Immortal-time bias (ITB) is known to be common in cohort studies and distorts the association estimates between treated and untreated groups. We used data from the last of two large studies in an Italian province on COVID-19 vaccines safety and effectiveness incurred this bias, and aligned the entire population on a single index date, to correct the ITB. We considered the "all-cause deaths" outcome to compare the survival curves between the unvaccinated group and the various vaccination statuses. The all-cause deaths Hazard Ratios in univariate analysis for unvaccinated (reference) versus vaccinated with 1, 2, 3/4 doses were 0.88 (CI95: 0.78 –1.00; p-value 0.044), 1.23 (1.16–1.32; p-value ≤0.001) and 1.21 (1.14–1.29; p-value ≤0.001), respectively. The multivariate values were 2.40 (2.00–2.88; p-value <0.0001), 1.98 (1.75–2.24; p-value <0.0001), 0.99 (0.90–1.09; ns). The possible explanations of the trend of the Hazard Ratios as vaccinations increase could be a harvesting effect; a calendar-time bias, accounting for seasonality and pandemic waves; a case-counting windows bias; a healthy-vaccinee bias; or some their combination. With two and even with 3/4 doses the calculated Restricted Mean Survival Time and Restricted Mean Time Lost have shown a small but significant downside for the vaccinated populations.

This paper aims to demonstrate how the detection of communities for epidemiological networks can be used to reduce the dimensionality of optimal control problems. A range of planted partition stochastic blockmodels are generated, where the underlying communities in the model vary in detectability. A high-performance computing workflow is then used to simulate and estimate reduced model dynamics for the networks, which in turn is used to find optimal control solutions.

In this paper, we consider the Cauchy problem of a time fractional nonlinear diffusion equation. According to the Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time for some sufficient conditions. We next give sufficient conditions for the existence of global solutions by using the result of Zhang and Sun. In conclusions, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

This work presents a Fault-Tolerant Model Predictive Control (FTMPC) algorithm applied to a simulation model for sewer networks. The control system will aim to prevent contaminated water from escaping the network, especially during periods of heavy rainfall, that can cause combined sewer overflows (CSO), while maintaining the flow of water towards the wastewater treatment plant (WWTP) as close as possible to its nominal value. The main purpose of the work is to preserve the operation of the predictive controller as much as possible, in accordance with its operational objectives, when there may be anomalies affecting the elements of the control system, mainly sensors and actuators. Comparing the results obtained considering various types of faults, with situations of normal controlled operation and with the behavior of the sewer network when no control is applied, will allow some conclusions to be drawn at the end.

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

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

Microgrid (MG) control is essential for efficient, reliable, and sustainable energy management in distributed energy systems. Genetic Algorithm-based energy management systems (GA-EMS) can optimally control a MG by finding global optima and handling complex, non-linear, and non-convex problems, but they can be computationally intensive, making real-time control challenging. Model Predictive Control (MPC)-based EMS predicts future behaviour over a defined horizon, ensuring optimal performance and constraint satisfaction but typically relies on linear models. This paper proposes a novel Genetic Predictive Control (GPC) method, combining GA and MPC to enhance resource allocation, balance multiple objectives, and adapt dynamically to changing conditions. Integrating GA with MPC significantly improves the handling of non-linearities and non-convexity in the system model, leading to more accurate and effective control. Comparative analysis shows that GPC significantly reduces excess power production—surplus power generated beyond load demand—improving resource allocation efficiency. For instance, in the Mutation–Random Selection scenario, GPC reduced excess power to 76.0W compared to 87.0W with GA. Additionally, GPC balances cost, emissions, and power efficiency. In the Crossover-Elitism scenario, GPC achieved a daily cost of $113.94 compared to GA's $127.80, and carbon emissions of 52.83 kg CO2e compared to GA's 69.71 kg CO2e, demonstrating GPC's cost efficiency and environmental benefits. While MPC optimizes a weighted sum of objectives, designing appropriate weights can be challenging and may result in non-convex problems. GA handles multiple, conflicting objectives through multi-objective optimization, providing Pareto-optimal solutions. GPC's dynamic adaptability maintains optimal performance by forecasting future load demands and adjusting control actions. GPC consistently achieves lower emissions than GA across various scenarios and, although it sometimes incurs higher costs, such as $113.94 compared to $131.90 in the Crossover–Random Selection scenario, its holistic approach balances these costs with other metrics, making it cost-effective in the long run. By reducing excess power production and emissions, GPC contributes to economic savings and promotes sustainable practices. These findings underscore GPC's potential as a versatile, efficient, and environmentally beneficial optimization tool for power generation systems.

(1) Background: The RDW-CV has predictive value in many pregnancy-related conditions. Re-search question: Can the RDW-CV be utilized predictively in pregnant patients with thrombo-philia? Aim of the study: To carry out a detailed analysis of the RDW-CV in pregnant patients with treated thrombophilia as compared with pregnant patients without thrombophilia who de-livered via cesarean section at term. (2) Methods: We studied 160 pregnant patients, including 80 pregnant patients with treated thrombophilia in the study group, and another 80 patients of a similar age and parity. The patients were referred to our hospital for delivery at term by means of a cesarean section between 1/10/2017 and 1/12/2021. Every patient received a sonogram during the first 1–2 days after the cesarean section, and their uterine evaluation was interpreted using the PUUS (Postpartum Uterine Ultrasonographic Scale). (3) Results: Our PUUS≥1 pregnant and postpartum patients with treated thrombophilia were the only group with an RDW-CV value over 14. No deep vein thrombosis was observed during hospitalization, showing that the antico-agulant treatment was necessary and effective. An RDW-CV of 14.5 was the highest value in the Rh-negative group of pregnant patients with treated thrombophilia. An RDW-CV of 14.48 was the highest level in the Rh-negative postpartum patients with treated thrombophilia. (4) Conclu-sion: An RDW-CV of ≥14 can predict uterine hematometra (PUUS≥1). The RDW-CV values were higher in Rh-negative patients.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

The extensive use of polypropylene (PP) in various industries has heightened interest in devel-oping efficient methods for recycling and optimising its mixtures. This study focuses on formu-lating predictive models for the Melt Flow Rate (MFR) and shear viscosity of PP blends. The in-vestigation involved characterising various grades, including virgin homopolymers, copolymers, and post-consumer recyclates, in accordance with ISO 1133 standards. The research examined both binary and ternary blends, utilising traditional mixing rules and symbolic regression to predict rheological properties. High accuracy was achieved with the Arrhenius and Cragoe models, at-taining R² values over 0.99. Symbolic regression further enhanced these models, offering signif-icant improvements. To mitigate overfitting, empirical noise and variable swapping were in-troduced, increasing the models' robustness and generalisability. The results demonstrated that the developed models could reliably predict MFR and shear viscosity, providing a valuable tool for improving the quality and consistency of PP mixtures. These advancements support the de-velopment of recycling technologies and sustainable practices in the polymer industry by opti-mising processing and enhancing the use of recycled materials.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

The implementation of systems condition monitoring is of utmost importance in ensuring effective maintenance, optimal efficiency, and adherence to established design criteria. This research presents a novel and economically efficient Digital Twin Model (DTM) designed for the purpose of Live Condition Monitoring (LCM) and Predictive Lifecycles. This study discusses the enhancement of DTs modelling by decreasing the number of dimensions from five to three: Physical, Digital, and Connection entities. The resulting model exhibits a notable improvement in accuracy and efficiency. The suggested Dynamic Time Model (DTM) enhances the empirical pre-set average load for both simulation and experimentation by 35.7%, which is equivalent to a 1.6-fold increase. The DTM demonstrates a significant enhancement in the empirical predefined average lifecycles of the system, as shown in the real-life case study. Specifically, the DTM achieves a 12-fold improvement compared to the simulated results and a nine-fold improvement compared to the experimental findings. The suggested Dynamic Time Management (DTM) demonstrates a significant enhancement in the average lifecycles of the system, with a 19.7% improvement (equivalent to 1.2 times greater) compared to the wireless DTM results obtained through the application of the real system load. The suggested Dynamic Time Warping (DTW) method's accuracy and efficiency are shown via a practical case study using the suspension system of a Peugeot 3008 vehicle.

