03.11.2022, MW = 5.0). Elastic response spectra computed from recordings at two levels of each structure are used, placed under and right above the isolating layer. At one building the existence of previous recordings and the particularity of the sensors allow a comparison with other two relatively recent medium intensity earthquakes. The assessment is carried out in terms of maximum acceleration amax, measured at certain levels in each structure, spectral acceleration amplitude SAmax and spectral-peak corresponding period. We find that the base-isolation methodology is effective in reducing the response of the building right above the isolating layer, an observation valid for both structures, all components of the recordings, and spectral acceleration values. Moreover, the outcomes from the modal evaluation performed prior to rehabilitation and seismic isolation process are presented, by pointing out a higher newly acquired fundamental period of the isolated structures.

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex anti-tumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these fields of research for more efficient development and effective treatments.

We introduce optically clear and resilient free-form micro-optical of pure (non-photosensitized) organic-inorganic SZ2080 material made by femtosecond 3D laser lithography (3DLL). This is advantageous for rapid printing of 3D micro-/nanooptics, including their integration directly onto optical fibers. A systematic study on the fabrication peculiarities and quality of resultant structures is performed. Comparison of microlenses’ resiliency to CW and femtosecond pulsed exposure is determined. Experimental results prove that pure SZ2080 is ∼3 fold more resistant to high irradiance as compared with a standard photo-sensitized material and can sustain up to 1.91 GW/cm² intensity. 3DLL is a promising manufacturing approach for high-intensity micro-optics for emerging fields in astro-photonics and atto-second pulse generation. Additionally, pyrolysis is employed to shrink structures up to 40% by removing organic SZ2080 constituents. This opens a promising route towards downscaling photonic lattices and creation of mechanically robust glass-ceramic structures.

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

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

In March 2020, the World Health Organization declared coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2, to be a pandemic. Since the declaration, Nigeria economy has been greatly impacted thus resulting in a recession. This paper considers a couple of misconceptions among Nigerian people in the COVID-19 pandemic era thereby causing the spread of the novel virus and hence making the situation difficult for the government to handle. In particular, we discuss the first and second waves of the pandemic as it affects the Nigerian people. The impact of the pandemic on animals and the role of mathematical epidemiologists in combatting the spread is discussed herein. We give some recommendations that could be adopted by the government and the good people of Nigeria to reduce the further spread of the virus.

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

Oil floating on the sea surface can be detected by both passive and active methods using the ultraviolet-to-microwave spectrum, whereas oil immersed below the sea surface can signal its presence only in visible light. This paper presents an optical model of a sea area deeply polluted by an oil suspension (10 ppm) located in a layer (thickness 5 m) separated from the sea surface by a clear layer (thickness 1 m). The impact of wavelength and state of the sea surface on reflectance changes is shown based on the results of Monte Carlo ray tracing. A two-wavelength index of reflectance is proposed to detect oil suspended in the water column (645-469 nm).

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

Antimicrobial resistance (AMR) is one of the greatest public health challenges we are currently facing. To develop effective interventions against this, it is essential to understand the processes behind the spread of AMR. These are partly dependent on the dynamics of horizontal transfer of resistance genes between bacteria, which can occur by conjugation (direct contact), transformation (uptake from the environment) or transduction (mediated by bacteriophages). Mathematical modelling is a powerful tool to investigate the dynamics of AMR, however its application to study the horizontal transfer of AMR genes is currently unclear. In this systematic review, we searched for mathematical modelling studies which focused on horizontal transfer of AMR genes. We compared their aims and methods using a list of predetermined criteria, and utilized our results to assess the current state of this research field. Of the 43 studies we identified, most focused on the transfer of single genes by conjugation in Escherichia coli in culture, and its impact on the bacterial evolutionary dynamics. Our findings highlight the existence of an important research gap on the dynamics of transformation and transduction, and the overall public health implications of horizontal transfer of AMR genes. To further develop this field and improve our ability to control AMR, it is essential that we clarify the structural complexity required to study the dynamics of horizontal gene transfer, which will require cooperation between microbiologists and modellers.

Byers Peninsula (62°34’-62°40’S-60°54’61°13’W), 60 km2 in size, is considered one of the largest ice-free areas in Antarctica. Since 2006, the Spanish Polar Program has taken part in a large number of environmental studies involving effects of climate changes, limnology and microbiology, live cycles, but not albedo. Surface albedo is one of the key physical parameters in the surface energy budget of polar regions. Most of Antarctica is covered by ice sheets; only about 0.44% of the area is permanently ice-free. However, in maritime Antarctica, the ice-free areas, corresponding to small islands, peninsulas, and coastal beaches, account for about 3% of the territory. To incorporate the contribution of these areas into global albedo models, it is necessary to relate the soil properties of the ice-free areas to the surface albedo response. Also, mapping soil properties and albedo have and special interest in these ice-free areas. Image classification using machine learning methods trained with georeferenced soil data could be useful for mapping soil properties and albedo in multispectral optical satellite images. A shallow neural network implemented using the Keras Python module was used to define and train models of soil properties using 15 explanatory variables corresponding to bands and spectral indices of a Sentinel image and a population of 49 soil samples taken from the top 5 centimeters of the soil profile. The soil samples were analyzed in the laboratory and a spectral library in the Vis-Nir range (350-2500 nm) was created. The albedo of the samples was integrated from the ADS spectra. At the same time, a linear regression model of albedo using the soil properties as explanatory variables was performed. The R2 fit of this new model was about 0.82 and the error of estimation was 4.1. The model was extended to the entire Byers Peninsula using the ML soil property models as explanatory variables. The RMSE of the extended models increased up to 8.2. We think that the main cause of this increase (2.6 points) is related to the error propagation, phenomenon due to the use of models as explanatory variables. However, another important part of the error increase could be due, among other reasons, to the use of an image that, although corrected, is not completely free of clouds.

