The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

Micro and small wood-processing enterprises represent the heart of the European forest-based industries, being among the key drivers of economic growth in rural, mountainous, and poor regions. Their economic efficiency is of fundamental importance for their existence and the pro-vision of income for the local population in rural areas. Data Envelopment Analysis (DEA) is nonparametric, linear-programming-based approach, commonly used to analyse the efficiency of organizational units. This method allows estimating the economic efficiency of a certain eco-nomic system without assumptions about the functional form between resources and products. Furthermore, DEA determines the efficiency frontier and gives results of whether an enterprise, i.e., a Decision Making Unit (DMU) is efficient or not. The main objective of this study was to investigate and evaluate the economic efficiency of micro and small wood-processing enterpris-es in the EU countries and reveal the hidden inputs that facilitate efficiency generation. The eco-nomic efficiency evaluation was carried out on the basis of the official statistical data for the mi-cro and small wood-processing companies in the EU member states for the period 2015-2020 by performing a two-stage DEA analysis. The data used were standardized by value per employee. In addition to the first stage of DEA, fractional regression probit and logit models with four contextual variables were used to reveal the influence of the hidden inputs in the model. The results showed that the micro and small wood-processing enterprises can be regarded as more scale-efficient than technically-efficient entities. The only contextual variable affecting the eco-nomic efficiency was Investments per Person Employed, improving the efficiency by 2% per 1% increase of the investments.

This paper aims to demonstrate that, beyond the small world of Riemann-Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to the different paths taken. Notions of time and scale sequences are introduced and general associated basic derivatives, namely right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to get both known and new fractional order derivatives. Several fractional derivatives are considered, mainly: Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.

This article aims to explore the existence and stability of solutions to differential equations involving a regularized ψ−Hilfer fractional derivative, which, compared to standard ψ−Hilfer fractional derivatives, provide a clear physical interpretation when dealing with initial conditions. We discovered that the regularized ψ−Hilfer fractional derivative can be represented as the inverse operation of the ψ−Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a regularized ψ−Hilfer fractional derivative. Additionally, we applied the Mönch’s fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a regularized ψ−Hilfer fractional derivative, and further discussed Ulam-Hyers-Rassias stability and semi-Ulam-Hyers-Rassias stability of these solutions. Finally, we illustrated our results through case studies.

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

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

Cervical cancer is one of the ailments that endangers the health of women all over the world and causes infertility. Fortunately, this disease can be avoided. Both the results and participation rates of the current preventative strategy remain poor. Hence, preventative or early detection methods remain challenging and open. In gynecology and computer science fields, few studies on identifying cervical cancer are based on behavior risk factor and machine learning. Moreover, various social and behavioral aspects might often make it more difficult to detect cervical cancer especially in low‑ and middle‑income countries (LMICs). Accordingly, focus on predicting the presence of cervical cancer through behavioral risk factors is the basic structure of this research. We proposed an approach to classify cervical cancer from a social-behavioral perspective using logistic regression to predict cervical cancer. We got significantly improved outcomes than the existing methods. Moreover, we used feature engineering to formulate less dimensionality as a pre-processing step and optimized parameters to be prepared for classification phase. The results proved that using the logistic regression with regularization type L1 had a promising performance. The accuracy of Logistic Regression (LR) L1 was 97.2%. Such results support the proposed work as a reliable classification predictive tool.

We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.

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

We introduce NodeFlow, a flexible framework for probabilistic regression on tabular data that combines Neural Oblivious Decision Ensemble (NODE) and Conditional Continuous Normalizing Flows (CNF). It offers improved modeling capabilities for arbitrary probabilistic distributions, addressing the limitations of traditional parametric approaches. In NodeFlow, the NODE captures complex relationships in tabular data through a tree-like structure, while the conditional CNF utilizes the NODE’s output space as a conditioning factor. The training process of NodeFlow employs standard gradient-based learning, facilitating end-to-end optimization of the NODEs and CNF-based density estimation. This approach ensures outstanding performance, ease of implementation, and scalability, making NodeFlow an appealing choice for practitioners and researchers. Comprehensive assessments on benchmark datasets underscore NodeFlow’s efficacy, revealing its achievement of state-of-the-art outcomes in multivariate probabilistic regression setup and its strong performance in univariate regression tasks. Furthermore, ablation studies are conducted to justify the design choices of NodeFlow. In conclusion, NodeFlow’s end-to-end training process and strong performance make it a compelling solution for practitioners and researchers. Additionally, it opens new avenues for research and application in the field of probabilistic regression on tabular data.

As argued by ‘Declaration of Concrete Environment (2010)’ of Korea and ‘Declaration of Asian Concrete Environment (2011)’ of six Asian countries, concrete as a single material has lately shown extremely large impact on environmental issues such as climate change. Assessment of environmental impact from concrete material and production has considerable importance. Concrete is a major material used in the construction industry that emits a large amount of substances with environmental impacts during its life cycle. Accordingly, technologies for the reduction in and assessment of the environmental impact of concrete from the perspective of Life Cycle Assessment must be developed. At present, the studies in relation to greenhouse gas emission from concrete are being carried out globally as a countermeasure against climate change. In this study, a sustainable concrete mix design algorithm was designed using correlation analyses, and its carbon emission and cost reduction performances were assessed. Using correlation analyses, the concrete strength, w/b and s/a ratios, and CO₂ emissions were identified as major variables of concrete mix design that influenced other variables. Also, this study aims to evaluate the CO₂ emission reduction performance of the algorithm-deduced sustainable concrete mix design, and therefore, the CO₂ emissions of the sustainable concrete mix design are compared with those of the actual concrete mix design applied to the construction of the office building A in South Korea.