Enhancing the management and monitoring of oil and gas processes demands developing precise predictive analytics techniques. Over the past two years, oil and its prediction have advanced significantly using conventional and modern Machine Learning techniques. Several review articles detail the developments in predictive maintenance and technical and non-technical aspects of influencing the uptake of big data. The absence of references for machine learning techniques impacts the effective optimization of predictive analytics in the oil and gas sector. This review paper offers readers thorough information on the latest machine learning methods utilized in this industry's predictive analytical modelling. The review covers forms of Machine Learning techniques used in predictive analytic modelling from 2021 to 2023 (91 articles). It provides an overview of the details of the papers that were reviewed, comprising of the model’s categories, the data's temporality, field, and name, the dataset's type, predictive analytics (classification or clustering or prediction), the models' input and output parameters, performance metrics, optimal model, and benefits and its drawbacks. Additionally, suggestions for future research directions are provided to raise the potential of the associated knowledge and increase the accuracy of oil and gas predictive analytics models.

Developments in artificial intelligence techniques allow for an improvement in sustainable mobility strategies with particular reference to energy consumption estimates of electric vehicles (EVs). This research proposes a vehicle energy model developed on the basis of Deep Neural Network (DNN) technology. The study also explores the potential application of the model developed for the movement data of new vehicles in the province of Enna, Sicily, Italy. which is characterized by numerous attractors and the increasing number of hybrid and electric cars circulating. The energy model for electric vehicles shows high accuracy and versatility, requiring vehicle velocity and acceleration as input data to predict energy consumption. The research article also provides recommendations for the energy modeling of electric vehicles and outlines additional steps for model development. The implemented methodological approach and its results can be used by transport decision makers to plan new transport policies in Italian cities aimed at optimizing vehicle charging infrastructure. They can also help vehicle users accurately estimate energy consumption, generate maps, and identify locations with the highest energy consumption.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

We investigate solutions of the classical Mathieu-Hill (MH) equation which describes the dynamics of trapped ions, based on the Floquet theory and the analytical model introduced in \cite{Blu89}. We show the equations of motion are equivalent to those of the harmonic oscillator (HO) and demonstrate methods to determine the solutions of the MH equation. The regions of stability and instability for the MH equation in case of a trapped particle are also discussed. What is more, we address both the damped HO and parametric oscillator (PO) for an ion confined in a Paul trap. The paper is a follow-up of a recently published paper in Photonics, 11 (6) 551.

Osteoarthritis and chronic pancreatitis comorbidity are insufficiently studied, and the reciprocal impact of these conditions remains poorly understood. This study aimed to investigate potential predictors for the development of osteoarthritis and chronic pancreatitis comorbidity, as well as complications associated with this comorbidity. A cohort of 150 patients was categorized into three groups: a control group (n=30), patients with osteoarthritis (n=68), and patients with comorbid osteoarthritis and chronic pancreatitis (n=52). Potential predictors for comorbidity development and associated complications were explored. The study revealed that concurrent osteoarthritis and chronic pancreatitis exacerbate each other's progression and contribute to malnutrition. Body Mass Index (BMI) emerged as a potential predictor for chronic pancreatitis development in osteoarthritis patients. In osteoarthritis patients, fecal elastase-1 levels were identified as potential predictors for exocrine pancreatic insufficiency. Factors such as WOMAC total score, fecal elastase-1, C-reactive protein (CRP), ferritin, retinol, tocopherol, 25-hydroxy vitamin D3, and BMI were found to influence comorbidity development between osteoarthritis and chronic pancreatitis. Additionally, Gastrointestinal Symptom Rating Scale-Diarrhea Syndrome (GSRS-DS), Gastrointestinal Symptom Rating Scale-Constipation syndrome (GSRS-CS), Qualitative Assessment of the Symptoms and Impact of Pancreatic Exocrine Insufficiency domain A (PEI-Q-A), retinol, tocopherol, and iron were identified as potential predictors for exocrine pancreatic insufficiency in osteoarthritis patients. In conclusion, the comorbidity of osteoarthritis and chronic pancreatitis exacerbates disease progression and complications, necessitating further investigation.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

The supply chain has incorporated products by putting them into hair scarfs. This study introduces the use of mini chips in health and beauty products and can reduce fatigue through enhanced sleep patterns. The mini chip could be placed in the scarf and used as a prototype. RFID technology provides the supply chain with specific information that is used to identify products and make communication easier. (Muhammad, et. al. 2013) This paper presents a new tool herein referred to as a scarf prototype which is developed to analyse EMG (electromyogram), ECG (electrocardiography), EEG (electroencephalogram), and EOG (electro-oculogram) signals that focuses in the area of sleep disorders. The mini chips used can be used to determine a solution for sleep disruption by using automated analytics. This could lead to improvement in our understanding of sleep disruption and overall sleep physiology. Automated technology allows repeated measurements, evaluation of sleep patterns, and provide suggestions to improve a person’s quality of sleep. This analysis compares the use of polysomnography and the scarf prototype. The analytics provide models and shows correlation between variables, such as EMG, ECG, EEG, and EOG. This study shows that the results from the scarf prototype is just as reliable as the original method, polysomnography.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

Due to the manufacturing process of Additive Manufacturing (AM) Parts the mechanical properties cannot be predicted. The scope of the present work is to propose a predictive tool for the mechanical properties of AM parts through the use of Adaptive Neuro-Fuzzy Inference System (ANFIS). The Adaptive Neuro-Fuzzy Inference System (ANFIS) combines neural networks with fuzzy logic to generate a mapping between the inputs and the output. Real data experiments from different AM technologies and materials compose the initial dataset so a detailed investigation is conducted to gain knowledge of how different parameters affect the UTS, the elongation and the Young modulus of each experiment. Experimental data were also use to train, check and verify the methodology. The method is tested for FFF technology, PLA material and 3 point bending stress, with interesting results.

Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their complete integrability. The Gardner equation is chosen as the key example for it comprises both the Korteweg-de Vries and modified Korteweg de Vries (mKdV) equations. The Gardner and Miura transformations which connect these equations are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case) whereas the focusing Gardner equation has the standard elastically colliding solitons. The paper’s aim is to provide a review of integrability properties and solutions of the Gardner equation and illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica but can be adapted for major computer algebra systems.