This paper presents a comprehensive investigation into the applicability and performance of two prominent growth models, namely the Verhulst model and the Montroll model, in the context of modeling tumor cell growth dynamics. Leveraging the power of Physics-Informed Neural Networks (PINNs), we aim to assess and compare the predictive capabilities of these models against experimental data obtained from the growth patterns of tumor cells. We employ a dataset comprising detailed measurements of tumor cell growth to train and evaluate the Verhulst and Montroll models. By integrating PINNs, we not only account for experimental noise but also embed physical insights into the learning process, enabling the models to capture the underlying mechanisms governing tumor cell growth. Our findings reveal the strengths and limitations of each growth model in accurately representing tumor cell proliferation dynamics. Furthermore, the study sheds light on the impact of incorporating physics-informed constraints on the model predictions. The insights gained from this comparative analysis contribute to advancing our understanding of growth models and their applications in predicting complex biological phenomena, particularly in the realm of tumor cell proliferation.

In this paper we study the influence of a small group of agents (i.e., a lobby) who is trying to spread a rumor in a population using the well known model suggested by Galam. In particular, lobbies are modeled as subgroups of people who strategically choose their seating in the social space in order to protect their opinion and influence the others. We consider different social gatherings and simulate the opinion dynamics comparing situations in which a lobby is present to those without lobby. Our results show how the lobby can influence the opinion dynamics in terms of the prevailing opinion and the mean time to reach unanimity. The approach we follow overcomes some of the issues that behavioral economics and psychology have recently encountered in terms of replicability. This approach relates to the methodological revolution which is slowly changing the perspective in psychology.

Condition monitoring of rotating shafts is essential for ensuring the reliability and optimal performance of machinery in diverse industries. In this context, as industrial systems become increasingly complex, the need for efficient data processing techniques is paramount. Deep learning has emerged as a dominant approach due to its capacity to capture intricate data patterns and relationships. However, a prevalent challenge lies in the black-box nature of many deep learning algorithms, which often operate without adhering to the underlying physical characteristics intrinsic to the studied phenomena. To address this limitation and enhance the fusion of data-driven methodologies with the fundamental physics of the system under study, this paper leverages physics-informed neural networks (PINNs). Specifically, a simple but realistic numerical case study of an extended Jeffcott rotor model, encompassing damping effects and anisotropic supports for a more comprehensive modelling, is considered. PINNs are used for the estimation of five parameters that characterize the health state of the system. These parameters encompass the radial and angular position of the static unbalance due to the disk installed on the shaft, the stiffness along the principal axes of elasticity, and the non-rotating damping coefficient. The estimation is conducted solely by exploiting the displacement signals from the centre of the disk and, to showcase the efficacy and precision provided by this novel methodology, various scenarios involving different constant rotational speeds are examined. Additionally, the impact of noisy input data is also taken into account within the analysis.

This study aimed at exploring what role artificial intelligence techniques could play in the futural numerical analysis. In this paper, a convolutional neural network techniques based on modified loss function is proposed as a surrogate of finite element method(FEM). Several surrogate-based physics-informed neural networks(PINNs) are developed to solve representative boundary value problems based on elliptic partial differential equations (PDEs). Results from the proposed surrogate-based approach are in good agreement with ones from conventional FEM. It is found that modification of the loss function could improve the prediction accuracy of the neural network. It is indicated that to some extent the artificial intelligence technique could replace conventional numerical analysis as a great surrogate model.

Emergent physics education research (PER) literatures have been disseminated through academic publications within the community. The growing body of literatures over years challenge Indonesian PER scholars to understand how the research community has been progressed and what possible future work that should be emphasized. Nevertheless, previous traditional method of thematic analysis performed serious limitation when the number of PER literatures exponentially increased. Dealing with this large volume of publications, one of the machine learning studies namely natural language processing (NLP) was employed in this study to automate our thematic analysis among Indonesian PER literatures that are still limited to be explored. One of the well-known NLP algorithm, latent Dirichlet allocation (LDA), has been performed to extract Indonesian PER topics and their associated development between 2014 and 2021. A total of 852 papers (~ 4 to 8 pages each) were collectively downloaded from five international conference proceedings organized by Indonesian PER researchers. Before their topics were modeled through LDA algorithm, our data corpus should be previously preprocessed through several common procedures of established NLP studies. Findings revealed that LDA has thematically quantified Indonesian PER topics and described their distinct development over certain period. The identified topics from this study demonstrated that Indonesian PER community has established robust development in eight distinctive topics to the present. They begin with initial interest in focusing research on physics laboratory and following the research based instruction in the late 2015. Indonesian PER scholars sustained to study continuous topic on 21st century skill until 2019 which gave way to a focus on developing relevant educational technology to address several forms of students’ performance including scientific literacy and problem solving. There is still lack of Indonesian PER literatures that have been attempted to address qualitative aspects of physics teaching and learning.

Focusing geophysics to improve recovery factor of hydrocarbon reservoirs adds value and contributes toward ZERO carbon footprint by increasing the recovery factor by of 30-40 % and thus reducing the cost/carbon emission per produced barrel. Thus, the Enhanced Oil Recovery (EOR) market is expected to grow more than 3.5% annually. This will be even more fueled by the Green-House-Gas (GHG) reduction and subsequent CO2 injection into the reservoirs as they are being produced. Presently, geophysics only ac-counts for a small percentage of this market, thus its growth is inevitable since more deterministic observation lead higher operating efficiency. Imaging the fluids (hydro-carbon, water, and CO2) is a key component to optimized production and injection. We designed a novel electromagnetic (EM) acquisition system that combines mul-ti-physics fluid imaging and acquires surface and borehole data with high fidelity. Borehole calibration is needed to upscale reservoir data and parameters to measurement scale. Multiple electromagnetic methods are used as well as microseismics in one layout for Exploration and Production (E & P) problems. Multi-components in electromagnetics allows resolving oil and water-bearing zones equally well while achieving the best ac-curacy suitable for repeat measurements. Because sedimentary basins are intrinsically anisotropic, considering 3-dimensional anisotropy is essential from measurement and 3D modeling viewpoint. Thus, the results have the better subsurface images. Here, we combine hardware design, methodology, 3D modeling, processing, and interpretations into an integrated technology and demonstrate the success with verifiable case histories.