Artificial neural networks are highly efficient tools for numerous kinds of tasks, which include forecasting, regression, and recognizing patterns in classification and pattern recognition. An artificial neural network is a model for processing information using essential components called artificial neurons that are inspired by the human brain. Two significant aspects of delayed neural networks dynamic activity are their stability and the synchronization phenomenon. This work presents a bidirectional associative memory (BAM) incommensurate fractional-order delay neural network model. The incommensurate fractional orders are calculated within the stability region through the corresponding eigenvalues and their points of equilibrium. The involved neuron states are synchronized with each other for the calculated incommensurate stable fractional orders. The reduction of the time delay will give more relaxation time for the state variable $w_4(t)$ to be stable as compared to the state variable $w_3(t)$ due to the induction of extra activation functions. The theoretical findings of this research have significance for providing guidance and controlling the dynamic behavior of artificial neural networks.

In traditional finance, option prices are typically calculated using crisp sets of variables. However, in a proposed new approach, the assumption is made that these parameters have a degree of fuzziness or uncertainty associated with them. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. To determine the belief degree associated with a particular option price, an interpolation search algorithm was proposed recently[1]. Interpolation is a mathematical technique used to estimate values between known data points. In this case, the algorithm is applied to determine the belief degree associated with a specific option price within the range of possible prices. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. It allows them to consider their risk preferences and beliefs about the uncertain parameters when selecting an option price. In this paper, we will review a unified framework for combining fractional Brownian motion with fuzzy processes and obtain a joint measure space. We start by constructing a product measure space that captures the randomness and fuzziness inherent in the respective processes. We begin with the usual Kolmogorov filtered probability space (Ω, F, ℙ), where ℙ represents the probability measure, Ω is the set of all possible outcomes or states that a random process can take and {Ft, t ∈ [0, T]} is an information filtration. We will review the work of Merton (1976) on option pricing when the underlying stock returns have jumps [2] and expand it to fuzzy fractional processes.

In this paper, we extend the KdVSKR equations in (1+1)-dimension and (2+1)-dimension to fractional KdVSKR equations with modified Riemann-Liouville derivative. The (2+1)-dimensional KdVSKR equation, which is a recent extension of (1+1)-dimensional KdVSKR equation, can model the resonances of solitons in shallow water. By means of the Hirota bilinear method, finite symmetry group method and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton-cnoidal interaction solution of the (1+1)-dimensional fractional KdVSKR equation has been derived for the first time. For the (2+1)-dimensional frac-tional KdVSKR equation, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. Impact of the fractional order on the shapes of these solutions has been illustrated by figures. Three-wave interaction solutions of fractional systems have not been reported in the existing references. The research idea in this paper can be applied to other fractional differential equations.

We consider fractional integral operators $(I-T)^d, d \in (-1,1)$ acting on functions $g: \mathbb{Z}^{\nu} \to \mathbb{R}, \nu \ge 1 $, where $T $ is the transition operator of a random walk on $\mathbb{Z}^{\nu}$. We obtain sufficient and necessary conditions for the existence, invertibility and square summability of kernels $\tau (\mathbf{s}; d), \mathmb{s} \in \mathbb{Z}^{\nu}$ of $(I-T)^d $. Asymptotic behavior of $\tau (\mathbf{s}; d)$ as $|\mathbf{s}| \to \infty$ is identified following local limit theorem for random walk. A class of fractionally integrated random fields $X$ on $\mathbb{Z}^{\nu}$ solving the difference equation $(I-T)^d X = \varepsilon$ with white noise on the right-hand side is discussed, and their scaling limits. Several examples including fractional lattice Laplace and heat operators are studied in detail.

Notion of median in one dimension is a foundational element in nonparametric statistics. It has been extended to multi-dimensional cases both in location and in regression via notions of data depth. Regression depth (RD) and projection regression depth (PRD) represent the two most promising notions in regression. Carrizosa depth DC is another depth notion in regression. Depth induced regression medians (maximum depth estimators) serve as robust alternatives to the classical least squares estimator. The uniqueness of regression medians is indispensable in the discussion of their properties and the asymptotics (consistency and limiting distribution) of sample regression medians. Are the regression medians induced from RD, PRD, and DC unique? Answering this question is the main goal of this article. It is found that only the regression median induced from PRD possesses the desired uniqueness property. The conventional remedy measure for non-uniqueness, taking average of all medians, might yield an estimator that no longer possesses the maximum depth in both RD and DC cases. These and other findings indicate that the PRD and its induced median are highly favorable among their leading competitors.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning & fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

(1) Background: The prediction of cervical lesions evolution is a challenge for clinicians. The prospective study aimed to determine and compare the predictive accuracy of cytology, HPV genotyping, and p16/Ki67 dual staining alone or in combination with personal risk factors for the prediction of progression, regression or persistence of cervical lesions in human papillomavirus (HPV)-infected patients; (2) Methods: This prospective study included HPV-positive patients with or without cervical lesions that underwent follow-up. Descriptive statistics and sensitivity analysis for individual or combined index tests were used for data analysis; (3) Results: The highest predictive performance for the progression of cervical lesions was achieved by a model that comprised a Pap smear suggestive of high-grade squamous intraepithelial lesion (HSIL), the presence of 16/18 HPV strains, a positive p16/Ki67 dual staining result along with the presence of at least 3 clinical risk factors, which had a sensitivity (Se) of 74.42%, a specificity of 97.92%, an area under the receiver operating curve (AUC) of 0.961, and an accuracy of 90.65%. The prediction of cervical lesions regression or persistence was modest; (4) Conclusions: Multiple testing or new biomarkers should be used to improve HPV-positive patient surveillance, especially for cervical lesion regression or persistence prediction.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