PURPOSE: Breast cancer tumors frequently have intratumor heterogeneity. Tumors with high intratumor heterogeneity have caused therapeutic resistance and have human epidermal growth factor receptor 2 (HER2) heterogeneity in response to HER2-targeted therapies. This study aimed to investigate whether high HER2 heterogeneity levels were clinically related to poor prognosis for HER2-targeted adjuvant therapies resistance in primary breast cancers. METHODS: This study included patients with primary breast cancer (n = 251) treated with adjuvant HER2-targeted therapies. HER2 heterogeneity was manifested by the shape of HER2 fluorescence in situ hybridization amplification (FISH) distributed histograms with HER2 gene copy number within a tumor sample. Those heterogeneity classified each tumor into the biphasic grade graph (high heterogeneity [HH]) group and the monophasic grade graph (low heterogeneity [LH]) group. Both groups were evaluated for disease-free survival (DFS) and overall survival (OS) for a median of ten years of annual follow-up. RESULTS: Of 251 patients with HER2-positive breast cancer, 46 (18.3%) and 205 (81.7%) were classified into the HH and LH groups, respectively. The HH group had more distant metastases and a poorer prognosis than the LH group (DFS: P < 0.001 (HH:63% vs LH:91% at 10 years), and OS: P = 0.012 (HH:78% vs LH:95% at 10 years). CONCLUSION: High HER2 heterogeneity is a poor prognostic factor in patients with HER2-positive breast cancer. A novel approach of heterogeneity, which is manifested by the shape of HER2 FISH distributions, might be clinically useful in the prognosis prediction of patients after HER2 adjuvant therapy.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

Abstract: Safety issues related to the electrification of more electric aircraft (MEA) need to be addressed because of the increasing complexity of aircraft electrical power systems and the growing number of safety-critical sub-systems that need to be powered. Managing the energy storage systems and the flexibility in the load-side plays an important role in preserving the system’s safety when facing an energy shortage. This paper presents a system-level centralized operation management strategy based on model predictive control (MPC) for MEA to schedule battery systems and exploit flexibility in the demand-side while satisfying time-varying operational requirements. The proposed online control strategy aims to maintain energy storage (ES) and prolong the battery life cycle, while minimizing load shedding, with fewer switching activities to improve devices lifetime and to avoid unnecessary transients. Using a mixed-integer linear programming (MILP) formulation, different objective functions are proposed to realize the control targets, with soft constraints improving the robustness of the model. Besides, an evaluation framework is proposed to analyze the effects of various objective functions and the prediction horizon on system performance, which provides the designers and users of MEA and other complex systems with new insights into operation management problem formulation.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

Geopolymers, made from aluminosilicate raw materials, offer significant environmental advantages over conventional concrete (CC) mixes. This study explores the compressive strength, setting time, and durability of geopolymer concrete (GPC) cylinders, some of which include an additional ordinary portland cement (OPC) mix. Consistent material composition and testing methods are emphasized to achieve reliable results. MATLAB was utilized to develop and assess a neural network model predicting the compressive strength of GPC based on key variables. The model was validated using 16 experimental samples and 1047 samples from various studies. The performance plot displayed the Mean Squared Error (MSE) over iterations, identifying the best training performance at epoch 658 with an MSE of 5.3408. The Error Histogram highlighted distribution errors between predicted and actual compressive strength values, with the highest range from -1.015 to 0.3587, meaning that the predicted values were mostly within a small margin of error from the actual values. This narrow error range indicates that the ANN model has high accuracy in its predictions, as most errors are small and clustered around zero, demonstrating reliable performance in estimating compressive strength. Regression analysis showed varying correlation coefficients (training set R=0.98373, test set R=0.88164, and whole set R=0.96982), indicating adequate predictive accuracy. The results demonstrate that properly trained neural networks can effectively predict the compressive strength of GPC, highlighting its potential as a sustainable construction material.

BReast CAncer gene 1 (BRCA1) and BReast CAncer gene 2 (BRCA2) encode for tumor suppressor proteins which are critical regulators of the homologous recombination (HR) pathway, the most precise and important DNA damage response mechanism. Dysfunctional HR proteins cannot repair double-stranded DNA breaks in mammalian cells, a situation called HR deficiency. Since their identification, pathogenic variants and other alterations of BRCA1 and BRCA2 genes have been associated with an increased risk of developing mainly breast and ovarian cancer. Interestingly, HR deficiency is also detected in tumors not carrying BRCA1/2 mutations, a condition termed “BRCAness”. One of the main mechanisms causing the BRCAness phenotype is the methylation of the BRCA1/2 promoters and this epigenetic modification is associated with carcinogenesis and poor prognosis mainly among patients with breast and ovarian cancer. BRCA1 promoter methylation has been suggested as an emerging biomarker of great predictive significance, especially concerning Poly (ADP-ribose) Polymerase inhibitors (PARP inhibitor-PARPi) responsiveness, along with or beyond BRCA1/2 mutations. However, as its clinical exploitation is still insufficient, the impact of BRCA1/2 promoter methylation status needs to be further evaluated. The current review aims to gather the latest findings about the mechanisms that underline BRCA1/2 function as well as the molecular characteristics of tumors associated with BRCA1/2 defects, by focusing on DNA methylation. Furthermore, we critically analyze their translational meaning and the validity of BRCA methylation biomarkers in predicting treatment response and we suggest a diagnostic pipeline that could be implemented in liquid biopsy to aid precision pharmacotherapy in BRCA-associated tumors.

Artificial intelligence (AI) is experiencing advances and integration in all medical specializations, and this creates excitement but also concerns. This narrative review aims at a critical assessment of the state of the art of AI in the field of endometriosis and adenomyosis. By enabling automation, AI may speed up some routine tasks, decreasing gynecologists’ risk of burnout, as well as enabling them to spend more time interacting with their patients, increasing their efficiency and patients’ perception of being taken care of. Surgery may also benefit from AI, especially through its integration with robotic surgery systems. This may improve the detection of anatomical structures and enhance surgical outcomes by combining intra-operative findings with pre-operative imaging. Not only, AI promises to improve the quality of care by facilitating clinical research and through the introduction of decision support tools that can enhance diagnostic assessment and predict treatment effectiveness and side effects, as well as reproductive prognosis and cancer risk. However, concerns exist regarding the fact that good quality data used in tool development and compliance with data sharing guidelines are crucial. Also, professionals are worried AI may render certain specialists obsolete. This said, AI is more likely to become a well-liked team member rather than a usurper.

The maneuverability of ships is influenced by several factors, including ship design, size, propulsion system, hull shape, and external conditions such as wind, waves, and currents. The size, shape, and arrangement of the hull, rudder, and propeller are decisive for maneuverability. Hydrodynamic forces such as bank effect and squat significantly impact the maneuverability of large ships in narrow channels. With the increasing trend of building ever-larger ships, the demand to evaluate the maneuvering performance of the ship at the design stage has become more critical than ever. Both experimental and computational methods are used to obtain accurate maneuvering characteristics of vessels. In this study, the methods for predicting ship maneuvering characteristics are analyzed using a systematic review based on the preferred reporting items for systematic reviews and meta-analyses (PRISMA). This article contributes to a deeper understanding of the hydrodynamic capabilities of ships and identifies possible future challenges in the field of ship hydrodynamics. The findings inform educators and the shipping industry about the importance of predicting the maneuvering performance of ships, with an emphasis on the education and training of seafarers needed to make timely decisions in critical situations.