Under the big unified framework of quantum gravitational field and quantum repulsive field, the earlier in this series of work has comprehensively expanded the general relativity and loop quantum ring gravitation theory, set up the quantum repulsive field equation corresponding to the quantum gravitational field equation, and then established the quantum hedge-unified field equation describing the interaction of quantum gravitational field and quantum repulsive field; On this basis, the quantum repulsive universe equation corresponding to the quantum gravitational universe equation has be established, thus a set of new equations describing the expansive universe model under the condition of fully considering the hedge effect of quantum gravitational field and quantum repulsion field, which can be called the expansive universe equation of quantum hedge-unified field theory, has be established. Now, let's go deep into the arche-unified physics behind the creation of the universe. Although all kinds of inflationary universe models can solve cosmological problems to a certain extent, there is no natural and reasonable analysis and explanation for all cosmological and physical consequences. For example, it is impossible to predict a large tensor-scale ratio and a relatively large spectral index run at the same time. At present, string theory, membrane theory, loop quantum gravity theory, super-gravitational holography principle and M theory, which are the theoretical basis of cosmology, are basically established by simplification in the case of breaking away from the extreme background conditions of the universe. While cosmology, which is deficient in nature, cannot provide strong support for particle physics to further advance to a wider field and a deeper level. Due to the lack of new ideas, the construction of existing theoretical models is difficult. Therefore, the existing research can only be further promoted by new astronomical observation. Unlike existing studies, we concentrate on the emergence of the big rip-rebound clusters of quantum chaotic-reticulate distribution between the outwards-push of the universe as a whole (related to pseudo-vacuum energy, Higgs field, dark energy, etc.) and the inwards-pull of the universe in local scale (related to dark matter, quantum gravity and initial gravity separated from high-dimensional supergravity, and the initial strong force separated from the grand unified force subsequently). On the one hand, we find a great impetus to make the inflation of the universe into firstly-imposed suppression, then-imposed acceleration and finally-imposed deceleration, which really explains why the universe expands at a critical rate and has the same temperature in different regions, on the other hand, we find a fundamental unit of matter and its emerging clusters evolving in the big bang, inflation and expansion of the universe accompanied by the great rip-rebound clusters of quantum chaos-reticulate distribution, which can be reduced to an arche-pulsator of neither punctiform particle nor linear string. From these two aspects, it can been seen that the evolution of the early universe is much more complicated than people originally thought. The complexity of the super inflation of the universe is mainly reflected in the big rip-rebound cluster emerging behind the gravitational disturbance (the pressure and tensor disturbance related to dark matter), the repulsive disturbance (the pressure and scalar disturbance related to dark energy), the cosmological disturbance (related to the interaction between high-dimensional supergravity and high-dimensional superrepulsion). This is a system of nonlinear stochastic differential dynamics, or a quantum statistical physical process of nonlinear nonequilibrium state. In the new research paradigms established in this series, the arche-conjugation between the high-dimensional supergravity and the high-dimensional superrepulsion, as well as between the quantum gravity and the quantum repulsion, is higher than the supersymmetry, and then becomes the core concept of the new theory. In this series, cluster-inflating configuration, spin network space and cosmic paradigm vectors are proposed, so the model of the super-inflated universe with quantum chaos-reticulate distribution emerged under the great impetus. The new model reveals that the unified inflation of the universe as a whole and the local inflation of the universe emerge together in the great impetus of the big rip-rebound cluster of quantum chaos-reticulate distribution. As a spin network model variable, the spatiotemporal mode variable is a vector composed of a series of variables, which variables include: dimension, curvature, range, expansion speed, dynamics, quantization, chaotic-reticulate distribution (inhomogeneity, concentration, fluctuation), synergy, and so on. Between particle physics and cosmology, this series of papers proposes the cosmic quantum evolution mode, the physical-sphere distributing configuration and the interaction situation variables, organizes the concepts, variables and models of these three levels, and establishes a systematic super-synergy paradigm. In this paradigm, the general Langevan equation and the general Fokker-Planck equation are established. For the quantum cosmic-sphere, a series of trend parameters are introduced to establish the dynamics of quantum gravitational mode and its master equation, and then to establish the operator distribution function and its motion equation of the action mode. For the Tachyon of upheaval in the rip-rebound-inflating of the universe, the hypothesis on the bifurcate-chaos wave of quantum is given, the quantum theory of the early photons in upheaval is set up, and the analysis on the particles of the ultrahigh energy cosmic ray from the γ ray burst is made. Finally, using Wigner-Ville distribution as a nonlinear time-frequency distribution, we establish the ultra-synergistic field equation of quantum-classic unifying action-sphere.

The beneficial effects of Lanthanide incorporation into 0.94Na0.5Bi0.5TiO3-0.06BaTiO3 (BNT-BT) matrix on its functional properties were investigated. The conventional solid-state method was used for synthesizing samples. The structural refinement revealed that all samples crystallized in R3c rhombohedral symmetry. Raman spectroscopy study was carried out using green laser excitation and revealed that no clear perceptible variation in frequency is observed. Dielectric measurements unveiled that the introduction of rare earth obstructed the depolarization temperature promoted in BNT-BT with decreasing the diffusive phase transition with increasing the lanthanide size. Only Dysprosium addition showed comparable diffusion constant and dielectric behavior as the unmodified composition. Further, the comparison of the obtained ferroelectric hysteresis and strain-electric field loops revealed that only Dy-phase exhibited interesting properties comparing parent composition. In addition, the incorporation of lanthanides Ln3+ into the BNT-BT matrix led to the development of luminescence characteristics in the visible and near infrared regions, depending on the excitation wavelengths. The simultaneous occurrence of photoluminescence and ferroelectric/piezoelectric properties opens up possibilities for BNT-BT-Ln to exhibit multifunctionality in a wide range of applications.Keywords: Sodium Bismuth Titanate; structural refinement; dielectric properties; ferroelectric properties; piezoelectric properties; Photoluminescence.

