Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

We study latching dynamics in the adaptive Potts model network, through numerical simulations with randomly and also weakly correlated patterns, and we focus on comparing its slowly and fast adapting regimes. A measure, Q, is used to quantify the quality of latching in the phase space spanned by the number of Potts states S, the number of connections per Potts unit C and the number of stored memory patterns p. We find narrow regions, or bands in phase space, where distinct pattern retrieval and duration of latching combine to yield the highest values of Q. The bands are confined by the storage capacity curve, for large p, and by the onset of finite latching, for low p. Inside the band, in the slowly adapting regime, we observe complex structured dynamics, with transitions at high crossover between correlated memory patterns; while away from the band latching transitions lose complexity in different ways: below, they are clear-cut but last so few steps as to span a transition matrix between states with few asymmetrical entries and limited entropy; while above, they tend to become random, with large entropy and bi-directional transition frequencies, but indistinguishable from noise. Extrapolating from the simulations, the band appears to scale almost quadratically in the p - S plane, and sublinearly in p - C. In the fast adapting regime the band scales similarly, and it can be made even wider and more robust, but transitions between anti-correlated patterns dominate latching dynamics. This suggest that slow and fast adaptation have to be integrated in a scenario for viable latching in a cortical system. The results for the slowly adapting regime, obtained with randomly correlated patterns, remain valid also for the case with correlated patterns, with just a simple shift in phase space.

A statistical analysis of semantic memory should reflect the complex, multifactorial structure of the relations among its items. Still, a dominant paradigm in the study of semantic memory has been the idea that the mental representation of concepts is structured along a simple branching tree spanned by superordinate and subordinate categories. We propose a generative model of item representation with correlations that overcomes the limitations of a tree structure. The items are generated through "factors" that represent semantic features or real-world attributes. The correlation between items has its source in the extent to which items share such factors and the strength of such factors: if many factors are balanced, correlations are overall low; whereas if a few factors dominate, they become strong. Our model allows for correlations that are neither trivial nor hierarchical, but may reproduce the general spectrum of correlations present in a data-set of nouns. We provide an estimate of the number of concepts that can be stored and retrieved by a large-scale cortical network, the Potts network, which is perhaps approximately 10⁷ with human cortical parameters. When this storage capacity is exceeded, however, retrieval fails completely only for balanced factors; above a critical degree of imbalance, a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: partial categorization seems to emerge spontaneously as a consequence of the dominance of particular factors, rather than being imposed ad hoc. We argue this to be a relevant model of semantic memory resilience in Tulving’s remember/know paradigms.

By framing the problem of determining the state of Schrodinger’s cat as a problem of searching for Hidden Markov Model (HMM), this work shows that Schrodinger’s cat is dead with stationary probabilities P(Cat = Dead) = 1 and P(Cat = Alive) = 0 consistently in various observation-based modelling of the HMM.

This paper investigates the transmission of educational attainment from parents to offsprings as a mediator of intergenerational class mobility in Europe. The study covers the last two decades with data drawn from a cross-national large scale sample survey, namely the European Social Survey (ESS), for the years 2002 - 2018. Interest has focused on the question of persistence of inequality of educational opportunities by examining attainment of nominal levels of education and the association between the educational attainment of the parent with the highest level of education and their descendants. The study covers also new trends in social mobility which consider education as a ‘positional good’ and a novel method of incorporating educational expansion into the transition probabilities is proposed, providing answers to whether the rising accessibility of educational qualifications attenuates the association between social origin and educational attainment. Therefore, the concept of positionality is taken into account in the estimation of intergenerational transition probabilities and to complement the analysis mobility measures are provided for both methods, nominal and positional. The proposed positional method is validated through a correlation analysis between the upward mobility scores (nominal and positional) with the Education Expansion Index (EEI) for the respective years. The upward mobility scores estimated via the positional method are higher correlated with the EEI for all years indicating a better alignment with the broader trends in educational participation and achievement.

Deciding when to replace dairy bulls presents a complex challenge for artificial insemination (AI) companies. These decisions encompass multiple factors, including a bull's age, predicted semen production, and estimated genetic merit. This study's purpose was to provide a practical, objective tool to assist in these decisions. We utilized a Markov Chain model to calculate the economic valuation of dairy bulls, incorporating key factors such as housing costs, collection and marketing expenses, and the bull's probable tenure in the herd. Data from a leading AI company were used to establish baseline values. The model further compared a bull's net present value to that of a potential young replacement, establishing a relative valuation (BullVal$). The range of BullVal$ observed spanned from -$316,748 to $497,710. Interestingly, the model recommended culling for 49% of the bulls based on negative BullVal$. It was found that a bull's net present value was primarily influenced by market allocation and pricing, coupled with the interaction of semen production and genetic merit. This study offers a robust, data-driven model to guide bull replacement decisions in AI companies. Key determinants of a bull's valuation included market dynamics, semen production rates, and genetic merit.

The Gol'denveizer problem of a torus can be described as follows: a toroidal shell is loaded under axial forces and the outer and inner equators are loaded with opposite balanced forces. Gol'denveizer pointed out that the membrane theory of shells is unable to predict deformation in this problem, as it yields diverging stress near the crowns. Although the problem has been studied by Audoly and Pomeau (2002) with the membrane theory of shells, the problem is still far from resolved within the framework of bending theory of shells. In this paper, the bending theory of shells is applied to formulate the Gol'denveizer problem of a torus. To overcome the computational difficulties of the governing complex-form ordinary differential equation (ODE), the complex-form ODE is converted into a real-form ODE system. Several numerical studies are carried out and verified by finite-element analysis. Investigations reveal that the deformation and stress of an elastic torus are sensitive to the radius ratio, and the Gol'denveizer problem of a torus can only be fully understood based on the bending theory of shells.

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

Sword-duels are interesting, from a game-theoretical perspective, as they correspond to sudden-death interactions between players (i.e., defeat means removal from the game), and where victory/defeat depend on not just skill, but also luck. Analyzing probabilities of victory streaks, given a certain level of self and others' skill, is thus relevant for any application domain that can be modeled in the same way. This paper takes inspiration from Miyamoto Musashi, famously undefeated for 61 duels, and implements a Markov-chain Monte-Carlo simulation approach to evaluate this scenario. Results suggest that a 61 victory streak can be probabilistically observed when skill level is roughly 6.5 times that of the average duelist, and with 95\% confidence when skill level is roughly 1000 times that of the average duelist. More generally, this paper provides a method for determining chances of victory streaks in game-theoretical sudden-death encounters, when both "skill" and "luck" contribute to the outcome of the encounter. Specific scenarios can be modeled by modifying the utilized Markov chain and adjusting sampled distributions as required.

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

Network coding approaches typically consider an unrestricted recoding of coded packets in the relay nodes for increased performance. However, this can expose the system to pollution attacks that cannot be detected during transmission, until the receivers attempt to recover the data. To prevent these attacks while allowing for the benefits of coding in mesh networks, the Cache Coding was proposed. This protocol only allows recoding at the relays when the relay has received enough packets to decode an entire generation of packets. At that point, the relay node recodes and signs the recoded packets with its own private key allowing for the system to detect and minimize the effect of pollution attacks and make relays accountable for changes on the data. This paper analyzes the delay performance of Cache Coding to understand the security-performance trade-off of this scheme. We introduce an analytical model for the case of two relays in an erasure channel relying on an Absorbing Markov Chain and a approximate model to estimate the performance in terms of the number of transmissions before successfully decoding at the receiver. We confirm our analysis using simulation results. We show that Cache Coding can overcome security issues of unrestricted recoding with only a moderate decrease in system performance.

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of those of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of $G$-type.