Fractional flow reserve (FFR) is regarded as the gold standard for assessing the functional significance of coronary artery lesions, yet it remains underutilized in clinical practice. Our objective was to investigate whether FFR results have the potential to alter treatment decisions for coronary lesions compared to visual assessments of angiographic images made by three operators at a high-volume interventional center. In this retrospective study, we aimed to reassess the angiographic images of 63 patients presenting with chronic coronary syndrome (n=39, 61.9%) and acute coronary syndrome (n=24, 38.1%) who underwent FFR. Three experienced interventional cardiologists (with >300 PCI procedures per year) reevaluated, blinded to FFR results, 105 ambiguous lesions in 63 patients to determine angiographic significance and treatment strategy. The observers reached a concordant agreement (≥2 operators made the same decision) to perform PCI in 60 (57.1%) of the lesions based on angiographic evaluation. Interestingly, 9 (15%) of these lesions were functionally non-significant (FFR >0.80). The observers agreed to defer PCI in 45 (42.9%) of the lesions; however, 4 (8.9%) of these were functionally significant (FFR ≤0.80) and required PCI. Thus, inter-observer concordance in visual-guided therapeutic decision-making is variable and not always confirmed by the functional significance of coronary lesions.

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated "peaks" and "fat" tails is also discussed.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

Functional partially linear regression model, contains a functional linear part and a non-parametric part, in which testing the linear relationship between the response and the functional predictor is of fundamental importance. When functional data cannot be approximated with a few principal components, based on a pseudo estimate for the unknown non-parametric component, we develop a U-statistic of order-two in this paper. Under some regularity conditions, we use the martingale central limit theorem to prove that the proposed test statistic is asymptotically normal. The finite sample performance with simulation studies and real data application are assessed to verify the proposed test procedure.

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

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

Chronic Obstructive Pulmonary Disease (COPD) is a disease characterized by local and systemic inflammation independently of the risk factor; during the exacerbations, such inflammation is accentuated and amplified. A practical inflammatory marker and one with an applicable predictive value in the follow-up has been sought. FeNO has shown an excellent performance in that respect within the context of asthma and has also been studied in tobacco-smoke COPD (COPD-TS). In Biomass-smoke COPD (COPD-BS), this, to our knowledge, has not been evaluated. Objective: To measure FeNO levels in patients with COPD-BS and to compare these with those of patients with stable COPD-TS and in healthy controls. Methods: Transversal, observational, descriptive, comparative, and analytical study. A total of 57 patients, including 23 with COPD-BS, 17 with COPD-TS, and 17 healthy control subjects. The measurement of FeNO was carried out on all of these by means of the on-line chemiluminescence technique; the values were expressed in parts per billion (ppb) for their analysis. Results: It was observed that the FeNO values were similar between COPD-BS and COPD-TS and were significantly different between the healthy and stable COPD (both groups). No correlation was found between pulmonary function and symptoms with FeNO in any of the groups. Conclusions: The level of FeNO in stable COPD is found to be increased in a similar manner in COPD-BS and COPD-TS, with a significant difference on comparing it with that of the healthy subjects.

Snow cover products are primarily derived from the Moderate-resolution Imaging Spectrometer (MODIS) and Advanced Very High-Resolution Radiometer (AVHRR) datasets. MODIS achieves both snow/non-snow discrimination and snow cover fractional retrieval, while early AVHRR-based snow cover products only focused on snow/non-snow discrimination. The AVHRR Climate Data Record (AVHRR -CDR) provides a nearly 40-year global dataset that has a potential to fill a gap in long term snow cover fractional monitoring. Our study selects the Qinghai-Tibet Plateau as the experimental area, utilizing AVHRR-CDR surface reflectance data (AVH09C1) and calibrating with MODIS snow product MOD10A1. The snow cover percentage retrieval from the AVHRR dataset is performed using Surface reflectance at 0.64μm (SR1) and Surface reflectance at 0.86μm (SR2), along with a simulated Normalized Difference Snow Index (NDSI) model. Also, in order to detect the effects of land cover type and topography on snow inversion, we tested the accuracy of the algorithm with and without these influences, respectively (vanilla algorithm & improved algorithm). The accuracy of the AVHRR snow cover percentage data product is evaluated using MOD10A1、 ground snow-depth measurements and ERA5. Results indicate that the logic model based on NDSI has the best fitting effect, with R-square and RMSE values of 0.83 and 0.10, respectively. Meanwhile, the accuracy was improved after taking into account the effects of land cover type and topography. The model is validated using MOD10A1 snow-covered areas, showing snow cover area differences of less than 4% across 6 temporal phases. Improved algorithm results in better consistency with MOD10A1 than vanilla algorithm. Moreover, the RMSE reaches greater levels when the elevation is below 2,000 meters or above 6,000 meters, and is lower when the slope is between 16° and 20°. Using ground snow-depth measurements as ground truth, the multi-year recall rates are mostly above 0.7, with an average recall rate of 0.81. Results also show a high degree of consistency with ERA5. The validation results demonstrate that the AVHRR snow cover percentage remote sensing product proposed in this study exhibits high accuracy in the Tibetan Plateau region, also demonstrating that land cover type and topographic factors are important to the algorithm. Our study lays the foundation for the global snow cover percentage product based on AVHRR-CDR，furthermore lays a basic work for generating a long-term AVHRR-MODIS fractional snow cover dataset.