It is claimed that classical mechanics (CM) in terms of its equivalent Koopman-von Neumann formulation (KvN) is indeed a ’real’ quantum theory since the formalism of quantum mechanics (FQM) does not, nor need it, exclude it as a such. This claim is made manifest by suggesting a common structure of which both KvN and ordinary quantum mechanics (OQM) correspond to unitary representations of, although unitarily inequivalent such. It is shown that OQM is obtained by enforcing the extra physical condition of quantized energy levels, which by itself does not constitute the ’quantum mystery’. It is furthermore shown that KvN in a physically realizable sense contain the hallmark quantum behavior of quantum interference. It is hence concluded that both CM and OQM are subjected to the same foundational issues. As the central part of both KvN and OQM is the introduction of probabilities via FQM it is suggested that the foundational issues regarding FQM are less about FQM itself and more about the concept of probability.

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

Based on three assumptions of our 4G model of final unification, we have developed simple logics for estimating the unified atomic mass unit, atomic electrochemical equivalents, Faraday constant and Avogadro number. We appeal the science community to review the following points. 1) Unified atomic mass or energy unit can be considered as ‘average rest energy of nucleons minus average binding energy per nucleon of all atomic nuclides plus electron rest energy’. 2) Electrochemical equivalent of any atomic ion is nothing but the ratio of its mass to its charge. 3) Faraday charge is nothing but the ratio of elementary charge to unified atomic mass unit. 4) Faraday mass can be considered as the inverse of Faraday charge. 5) Avogadro number is nothing but the inverse of unified atomic mass unit. 6) Number of atoms per kg can be called as Kg-mole and number of atoms per gram can be called as gram-mole. Following our 4G model, starting form A=5 to 340, for isobars, ‘average binding energy per nucleon’ having maximum binding energy can be estimated with a simple relation of the form, BE/A=A^-1[1-(0.5+0.000935A²)-A^1/3]10.1MeV. It needs a review and fine tuning.

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.

In this paper, the computational fluid dynamics (CFD) method has been used to simulate the gas flow and the catalytic hydrogenation process of the C-2 hydrogenation adiabatic reactor in a practical ethylene production unit of a chemical plant. The laminar finite-rate model was used for the chemical reaction model. The standard two-equation model was used for the turbulence model. The exponent-function kinetic model was used for the reaction dynamics model. The simulation results were in good agreement with the actual industrial data obtained from the C-2 hydrogenation reactor, and the distributions of reaction parameters such as temperature and component concentrations in the reactor were further analyzed. Based on the validated CFD models, the structure and operating conditions of the reactor, as well as hydrogen load distribution ratios, are simulated for comparing the comprehensive performance metrics of ethylene selectivity and acetylene conversion rate; as a result, we can obtain the optimal temperature of 312 K, the optimal hydrogen/acetylene ratio of 0.10 as well as the optimal hydrogen load distribution ratio of 4:4:2, and the diameter/height ratio exerts a marginal effect on the selectivity, conversion rate and harmonic mean of the reactor.

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

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

This 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.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

Hidden markov models are a very useful tool in the modelling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden markov model to analyze the underlying structure of an ancient and complex manuscript, known as Voynich's manuscript, that remains still undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscript we train the network by means of the $\alpha$ and $\beta$-pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices in order to compare with known languages concerning the frequency of consonant and vowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.

This paper proposes a new approach to investigation into the aesthetics. Specifically, it argues that it is possible to explain the aesthetic and its underlying dynamic relations with axiomatic structure (the octahedral axiom derived category) based on contemporary mathematics – namely, category theory – and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there was a way to describe the structure of aesthetics with the language of mathematical structures and mathematical axioms – a language completely devoid of arbitrariness – then we would make possible a synthetical argument about the essential human activity of “the aesthetics”, and we would also gain a new method and viewpoint on the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one hypothesis as a first step in constructing the science of dynamic generative aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the functional structure of aesthetics.

The rationalization of single molecule magnets’ (SMMs) magnetic properties by quantum mechanical approaches represents a major task in the field of the Molecular Magnetism. The fundamental interpretative key of molecular magnetism is the phenomenological Spin Hamiltonian and the understanding of the role of its different terms by electronic structure calculations is expected to steer the rational design of new and more performing SMMs. This paper deals with the ab initio calculation of isotropic and anisotropic exchange contributions in the Fe(III) dimer [Fe₂(OCH₃)₂(dbm)₄]. This system represents the building block of one of the most studied Single Molecule Magnets ([Fe₄RC(CH₂O)₃)₂(dpm)₆] where R can be an aliphatic chain or a phenyl group just to name the most common functionalization groups) and its relatively reduced size allows the use of a high computational level of theory. Calculations were performed using CASSCF and NEVPT2 approaches on the X-ray geometry as assessment of the computational protocol, which has then be used to evinced the importance of the outer coordination shell nature through organic ligand modelization. Magneto-structural correlations as function of internal degrees of freedom for isotropic and anisotropic exchange contributions are also presented, outlining for the first time the extremely rapidly changing nature of the anisotropic exchange coupling.