Snap-fit is a commonly used jointing/connention mechanism, and its easy installation and difficult removal are the result of the coordinated interaction between friction, geometric shape, and elasticity. This paper presents a detailed study on the assembly/disassembly forces of thin-walled torus snap-fit through finite element simulation, experimental testing, and data fitting of approximate analytical solutions. The research reveals that the non-zero Gaussian curvature of the torus has a significant impact on the mechanical performance of the torus snap fit. The findings in this study are of great significance for future design of high-performance structural connections.

The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.

In this work, we explore a the different forms of a new type of modified gravity, namely f(φ) gravity. We construct the Big Rip type for the energy density and the curvature of the universe. We show that dark energy is a result of the transformation of the field φ mass (dark matter) to energy. In addition, we provide that Ω_{m}≈0,050, Ω_{DM}≈0,2, Ω_{DE}≈0,746, is in excellent agreement with observation data. We explore a generalized formalism of braneworld modified gravity. We also construct a new field equations, which generalize the Einstein field equations. We provide a relation between the extra dimension in 3-brane with the vacuum energy density. We show that the energy density of matter depends directly on the number of dimensions. We manage to find the value of the Gauss-Bonnet coupling α=1/4 which is a good agreement with the results in the literature, this correspondence creates a passage between f(R) gravity and Gauss-Bonnet gravity, this comparison leads to a number of bulk dimensions equal to D=10¹²¹+4.

The spectrums of one type of object under different conditions have the same features (up, down, protruding, concave) at the same spectral positions, which can be used as primary parameters to evaluate the difference among remotely sensed pixels. Wavelet-feature correlation ratio Markov clustering algorithm (WFCRMCA) for the remotely sensed data is proposed based on an accurate description of abrupt spectral features and an optimized Markov clustering in the wavelet feather space. The peak points can be captured and identified by applying a wavelet transform to spectral data. The correlation ratio between two samples is a statistical calculation of the matched peak point positions on the wavelet feature within an adjustable spectrum domain or a range of wavelet scales. The evenly sampled data can be used to create class centers, depending on the correlation ratio threshold at each Markov step, accelerating the clustering speed by avoiding the computation of Euclidean distance for traditional clustering algorithms, such as K-means and ISODATA. Markov clustering applies several strategies, such as a simulated annealing method and gradually shrinking the clustering size, to control the clustering convergence. At each clustering tempera-ture, it can obtain the best class centers quickly. The experimental results of the Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS) and Thermal Mapping (TM) data have verified its ac-ceptable clustering accuracy and high convergence velocity.

A correctly obtained Land-use/land-cover (LULC) prediction map is essential to under-standing and assessing future patterns. In the study, the LULC map of Urmia/Iran in 2030 was produced using two different prediction methods CA-Markov and Artificial Neural Network (ANN). In general, the study followed a methodology consisting of three steps. In the first steps, Landsat satellite images acquired in 2000, 2010 and 2020 were classified with maximum likelihood algorithm and LULC maps were prepared for each year. In the second stage, to investigate the LULC prediction methods' validation (CA-Markov and ANN) the LULC prediction map of 2020 was produced using the LULC map of 2000 and 2010; In this step, the predicted LULC map of 2020 and the actual LULC map of 2020 were evaluated by correctness, completeness and quality indexes. Finally, The LULC map for 2030 was prepared using all two algorithms and the change map was extracted. The results show that the area of soil and vegetation decreased, and built-up regions increased during the research period. The methods validation results show that the two algorithms are much closer to each other. Nevertheless, in general, ANN has the highest completeness (96.21%) and quality (93.8%) and CA-Markov the most correctness (96.47). This study shows that the CA-Markov algorithm is most successful in predicting the future that had larger areas and a higher percentage in the region (urban and vegetation cover) and the ANN algorithm in predicting phenomena that had smaller levels with fewer percentages (soil and rock).

Congestion pricing has received lots of attention in the scientific discussion. Congestion pricing means that the operator increases prices at the time of congestion and the traffic demand is expected to decrease. In a certain sense, shadow prices are an optimal way of congestion pricing: users are charged shadow prices, i.e., the expectations of future losses because of blocked connections. The shadow prices can be calculated exactly from Howard’s equation, but this method is difficult. The paper presents simple approximations to the solution of Howard’s equation and a way to derive more exact approximations. If users do not react by lowering their demand, they will receive higher bills to pay. Many users do not react to increased prices but would want to know how the congestion pricing mechanism affects the bills. The distribution of the price of a connection follows from knowing the shadow prices and the probability of a congestion state. There is another interesting distribution. The network produces profit to the operator, or equivalently, blocked connections produce a cost to the operator. The average cost rate can be calculated from Howard’s equation, but the costs have some distribution. The distribution gives the risk that the actual costs exceed the average costs, and the operator should include this risk to the prices. The main result of this paper shows how to calculate the distribution of the costs in the future for congestion pricing by shadow prices and for congestion pricing with a more simple pricing scheme that produces the same average costs.

The purpose of this study is to estimate the mean transitioning probabilities from a Healthy state to malaria positive uncomplicated state or to malaria positive severe state. It also classifies the various transitioning probabilities of moving through the various states based on some baseline characteristics. Malaria test results for 2019 over a 12-month period were collected from the University of Ghana school clinic. An H-U model for the study was developed and the transition rates from the cross-sectional data are indicated. With two states Healthy (H) and Uncomplicated (U) forming a state space, there were four possible transitions. The results show that the probability of transitioning from a Healthy state to a malaria positive state is 0.03% while the probability that an individual will remain at Healthy state (H) after the test is 99.73%. It was found that if an individual is already positive and has taken medication the probability that its second test came out negative is 6.45% while the chances that it will remain positive but uncomplicated is 93.55%. The study also showed that in the long run, about 95.98% of persons who visited the student clinic with malaria symptoms recorded negative tests for malaria parasite while about 4% recorded positive for malaria. In terms of disaggregation by gender, it was realized that the number of reported negative test results were higher for females (97.08%) than for males (96.13%). However, the infection rate is higher for males (3.87%) than females (2.92%). It is recommended that in as much as the University of Ghana has two health centers (a clinic and hospital), there should be a centralized system to track students’ health so research done would not be biased.

Runtime verification (RV) is a lightweight approach to detecting temporal errors of system at runtime. It confines the verification on observed trajectory which avoids state explosion problem.To predict the future violation, some work proposed the predictive RV which uses the information from models or static analysis. But for software whose models and codes cannot be obtained, or systems running under uncertain environment, these predictive methods cannot take effect. Meanwhile, RV in general takes multi-valued logic as the specification languages, for example the " true, false and inconclusive" in three-valued semantics. They cannot give accurate quantitative description of correctness when "inconclusive" is encountered. We in this paper present a RV method which learns probabilistic model of system and environment from history traces and then generates probabilistic runtime monitor to quantitatively predict the satisfaction of temporal property at each runtime state. In this approach, Hidden Markov Model (HMM) is firstly learned and then transformed to Discrete Time Markov Chain (DTMC). To construct incremental monitor, the monitored LTL property is translated into Deterministic Rabin Automaton (DRA). The final probabilistic monitor is obtained by generating the product of DTMC and DRA, and computing the probabilities for each state. With such method, one can give early warning once the probability of correctness is lower than pre-defined threshold, and have the chance to do adjustment in advance. The method has been implemented and experimented on real UAS (Unmanned Aerial Vehicle) simulation platform.

LiFePO₄ (LFP) or Lithium-ion battery with its advantages compared to common current motorcycle battery is an appropriate alternative in substituting wet and dry cell battery. Huge amount of demand of motorcycle along with the battery in Indonesia also make it an interesting product for business. In order to assess the commercial potential for such a new technology, market share needs to be estimated as well as the techno-economic feasibility. Hence, market share prediction using the residents of Surakarta Region and techno-economic analysis using NPV, IRR and PBP indicators have been conducted in this study. Calculation using markov chain method shows that LFP battery tends to dominate the market after certain period. Techno-economic analysis also figures out that the commercialization is feasible in three conditions - first mover, even with market leader and equilibrium point. Therefore, there is a great commercial potential for LFP battery especially in Indonesia.