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.

Extreme Ultraviolet (EUV) photolithography process, is a cornerstone of semiconductor manufacturing and operates under demanding precision standards realized via nanometer-level overlay (OVL) error modeling. This procedure allows the machine to anticipate and correct OVL errors before impacting the wafer, thereby facilitating near-optimal image exposure while simultaneously minimizing the overall OVL error. Such models are usually high dimensional and exhibit rigorous statistical phenomena such as collinearities that play a crucial role in the process of tuning their parameters. Ordinary Least Squares (OLS) is the most widely used method for parameters tuning of Overlay models but in most cases it fails to compensate for such phenomena. In this paper we propose the usage of Ridge Regression, a widely known Machine Learning (ML) algorithm especially suitable for datasets that exhibit high multicollinearity. The proposed method has been applied in perturbed data from a 300 mm wafer fab and the results show reduced residuals when ridge regression is applied instead of OLS.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of dual-phase-lag heat conduction model with the Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag-Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

AbstractBackground: In Ethiopia, 8.6% of maternal deaths are attributed to abortion. Despite the legalization of abortion and improved accessibility of safe abortion services, almost six in 10 abortions in Ethiopia are performed outside of the health facility. Abortion considered as an indicator for various aspects of reproductive health and healthcare access within a particular region or country. Despite the significance of the problem, there is a limited understanding of the magnitude of abortion and the contributing factors in the study area. Therefore, this study aimed to assess the prevalence of abortion and determinant factors among reproductive-age women in the Sidama regional state of Ethiopia.Methods: A community-based cross-sectional study was conducted from October to November 11, 2022, among 1,130 women of reproductive age. We utilized a multi-stage sampling method to select eligible women. A structured and pretested questionnaire was utilized to collect the data using Open Data Kit (ODK) mobile application. Due to the hierarchical nature of the data, a multilevel logistic regression model was applied. Variables with p-values < 0.25 on bi-variable analysis were included in a multivariable regression model. In the multivariable regression model, variables with a p-value < 0.05 were declared as statistically significant factors of abortion. Results: Nearly one-fifth (19.5%) of the women had a history of abortion. From the individual level determinates; women with formal education (AOR=0.44; 95% CI: 0.24-0.79), and planned pregnancy (AOR=0.41; 95% CI: 0.28-0.61) had lower odds of abortion. While from the community related factors; urban residence increased the odds of abortion (AOR=2.25; 95% CI: 1.20-4.20) as compared to the rural residence.Conclusion: the prevalence of abortion among reproductive age women of Northern Zone of Sidama Region was high. Education and a planned pregnancy serve as protective factors for abortion, while the risk of abortion increased among women reside in urban area. Therefore, to lower the abortion rate, it is better to implement a comprehensive approach, focusing on education, family planning, and urban-specific intervention.

Background: Diagnostic accuracy of Parkinson’s disease (PD), a synucleinopathy, based on diagnostic criteria is suboptimal. A biomarker for synucleinopathies is pivotal both from a clinical and from a research aspect. CSF a-synuclein has been extensively studied over the past two decades as a candidate biomarker of synucleinopathies. Herein we present data on studies focusing on total, phosphorylated and oligomeric CSF a-synuclein in PD. Methods: Pubmed, Scopus and Web of Science were searched for studies with &gt;10 PD patients and control subjects, with data (mean, SD) on total, phosphorylated or oligomeric a-synuclein. Cohen’s d, as a measure of effect size, was calculated for all a-synuclein forms. Subgroup analysis and meta-regression were performed in an effort to explain between-study heterogeneity. Results: Thirty studies on total, six studies on oligomeric and one study on phosphorylated a-synuclein were included. Total a-synuclein was decreased and oligomeric a-synuclein increased in PD patients vs. controls. Effect size was medium for total and high for oligomeric a-synuclein. A-syn forms provided suboptimal combined sensitivity/specificity for the differentiation of PD from controls. There was significant between-study heterogeneity. PD cohort characteristics (sex, age, disease duration, UPDRS, H&amp;Y) and study characteristics (study design, healthy vs. neurological controls, control for CSF blood contamination, method of a-syn measurement) could not account for between-study heterogeneity. Publication bias was limited. Conclusions: CSF a-synuclein levels lack sufficient accuracy to be used as biomarkers for PD. Standardization of (pre)analytical variables may improve the discriminatory power of a-synuclein forms in the future.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

Traditional computer vision techniques aim to extract meaningful information from images but often depend on manual feature engineering, making it difficult to handle complex real-world scenarios. Fractional Calculus (FC), which extends derivatives to non-integer orders, provides a flexible way to model systems with memory effects and long-term dependencies, making it a powerful tool for capturing fractional rates of variation. Recently, Neural Networks (NNs) have demonstrated remarkable capabilities in learning complex patterns directly from raw data, automating computer vision tasks and enhancing performance. Therefore, the use of fractional calculus in neural network-based computer vision is a powerful method to address existing challenges by effectively capturing complex spatial and temporal relationships in images and videos. This paper presents a survey of Fractional Calculus Neural Network-based (FC NN-based) computer vision techniques for denoising, enhancement, object detection, segmentation, restoration, and NN compression. The survey compiles existing FFC NN-based approaches, elucidates underlying concepts, and identifies open questions and research directions. By leveraging FC's properties, FC NN-based approaches offer a novel way to improve the robustness and efficiency of computer vision systems.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