Color centers in diamond and nanodiamonds can be utilized as quantum sensors for measuring various physical parameters, particularly magnetic and electric fields, as well as temperature. Due to its small size and possible surface functionalization, fluorescent nanodiamonds are attractive systems for biological and medical applications since they can be used for intracellular experiments. This review focuses on fluorescent nanodiamonds for thermometry with nanoscale spatial resolution for living systems. The current state of the art, possible further development, and potential limitations will be discussed here.

Depth-sensing technology has led to broad applications of inexpensive depth cameras that can capture human motion and scenes in 3D space. Background subtraction algorithms can be improved by fusing color and depth cues, thereby allowing many issues encountered in classical color segmentation to be solved. In this paper, we propose a new fusion method that combines depth and color information for foreground segmentation based on an advanced color-based algorithm. First, a background model and a depth model are developed. Then, based on these models, we propose a new updating strategy that can eliminate ghosting and black shadows almost completely. Extensive experiments have been performed to compare the proposed algorithm with other, conventional RGB-D algorithms. The experimental results suggest that our method extracts foregrounds with higher effectiveness and efficiency.

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

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

The planned closure of potash mines, achieved through the injection of highly mineralized brines into the worked-out area, is a complex and not fully studied process. A critical concern arises when brines obstruct the aerodynamic connections between the flooded mine's airspace and the atmosphere, potentially leading to the formation of closed cavities where explosive gases can accumulate. To address this hazard, it is imperative to develop systems capable of extracting the gas-air mixture from the unflooded domed portions of the worked-out area. This is the focus of this study, in which we analyze gas-dynamic processes within the potassium mine worked-out area during planned flooding. Two distinct scenarios are examined: the first involves controlled flooding with saturated brines, while the second contemplates flooding resulting from a hypothetical breakthrough of supra-salt strata, leading to the ingress of groundwater into the worked-out area. A novel mathematical model is introduced to predict the evolution of gas-air mixture parameters in the unflooded dome segment of the worked-out area. Utilizing this model, we assess the effectiveness of proposed measures designed to eliminate explosive gases from the worked-out area. Specifically, a pipeline system is proposed for the removal of gases, followed by their dilution below the maximum permissible concentrations in the effluent jet. The findings from this study contribute valuable insights into ensuring the safe and efficient closure of potash mines, shedding light on potential risks and effective mitigation strategies for gas-related hazards during planned flooding.

We propose a new theory beyond the standard model of elementary-particle physics. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. No serious undetermined parameters are assumed. Furthermore, the relations between the forces at the quantum-mechanics level is made clear. Using these relations, we quantize Einstein’s gravitational equation: Beginning with the zero-point energy of the vacuum, and after quantizing Newtonian gravity equation, we combine the energies of a static electromagnetic field and gravity in a quantum spacetime. Applying these results to the Einstein gravity equation, we substitute the energy density derived from the zero-point energy in addition to redefining differentials in a quantized spacetime. This is how we derive the quantized Einstein gravitational equation without assuming the existence of macroscopic masses. For the weak interaction, by considering plane-wave electron and the zero-point energy, we obtain a wavefunction that represents a β collapse. In this process, from a different point of view than Weinberg-Salam theory, we derive the masses of the W and Z bosons and the neutrino, and we calculate the radius and lifetime of the neutron. For the strong interaction, we previously reported an analytical theory for calculating the mass of a proton by providing a specific linear attractive potential obtained from the zero-point energy, which agrees well with the measurements. In the present study, we further calculate the strong interaction between two nucleons, i.e., the mass of the pi-meson. The resulting calculated quantities agree with the measurements, which verifies our proposed theory.

The use of naturally available materials not conforming to traditional specifications or standards, in the base and sub-base layers of road pavement structures, stabilised with New-age (Nano) Modified Emulsions (NME), have been tested, implemented and successfully verified through Accelerated Pavement Testing (APT) in South Africa. This was made possible through the development and use of a design procedure addressing fundamental principles and based on scientific concepts, which are universally applicable. The understanding of and incorporation of the chemical interaction between the mineralogy of the materials and a NME stabilising agent (compatibility between the chemistry of the reactive agents and material mineralogy) into the design approach is key to achieving the required engineering properties. Stabilised materials evaluation is done using tests indicative of the basic engineering properties (physics) of compressive strengths, tensile strengths and durability. This article describes the basic materials design approach developed to ensure that organofunctional nano-silane modified emulsions can successfully be used for pavement layer construction utilising naturally available materials, at a low risk. The enablement of the use of naturally available materials in all pavement layers can have a considerable impact on the unit cost and life-cycle costs of road transportation infrastructure. TRANSLATE with x English ArabicHebrewPolish BulgarianHindiPortuguese CatalanHmong DawRomanian Chinese SimplifiedHungarianRussian Chinese TraditionalIndonesianSlovak CzechItalianSlovenian DanishJapaneseSpanish DutchKlingonSwedish EnglishKoreanThai EstonianLatvianTurkish FinnishLithuanianUkrainian FrenchMalayUrdu GermanMalteseVietnamese GreekNorwegianWelsh Haitian CreolePersian TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster Portal Back

The purpose of this paper is to find a quantum formulation of entropic gravity, incorporating the bijective theory. In a first part, we will describe the basis of the bijective theory. In a second part, we will incorporate the stress energy quantum tensor defined in the linear approximation of the Einstein’s equation in its quantum version to entropy. In the third part, we will integrate the bijective theory with the newly created relativistic quantum entropy. This will lead us four part where we will formalize quantum entropic gravity.