This study analyses regional development in one of the poorest provinces in China, Guizhou Province, between 2000 and 2012 using a multiscale and multi-mechanism framework. In general, regional inequality has been declining since 2000. In addition, economic development in Guizhou Province presented spatial agglomeration and club convergence, which shows how the development pattern of one core area, two-wing areas and a contiguous area at the edge of the province have been developed between 2006 and 2012. Multilevel regression analysis revealed that industrialization and investment level were the primary driving forces of regional economic disparity in Guizhou Province. The influences of marketization and decentralization on regional economic disparity were relatively weak. Investment level reinforced regional economic disparity and the development of core-periphery structure in the province. However, investment level actually weakened the regional economic disparity in Guizhou Province when the variable of time was considered. In addition, both the topography and urban–rural differentiation were the two main reasons for forming a core-periphery structure in Guizhou Province.

The formulation used by the most of studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of the torus, application of those formulations has encountered great difficulty. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of the torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency.

The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while for smaller black holes higher curvature corrections become important. We will show that if one is limited by positive values of the coupling constants, then the dynamical instability of black holes serves as an effective cut-off of influence of higher curvature corrections in the 4D Einstein-Lovelock approach: the higher is the order of the Lovelock term, the smaller is the maximal value of the coupling constant allowing for stability, so that effectively only a first few orders can deform the observable values seemingly. For negative values of coupling constants this is not so, and, despite some suppression of higher order terms also occurs due to the decreasing threshold values of the coupling constant, this does not lead to an noticeable opportunity to neglect higher order corrections. In the case a lot of orders of Lovelock theory are taken into account, so that the black-hole solution depends on a great number of coupling constants, we propose a compact description of it in terms of only two or three parameters encoding all the observable values.

Background: The first few minutes after birth are the most dangerous for the survival of an infant. Babies in neonatal intensive care units are either under heated or overheated, and hypothermic infants remain hypothermic or develop a fever. As a result, special attention must be paid to monitoring and maintaining the time of recovery from hypothermia states. Despite numerous studies, only a few have examined the transition from neonatal hypothermia and associated risk factors in depth. Method: A retrospective observational study was conducted to track axillary temperatures taken at the time of neonatal intensive care unit admission, which were then tracked every 30 minutes until the newborn's temperature stabilized. All hypothermic neonates admitted to the neonatal intensive care unit between January 2018 and December 2020 was included in the study. Temperature data were available at birth and within the first three hours of admission for 391 eligible hypothermic neonates. The effect of factors on the transition rate in different states of hypothermia was estimated using a multi-state Markov model. Result: The likelihood of progressing from mild to severe hypothermia was 5%, while the likelihood of progressing to normal was 34%. The average time spent in a severe hypothermia state was 48, 35, and 24 minutes for three different levels of birth weight, and 53, 41, and 31 minutes for low, moderate, and normal Apgar scores, respectively. Furthermore, the mean sojourn time in a severe hypothermia state was 48, 39, and 31 minutes for three different levels of high, normal, and low pulse rate, respectively. Conclusion: For hypothermic survivors within the first three hours of life, very low birth weight, low Apgar, and high pulse rate had the strongest association with hypothermia and took the longest time to improve/recover. As a result, there is an urgent need to train all levels of staff dealing with maintaining the time of recovery from neonatal hypothermia.

Purpose: To construct a hidden Markov model (HMM) for vigilance assessment to improve the real-time performance and accuracy of current vigilance measurement. Methods: ECG signal was collected by sensors, while the noise and baseline drift was eliminated from the original ECG signal. 10 volunteers were randomly selected. Their heart rate variability (HRV) were measured and trained parameters of the modified Hidden Markov model for vigilance assessment. Then, these data were collected to optimize using the Baum-Welch algorithm and obtained the state transition probability matrix A ̂ and the observation probability matrix B ̂. Finally, the data of three volunteers with different transition patterns of mental state were selected randomly and used the Viterbi algorithm to find the optimal state, which compared with the actual state. Results: The constructed vigilance assessment model had a high accuracy rate the accuracy rate of data prediction for these three volunteers exceeded 80%. Conclusion: The Hidden Markov model for vigilance assessment can accurately predict the vigilance level and indicate broad application prospects.

Flexible implementations of Monte Carlo Tree Search (MCTS), combined with domain specific knowledge and hybridization with other search algorithms, can be a very powerful for the solution of problems in complex planning. We introduce mctreesearch4j, a standard MCTS implementation written as a standard JVM library following key design principles of object oriented programming. We define key class abstractions allowing the MCTS library to flexibly adapt to any well defined Markov Decision Process or turn-based adversarial game. Furthermore, our library is designed to be modular and extensible, utilizing class inheritance and generic typing to standardize custom algorithm definitions. We demon- strate that the design of the MCTS implementation provides ease of adaptation for unique heuristics and customization across varying Markov Decision Process (MDP) domains. In addition, the implementation is reasonably performant and accurate for standard MDP’s. In addition, via the implementation of mctreesearch4j, the nuances of different types of MCTS algorithms are discussed.

This paper presents a simple and fast technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov Modulated Poisson Process models has been performed.

Aim: This research is aimed at examining the cost-effectiveness of olanzapine versus risperidone in dementia patients with behavioural and psychological symptoms in Thailand. Methods: An existing Markov model based on a critical review through the comprehensive literature search and a justification for the most appropriate model for a Thai setting was adapted to simulate the disease progression of patients with dementia with behavioural disturbances until their need for full-time care (FTC). The time to the FTC state was estimated by a predictive equation developed by Rive et al. (2010). The model was conducted to assess the expected costs and outcomes associated with olanzapine compared with risperidone for Thai patients with BPSD aged 60 years and above. This model performed over a five-year time horizon with a one-month cycle length based on a societal perspective. The incremental cost-effectiveness ratio was used as the estimated outcome. Sensitivity analyses were also conducted to demonstrate the robustness of the results. Results: Over 5 years, olanzapine was found to be a cost-effective therapeutic option for the treatment of behaviourally disturbed patients with dementia compared with risperidone, in Thailand from a societal perspective (ICER < THB 160,000). The model underwent extensive sensitivity analyses, which also confirmed that olanzapine was the dominant strategy following the base-case findings. Conclusions: By comparison with risperidone, the model suggests that olanzapine can be regarded as a cost-effective therapeutic strategy for the management of patients with behavioural and psychological symptoms in Thailand.

Autonomous shuttles have been used as end mile solutions for smart mobility in smart cities. The urban driving conditions of smart cities with many other actors sharing the road and the presence of intersections have posed challenges to the use of autonomous shuttles. Round intersections are more challenging as it is more difficult to perceive the other vehicles in and near the intersection. Thus, this paper focuses on decision making of autonomous vehicles for handling round intersections. The round intersection is introduced first, followed by introductions of the Markov Decision Process (MDP), the Partially Observable Markov Decision Process (POMDP) and the Object Oriented Partially Observable Markov Decision Process (OOPOMDP) which are used for decision making with uncertain knowledge of the motion of the other vehicles. The Partially Observable Monte-Carlo Planning (POMCP) algorithm is used as the solution method and OOPOMDP is applied to decision making for autonomous vehicles in round intersections. Decision making is formulated first as a POMDP problem, and the penalty function is formulated and set accordingly. This is followed by improvement of decision making with policy prediction. Augmented objective state and policy-based state transition are introduced and simulations are used to demonstrate the effectiveness of the proposed method for collision free handling of round intersections by the ego vehicle.

By generalizing the notion of pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls do not have the proper generalized 1-type Gauss map. In fact, it is harmonic.