Neural Fractional Differential Equations (Neural FDE) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represented by a fractional derivative, with a neural network component, forming an initial value problem. During the learning process, both the order of the derivative and the parameters of the neural network must be optimised. In this work, we investigate the non-uniqueness of the optimal order of the derivative and its interaction with the neural network component. Based on our findings, we perform a numerical analysis to examine how different initialisations and values of the order of the derivative (in the optimisation process) impact its final optimal value. Results show that the neural network on the right-hand side of the Neural FDE struggles to adjust its parameters to fit the FDE to the data dynamics for any given order of the fractional derivative. Consequently, Neural FDEs do not require a unique α value, instead, they can use a wide range of α values to fit data. This flexibility is beneficial when fitting to given data is required, and the underlying physics is not known.

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

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

Objective: To evaluate the variables influencing the length of stay (LoS) for COVID-19 ICU patients at Tygerberg Hospital (Cape Town) and to identify the covariates that significantly influenced it and any potential risk factors associated with LoS. Methods and Results: Poisson, negative binomial (NB), Hurdle–Poisson, and Hurdle–NB regression models were used to model the LoS in this prospective cohort study. The fitted models were compared using the Akaike information criterion (AIC), Vuong’s test criteria, and Rootograms. Based on the chosen performance criteria, the NB model provided the best fit outperforming other candidate models. The baseline LoS count was 8 days. On average, antibiotics reduced LoS by 0.74-fold (95% CI 0.62-0.89) compared to not taking antibiotics. The second wave had a significant effect on the average LoS, which decreased by 0.36-fold (95% CI 0.14-0.93) compared to the first wave. Average LoS increased by 1.01-fold (95% CI 1.01-1.02) for every one-year increase in the age of the patient and by 1.02-fold (95% CI 1.01-1.03) for every 1 unit increase in neutrophils. A 1 ng/L increase in log (TropT) levels decreased the average LoS by 0.87-fold (95% CI 0.81-0.93) similarly, a unit increase in the PF ratio decreased the average LoS by 0.998-fold (95% CI 0.997-0.999) respectively. Conclusion: The study identified common clinical characteristics associated with length of stay in ICU for COVID-19 patients, including age at admission, PF ratio, neutrophils, TropT, Wave, and antibiotic use. These results can aid in identifying risk factors for increased length of stay, assist in healthcare systems planning, and aid in evaluating different models for analysing this type of data.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections, out of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behaviour of our proposed test is examined through extensive Monte Carlo experiments under various data generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labour wage of 36 countries agricultural markets.

In this work we looked for a stable and accurate procedure to perform feature selection in datasets with a much higher number of predictors than individuals, as in Genome-Wide Association Studies. Due to the instability in feature selection when many potential predictors are measured, a variable selection procedure is proposed that combines several replications of shrinkage regression models. A weighted formulation is used to define the final predictors. The procedure is applied to investigate Single Nucleotide Polymorphisms (SNPs) predictors associated to Alzheimer’s disease in the Alzheimer’s disease Neuroimaging Initiative (ADNI) dataset. Two data scenarios are investigated: one considering only the set of SNPs and another with the covariates age, sex, educational level and APOE4 genotype. The SNP rs2075650 and the APOE4 genotype are given as risk factors for AD, which is in line with the literature, and other four new SNPs are pointed, opening new hypotheses for in vivo analyses. These experiments demonstrate the potential of the new method for stable feature selection.

As prominent oil producers, the Gulf Cooperation Council (GCC) countries have played a significant role in the global energy market. However, as the world's attention increasingly shifts towards environmental sustainability, understanding the implications of the GCC's economic activities on CO2 emissions becomes indispensable. This research paper investigates the relationship between specific economic indicators and their impact on CO2 emissions in the GCC from 2001 to 2021. The study employs quantile regression, a powerful statistical method that estimates the conditional quantiles of a response variable given a set of predictor variables. The findings reveal several important insights: Financial institution efficiency is significant and negative at a 1% level at the lower (10th) -83537.3 and the higher quantile (90th) -549002.3. The relationship between GDP per capita and CO2 emissions varies across quantiles, highlighting the complexity of the growth-environment nexus. Total patents exhibit a positive and significant relationship with emissions, underscoring the importance of directing innovation towards environmentally sustainable solutions. Renewable energy consumption displays a nuanced relationship with CO2 emissions, with a stronger negative impact observed at higher consumption levels. This underscores the potential of renewable energy to mitigate emissions when integrated at scale. The study's outcomes hold crucial policy implications for the GCC countries as they seek to align economic growth with environmental sustainability. The findings emphasize the importance of fostering financial institution efficiency, promoting green innovation, and expanding renewable energy sources to reduce emissions