Seeds from several Ribes taxa were surveyed for phenolic compounds and in vitro antiproliferative activity against HT-29 colorectal cancer cells. Total phenolic compounds were analysed through the Folin-Ciocalteu procedure, while phenolic profiles were analysed by LC coupled to a single mass spectrometer Orbitrap using an electrospray interface (ESI). Antitumor effects were established using the MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay. Total phenolics ranged from 11.4 in R. alpinum to 94.8 mg of caffeic acid equivalents (CAE)/g in R. nigrum 'Koksa'. Concerning phenolic compounds, four were hydroxylated benzoic acids, four cinnamic acid derivatives, eight flavonoids, and nine flavonoid glycosides. The growth inhibition against HT-29 cancer cells was exercised much better by R. nigrum 'Koksa' and Ribes 'Erkeeni' (GI50 37 and 42 µg/ml). All Ribes extracts, except R. nigrum 'Hara katarlik', showed higher activity than that of R. rubrum (GI50 at 72 h: 99 µg/ml). Interestingly, the highly bioactive extract from Ribes 'Erkeeni' contains all detected phenolics, while R. nigrum 'Koksa' lacks only populnin. Therefore, the high bioactivity found for such extracts could be due to a synergy due to all detected compounds. This work constitutes a comprehensive action for expanding knowledge on the phenolic profiles and antitumor activity of GLA-rich Ribes seeds.

Deep Neutral Networks (DNNs) were initially proposed towards the midst of the 20th century, motivated by the neural structure and mechanism of the human brain. Thanks to major ad-vancements in computational resources, during the past decade DNN-based systems have demonstrated unprecedented performance in terms of accuracy and speed. However, recent work has shown that such models may not be sufficiently robust during the inference process. Furthermore, due to the data-driven learning nature of DNNs, designing interpretable and gen-eralizable networks is a major challenge, especially in critical applications, such as medical Computer Aided Diagnostics (CAD) and other medical imaging tasks, including classification, regression and reconstruction. Within this context, a line of physics-driven approaches for deep learning has recently emerged, aimed at improving the stability and generalization capacity of DNNs for medical imaging applications. In this paper, we review recent work focused on phys-ics-driven or prior-information learning for a variety of imaging modalities and medical applica-tions. We discuss how the inclusion of domain-related knowledge into the learning process and networks’ design supports their stability and generalization capability. In addition, we highlight current and future challenges within this scope.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

The ability to self-direct a research program determines graduate degree completion. Yet, research on incompletion of graduate physics programs assume students’ present level of self-direction adequate and neglects to recognize a lack of self-directed learning as key. One theoretical mathematical physicist focused on changing this challenge of physics graduate education by promoting self-directed learning through the type research flow that has been found to bring the greatest satisfaction to researchers with respect to their insights. This he provided through his space, time, open mindedness and theoretical contributions with his students and in collaboration with his colleagues. A self-directed learner himself, David J. Rowe developed methods of mentoring for encouraging physics graduate students to recognize symmetry as valuable in identifying solutions to problems quickly—helping these students take the lead in finding insightful resolutions to complex, multidimensional, mathematical physics uncertainties. How Rowe set about supporting self-directed learning in his graduate physics education interactions will be examined with the use of narrative research to interpret the texts and conversations with the author he made available. His techniques will be presented and recommendations made regarding how Rowe’s work in this regard can be modeled to improve self-direction in STEM graduate education.

Deep learning machines are computational models composed of multiple processing layers of adaptive weights to learn representations of data with multiple levels of abstraction. Their structure is mainly reflecting the intuitive plausibility of decomposing a problem into multiple levels of computation and representation since it is believed that higher layers of representation allow a system to learn complex functions. Surprisingly, after decades of research, from learning and design perspectives these models are still deployed in a heuristic manner. In this paper, deep learning feed-forward machines are modeled from a statistical mechanics point of view as disordered physical systems where its macroscopic behavior is determined in terms of the interactions defined between the basic constituent of these models, namely, the artificial neuron. They are viewed as the equilibrium states of a theoretical body that is subject to the law of increase of the entropy. The study of the changes in energy of the body when passing from one equilibrium state to another is used to understand the structure and role of the phase space of the system, the stability of the equilibrium states, and the resulting degree of disorder. It is shown that the topology of these models is strongly linked to their stability and resulting level of disorder. Furthermore, the proposed theoretical characterization permit to assess the thermodynamic efficiency with which information can be processed by these models, and to provide a practical methodology to quantitatively estimate and compare their expected learning and generalization capabilities. These theoretical results provides new insights to the theory of deep learning and their implications are shown to be consistent through a set of benchmarks designed to experimentally assess their validity.

We study in this paper the time evolution of stock markets using a statistical physics approach. We consider an ensemble of agents who sell or buy a good according to several factors acting on them: the majority of the neighbors, the market ambiance, the variation of the price and some specific measure applied at a given time. Each agent is represented by a spin having a number of discrete states q or continuous states, describing the tendency of the agent for buying or selling. The market ambiance is represented by a parameter T which plays the role of the temperature in physics: low T corresponds to a calm market, high T to a turbulent one. We show that there is a critical value of T, say T_c, where strong fluctuations between individual states lead to a disordered situation in which there is no majority: the numbers of sellers and buyers are equal, namely the market clearing. The specific measure, by the government or by economic organisms, is parameterized by $H$ applied on the market at the time t₁ and removed at the time t₂. We have used Monte Carlo simulations to study the time evolution of the price as functions of those parameters. In particular we show that the price strongly fluctuates near T_c and there exists a critical value H_c above which the boosting effect remains after H is removed. Our model replicates the stylized facts in finance (time-independent price variation), volatility clustering (time-dependent dynamics) and persistent effect of a temporary shock. The second party of the paper deals with the price variation using a time-dependent mean-field theory. By supposing that the sellers and the buyers belong to two distinct communities with their characteristics different in both intra-group and inter-group interactions, we find the price oscillation with time. Results are shown and discussed.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

From 1964 to the early 1970s, Orson Anderson led a research program at the Lamont Geological Observatory in the newly-emerging field of “mineral physics”. In collaboration with colleagues Edward Schreiber and Naohiro Soga, Orson exploited the techniques of physical acoustics to study the behavior of the sound velocities of minerals at elevated pressures and temperatures. This research program also included semi-empirical studies of relationships between the bulk modulus and the molar volume of solids and the use of lattice dynamics to calculate the elastic moduli of cubic structures as a function of pressure to predict instabilities, as well as theoretical investigations of the Lagrangian vs. Eulerian formulations of finite strain equations of state.