For massive multiple-input multiple-output (MIMO) communications, the minimum mean square error (MMSE) scheme provides close to optimal recognition but involves inverting the high-dimensional matrix. A Gauss-Seidel (GS) detector based on conjugate gradient and Jacobi iteration (CJ) joint processing is introduced to address this problem. Firstly, the signal is initialized with the best of the three initialization regimes for faster algorithm convergence. Secondly, the signal is processed together with CJ. Finally, the pre-processed result is transferred to the GS detector. The simulation results indicate that the proposed iterative algorithm has a lower BER performance than the GS and improved iterative scheme based on GS in channels with different correlation levels.

For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic, and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrance theory. A numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.

Background: Current obstructive sleep apnea treatment relies on manual PAP titration, but it has limitations. Complex interactions during titration and variations in SpO2 data accuracy pose challenges. Patients with co-occurring chronic hypercapnia may require precise oxygen titration. To address these issues, we propose a Clinical Decision Support System using Markov Decision Processes. Methods: This study, compliant with data protection laws, focused on adults with OSA-induced hypoxemia utilizing supplemental oxygen and CPAP/BiPAP therapy. PAP titration, conducted over one night, involved vigilant monitoring of vital signs and physiological parameters. Adjustments to CPAP pressure, potential BiLevel transitions, and supplemental oxygen were precisely guided by patient metrics. Markov Decision Processes outlined three distinct phases for sleep disorder management, incorporating expert medical insights. Results: In our study involving 14 OSA patients (average age: 63 years, 27% females, BMI 41 kg m−2), significant improvements were observed in key health parameters. The initial AHI of 61.8 events per hour significantly decreased to an average of 18.0 events per hour after PAP and oxygen titration (p < 0.0001), indicating a substantial reduction in sleep-disordered breathing severity. Concurrently, SpO2 levels increased significantly from an average of 79.7% before titration to 89.1% after titration (p < 0.0003). Pearson correlation coefficients demonstrated aggravation of hypercapnia in 50% of patients (N=5) with initial hypercapnia during the increase of CPAP pressure. However, transitioning to BiPAP exhibited a reduction in pCO2 levels, showcasing its efficacy in addressing hypercapnia. Simultaneously, BiPAP therapy correlated with a substantial increase in SpO2, underscoring its positive impact on oxygenation in OSA patients. Markov dynamic process analysis demonstrated realistic patient behavior during stable night conditions, emphasizing minimal apnea and good toleration to high CPAP pressure. Conclusions: the development of a framework for Markov Decision Processes of PAP and oxygen titration algorithms holds promise for providing algorithms for deviation in pCO2 and SpO2 markers. While challenges remain, including the need for high-quality data, the potential benefits in terms of patient management and care optimization are substantial, and this approach represents an exciting frontier in the realm of telemedicine and respiratory healthcare. Obstructive sleep apnea, PAP titration, hypoxia, hypercapnia, Markov decision processes

This research focuses on exploring gravitational lensing of the wormhole in Einstein-bumblebee gravity with an antisymmetric tensor. The Gibbons and Werner technique based on the Gauss-Bonnet theorem is utilized to calculate the bending angle of light. The effects of non-plasma and plasma medium on the bending angles are investigated. Furthermore, we examine the deflection angle $\Tilde{\alpha}$ in relation to the impact parameter $\sigma$ and minimal radius $r_{0}$ in both non-plasma and plasma mediums. Our findings indicate that the deflection angle is positively correlated with $r_{0}$, meaning that larger values of $r_{0}$ result in larger deflection angles and smaller values of $r_{0}$ result in smaller deflection angles. On the other hand, the deflection angle $\Tilde{\alpha}$ is inversely related to the impact parameter $\sigma$.

In applied mathematics, statistics, operation research, physics, and engineering mathematics, confluent representations of hypergeometric functions in one and two variables are known to exist, and their occurrence in a variety of applications is also well recognised. In this article, we intend to present a new derivation of the extended Watson summation theorem for the Kim et al. given series 4F3. We assessed four attractive integrals involving generalized hypergeometric function as an application. With a few particular cases, this note will come to an end. In the results given above, symmetry appears on its own.

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

In this article, we demonstrate the weak gravitational lensing in the context of Bocharova-Bronnikove-Melnikov-Bekenstein (BBMB) black hole. To this desire, we derive the deflection angle of light in a plasma medium by BBMB black hole using the Gibbons and Werner method. First, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically symmetric spacetime of BBMB black hole. Moreover, we also analyze the graphical behavior of deflection angle by BBMB black hole in the presence of plasma medium.

In this paper, we define Ulisse Dini-type helicoidal hypersurface with spacelike axis in Minkowski 4-space ${\mathbb{E}}_1^4$ . We compute the Gaussian and the mean curvature of the hypersurface. Moreover, we obtain some special symmetry to the curvatures when they are flat and maximal.

Starting with a particle in the cube system, we investigate the exotic possibility that the quantum numbers (n_x,n_y,n_z) satisfy the Markov equation. We find that the proposed particle in the Markov-cube system follows from a non-classical information entropic space by the quantum potential Q. We study the classical correspondents of the proposed particle in the Markov-cube system. According to our proposition, this particle identified by detailed measurements of the confinement particle-energy levels is an artifact or occurs in nature.

In this paper, a Markov random field model is proposed to determine a site’s light pollution risk level. The specific data of 12 indicators of five typical cities in China is first collected to establish a hierarchical indicator system using an R-type clustering algorithm. Then, the entropy weight method is used to filter, determine 10-factor indicators, three potential impact indicators, and a light pollution risk index, and establish an undirected probability map model. A light pollution measurement based on Markov random field is obtained, and a location-based light pollution risk assessment index (LBLPRAI) is proposed. LBLPRAI of different types of sites is analyzed, and three possible intervention strategies are proposed to solve the light pollution problem: road lighting system planning, increasing vegetation coverage, and building system planning. Finally, the simulated annealing algorithm is used to determine the best intervention strategy, and it is concluded that the use of strategy 1 in the urban community 2 is the most effective measure, which can reduce the risk level of light pollution by 17.2%.

This paper investigates the dynamic tail dependence risk between BRICS economies and world energy market in the context of the COVID-19 financial crisis of 2020, to determine optimal investment decisions based on risk metrics. For this purpose, the study employs a combination of novel statistical techniques ranging from Markov Switching, GARCH and Vine copula. Using a dataset consisting of daily stock and world crude oil prices; we find high probability of transition between lower and higher volatility regimes. Furthermore, our results based on the C-Vine copula confirm the existence of two types of tail dependence: - symmetric tail dependence between South Africa and China; South Africa and Russia; and lower tail dependence between South Africa and India; South Africa and Brazil; South Africa and Oil. For the purpose of diversification in these markets, we formulate an asset allocation problem using C-vine copula-based returns and optimize it using Particle Swarm algorithm with a rebalancing strategy. The results show an inverse relationship between the risk contribution and asset allocation of South Africa and oil market supporting the existence of lower tail dependence between them. This suggests that when South African stocks are in distress, investors tend to shift their holdings in oil market. Similar results are found between China and oil. In the upper tail, South African asset allocation is found to have an inverse relationship with that of Brazil, Russia and India suggesting that these three markets might be good investment destinations when things are not good in South Africa and vice-versa.

This article proposes a monitoring system that allows to track transitions between different stages in the berry harvesting process (berry picking, waiting for transport, transport, and arrival to the packing) solely using information from temperature and vibration sensors located in the basket. The monitoring system assumes a characterization of the process based on Hidden Markov Models and uses the Viterbi algorithm to perform inference and estimate the most likely state trajectory. The obtained state trajectory estimate is then used to compute a potential damage indicator in real-time. The proposed methodology does not require information about the weight of the basket to identify each of the different stages, which makes it effective and more efficient than other alternatives available in the industry.