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

Expectation maximization (EM) algorithm is a powerful mathematical tool for estimating statistical parameter when data sample contains hidden part and observed part. EM is applied to learn finite mixture model in which the whole distribution of observed variable is average sum of partial distributions. Coverage ratio of every partial distribution is specified by the probability of hidden variable. An application of mixture model is soft clustering in which cluster is modeled by hidden variable whereas each data point can be assigned to more than one cluster and degree of such assignment is represented by the probability of hidden variable. However, such probability in traditional mixture model is simplified as a parameter, which can cause loss of valuable information. Therefore, in this research I propose a so-called conditional mixture model (CMM) in which the probability of hidden variable is modeled as a full probabilistic density function (PDF) that owns individual parameter. CMM aims to extend mixture model. I also propose an application of CMM which is called adaptive regressive model (ARM). Traditional regression model is effective when data sample is scattered equally. If data points are grouped into clusters, regression model tries to learn a unified regression function which goes through all data points. Obviously, such unified function is not effective to evaluate response variable based on grouped data points. The concept “adaptive” of ARM means that ARM solves the ineffectiveness problem by selecting the best cluster of data points firstly and then evaluating response variable within such best cluster. In order words, ARM reduces estimation space of regression model so as to gain high accuracy in calculation.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

Caudal regression syndrome (CRS) is a congenital abnormality characterized by an incomplete development of the spinal cord (SC) and other abnormalities. We studied a 9-months old CRS child presenting: interruption of SC at L2-L3 level, sacral agenesis, lack of innervation of the inferior limbs (flaccid paraplegia) and neurogenic bladder and bowel. Given the effects of growth hormone (GH) on the proliferation, differentiation and migration of neural stem cells (NSCs), we treated him with GH and rehabilitation, trying to induce the recovery of main sequelae. GMFM-88 test score was 12.31%. After a blood analysis, GH treatment (0.3 mg/day, 5 days/week, 3 months and then 15 days without GH) and rehabilitation commenced. This protocol was followed during 5 years, being the last GH dose 1 mg/day. Blood analysis and physical exams were performed every 3 months initially and every 6 months later. Six months after commencing the treatment GMFM-88 score increased to 39.48%. Responses to sensitive stimuli appeared in most of the territories explored; 18 months later sensitive innervation was complete and the patient moved any muscle over the knees and controlled his sphincters. Three years later he walked with the help of canes, there was plantar flexion and GMFM-88 score was 78.48%. In summary, GH plus rehabilitation may be useful for innervating distal territories, below the level of the incomplete spinal cord in CRS. Most likely, GH acts on ependymal SC NSCs, as the hormone does in the neurogenic niches in the brain.

COVID-19 is the most severe health crisis of the 21st century. COVID-19 presents a threat to almost all countries world-wide. The restriction of human mobility is one of the strategies used to control the transmission of COVID-19. However, it has yet to be determined how effective this restriction is in controlling the rise in COVID-19 cases, particularly in major capital cities such as Jakarta, Indonesia. Using Facebook's mobility data, our study explores the impact of restricting human mobility on COVID-19 case control in Jakarta. Our main contribution is showing how the restriction of human mobility data can give important information about how COVID-19 spreads in different places. We proposed modifying a global regression model into a local regression model by accounting for the spatial and temporal interdependence of COVID-19 transmission across space and time. We applied Bayesian hierarchical Poisson spatiotemporal models with spatially varying regression coefficients. We estimated the regression parameters using an Integrated Nested Laplace Approximation. We found that the local regression model with spatially varying regression coefficients outperforms the global regression model based on DIC, WAIC, MPL, and R2 criteria for model selection. In Jakarta's 44 districts, the impact of human mobility varies significantly. The impacts of human mobility on the log relative risk of COVID-19 range from –4.445 to 2.353. The prevention strategy involving the restriction of human mobility may be beneficial in some districts but ineffective in others. Therefore, a cost-effective strategy had to be adopted.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

In this paper, we present a relapse based demonstrating way to deal with investigate various arrangement MTC information. A commonplace use of this displaying approach incorporates three stages: first, define a model that approximates the connection between quality articulation and trial factors, with boundaries consolidated to address the exploration premium; second, utilize least-squares and assessing condition methods to gauge boundaries and their relating standard blunders; third, register test insights, P-qualities and NFD as proportions of factual criticalness. The benefits of this methodology are as per the following. To begin with, it tends to the exploration interest in a particular, precise way, and maximally uses all the information and other important data. Second, it represents both orderly and irregular varieties related with the information, and the consequences of such examination give not just quality explicit data applicable to the exploration objective, yet additionally its dependability, in this way helping agents to settle on better choices for subsequent investigations. Third, this methodology is truly adaptable, and can undoubtedly be stretched out to different sorts of MTC considers or other microarray explores by detailing various models dependent on the test plan of the investigations.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

(1) Background The SKT is a short cognitive performance test designed to assess impairments in memory and cognitive abilities such as attention and speed of information processing. In 2019, new regression-based norms for the English version of the SKT were calculated applying data from older cognitively healthy adults living in the US, Ireland and Australia (the norming sample) The study has two aims: to establish valid cut-offs for distinguishing between no cognitive impairment, mild cognitive impairment (MCI) and dementia (1), and to cross-validate the new norms for detecting MCI and dementia (2) in a community sample of older adults with clinical diagnoses; (2)Methods: The validation sample included 142 older adults (mean age=87.7, SD=3.55) from the Sydney Memory and Aging Study (MAS Study). Participants were classified as having normal cognition, MCI, or dementia through a consensus diagnosis as well as by the SKT; (3)Results: The sensitivity of the SKT for the differentiation of cognitive impairment (MCI or dementia) from normal cognition was 80.6%. The convergence between the SKT and the consensus diagnoses was 60.1% for all three diagnostic groups. The correlation between the SKT and the Addenbrooke’s Cognitive Examination III (ACE-III), a well validated measure of cognitive ability in older adults, was r = 0.3;. (4) Conclusions: In sum, it can be stated that the SKT is a valid tool for detecting early stages of cognitive impairment, performing very well in discriminating between no cognitive impairment and cognitive impairment (MCI or dementia).