This brief review highlights some current issues in Galactic stellar nucleosynthesis, and some recent laboratory studies by the Wisconsin atomic physics group that have direct application to stellar spectroscopy, in order to advance our understanding of the chemical evolution of our Galaxy. The relevant publication history of the lab studies are summarized, and investigations into the abundances of neutron-capture and iron-peak elements in low metallicity stars are described. Finally, new initatives in near-infrared spectroscopy are briefly explored.

Biodiversity conservation questions human practices towards biodiversity and, therefore, largely conflicts with ordinary societal aspirations. Decisions on the location of protected areas, one of the most convincing conservation tools, reflect such a competitive endeavor. Operations Research (OR) brings a set of analytical models and tools capable of resolving the conflicting interests between ecology and economy. Recent technological advances have boosted the size and variety of data available to planners, thus challenging conventional approaches bounded on optimized solutions. New models and methods are requested to use such a massive amount of data in integrative schemes addressing a large variety of concerns. Here, we provide an overview on the past, present and future challenges that characterize spatial conservation models supported by OR. By enlarging the spatial, temporal, taxonomic and societal horizons of biodiversity conservation planners navigate around multiple bio-socioeconomic equilibria and are able to decide on cost-effective strategies to improve biodiversity persistence.

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.

Nanocomposites of TiO₂ Degussa P25 nanoparticles/activated carbon (TiO₂/AC ) were prepared at various mass ratios of (4:1), (3:2), (2:3), and (1:4) by a facile process. The effects of TiO₂/AC mass ratios on the structural, morphological, and photocatalytic properties were systematically studied in comparison with bare TiO₂ and bare AC. TiO₂ nanoparticles exhibited dominant anatase and minor rutile phases, and a crystallite size of approximately 21 nm; while AC had XRD peaks of graphite and carbon, and a crystallite size of 49 nm. The composites exhibited tight decoration of TiO₂ nanoparticles on micron-/submicron AC particles, and uniform TiO₂/AC composites were obtained as evidenced by the uniform distribution of Ti, O, and C in an EDS mapping. Moreover, Raman spectra show the typical vibration modes of anatase TiO₂ (e.g., E_1g⁽¹⁾, B_1g⁽¹⁾, E_g⁽³⁾) and carbon materials with D and G bands. The TiO₂/AC with (4:1), (3:2), and (2:3) possessed higher reaction rate constants (k) in photocatalytic degradation of methylene blue (MB) than that of either TiO₂ or AC. Among the investigated materials, TiO₂/AC = 4:1 achieved the highest photocatalytic activity with a high k of 55.2×10^-3 min^-1 and an MB removal efficiency of 96.6% after 30 min treatment under UV-Vis irradiation (120 mW/cm²). The enhanced photocatalytic activity for TiO₂/AC is due to the synergistic effect of the high adsorption capability of AC and the high photocatalytic activity of TiO₂. Furthermore, TiO₂/AC promotes the separation of photoexcited electron/hole (e^-/h⁺) pairs to reduce their recombination rate and thus enhance photocatalytic activity. The optimal TiO₂/AC composite in this study can be used for treating industrial or household wastewater with organic pollutants.

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

{\bf Abstract.} \\ {\bf Background:} Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 burden among the Rohingya refugees of Bangladesh to keep up with the disease outbreak's pace, health needs, and disaster preparedness. \noindent{\bf Methodology and Findings:} To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a modified Susceptible-Exposed-Infectious Recovered (SEIR) transmission model. All the values of different parameters used in this model were from the Bangladesh Government’s database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and good fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be good control over the transmission of the COVID-19 disease. At the end of December 2020, there will be only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number ($ \mathcal{R}_{0} $) has been estimated to be 0.7563. \noindent{\bf Conclusion:} Our analysis suggests that, due to the extensive precautions from the Bangladesh government as well as other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. Although detailed and pragmatic preparedness should be adopted for the worst scenario.

The assessment of soil contamination in the vicinity of integrated siderurgical plants is of outmost importance for agroecosystems and human health, and sensitive techniques should be employed for accurate assessment of chemical elements (metals, potential toxic elements, rare earths, radioelements) in soil and further evaluation of potential ecological and safety risk. In this paper a total of 45 major, minor and trace elements (Al, As, Au, Ba, Br, Ca, Cd, Ce, Co, Cr, Cs, Cu, Dy, Eu, Fe, Hf, Hg, I, K, La, Mg, Mn, Mo, Na, Nd, Ni, Pb, Rb, Sb, Sc, Sm, Sn, Sr, Ta, Tb, Th, Ti, Tm, U, V, W, Y, Yb, Zn and Zr) were quantified in soils located around a large siderurgical works (Galati, SE Romania) using instrumental neutron activation analysis (INAA) in combination with X-ray fluorescence (XRF) and inductively coupled plasma mass spectrometry (ICP-MS). The statistical analysis results and vertical distribution patterns for three depths (0-5 cm, 5-20 cm, 20-30 cm) indicate inputs of toxic elements in the sites close to the ironmaking and steelmaking facilities and industrial wastes dumping site. For selected elements, a comparison with historical, legislated and world reported concentration values in soil was performed and depth migration, contamination and toxic risk indices were assessed. The distribution of major, rock forming elements was closer to the Upper Continental Crust (UCC), and to the Dobrogea loess, finding confirmed by the ternary diagram of the incompatible trace elements Sc, La and Th, as well as by the La to Th rate. At the same time, the La/Th vs. Sc and Th/Sc vs. Zr/Sc bi-plots suggested a felsic origin and a weak recycling of soils mineral components.