For offshore wind power generation, accessibility is one of the main factors that has great impact on operation and maintenance due to constraints on weather conditions for marine transportation. This paper presents a framework to explore the accessibility of an offshore site. At first, several maintenance types are defined and taken into account. Next, a data visualization procedure is introduced to provide an insight into the distribution of access periods over time. Then, a rigorous mathematical method based on finite state Markov chain is proposed to assess the accessibility of an offshore site from the maintenance perspective. A five-year weather data of a marine site is used to demonstrate the applicability and the outcomes of the proposed method. The main findings show that the proposed framework is effective in investigating the accessibility for different time scales and is able to catch the patterns of the distribution of the access periods. Moreover, based on the developed Markov chain, the average waiting time for a certain access period can be estimated. With more information on the maintenance of an offshore wind farm, the expected production loss due to time delay can be calculated.

Assessment of the environmental impact of organic chemicals has become an important subject in chemical science. Efficient quantitative descriptors of their impact are their partition coefficients logPow, logKoa and logKaw. We present a group-additivity method that has proven its versatility for the reliable prediction of many other molecular descriptors for the calculation of the first two partition coefficients and indirectly of the third with high dependability. Based on the experimental logPow data of 3332 molecules and the experimental logKoa data of 1900 molecules at 298.15K the respective partition coefficients have been calculated with cross-validated standard deviations of only 0.42 and 0.48 log units and a goodness of fit Q^2 of 0.9599 and 0.9717, respectively, in a range of ca. 17 log units for both descriptors. The third partition coefficient logKaw has been derived from the calculated values of the former two descriptors and compared with the experimentally determined logKaw values of 1937 molecules, yielding a standard deviation of 0.67 log units and a correlation coefficient R^2 of 0.9467. This approach enabled the quick calculation of 29462 logPow, 27069 logKoa and 26220 logKaw values for the more than 37100 molecules of ChemBrain's database available to the public.

The main goal of this paper is to study the weak gravitational lensing by Horndeski black hole in weak field approximation. In order to do so, we exploit the Gibbons-Werner method to the optical geometry of Horndeski black hole and implement the Gauss-Bonnet theorem to accomplish the deflection angle of light in weak field region. Furthermore, we have endeavored to extend the scale of our work by comprising the impact of plasma medium on the deflection angle as properly. Later, the graphical influence of the deflection angle of photon on Horndeski black hole in plasma and non-plasma medium is examined.

In this paper, first we use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.

In this paper, we discuss the weak gravitational lensing in the context of stringy black holes. Initially, we examine the deflection angle of photon by charged stringy black hole. For this desire, we compute the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically balanced spacetime of stringy black hole. We also analyze the influence of plasma medium in the weak gravitational lensing for stringy black hole. Moreover, the graphical impact of coupling constant $\alpha$, impact parameter $b$ , black hole charge $Q$ on deflection angle by charged stringy black hole has been studied in plasma as well as non-plasma medium.

Relationships between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem are discussed. Whether a function similar to Chebyshev’s second function is square-root close to a line having a slope different from 1 is discussed. The nontrivial zeros of the Riemann zeta function can be used to approximate many functions in analytic number theory. For example, it could be said that the nontrival zeta function zeros and the Möbius function generate in essence the same function - the Mertens function. A different approach is to start with a sequence that is analogous to the nontrivial zeros of the zeta function and follow the same procedure with both this sequence and the nontrivial zeros of the zeta function to generate in essence the same function. A procedure for generating such a function is given.

The paper proves a theorem about the structure of the distribution function on which the extremum of fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters, hence the problem is greatly simplified since it is reduced to the search for an extremum of some function.

To assess the degree to which it has met its commitments under the Paris Agreement, Morocco is called upon to carry out carbon assessments and transparent evaluations. Within the forestry sector, little is known about the role of Morocco’s forests in contributing to carbon uptake. With this aim, we applied for the first time in literature the 3-PG model to Cedrus atlantica ((Endl.) Manetti ex Carrière, 1855), which represents about 131.800 ha of Morocco’s forest area (i.e. Azrou forest). Through the Differential Evolution - Markov Chains (DE-MC) we tested and assessed the sensitivity and calibrated the 3-PG model. This process-based model provided significant results regarding the carbon sequestration capacity. The results showed the following: i- Parameters related to stand properties, canopy structure, and processes, as well as biomass partitioning, are the most important or sensitive for the performance of the model; ii- The DE-MC method optimized the values of the 3-PG parameters which was confirmed by the means of Gelman-Rubin convergence test; iii- According to the predictions of the calibrated 3-PG, the Net Primary Production in the pure Azrou forest varies between 0.32 and 7.88 tC.ha−1.yr−1, it is equal in average to 4.9 tC.ha−1.yr−1, which given the total area corresponds to 7078 tC.yr−1.

This paper investigates the cooperative anti-jamming distributed channel selection problem in UAV communication networks. Considering the existence of malicious jamming and co-channel interference, a location-aware cooperative anti-jamming scheme is designed for the purpose of maximizing the users' utilities. Users in the UAV group cooperate with each other via location information sharing. When the received interference energy is lower than mutual interference threshold, users conduct channel selection strategies independently. Otherwise, users take joint actions with a cooperative anti-jamming pattern under the impact of mutual interference. Aimed at the independent anti-jamming channel selection problem under no mutual interference, a Markov Decision Process framework is introduced, whereas for the cooperative anti-jamming channel selection case under the influence of co-channel mutual interference, a Markov game framework is employed. Furthermore, motivated by reinforcement learning with a ``Cooperation-Decision-Feedback-Adjustment" idea, we design a location-aware cooperative anti-jamming distributed channel selection algorithm (LCADCSA) to obtain the optimal anti-jamming channel strategies for the users with a distributed way. In addition, the channel switching cost and cooperation cost, which have great impact on the users' utilities, are introduced. Finally, simulation results show that the proposed algorithm converges to a stable solution with which the UAV group can avoid the malicious jamming as well as co-channel interference effectively.

Markov chain Monte Carlo sampling propagators, including numerical integrators for stochastic dynamics, are central to the calculation of thermodynamic quantities and determination of structure for molecular systems. Efficiency is paramount, and to a great extent, this is determined by the integrated autocorrelation time (IAcT). This quantity varies depending on the observable that is being estimated. It is suggested that it is the maximum of the IAcT over all observables that is the relevant metric. Reviewed here is a method for estimating this quantity. For reversible propagators (which are those that satisfy detailed balance), the maximum IAcT is determined by the spectral gap in the forward transfer operator, but for irreversible propagators, the maximum IAcT can be far less than or greater than what might be inferred from the spectral gap. This is consistent with recent theoretical results (not to mention past practical experience) suggesting that irreversible propagators generally perform better if not much better than reversible ones. Typical irreversible propagators involve a parameter controlling the mix of ballistic and diffusive movement. To gain insight into the effect of the damping parameter for Langevin dynamics, its optimal value is obtained here for a multidimensional quadratic potential energy function.

In a continuation and extension of an earlier publication, the calculation of the refractivity and polarizability of organic molecules at standard conditions is presented, applying a commonly applicable computer algorithm based on an atom-group additivity method, where the molecules are broken down into their constituting atoms, these again being further characterized by their immediate neighbor atoms. The calculation of their group contributions, carried out by means of a fast Gauss–Seidel fitting calculus, used the experimental data of 5988 molecules from literature. An immediate subsequent ten-fold cross-validation test confirmed the extraordinary accuracy of the prediction of the molar refractivity, indicated by a correlation coefficient R^2 and a cross-validated analog Q^2 of 0.9997, a standard deviation σ of 0.38, a cross-validated analog S of 0.41, and a mean absolute deviation of 0.76%. The high reliability of the predictions has been exemplified with three classes of molecules: ionic liquids, silicon- and boron-containing compounds. The corresponding molecular polarizabilities have been calculated indirectly from the refractivity using the inverse Lorentz-Lorenz relation. In addition, it could be shown that there is a close relationship between the "true" volume and the refractivity of a molecule, revealing an excellent correlation coefficient R^2 of 0.9645 and a mean absolute deviation of 7.53%.