With the use of linear regression modeling, this study sought to forecast and analyze rainfall patterns in Ethiopia. The dataset included historical rainfall data as well as pertinent independent variables. The R-squared score and mean squared error (MSE) were used to assess the effectiveness of the linear regression model. The results showed that the model's ability to forecast and analyze rainfall patterns was not very good. Only around 5.3% of the variance in rainfall could be explained by the chosen independent variables, according to the R-squared score of 0.053. This low number indicated that there was little correlation between the selected variables and rainfall, and that a sizable percentage of the variation in the dependent variable was not captured by the model. The model's accuracy in forecasting rainfall was shown to be quite low by the MSE error, with significant squared discrepancies between the expected and actual amounts. These results support the notion that the linear regression model as it is now designed is not appropriate for studying or forecasting Ethiopia's rainfall patterns. Alternative modeling approaches, the inclusion of other pertinent factors, and the assurance of the availability of high-quality data that faithfully captures the intricate dynamics of rainfall in the area all require more investigation.

This study investigates the suitability of the timestamp approach algorithm for predicting blood pressure (BP) using wearable and comfortable devices, showcasing its accuracy even with low-frequency sampled signals. Developed within the SINTEC European project, the algorithm utilizes Electrocardiogram (ECG) and Photoplethysmogram (PPG) sensors, demonstrating promising results in both laboratory and hospital settings. The research emphasizes the algorithm’s potential to transform continuous and non-invasive BP monitoring through wearable technology, offering frequent measurements with minimal discomfort. While the study shows promise, further exploration is needed, focusing on optimizing machine learning coefficients for long-term monitoring applications and addressing potential changes over time. Technological improvements, including the implementation of edge computing algorithms, hold the key to enhancing BP accuracy, denoising techniques, and integrating alarm systems for future wearable solutions. This study emphasizes the adaptability of the algorithm for diverse healthcare environments, paving the way for broader applications in convenient and reliable BP monitoring.

Like traditional single label learning, multi-label learning is also faced with the problem of dimensional disaster.Feature selection is an effective technique for dimensionality reduction and learning efficiency improvement of high-dimensional data. In this paper, Logistic regression, manifold learning and sparse regularization were combined to construct a joint framework for multi-label feature selection (LMFS). Firstly, the sparsity of the eigenweight matrix is constrained by the $L_{2,1}$-norm. Secondly, the feature manifold and label manifold can constrain the feature weight matrix to make it fit the data information and label information better. An iterative updating algorithm is designed and the convergence of the algorithm is proved.Finally, the LMFS algorithm is compared with DRMFS, SCLS and other algorithms on eight classical multi-label data sets. The experimental results show the effectiveness of LMFS algorithm.

In this project, we use a statistical multiple regression to study the impact of eight various predictors (relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, glazing area distribution) to estimate the cooling load energy efficiency of residential buildings. We try to analyze and visualize the effect of each predictor with each of the response variable using different classical statistical analysis tools used in describing linear models, in such a way so that we can find out the most strongly related predictor variables. Before starting all of this, we use the idea of model selection by stepwise regression technique and compare the AIC of these models and identified a better model between all of them. Then, we compare a classical linear regression approach by simulations on 768 diverse residential buildings show that we can predict CL with low mean absolute error. By using ANOVA we determine variation in the different residuals. Also, we use non constant variance test to verify it. Furthermore, we check leverage and influence points as well as outliers as well as determined cook distance for influential points. By taking box cox transformation and weights, we also introduce WLS technique to fit the model for better results and did all type of important analysis to understand the energy efficiency. Finally, we show 5-fold cross validation to verify our model.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

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

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

Making sustainable business models, especially in manufacturing, is a key approach for organizations to adopt in order to create more sustainable processes. New technologies are needed to implement new policies that can minimize the economic, environmental, and social consequences of industrial activity. Sustainable maintenance is decisive to guarantee the availability, reliability, and safety of assets, surpassing traditional maintenance policies and embracing the principles of the circular economy. The main objective of Maintenance 4.0 is to increase the lifespan and availability of the equipment by preventing unplanned downtime, reducing planned shutdowns, and improving safety. This research focuses on the integration of advanced Industry 4.0 tools with conventional monitoring and control techniques in process industries. The article suggests that while complex neural networks might provide good predictions, simpler solutions can generalize well and have lower prediction errors because they can capture the underlying relationships between variables in a specific asset better. The combination of maintenance function, Industry 4.0 tools, and advanced statistical solutions to obtain sustainable processes can facilitate organizational change and aid decision-making in equipment management. These solutions seek to reduce interruptions and expenses through the unnecessary utilization of labor and spare parts. All these considerations improve communication and data processing, resulting in improved maintenance of a hydrogen compressor in the petrochemical industry.

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained increasing attention due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring for future research.