The study aimed to analyze thoracic and lumbar erector spinae muscle activations during 3D elongation exercises in individuals with adolescent idiopathic scoliosis (AIS). Participants included 24 adolescents, meeting specific criteria such as a Cobb angle between 10° and 20°, and not having undergone surgical or brace treatments. EMG data were collected to evaluate muscle activations. The study found no significant interaction between exercise type and the side of the curve, but a significant main effect of exercise type on muscle activation, irrespective of Cobb angle. Different exercise types significantly affected muscle activity, with the highest activations in the TheraBand exercise, followed by manual and without equipment conditions. This suggests that exercise type significantly impacts muscle engagement in AIS patients, providing valuable insights for targeted exercise program design. The study, however, focused on short-term muscle activation, not long-term Cobb angle progression, pointing to the need for further research in this area.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

Though early-stage colorectal cancer has a high 5-year survival rate of 65-92% depending on the specific stage, this probability drops to 13% after the cancer metastasizes. Frontline treatments for colorectal cancer such as chemotherapy and radiation often produce dose-limiting toxicities in patients and acquired resistance in cancer cells. Additional targeted treatments are needed to improve patient outcomes and quality of life. Immunotherapy involves treatment with peptides, cells, antibodies, viruses, or small molecules to engage or train the immune system to kill cancer cells. Preclinical and clinical investigations of immunotherapy for treatment of colorectal cancer including immune checkpoint blockade, adoptive cell therapy, monoclonal antibodies, oncolytic viruses, anti-cancer vaccines, and immune system modulators have been promising, but demonstrate limitations for patients with proficient mismatch repair enzymes. In this review, we discuss preclinical and clinical studies investigating immunotherapy for treatment of colorectal cancer and predictive biomarkers for response to these treatments. We also consider open questions including optimal combination treatments to maximize efficacy, minimize toxicity, and prevent acquired resistance and approaches to sensitize mismatch repair proficient patients to immunotherapy.

Using data-driven models to solve predictive maintenance problems has been prevalent for original equipment manufacturers (OEMs). However, such models fail to solve two tasks that OEMs are interested in: (1) Making the well-built failure prediction models working on existing scenarios (vehicles, working conditions) adaptive to target scenarios. (2) Finding out the failure causes, furthermore, determining whether a model generates failure predictions based on reasonable causes. This paper investigates a comprehensive architecture towards making the predictive maintenance system adaptive and interpretable by proposing (1) an ensemble model dealing with time-series data consisting of a long short-term memory (LSTM) neural network and Gaussian threshold to achieve failure prediction one week in advance and (2) an online transfer learning algorithm and a meta learning algorithm, which render existing models adaptive to new vehicles with limited data volumes. (3) Furthermore, the Local Interpretable Model-agnostic Explanations (LIME) interpretation tool and super-feature methods are applied to interpret individual and general failure causes. Vehicle data from Isuzu Motors, Ltd., are adopted to validate our method, which include time-series data and histogram data. The proposed ensemble model yields predictions with 100% accuracy for our test data on engine stalling problem and is more rapidly adaptive to new vehicles with smaller error following application of either online transfer learning or the meta learning method. The interpretation methods help elucidate the global and individual failure causes, confirming the model credibility.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

Background: Malignant pleural mesothelioma (MPM) is an atypical, belligerent tumor that matures into cancer in the pleura, a stratum of tissue bordering the lungs. Pleural mesothelioma is a common type of mesothelioma that accounts for about 75 percent of all mesothelioma diagnosed yearly in the United States. Diagnosis of mesothelioma takes several months and is expensive. Given the difficulty of diagnosing MPM, early identification is crucial for patient survival. Our study implements artificial intelligence and recommends the best fit model for early diagnosis and prognosis of MPM. Method: We retrospectively retrieved patient’s medical reports generated by Dicle University, Turkey and implemented multi-layered perceptron (MLP), voted perceptron (VP), Clojure classifier (CC), kernel logistic regression (KLR), stochastic gradient decent SGD), adaptive boosting (AdaBoost), Hoeffding tree (VFDT), and primal estimated sub-gradient solver for support vector machine (s-Pegasos). We evaluated the models, compared and tested using paired T-test (corrected) at 0.05 significance based on their respective classification accuracy, f-measure, precision, recall, root mean squared error, receivers characteristic curve (ROC), and precision-recall curve (PRC). Results: In phase-1 SGD, AdaBoost.M1, KLR, MLP, VFDT generates optimal results with the highest possible performance measures. In phase-2, AdaBoost with a classification accuracy of 71.29% outperformed all other algorithms. C-reactive protein, platelet count, duration of symptoms, gender, and pleural protein were found to be the most relevant predictors that can prognosticate mesothelioma. Conclusion: This study confirms that data obtained from biopsy and imagining tests are strong predictors of mesothelioma but are associated with high cost, however, can identify mesothelioma with optimal accuracy. Predictive analytics without using biopsy results can diagnose mesothelioma with acceptable accuracy. Implementation of phase-2 followed by phase-1 can address diagnosis expenses and maximize disease prognosis. Additionally, results indicate improved MPM diagnosis using AI methods dependent upon the specific application.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

In the present work, a predictive modelling and optimization with the adaptive network based fuzzy inference system(ANFIS) modelling of mechanical properties of laser-coated NB/SiC/Ni welds was studied based on Taguchi design by laser cladding. An ANFIS model based on a Sugeno type fuzzy inference system was developed for predicting the hardness properties of SiC/BN/Ni welds by laser cladding with experimental data required for network training and prediction. Based on analysis of variance, three important factors were taken as inputs for the fuzzy logic inferences, while the hardness properties was taken as the output of the ANFIS. The microstructure of welds were analysed using scanning electron microscopy with an energy dispersive X-Ray spectrometer. Highly developed leaf-like dendrites and eutectic crystals were found in some areas of the melting zone for the BN/SiC/Ni weld, which was significantly hardened. The ANFIS model based on Taguchi's design provides a better pattern of response because the predicted and experimental values were highly similar. As a result, a satisfactory result was achieved between the predicted and experimental values of hardness in laser-coated NB/SiC/Ni welds, whereby the success and validity of the method was verified.

While some research supports utilizing plain radiography for measuring biomechanical alignment of the spine for prognosis and treatment, there are contrasting viewpoints regarding both the value and utilization of these procedures in conservative care. Evaluation of both conservative and non-conservative approaches to spinal care revealed vast differences in radiographic utilization and interpretation between orthopedic surgeons, primary care physicians, chiropractic physicians, and physical therapists, which may account for the different viewpoints and rationale in the literature. A research summary is provided regarding the various methods of spinal analysis utilized by these professions to help determine if there is any unique diagnostic or prognostic value associated with radiographic utilization that could assist in advancing conservative spinal assessment and treatment. Understanding any unique value provided through biomechanical assessment utilizing plain radiography of the spine established in the literature may help chiropractic physicians determine the appropriate use of radiographic procedures in clinical practice and how to coordinate efforts with other conservative and non-conservative professions to improve spinal healthcare.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.

A proportion of osteoarthritis (OA) patients are unsatisfied with post-operative outcomes following total joint replacement surgery (TJR), with insufficient pain relief or poor functional improvement. Predicting those will have poor outcomes would be beneficial for patients and clinicians. The aim of this study was to determine the relationship between baseline anthropometric data and the concentration of pre-operative serum and peri-operative synovial fluid (SF) cytokines with 7-month post-operative outcomes in a cohort of knee and hip OA patients. 160 OA patients were recruited who were scheduled for TJR. The concentration of 24 cytokines were measured in blood and SF by multiplex assay. EQ5Dindex health status was assessed pre-operatively and at 7-months post-operatively. 13% of patients were identified as non-responders based on EQ5Dindex. Compared to responders, non-responders were of higher BMI, had greater waist and hip circumference and had higher levels of SF leptin but lower levels of SF Resistin (p&lt;0.05). Linear regression analysis found a significant relationship between pre-operative body weight and post-operative response (ΔEQ5Dindex; r=0.222, p=0.049). The combination of body weight with SF amphiregulin and SF IL-6 provided an improved predictive model of post-operative response (r=0.470, p=0.035).