Byers Peninsula is considered one of the largest ice-free areas in Maritime Antarctica. Since 2006, the Spanish Polar Program has taken part in a large number of environmental studies involving effects of climate changes in lives cycles, limnology and microbiology. Soils from maritime Antarctica are generally weakly developed and have chemical, physical and morphological characteristics strongly influenced by the parent material. However, biological activity during the short Antarctic summer promotes intense transference of nutrients and organic matter in areas occupied by different species of birds and marine mammals. To mapping and monitoring those areas with high biological occupation, could be very useful to have models of edaphic properties prepared from satellite images. In this approach, Deep Learning and Linear Regression models of soil properties and spectral indexes as explicative variables were performed. We training models of soil properties closely related to biological activity such as Dissolved Organic Carbon (DOC) and the iron fraction associated with organic matter (Fe). We tested the best approach to model the spatial distribution of DOC, Fe and pH by training models of Linear Regression and Deep Learning over Sentinel2 and WorldView2 images. The most robust models were used to track possible areas with ornithogenic soils as well as areas of the Byers Peninsula that could support the highest biological development.

This research paper examines a cosmological model in flat space-time via $f(R,G)$ gravity where $R$ and $G$ are respectively the Ricci scalar and Gauss-Bonnet invariant. Our model assumes that $f(R,G)$ is an exponential function of $G$ combined with a linear combination of $R$. We scrutinize the observational limitations under a power law cosmology that relies on two parameters - $H_0$, the Hubble constant, and $q$, the deceleration parameter, utilizing the 57-point $H(z)$ data, 8-point BAO data, 1048-point Pantheon data, joint data of $H(z)$ + Pantheon, and joint data of $H(z)$ + BAO + Pantheon. The outcomes for $H_0$ and $q$ are realistic within observational ranges. We have also addressed Energy Conditions, $Om(z)$ analysis and cosmographical parameters like Jerk, Lerk and Snap. Our estimate of $H_0$ is remarkably consistent with various recent Planck Collaboration studies that utilize the $\Lambda$CDM model. According to our study, the power law cosmology within the context of $f(R,G)$ gravity provides the most comprehensive explanation for the important aspects of cosmic evolution.

Specialized classes of proteins, working together in a tightly orchestrated manner, induce and maintain highly curved cellular and organelles membrane morphology. Due to the various ex- perimental constraints, including the resolution limits of imaging techniques, it is non-trivial to accurately elucidate interactions among the various components involved in membrane deformation. The spatial and temporal scales of the systems also make it formidable to investigate them using simulations with molecular details. Interestingly, mechanics-based mesoscopic models have been used with great success in recapitulating the membrane defor- mations observed in experiments. In this review, we collate together and discuss the various mechanics based mesoscopic models for protein-mediated membrane deformation studies. In particular, we provide an elaborate description of a mesoscopic model where the membrane is modeled as a triangulated sheet and proteins are represented as either nematics or fila- ments. This representation allows us to explore the various aspects of protein-protein and protein-membrane interactions as well as examine the underlying mechanistic pathways for emergent behavior such as curvature-mediated protein localization and membrane deforma- tion. We also put forward current efforts in the field towards back-mapping these mesoscopic models to finer-grained particle based models - a framework that could be used to explore how molecular interactions propagate to physical scales and vice-versa. We end the review with an integrative-modeling based road map where experimental imaging micrograph and biochemical data are combined with mesoscopic and molecular simulations methods in a theoretically consistent manner to faithfully recapitulate the multiple length and time scales in the membrane remodeling processes.

Recent experimental research has shown that mass is linked to Compton periodicity. We suggest a new way to look at mass: Namely that mass at its most fundamental level can simply be seen as reduced Compton frequency over the Planck time. In this way, surprisingly, neither the Planck constant nor Newton's gravitational constant are needed to observe the Planck length, nor in any type of calculation or gravitational predictions. The Planck constant is only needed when we want to convert back to the more traditional and we would say arbitrary mass measures such as kg. The theory gives the same predictions as Einstein's special relativity theory, with one very important exception: anything with mass must have a maximum velocity that is a function of the Planck length and the reduced Compton wavelength. For all observed subatomic particles, such as the electron, this velocity is considerably above what is achieved in particle accelerators, but always below the speed of light. This removes a series of in finity challenges in physics. The theory also offers a way to look at a new type of quantum probabilities. As we will show, a long series of equations become simpli ed in this way. Further Newton's gravitational constant G is clearly not needed for gravity calculations or predictions; it is the Planck length and the speed of light (gravity) that are essential for gravity, and both can be measured easily with no knowledge of G.

We suggest that momentum should be rede ned in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.

Since general relativity (GR) has already established that matter can simultaneously have two different values of mass depending on its context, we argue that the missing mass attributed to non-baryonic dark matter (DM) actually obtains because there are two different values of mass for the baryonic matter involved. The globally obtained "dynamical mass'' of baryonic matter can be understood as a small perturbation to a background spacetime metric even though it's much larger than the locally obtained "proper mass". Having successfully fit the SCP Union2.1 SN Ia data without accelerating expansion or a cosmological constant, we employ the same ansatz to compute dynamical mass from proper mass and explain galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (Planck 2015 data) without DM. We compare our fits to modified Newtonian dynamics (MOND), metric skew-tensor gravity (MSTG) and scalar-tensor-vector gravity (STVG) for each data set, respectively, since these modified gravity programs are known to generate good fits to these data. Overall, we find our fits to be comparable to those of MOND, MSTG and STVG. While this favorable comparison does not establish the validity of our proposition, it does provide confidence in using the fits to pursue an underlying action. Indeed, the functional form of our ansatz reveals an interesting structure in these fits.