In this article, we calculate the deflection angle of tidal charged black hole (TCBH) in weak field limits. First we obtain the Gaussian optical curvature and then apply the Gauss-Bonnet theorem on it. With the help of Gibbons-Werner method, we are able to calculate the light's deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light's deflection angle in the presence of plasma medium and also check the graphical behavior in the presence of plasma medium. Moreover, we investigate the shadow of TCBH.For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH's shadow in the plasma medium. Hence, we discuss the shadow of the TCBH using the $M87^{*}$ parameters announced by the Event Horizon Telescope.

The catenary shells of revolution are widely used in constructions due to their unique mechanics' feature. However, no publications on this type of shells can be found in the literature. To have a better understanding of the deformation and stress of the catenary shells of revolution, we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations. Numerical simulations are carried out based on both Reissner-Meissner mixed formulations and displacement formulations. Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter $c$, and reveal that the mechanics of the catenary shells of revolution does much better than the spherical shells. Two complete codes in Maple are provided.

In this paper, by considering Einstein-Hilbert-Bumblebee (EHB) gravity around global monopole field, we derive exactly a black hole spacetime metric. To test the effect of global monopole field and bumblebee field, which causes the spontaneous Lorentz symmetry breaking, we calculate the weak deflection angle using the Gauss-Bonnet theorem.

In this paper, we use a new asymptotically flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity to study the weak gravitational lensing and its shadow cast. To this end, we first compute the weak deflection angle of generalized ECKS black hole using the Gauss–Bonnet theorem in plasma medium and in vacuum. Next by using the Newman-Janis algorithm without complexification, we derive the rotating generalized ECKS black hole and in the sequel study its shadow. Then, we discuss the effect of the ECKS parameter on the shadow of the black hole and weak deflection angle. In short, the goal of this paper is to give contribution to the ECKS theory and look for evidences to understand how the ECKS parameter effects the gravitational lensing.

In this paper, we analyze the deflection angle of light by Brane-Dicke wormhole in the weak field limit approximation to find the effect of the Brane-Dicke coupling parameter on the weak gravitation lensing. For this purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and optical geometry in order to calculate the deflection angle. Furthermore, we verify our results by considering the most familiar geodesic technique. Moreover, we establish the quantum corrected metric of Brane-Dicke wormhole by replacing the classical geodesic with Bohmian trajectories, whose matter source and anisotropic pressure are influenced by Bohmian quantum effects and calculate its quantum corrected deflection angle. Then, we calculate the deflection angle by naked singularities and compare with the result of wormhole's. Such a novel lensing feature might serve as a way to detect wormholes, naked singularities and also the evidence of Brane-Dicke theory.

The problem of optimal scheduling in a system with parallel queues and a single server has been extensively studied in the queueing theory. However, such systems have mostly been studied by assuming homogeneous attributes of arrival and service processes, or in heterogeneous case a Markov random process was usually assumed. In this paper, we explore the possibility of combining simulation and neural network paradigms for optimal scheduling in a heterogeneous system with an arbitrary inter-arrival and service time distributions. The service of any queue by the server is exhaustive. Further routing of the server after the queue has been emptied is as instructed by the trained neural network. Any change in the queue that currently has a server is accompanied by a switching cost. The simulated annealing optimization algorithm which is used to optimize the parameters of the neural network was adapted for numerically evaluated average cost function. A Markov decision problem was formulated for the corresponding markovian queueing system to verify the results of solving the optimization problem. In addition to comparing the actual values of the average cost, the parameter values of the neural network trained on the optimal control policy of the Markov model are also used to determine the domains of parameters required for the simulated annealing defined on a finite discrete domain. Numerical analysis shows the effectiveness of this approach. Moreover, a comparison of the results for different distributions illustrates the insensitivity of the optimal control policy to the shape of the distributions for the same two first moments. Thus, the optimal control policy for an exponential model can be used as a suboptimal one for the general system.

Since the conventional split-merge algorithm is sensitive to the object scale variance and splitting starting point, a piecewise split-merge polygon approximation method is proposed to extract the object contour features. Specifically, the contour corner is used as the starting point for the contour piecewise approximation to reduce the sensitivity of the contour segment on the starting point; then, the split-merge algorithm is used to implement the polygon approximation for each contour segments. Both the distance ratio and the arc length ratio instead of the distance error are used as the iterative stop condition to improve the robustness to the object scale variance. Both the angle and length as two features describe the shape of the contour polygon, and affect each other along the contour order relationship. Since they have a strong coupling relationship. To improve the description correction of the contour, these two features are combined to construct a Coupled Hidden Markov Model to detect the object by calculating the probability of the contour feature. The proposed algorithm is validated on ETHZ Shape Classes and INRIA Horses standard datasets. Compared with other contour-based object detection algorithms, the proposed algorithm reduces the complexity of contour description, improves the robustness of contour features to scale variance, and has a higher object detection rate.

The fifth Generation (5G) mobile networks use millimeter Waves (mmWaves) to offer giga bit data rates. However, unlike microwaves, mmWave links are prone to user and topographic dynamics. They easily get blocked and end up forming irregular cell patterns for 5G. This in turn cause too early, too late, or wrong handoffs (HOs). To mitigate HO challenges, sustain connectivity and avert unnecessary HO, we propose a HO scheme based on Jump Markov Linear System (JMLS) and Deep Reinforcement Learning (DRL). JMLS is widely known to account for abrupt changes in system dynamics. DRL likewise emerges as an artificial intelligence technique for learning highly dimensional and time-varying behaviors. We combine the two techniques to account for time-varying, abrupt, and irregular changes in mmWave link behaviour by predicting likely deterioration patterns of target links. The prediction is optimized by meta training techniques that also reduces training sample size. Thus, the JMLS-DRL platform formulates intelligent and versatile HO policies for 5G. Results show our proposed prediction scheme about target link behavior post HO to be highly reliable. The scheme also averts unnecessary HOs thus ably supports longer dew time.

Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, also surface waves retrieved through the application of seismic interferometry are exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a two-dimensional grid of localized depth-dependent velocity profiles are obtained. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation on the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. Also, it adapts model resolution to the amount of noise on the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from (time-averaged) station-station cross correlations by the Reykjanes seismic network.

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

Although, promotion of urbanization culture in recent decades has made inevitable development of cities in the world, however, the development can be guided in a direction that leave, to the extent possible, minimum socioeconomic and environmental impacts. For this, it is required to first forecast auto-spreading orientation of cities and suburbs in rural areas over time and then avoid shapeless growth of cities. This paper is an attempt to develop a dynamic hybrid model based on logistic regression (LR), Markov chain (MC), and cellular automata (CA) for prediction of future urban sprawl in fast-growing cities. The model was developed using 12 widely-used urban development criteria, whose significant coefficient was determined by logistic regression, and validated by relative operating characteristic (ROC) analysis. The validated model was run in Guilan, a tourist province in northern Iran with a very high rate of urban development. For this, changes in the area of urban land use were detected over the period of 1989 to 2013 and then, future sprawl of the province was forecasted by the years 2025 and 2037. The analysis results revealed that the area of urban land use was increased by more than 1.7 % from 36012.5 ha in 1989 to 59754.8 ha in 2013, and the area of Caspian Hyrcanian forestland was reduced by 31628 ha. The results also predicted an alarming increase in the rate of urban development in the province by the years 2025 and 2037, during which urban land use is predicted to develop 0.9 % and 1.38 %, respectively. The development pattern is expected to be uneven and scattered, without following any particular direction. The development will occur close to the existing or newly-formed urban basements as well as around major roads and commercial areas. This development, if not controlled, will lead to the loss of 13863 ha of Hyrcanian forests and if the trend continues, 21013 ha of Hyrcanian forests and 20208 ha of Barren/open lands are expected to be destroyed by the year 2037. In general, the proposed model is an efficient tool for the support of urban planning decisions and facilitates the process of sustainable development of cities by providing decision-makers with an overview on future development of cities where the growth rate is very fast.

Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc…Using the PBN, many formulas, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi’s state function or Peliti’s standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman-Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential Applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT.

The improvement of agricultural low-carbon efficiency is an important path to promote the realization of the "double carbon" goal in the Yellow River Basin. In the context of rapid urbanization development, it is of great significance to explore whether the promotion of urbanization will affect the agricultural low-carbon efficiency. Based on the panel data of 75 cities in the Yellow River Basin from 2000 to 2020, this paper uses super-DEA model, three-dimensional kernel density model and Markov chain model to measure and analyze the spatio-temporal evolution of agricultural low-carbon efficiency in the Yellow River Basin, on this basis, the panel Tobit model is used to analyze the relationship between urbanization and low-carbon efficiency in agriculture. The results show that: (1) The level of agricultural low-carbon efficiency in the Yellow River Basin is low and has not reached the effective state, showing a slow downward trend in general, among which, the agricultural low-carbon efficiency in the lower reaches is higher than that in the middle reaches, and the upper reaches is the lowest. (2) The agricultural low-carbon efficiency in the Yellow River Basin has a negative trend of transferring to the low level on the whole, and tends to maintain the original state level, and it is difficult to realize the leapfrog transfer between states. Agricultural low-carbon efficiency has obvious spatial spillover effect and "club convergence" phenomenon, high efficiency area has a positive driving effect on the neighborhood area, while low efficiency area has a negative impact on the neighborhood area. (3) The level of urbanization has a significant positive impact on the low-carbon efficiency of agriculture in the upper, middle and lower reaches of the Yellow River Basin, which plays an important role in promoting the green development of agriculture. Finally, based on the above research conclusions, relevant policy recommendations were put forward, in order to provide references for promoting the improvement of low-carbon agricultural efficiency and promoting high-quality agricultural development in the Yellow River Basin.

Steam Generator Level Control System (SGLCS) is one of the key instrumentations and control subsystems to ensure the safe operation of nuclear power plants. It is highly recommended to perform reliability analysis for SGLCS for making better maintenance strategy. SGLCS is a digital control system with complex redundant configuration and failure\self-diagnosis\repair action, traditional fault tree is not applicable due to its static property, Markov model is not a good choice too because of heavy burden of creating state transition graph for even medium-size system. Boolean Logic Driven Markov Process (BDMP) can describe complex failure-repair state transition via ‘trigger link’ and three kinds of leaf nodes, as well as keep compact and easy-read struct like fault tree. So BDMP is adopted to analysis reliability of SGLCS. Graphical BDMP modeling environment KB3 and Monte Carlo simulator YAMS is used for BDMP modeling and quantitative analysis respectively, and unavailability of SGLCS is obtained. The contribution of three parts of SGLCS to the unavailability of the system is also evaluated, and it is found that the water supply flow control part contributes the most to the failure of SGLCS.

Urban growth in various cities across the world, especially in developing countries, leads to land use change. Thus, predicting future urban growth in the most rapidly growing region of Nigeria becomes a significant endeavor. This study analyzes land use and land cover (LULC) change and predicts the future urban growth of the Lagos metropolitan region, using Cellular Automata (CA) model. To achieve this, the GlobeLand30 datasets from years 2000 and 2010 were used to obtain LULC maps, which were utilized for modeling and prediction. Change analysis and prediction for LULC scenario for 2030 were performed using LCM and CA_Markov chain modeling. The results show a substantial growth of artificial surfaces, which will cause further reductions in cultivated land, grassland, shrubland, wetland, and waterbodies. There was no appreciable impact of change for bare land, as its initial extent of cover later disappeared completely. Additionally, artificial surfaces/urban growth in Lagos expanded to the neighboring towns and localities in Ogun State during the study period, and it is expected that such growth will be higher in 2030. Lastly, the study findings will be beneficial to urban planners and land use managers in making key decisions regarding urban growth and improved land use management in Nigeria.

Water resource is considered as a significant factor in development of regional environment and society. Water consumption prediction can provide important decision basis for the regional water supply scheduling optimisations. According to the periodicity and randomness nature of the daily water consumption data, a Markov modified autoregressive moving average (ARIMA) model is proposed in this study. The proposed model, combined with the Markov chain, can correct the prediction error, reduce the continuous superposition of prediction error, and improve the prediction accuracy of future daily water consumption data. The daily water consumption data of different monitoring points are used to verify the effectiveness of the model, and the future water consumption is predicted, in the study area. The results show that the proposed algorithm can effectively reduce the prediction error compared to the ARIMA.

Although the signaling function of Na/K ATPase is been studied for decades, the chasm between the pumping function and the signaling function of Na/K – ATPase is still an open issue. This article explores the relationship between ion pumping and signaling with attention to the amplification of oxidants through this signaling function. Starting with some experimental observations published by our laboratories and others, we develop some predictions regarding cellular oxidant stress.

Human footprint is having a unique set of ridges unmatched by any other human being, and therefore it can be used in different identity documents for example birth certificate, Indian biometric identification system AADHAR card, driving license, PAN card, and passport. There are many instances of the crime scene where an accused must walk around and left the footwear impressions as well as barefoot prints and therefore it is very crucial to recovering the footprints to identify the criminals. Footprint-based biometric is a considerably newer technique for personal identification. Fingerprints, retina, iris and face recognition are the methods most useful for attendance record of the person. This time world is facing the problem of global terrorism. It is challenging to identify the terrorist because they are living as regular as the citizens do. Their soft target includes the industries of special interests such as defense, silicon and nanotechnology chip manufacturing units, pharmacy sectors. They pretend themselves as religious persons, so temples and other holy places, even in markets is in their targets. These are the places where one can obtain their footprints easily. The gait itself is sufficient to predict the behaviour of the suspects. The present research is driven to identify the usefulness of footprint and gait as an alternative to personal identification.

Experimental recordings of the collective activity of interacting spiking neurons exhibit random behavior and memory effects, thus the stochastic process modeling the spiking activity is expected to show some degree of time irreversibility. We use the thermodynamic formalism to build a framework, in the context of spike train statistics, to quantify the degree of irreversibility of any parametric maximum entropy measure under arbitrary constraints, and provide an explicit formula for the information entropy production of the inferred Markov maximum entropy process. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named interacting multiple model fifth-degree spherical simplex-radial cubature filter (IMM5thSSRCKF) is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM) filter and fifth-degree spherical simplex-radial cubature filter (5thSSRCKF). The proposed algorithm makes use of Markov process to describe the switching probability among the models, and uses 5thSSRCKF to deal with the state estimation of each model. The 5thSSRCKF is an improved filter algorithm, which utilizes the fifth-degree spherical simplex-radial rule to improve the filtering accuracy. Finally, the tracking performance of the IMM5thSSRCKF is evaluated by simulation in a typical maneuvering target tracking scenario. Simulation results show that the proposed algorithm has better tracking performance and quicker model switching speed when disposing maneuver models compared with IMMUKF, IMMCKF and IMM5thCKF.

: The silicon single crystals for semiconductor application is usually grown by Czochralski (CZ) method. This paper researches 300mm silicon Czochralski (CZ) crystal growth with CUSP magnetic field for IGBTs substrate application. The different positions of Zero-Gauss plane (ZGP) under CUSP magnetic field are simulated and compared to numerical analysis, investigated melt convection, melt flow velocity near to quartz crucible wall, diffusion boundary layer and effect of initial oxygen concentration in the silicon crystal, and the shape of solid/liquid interface was discussed. The results show that the change of the ZGP of the CMF mainly affects the convection in the melt, which leads to the difference of the thickness of the boundary layer near to the wall of the quartz crucible, and was found to be the key to reduce the oxygen dissolution from the crucible wall and oxygen diffuse into the crystal, along with the differences in the shape of the crystal-melt interface. In addition, we have carried out actual industrial single crystal production under the three configurations. The results show that the experimental data of oxygen content and shape of the crystal-melt interfaces in silicon crystal are consistent with the numerical results.