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .

Background: Large-cell neuroendocrine carcinoma presents significant treatment challenges owing to its rarity and limited therapeutic options. The LANCE study was designed to explore the survival benefits of incorporating atezolizumab in chemotherapy for metastatic LCNEC. Methods: In this non-randomized study, patients with metastatic LCNEC were treated with ei-ther standard chemotherapy plus atezolizumab or standard chemotherapy alone. The primary outcomes measured were progression-free survival (PFS) and overall survival (OS), with an ex-ploratory analysis of miR375 in plasma as a potential biomarker. Results: Of the 22 screened patients, 17 met the inclusion criteria and were stratified into the atezolizumab and chemotherapy (n=10) or chemotherapy alone(n=7) groups. After a median follow-up of 23.3 months, the 12-month survival rate for the atezolizumab group was 57.1% (95% CI: 32.6%-100%) and 45.7% at 24 months (95% CI: 22.4%-93.2%). In contrast, the chemotherapy group had a 14.3% survival rate at both 12 and 24 months (95% CI: 2.33%-87.7%). The log-rank test for survival showed a statistically significant difference in the atezolizumab-treated group (chi-squared = 4, df = 1, p = 0.04). A non-significant correlation was found between disease pro-gression and elevated levels of miR375. Conclusions: This pilot study suggests that atezolizumab combined with chemotherapy may be effective in treating metastatic LCNEC. The non-significant correlation between plasma miR375 levels and disease progression suggests its biomarker potential, warranting further validation research.

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which yields best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, thus incorporating, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizing the results produced by extant data assimilation and data adjustment procedures. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC). The application of the 4th-BERRU-PM methodology to energy systems is illustrated by means of the above-mentioned OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation involving 21976 imprecisely known parameters, the solution of which is representative of “large-scale computations.” The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

This study investigates the application of frequency augmentation techniques to improve condition-based maintenance (CBM+) systems for airborne weapon systems, focusing on the predictive accuracy of velocity and acceleration parameters. Utilizing MIL-STD-1553B MUX data from 138 sorties of fixed-wing aircraft, we explored six augmentation methods, including traditional interpolations (linear, quadratic, cubic spline) and advanced machine learning models (K-Nearest Neighbor, LSTM, and Bi-LSTM). Our findings indicate that while traditional methods like linear interpolation are more effective for velocity parameters, advanced ML techniques, particularly Bi-LSTM, provide better results for acceleration parameters, which exhibit more complex and rapid variability. The study underscores the necessity of tailoring augmentation approaches to specific parameter characteristics and highlights the potential of ML models in capturing intricate patterns within time-series data. These insights are critical for advancing CBM+ systems in military avionics, enhancing reliability and operational efficiency through improved data processing strategies. Future work should explore more performant augmentation techniques, such as by integrating multi-dimensional datasets, and explore ways to develop automated tools for a more powerful predictive maintenance framework.

Caudal type homeobox transcription factor 2 (CDX2) is a gastrointestinal cancer biomarker that regulates epithelial development and differentiation. Absence or low levels of CDX2 have been associated with poor prognosis and proposed as a chemotherapy response predictor. Tumour tissue of 668 patients with stage I-IV colorectal cancer were stained for CDX2 and stratified into two subgroups according to expression levels. Statistical tests evaluated CDX2 relationship with survival and chemotherapy response. Of 646 samples successfully stained, 51 (7.9%) had low and 595 (92.1%) had high CDX2 levels. Low CDX2 staining was associated with poor differentiation, presence of lymphovascular or perineural invasion, and more common in colon and right sided tumours. Overall survival (p&lt;0.001) and disease-free survival (p=0.009) was lower in low CDX2 expressing patients. Multivariable analysis validated CDX2 as an independent poor prognostic factor after excluding confounding variables. There was no statistically significant improvement in survival with adjuvant chemotherapy in stage II colon cancer (p=0.11). In the rectal cohort, there was no relationship between CDX2 levels and therapy response. While confirming the prognostic utility of CDX2 in colorectal cancer, our study highlights larger studies are required to confirm utility as a predictive chemotherapy biomarker, especially in left sided and rectal cancers.

Zinc, an essential trace mineral, plays a crucial role in over 300 enzymes that are vital for major metabolic pathways. Zinc deficiency can cause various symptoms and sometimes lead to serious conditions, especially after surgery. Therefore, recognising the prevalence and predictors of zinc deficiency before surgery is essential for preventing associated symptoms. Although zinc deficiency is linked to several diseases, its association with orthopaedic disorders remains unclear. This retrospective study aimed to explore the prevalence and predictors of zinc deficiency in orthopaedic inpatients prior to surgery. This retrospective case-control study aimed to investigate the prevalence and predictors of zinc deficiency in orthopaedic inpatients. Patients admitted to the Department of Orthopaedic Surgery at Teikyo University Chiba Medical Center between 15 February 2022 and 31 August 2022 were included. The case-control design categorised patients into zinc deficiency (case) and non-deficiency (control) groups based on serum zinc concentrations (< 60 µg/dL). The data retrieved from the centre’s database included demographics, comorbidities, reasons for hospitalisation, fracture details, medication use, and laboratory values. Statistical tests included Fisher’s exact test for categorical variables and a two-sample t-test for continuous vari-ables. To identify factors associated with zinc deficiency, multivariate analysis ( backward stepwise regression model) was performed for items that were significantly different from the univariate analysis. A total of 156 orthopaedic patients were included in this study. Forty-seven patients (30.1%) had a zinc deficiency. The fracture rate was significantly higher in the case group than in the control group (68.1 % vs. 33.9 %; p < 0.001); spinal disease was significantly less common in the case group than in the control group (2.1 % vs. 31.2 %; p < 0.001); and OA was significantly less common in the case group than in the control group (8.5 % vs. 22.9 %; p = 0.04). The case group had signif-icantly higher rates of fragility and hip and pelvic fractures than did the control group. Spinal disease was less common in the case group than in the control group. Laboratory findings revealed significantly lower mean serum zinc (46.2 µg/dL) in the case group than in the control group (76.3 µg/dL), accompanied by lower albumin and haemoglobin concentrations. Hypoalbuminemia and anaemia were more prevalent in the case group than in the control group. Multivariate logistic regression identified age ≥ 60, anaemia, hip fracture, and hypoalbuminaemia as independent predictive factors for zinc deficiency, while spinal disease was associated with decreased risk. This study identified zinc deficiency in 30.1% of orthopaedic inpatients based on serum zinc concen-trations. Furthermore, age ≥ 60, anaemia, hip fracture, and hypoalbuminaemia were determined as independent predictive factors for zinc deficiency.

Abstract: Background and Objectives: A growing number of epidemiologic studies have found that diabetes mellitus may increase cancer risk and is implicated in numerous other metabolic and inflammatory disorders. The increase in pro-inflammatory cytokines plays a major role in insulin resistance and leads to hypoalbuminemia, and micro- and macrovascular diabetes complications, including kidney disease and anemia. This study aimed to investigate the utility of CEA, CRP, serum albumin level, hemoglobin, and LDH as biomarkers for cancer risk and the biological implications of diabetes on the evolution and prognosis of oncological patients. Material and methods: We conducted a retrospective, longitudinal, observational study, on a total group of 434 patients, 217 diagnosed with a form of cancer and with type 2 diabetes as a comorbidity, and the other 217 – control group, without diabetes. These patients were admitted to the oncology clinic. In subgroups, the same number of patients was considered, depending on the location of the oncological pathology. Anemia, hypoalbuminemia, elevated lactate dehydrogenase, glycated hemoglobin, and C-reactive protein levels are more pronounced in subjects with type 2 diabetes and cancer. Conclusions: The presence of diabetes negatively affects the clinical and biological prognosis of cancer patients.

Globally, there is massive uptake and explosion of data and challenge is to address issues like scale, pace, velocity, variety, volume and complexity of the data. Considering the recent epidemic in China, modeling of COVID-19 epidemic for cumulative number of infected cases using data available in early phase was big challenge. Being COVID-19 pandemic during very short time span, it is very important to analyze the trend of these spread and infected cases. This predictive analytics can be empowered using Information, Communication and Technologies (ICT) services, tools and applications. This paper presents medical perspective of COVID-19 towards epidemiological triad and the study of state-of-the-art. The main aim this paper is to present different predictive analytics techniques available for trend analysis, different models and algorithms and their comparison. Finally, this paper concludes with prediction of COVID-19 using Prophet algorithm indicating more faster spread in short term. These predictions will be useful to government and healthcare communities to initiate appropriate measures to control this outbreak in time.

Sorafenib is an oral kinase inhibitor that enhances survival in patients affected by advanced hepatocellular carcinoma (HCC). According to the results of two registrative trials, this drug represents a gold quality standard in the first line treatment of advanced HCC. Recently, lenvatinib showed similar results in terms of survival in a non-inferiority randomized trial study considering the same subset of patients. Unlike other targeted therapies, currently predictive and prognostic markers in HCC patients treated with sorafenib are lacking. Their identification could help clinicians in the daily management of these patients, mostly in light of the new therapeutic options available in the first.

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

COVID-19 outbreak started in the Chinese city of Wuhan and spread around the globe in months due to its high contagious level. Hence, this disease posed a great challenge to researchers and mathematicians. Numerous mathematical models have been suggested to visualize the spreading speed and trends of this pandemic. In this paper, a comparison of a widely established and accepted method, the Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model with a newly-proposed fractional-order SEIQRDP is studied. Densely populated Countries of Asia (Pakistan, India, and Bangladesh) have been chosen as data sets and both algorithms have been applied to their data. The same comparison technique has also been used on the data of two polar countries, New Zealand and Russia, that validated our findings. Error comparison of both algorithms has been recorded in a tabulated form which shows multi-fold erroneous trends over WHO data of selected countries.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

We still do not have satisfactory answers about the inflationary and accelerating expansions of the universe, the missing mass problem, and the origins of the four fundamental forces and the quantum phenomena. Here, we introduce a new model of matter and space and a postulate on a constant of motion, and then show that an equation of motion derived from the constant of motion could provide new understandings of the above problems. For example, we show that there is a natural inflation scenario and that the co-moving distance to the closest accelerating supernova is clearly given as $c/(\sqrt{3} H)$ ($\sim$8.1 billion ly). In addition, we show that, in a system including a proton and an electron, the equation of motion has eight acceleration terms, some of which are suspected to be responsible for the four fundamental forces and the galaxy rotation anomaly. From further discussion, we conjecture that in order to understand the gravitational and strong interactions and the quantum phenomena, it is necessary to consider the expansion of the universe. The lensing mass distribution is explained, based on another postulate on a method of representing superposition.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

This paper secures the analytical soliton solutions of the perturbed NLSE gives to (1). The existence criteria have been demonstrated and the wave speed of the soliton befall out. To achieve all the results obtained we used the mathematical technique. In view of the results obtained, some new additional one have been reported in left-handed metamaterials.

Dams significantly impact the environment, industry, residential areas, and agriculture. Efficient dam management can mitigate negative impacts and enhance benefits such as flood and drought reduction, energy efficiency, water access, and improved irrigation. This study tackles the critical issue of predicting dam occupancy levels precisely within the framework of Integrated Water Resource Management (IWRM). Our research proposes that combining the physical model of evapotranspiration using the Penman–Monteith equation with data-driven models based on historical reservoir data, weather data, and consumption data is essential for accurately predicting occupancy levels. We implemented various prediction models, including Random Forest, Extra Trees, Long Short-Term Memory, Orthogonal Matching Pursuit CV, and Lasso Lars CV. To strengthen our proposed model with robust evidence, we conducted a statistical test on the MAPE values. We achieved a remarkable accuracy in predicting the occupancy level one month ahead, with an error margin of just 1% using Extra Trees. This study represents a pioneering effort in providing guidance and proposing a hybrid model in this field.

For decades since the central dogma, cancer biology research has been focusing on the involvement of genes encoding proteins. It has been not until more recent times that a new molecular class has been discovered, named non-coding RNA (ncRNA), which has been shown to play crucial roles in shaping the activity of cells. An extraordinary number of studies into shown that ncRNAs represent an extensive and prevalent group of RNAs, including both oncogenic or tumor suppressive molecules. Henceforth, various clinical trials involving ncRNAs as extra ordinary biomarkers or therapies have started to emerge. In this review, we will focus on the prognostic and diagnostic role of ncRNAs for breast cancer.

Alzheimer’s disease (AD) predominantly occurs as a late-onset form (LOAD), involving neurodegeneration and cognitive decline with progressive memory loss. Over time, risk factors and aging promote accumulation of well-known AD hallmarks in oxidative stress, amyloid-beta and tau protein pathology, as well as inflammation. Homeostatic glial functions regulate and suppress these AD hallmarks; however, other glial states involve increased pro-inflammatory cytokine release and further hallmark accumulation. Different stresses can additionally induce cellular senescence, or an irreversible differentiation process resulting in decreased supportive functions and increased, pro-inflammatory cytokine release. While these pathophysiological underpinnings all contribute to LOAD, they require temporal and mechanistic integration. This Perspective proposes that traditional AD hallmarks induce glial senescence in LOAD, where sufficient senescent glia exacerbate ongoing AD pathology and primarily drive LOAD into clinical, cognitive decline. We first explore age-related increases in pro-inflammatory glial activity, and then discuss emerging evidence linking oxidative stress, neurons containing tau pathology, and amyloid-beta to microglia, oligodendrocyte progenitor, and astrocyte senescence. Our evidence-based model mainly predicts that senescent astrocytes and oligodendrocyte progenitors together pressure microglia to phagocytose neurons containing tau pathology, where resulting senescent microglia create neuritic plaques and induce paracrine senescence transitioning into and progressing clinical, dementia presentation. This predictive model accounts for why medications used to treat LOAD fail, as previous treatments have not reduced senescent glial burden. It is also coherent with the predominant hypotheses surrounding LOAD involving the amyloid cascade, tau, glia and inflammation, creates testable hypotheses about LOAD, and increases rationale in testing senolytics as targeted treatments for LOAD arrest and reversal.