In this paper, we introduce as a pedagogical strategy an internal division-free, straightforward, and symmetrically progressing algorithm in manually computing matrix inverse and solving systems of linear equations by revisiting the application of elementary row operations in the Gauss-Jordan reduction method and connecting it to the determinant method. The proposed cross-multiplication-flip (CMF) algorithm employs cross-multiplication similar to the butterfly movement in computing determinants as a strategic application of elementary row operations to efficiently reduce the rows and then applies flipping of rows and entries to put an upper triangular matrix into lower triangular form to continue the reduction process.

Spherically symmetric solution in 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics (ModLogNED) is found. This solution at infinity possesses the charged black hole Reissner--Nordstr\"{o}m behavior. We study the black hole thermodynamics, entropy, shadow, energy emission rate and quasinormal modes. It was shown that black holes can possess the phase transitions and at some range of event horizon radii black holes are stable. The entropy has the logarithmic correction to the area law. The shadow radii were calculated for variety of parameters. We found that there is a peak of the black hole energy emission rate. The real and imaginary parts of the quasinormal modes frequencies were calculated. The energy conditions of ModLogNED are investigated.

In this paper, we study the weak deflection angle using Gauss-Bonnet theorem and bounding greybody factor for electric and magnetic black holes in the background of nonlinear electrodynamics. Using Gibbons and Werner's approach, first we acquire the Gaussian optical curvature to use in Gauss-Bonnet theorem and calculate the bending angle for spherically symmetric electric and magnetic black holes in both non-plasma and plasma mediums in the weak field limits. Later, we calculate the rigorous bounds of the greybody factor for the given black holes. Furthermore, we look into the graphical behaviour of bending angles and greybody bounds at some specific values of multiple parameters as well as black holes charges. It is to be mention here that all the results for the electric and magnetic charged black holes solutions reduce into the Schwarzschild black hole solution in the absence of the black holes charges.

Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found.

The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.

The logarithmic correction to Bekenshtein$-$Hawking entropy in the framework of 4D Einstein - Gauss - Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations which mimics the quantum correction to the area low. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters.

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the quasinormal modes of Hayward black hole in Einstein Gauss-Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein-Lovelock gravity. By utilizing the WKB resonance technique, we examine the quasinormal modes frequencies $\omega$ by shifting the charge parameter $Q$ (it is also identified with the cosmological constant), circular harmonic index $l$, and mass of scalar field $m$. We also study the relaxation rate for those black holes and find out that the relaxation rate increases with increasing values of $Q$. We observe that real and imaginary components of the quasinormal modes are not linear functions as similar to Reisnner Nordstr\"{o}m-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

We study the light rays in a static and spherically symmetric gravitational field of null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations show how gravitational lensing is affected by the NAT field. We also show once again that the bending of light stems from a global and topological effect.

In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $\gamma$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investigate the impact of plasma medium on weak gravitational lensing by asymptotically flat charged hairy black hole with a dilaton potential. Our analytically analyses show the effect of the hair on the deflection angle in weak field limits.

In this paper, we proposed a new model of non-linear electrodynamics with parameter. Firstly, we study the weak limit approximation and by using the Gauss Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole and effect of bnon-linear electrodynamics. In doing so, we find the corresponding optical metric after that we calculate the Gaussian curvature which is used in Gauss Bonnet theorem. Then we show the deflection angle in the leading order terms. We also analyzed that our results reduces into Maxwell's electrodynamics and RN solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

The transportation industry is rapidly transitioning from Internal Combustion Engine (ICE) based vehicles to Electric Vehicles (EVs) to promote clean energy. However, large-scale adoption of EVs can compromise the reliability of the power grids by introducing large uncertainty in the demand. Demand response with a controlled charge scheduling strategy for EVs can mitigate such issues. In this paper, a deep reinforcement learning- based charge scheduling strategy is developed for individual EVs by considering user’s dynamic driving behavior and charging preferences. The temporal dynamics of user’s anxiety about charging the EV battery is rigorously addressed. A dynamic weight allocation technique is applied to continuously tune user’s priority for charging and cost-saving with respect to charging duration. The sequential charging control problem is formulated as a Markov decision process, and an episodic approach to the deep deterministic policy gradient (DDPG) algorithm with target policy smoothing and delayed policy update techniques is applied to develop the optimal charge scheduling strategy. A real-world dataset that captures user’s driving behavior, such as arrival time, departure time, and charging duration, is utilized in this study. The extensive simulation results reveal the effectiveness of the proposed algorithm in minimizing energy cost while satisfying user’s charging requirements.

We present a new analytical method to find the asymptotic stable equilibria states based on the Markov chain technique. We reveal this method on the SIR-type epidemiological model that we developed for viral diseases with long-term immunity memory pandemic. This is a large-scale model containing 15 nonlinear ODE equations, and classical methods have failed to analytically obtain its equilibria. The proposed method is used to conduct a comprehensive analysis by a stochastic representation of the dynamics of the model, followed by finding all asymptotic stable equilibrium states of the model for any values of parameters and initial conditions.

This study identifies the optimal management policy of a given energy storage system (ESS) installed in a grid-connected wind farm for maximizing the monetary benefits and provides guidelines for defining the economic value of the ESS under the optimal management policy and selecting the optimal size of the ESS based on the economic value. Considering stochastic models for wind power and electricity price, we develop a finite-horizon periodic-review Markov decision process (MDP) model to seek the optimal management policy. We also use a simple optimization model to find the optimal storage capacity and charging/discharging capacity of the ESS. By applying our analytic approach to a real-world grid-connected wind farm located in South Korea, we verify the usefulness of this study. Our numerical study shows that the economic value of the ESS is highly dependent on the management policy, wind electricity variability, and the electricity price variability. Thus, the optimal size of ESS should be carefully determined based on the locational characteristics and management policy even with limited investments. Furthermore, this study provides a meaningful policy implication on how much a subsidy the government should provide for installing ESS in a wind farm.

Bayesian analysis for masked data under competing risk frameworks is studied for the purpose of assessing the impact of covariates on the hazard functions when the failure time is exactly observed for some subjects but only known to lie in an interval of time for the remaining subjects. Such data, known as partly interval-censored data, usually result from periodic inspection. Dirichlet and Gamma processes are assumed as priors for masking probabilities and baseline hazards. The Markov Chain Monte Carlo (MCMC) technique is employed for the implementation of the Bayesian approach. The effectiveness of the proposed model is tested through numerical studies, including simulated and real data sets.

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

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

In this work, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss-Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss-Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of NLED, plasma, and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

In this paper, we examine the weak deflection angle and greybody factor of magnetized regular black hole. We implement the Gauss-Bonnet theorem on magnetized regular black hole to get the deflection angle. Moreover, we analyze the influence of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. We observe the graphical behaviour of plasma and non-plasma mediums on deflection angle of magnetized regular black hole. Lastly, we study the rigorous bound phenomenon of the greybody factor of magnetized regular black hole. For this purpose we calculate greybody factor results and analyze the graphical behaviour of greybody bound for the different values of the parameters.

In this paper, we study light rays in a Kazakov-Solodukhin black hole. To this end, we use the optical geometry of the Kazakov-Solodukhin black hole within the Gauss-bonnet theorem. We first show the effect of the deformation parameter $a$ on the Gaussian optical curvature, and then we use the modern method popularized by Gibbons and Werner to calculate the weak deflection angle of light. Our calculations of deflection angle show how gravitational lensing is affected by the deformation parameter $a$. Moreover, we demonstrate the effect of a plasma medium on weak gravitational lensing by the Kazakov-Solodukhin black hole. We discuss that the increasing the deformation parameter $a$, will increase the weak deflection angle of the black hole. Our analysis also uncloak how one may find a observational evidence for a deformation parameter on the deflection angle.