Modularity is arguably one of the most influential theses guiding research on brain and cognitive function since phrenology. This paper considers the following question: is modularity entailed by recent Bayesian models of brain and cognitive function, especially the predictive processing framework? It starts by considering three of the most well-articulated arguments for the view that modularity and predictive processing work well together. It argues that all three kinds of arguments for modularity come up short, albeit for different reasons. The analysis in this paper, although formulated in the context of predictive processing, speaks to broader issues with how to understand the relationship between functional segregation and integration and the reciprocal architecture of the predictive brain. These conclusions have implications for how to study brain and cognitive function. Specifically, when cognitive neuroscience works within an acyclic Markov decision scheme, adopted by most Bayesian models of brain and cognitive function, it may very well be methodologically misguided. This speaks to an increasing tendency within the cognitive neurosciences to emphasise recurrent and reciprocal neuronal processing captured within newly emerging dynamical causal modelling frameworks. The conclusions also suggest that functional integration is an organising principle of brain and cognitive function.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, momentum spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant, in contrast to the Dirac equation, which lacks this invariance. This novel equation permitted the construction of a relativistically invariant procedure for the second quantization of the fermion field in spinor coordinate space.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations converting the defined Lax pairs to some simpler forms and reducing the variety of the Lax pairs this way are found. The direct method and its possible applications to other types of evolution equations are discussed.

Predictive maintenance technologies have emerged as a transformative force in retail supply chain management, offering the potential to significantly enhance operational efficiency, reduce costs, and improve customer satisfaction. This study explores the implementation and impact of predictive maintenance within the retail sector, focusing on its benefits, challenges, technological tools, and future directions. The findings indicate that predictive maintenance enables a proactive approach to equipment management, leading to substantial reductions in downtime and maintenance costs, extended equipment lifespan, and enhanced sustainability through reduced energy consumption and waste. However, the adoption of these technologies is not without challenges. High initial costs, the need for specialized skills in data analytics and IoT, issues with data quality and reliability, organizational resistance, and cybersecurity concerns present significant barriers to successful implementation. Technological tools such as IoT sensors, data analytics platforms, machine learning algorithms, and digital twins are crucial for the effective functioning of predictive maintenance systems, providing real-time data monitoring and analysis that improve decision-making and maintenance planning. The study also highlights promising future trends, including advancements in AI, machine learning, IoT, and blockchain technologies, which are expected to further enhance predictive maintenance capabilities. To fully realize the potential of predictive maintenance, companies must address the identified challenges, invest in workforce development, and implement robust data security measures. Future research should focus on exploring these advancements, understanding the broader environmental impacts, and conducting cross-industry analyses to identify best practices. Overall, while predictive maintenance offers substantial benefits, its successful integration requires a nuanced approach that balances technological innovation with strategic and operational considerations.

This study addressed algorithmic bias in predictive policing, focusing on the Chicago Police Department's Strategic Subject List (SSL) dataset. We specifically focused on identifying and mitigating age-related biases, a notably underexplored area in prior research. Our research introduced Conditional Score Recalibration as a bias mitigation strategy alongside the well-established Class Balancing technique. Conditional Score Recalibration involved reassessing and adjusting risk scores for individuals initially assigned moderately high-risk scores in the dataset. This recalibration marked such individuals as low risk if they met three conditions, namely: no prior arrests for violent offenses, no previous arrests for narcotic offenses, and having never been involved in shooting incidents. These fairness strategies were implemented on the Random Forest model, and the fairness metrics employed included Equality of Opportunity Difference, Average Odds Difference, and Demographic Parity. The results showed a significant improvement in model fairness, particularly for age biases, without compromising the model's accuracy. These findings challenged the often-assumed trade-off between fairness and accuracy, underscoring the feasibility of achieving fairness without compromising accuracy.

Fuel consumption, subsequent emissions and safe operation of class 8 vehicles are of prime importance in recent days. It is imperative that the vehicle operates in its true optimal operating region given a variety of constraints such as road grade, load, gear shifts, Battery State of charge (for hybrid vehicles), etc. In this paper a research study is conducted to evaluate the fuel economy and subsequent emission benefits when applying predictive control to a mild hybrid line haul truck. The problem is solved using a combination of dynamic programming with back tracking and model predictive control. The specific fuel saving features that are studied in this work are dynamic cruise control, gear shifts, vehicle coasting and torque management. These features are evaluated predictively as compared to a reactive behavior. The predictive behavior of these features are a function of road grade. The result and analysis shows significant improvement in fuel savings along with NOx benefits. Out of the control features dynamic cruise (predictive) control and dynamic coasting showed the most benefits while predictive gear shifts and torque management (by power splitting between battery and engine) for this architecture did not show fuel benefits but provided other benefits in terms of powertrain efficiency.

A novel machine learning approach is presented in this paper, based on extracting latent information and using it to assist decision making on ambulance attendance and conveyance to a hospital. The approach includes two steps: in the first, a forward model analyzes the clinical and, possibly, non-clinical factors (explanatory variables), predicting whether positive decisions (response variables) should be given to the ambulance call, or not; in the second, a backward model analyzes the latent variables extracted from the forward model to infer the decision making procedure. The forward model is implemented through a machine, or deep learning technique, whilst the backward model is implemented through unsupervised learning. An experimental study is presented, which illustrates the obtained results, by investigating emergency ambulance calls to people in nursing and residential care homes, over a one-year period, using an anonymized data set provided by East Midlands Ambulance Service in United Kingdom.

In this paper, the power quality of interconnected microgrids is managed using a Model Predictive Control (MPC) methodology which manipulates the power converters of the microgrids in order to achieve the requirements. The control algorithm is developed for the microgrids working modes: grid-connected, islanded and interconnected. The results and simulations are also applied to the transition between the different working modes. In order to show the potential of the control algorithm, a comparison study is carried out with classical Proportional-Integral Pulse Width Modulation (PI-PWM) based controllers. The proposed control algorithm not only improves the transient response in comparison with classical methods but also shows an optimal behavior in all the working modes, minimizing the harmonics content in current and voltage even with the presence of non-balanced and non-harmonic-free three-phase voltage and current systems

The goal of this contribution is an application of the Linear General Model Predictive Control (LGMPC). In this paper, stability of the LGMPC is proven by means of a demonstration of a Theorem stating a sufficient and constructive condition. This condition can be applied for calculating the weight matrices of the cost function in the optimisation problem in LGMPC. Lower bounds conditions are found for one of these matrices and then a system with saturation is taken into consideration. The conditions could be interpreted and discussions through physical aspects. The obtained results were tested by means of computer simulations and an example with a recover water process is considered.

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

This paper addresses challenges and solutions in urban development and infrastructure resilience, particularly in the context of Japan's rapidly urbanizing landscape. It explores the integration of smart city concepts to combat land subsidence and liquefaction, phenomena highlighted by the 2011 Great East Japan Earthquake. Using advanced technologies such as smart sensing and predictive analytics through kriging and ensemble learning, the study aims to improve the accuracy of geotechnical investigations and urban planning. By analyzing data from 433 geotechnical surveys in Setagaya, Tokyo, it develops predictive models to accurately determine the depth of bearing layers critical to urban infrastructure. The results demonstrate the superiority of ensemble learning in predicting the depth of bearing layers, with significant implications for smart city development and the sustainability of urban environments. This interdisciplinary approach not only seeks to mitigate risks associated with geological disturbances, but also promotes sustainable urban growth that prioritizes safety and prosperity. Through advanced technology and comprehensive research, the study underscores the potential of smart cities to address urban complexities and ensure a resilient, sustainable future.

Multi-junction solar cells comprised of stacked III-V semiconductor junctions represent the highest-efficiency photovoltaic technology, with recent demonstrations exceeding 47% efficiency . Optimizing the design and thickness of each junction is critical for maximizing performance . This work utilizes Silvaco TCAD tools to systematically optimize a 5-junction cell based on AlInP, AlGaInP, AlGaInAs, GaInP, GaAs, InGaAs, and Ge similar to recent record cells . The junction thicknesses are varied using a predictive profiler to sample the parameter space . For each combination, the spectral absorption and I-V characteristics are simulated to determine the efficiency . Statistical analysis identifies the optimal thickness set that maximizes performance to 26% under 1 sun illumination .

In cricket, particularly the twenty20 format is most watched and loved by the people, where no one can guess who will win the match until the last ball of the last over. In India, The Indian Premier League (IPL) started in 2008 and now it is the most popular T20 league in the world. So we decided to develop a machine learning model for predicting the outcome of its matches. Winning in a Cricket Match depends on many key factors like a home ground advantage, past performances on that ground, records at the same venue, the overall experience of the players, record with a particular opposition, and the overall current form of the team and also the individual player. This paper briefs about the key factors that affect the result of the cricket match and the regression model that best fits this data and gives the best predictions. Cricket, the mainstream and widely played sport across India which has the most noteworthy fan base. Indian Premier League follows 20-20 format which is very unpredictable. IPL match predictor is a ML based prediction approach where the data sets and previous stats are trained in all dimensions covering all important factors such as: Toss, Home Ground, Captains, Favorite Players, Opposition Battle, Previous Stats etc, with each factor having different strength with the help of KNIME Tool and with the added intelligence of Naive Bayes network and Eulers strength calculation formula.

BACKGROUND AND AIMS: Cardiovascular disease and colorectal cancer (CRC) are significant health problems and share some risk factors. The aim of our study was to develop and validate a predictive score for advanced colorectal neoplasia (CRN) based on risk factors for cardiovascular disease and CRC. MATERIALS AND METHODS: A cross-sectional study comprising a derivation cohort and an external validation cohort of 1049 and 308 patients respectively. A prediction score for advanced CRN (CRNAS: Colorectal Neoplasia Advanced Score) was developed from a logistic regression model, comprising sex, age, first-degree family history for CRC, systolic and diastolic blood pressure, total cholesterol, HDL-cholesterol, body mass index, diabetes, smoking, and antihypertensive treatment. Other cardiovascular risk scores (Framingham-Wilson, REGICOR, SCORE and FRESCO) were also used to predict the risk of advanced CRN. The discriminatory capacity of each score was evaluated using the area under the curve (AUC). RESULTS: CRN were found in 379 subjects from the derivation cohort (36%) including 228 patients (22%) with an advanced CRN. Male sex, age, diabetes, and smoking were identified as independent risk factors for advanced CRN. The newly created score (CRNAS), showed an AUC of 0.68 (95% CI: 0.64-0.73) for advanced CRN, which was better than cardiovascular risk scores (p

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind soil erosion and common soil erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. The main objective of this paper is to estimate the best exponent of the MUSLE, and to estimate the best combination of the exponent and topographic factor of the MUSLE under hydro-climatic conditions of Ethiopia. For the sake of calibration procedure, the main parameters of the MUSLE which directly affect soil erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which have no any physical meaning (i.e coefficient a and exponent b) are estimated through calibration. It is verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e approximately 100\%). For the best combination of the exponent and topographic factor, the performance of the MUSLE is greater than or equal to 80\% for all four watersheds under our consideration, we expect the same for other watersheds of Ethiopia.

Basophils are initiators of the Th2 response related to the progression of canine visceral leishmaniasis (CanL). Miltefosine has been presented as an alternative in treatment due to its leishmanicide and immunomodulatory effects. Many blood cells have been used as predictive biomarkers, but none of them focused on the immunomodulatory action of miltefosine in the different stages of the disease. Identifying the predictive hematological biomarkers in dogs with visceral leishmaniasis treated with miltefosine. The animals were divided into three groups: sick dogs; infected dogs, dogs exposed. The animals were submitted to differential blood cell count and CanL diagnosis, through DPP, ELISA and qPCR. The groups were monitored from the time zero (T0) before treatment, and the times twenty (T20) and thirty (T30) days after the beginning of treatment using miltefosine at a dose of 1mL/10kg per day for 28 days. Basophils showed an exponential increase in the infected and sick group with an increase of IgG, suggesting a Th2 response. In the exposed group there was reduction of basophils with increase in monocytes and IgG reduction, suggesting a Th1 response. We suggest basophils as a predictive biomarker of immunomodulation in the treatment of CanL with miltefosine.

This paper presents the perturbation theory for the double–sine–Gordon equation. We obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution.. In the particular case λ = 0 we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ=-1/8, we derive a phase-locked solution with the same frequency of the linear case. In general we obtain both coherent (solitary waves, lumps and so on) solutions as well as fractal solutions. We can demonstrate the existence of envelope wobbling solitary waves, because of the phase modulation depending on the solution amplitude and on the position. The main conclusion is that it is too reductive focus only on coherent solutions for the double sine-Gordon equation, because of the very rich behavior for the DSG nonlinear equation, including wobbling chaotic and fractal solutions.

Although there is a common physiological notion that the origin of the membrane potential is attributed to transmembrane ion transport, it is theoretically possible to explain its generation by the mechanism of ion adsorption. It was previously suggested that the ion adsorption mechanism led even to the potential formulas which are even identical to either the famous Nernst equation or Goldman-Hodgkin-Katz equation. Our further analysis shown in this paper indicates that the potential formula based on the ion adsorption mechanism leads to one equation which is the function of material surface charge density and the material surface potential. Furthermore, we confirmed that the equation holds in all the different experimental systems we studied. Although we have not succeeded in elucidating why such an equation is established, the equation appears to be the key equation governing the characteristics of the membrane potential regardless of the systems in question.

HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

A contemporary technique for calculating seismic risk is earthquake nowcasting (EN), which analyzes the progression of the earthquake (EQ) cycle in fault systems. 'Natural time' is a novel idea of time that serves as the foundation for EN assessment. The earthquake potential score (EPS), which has been discovered to have useful uses regionally and worldwide, is a unique tool EN uses to predict seismic risk. For the estimation of the EPS for the occurrences with the highest magnitude among these applications, we have since 2021 concentrated on Greece territory, applying sophisticated Artificial Intelligence (AI) algorithms, both wise (semi)supervised and unsupervised models, along with a customized dynamic sliding window technique that performs as a stochastic filter able to fine-tune the geo seismic occurrences. Long short-term memory (LSTM) neural networks, random forests, and clustering (geospatial) models are three machine learning techniques that are particularly good at finding patterns in vast databases and may be used to enhance earthquake prediction performance. In this study, we attempt to forecast whether practical Machine-learning and AI/Game-theoretic-based approaches can help predict big earthquakes and the normal future seismic cycle for 6-12 months. Specifically, we focus on answering two questions for a given region: (1) Is there a chance that a significant earthquake—say, one with a magnitude of M ≥ 6.0 will happen in the upcoming year? (2) What is the largest earthquake magnitude predicted in the upcoming year, and with which exact geographic coordinates (GCS)? Our results are quite promising and project a high precision accuracy score (≥ 98%) for seismic nowcasting in terms of four predictive parameters: the approximate (a) latitude, (b) longitude, (c) focal depth, and (d) magnitude of the phenomena.