Predicting copper price is essential for making decisions that can affect companies and governments dependent on the copper mining industry. Copper prices follow a time series that is non-linear, non-stationary, and which have periods that change as a result of potential growth, cyclical fluctuation and errors. Sometimes the trend and cyclical components together are referred to as a trend-cycle. In order to make predictions, it is necessary to consider the different characteristics of trend-cycle. In this paper, we study a copper price prediction method using Support Vector Regression. This work explores the potential of the Support Vector Regression with external recurrences to make predictions at 5, 10, 15, 20 and 30 days into the future in the copper closing price at the London Metal Exchanges. The best model for each forecast interval is performed using a grid search and balanced cross-validation. In experiments on real data-sets, our results obtained indicate that the parameters (C, ε, γ) of the model Support Vector Regression do not differ between the different prediction intervals. Additionally, the amount of preceding values used to make the estimates does not vary according to the predicted interval. Results show that the support vector regression model has a lower prediction error and is more robust. Our results show that the presented model is able to predict copper price volatilities near reality, being the RMSE equal or less than the 2.2% for prediction periods of 5 and 10 days.

Regression models form the core of the discipline of econometrics. One of the basic assumptions of classical linear regression model is that the values of the explanatory variables are fixed in repeated sampling. However, in most of the real life cases, particularly in economics the assumption of fixed regressors is not always tenable. Under a non-experimental or uncontrolled environment, the dependent variable is often under the influence of explanatory variables that are stochastic in nature. There is a huge literature related to stochastic regressors in various aspects. In this paper, a historical perspective on some of the works related to stochastic regressor is being tried to pen down based on literature search.

In Taiwan, mountainous areas account for approximately two-thirds of the total area. The steep terrain and concentrated rainfall during typhoons cause landslides, which pose a considerable threat to mountain settlements. Therefore, models for analyzing rainfall-induced landslide hazards are urgently required to ensure adequate land use in mountainous areas. In this study, focusing on Pingtung County in southern Taiwan, we developed a landslide hazard index (IRL) to land use. Using FORMOSA-2 and SPOT-5 satellite images, data were collected before and after four typhoons (one in 2009 and three in 2013). The ArcGIS random tree classifier was used for interpreting satellite images to explore surface changes and disasters, which were used to analyze slope disturbances. The product of the maximum 3-h rolling rainfall intensity and effective accumulated rainfall was used as a rainfall trigger index (IRT). Considering environmental and slope disturbance factors, an index of slope environmental strength potential (ISESP) was developed through logistic regression (LR). Landslide hazard to land use was estimated using IRT and ISESP. The average coefficient of agreement (Kappa) was approximately 0.71 (medium to high accuracy); the overall accuracy of slope environmental strength potential analysis was approximately 80.4%. At a constant ISESP, IRT increased with the increasing hazard potential of rainfall-induced landslides. Furthermore, IRT and ISESP were positively correlated with landslide occurrence. When large ISESP values occur (e.g., fragile environment and high land development intensity), small IRT values may induce landslides.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

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

This paper uses the numerical results of surveys sent to Huelva’s (Andalusia, Spain) households to determine the degree of knowledge they have about the urban water cycle, needs, values, and attitudes regarding water in an intermediary city with low water stress. In previous research, we achieved three different households’ clusters. The first one grouped households with high knowledge of the integral water cycle and a positive attitude to smart devices at home. The second cluster described households with low knowledge of the integral water cycle and high sensitivity to price. The third one showed average knowledge and predisposition to have a closer relationship with the water company. This paper continues with this research line, applying Classification and Regression Trees (CART) to determine which hierarchy of variables/factors/ independent components obtained from the surveys are the decisive ones to predict the range of household water consumption in Huelva. Positive attitudes towards improved cleaning habits for personal or household purposes are the highest hierarchy component to predict the water consumption range. Second in the hierarchy, the variable Knowledge Global Score about the integral urban water cycle, associated with water literacy, also contributes to predicting the water consumption range. Together with the three clusters obtained previously, these results will allow us to design water demand management strategies (WDM) fit for purpose that enable Huelva’s households to use water more efficiently.

This work evaluates the surface water quality in terms of physico-chemical parameters of the Brahmani River, Odisha using statistical analysis involving the calculation of correlation coefficient and regression equation. Besides this, the work also highlights and draws attention towards the “Water Quality Index” in a simplified format which may be used at large and could represent the reliable picture of water quality. Surface water quality data is taken from OSPCB of various location i.e. Panposh D/S, Rourkela D/S, Rengali, Talcher U/S, Kamalanga D/S, Bhuban, Pattamundai and was assessed for summer, monsoon, winter for the years 2011, 2012, 2013, 2014 and 2015. Average of values, minimum of values and maximum of values of water quality parameters were obtained seasonally over the above mentioned years. Besides this, the standard deviation for the water quality parameters was also obtained for water quality parameters namely pH, Temperature, DO, TDS, Alkalinity, EC, Na+, Ca2+, Mg2+, K+, F-, Cl-, NO3-, SO42- and PO42-. Seasonal changes in various physical and chemical parameters were analysed.The values obtained were compared with the guideline values for drinking water by Bureau of Indian Standard (BIS). A systematic correlation and regression study is carried out for three seasons, showed linear relationship among different water quality parameters. This provides an easy and rapid method of monitoring water quality. Highly significant (0.8< r <1.0), moderately significant (0.6< r <0.8) and significant (0.5< r <0.6) correlations between the parameters have been worked out. High correlation coefficient has been observed between TDS,EC-Na+, Ca2+, Cl-, SO42- ; Na+- Cl-. From the collected quantities, certain parameters were selected to derive WQI for the variations in water quality of each designated sampling site. WQI of Brahmani River ranged from 36.7 to 44.1 which falls in the range of good quality of water.Panposh D/S and Rourkela D/S showed poor water quality in summer and winter season. It is shown that WQI may be a useful tool for assessing water quality and predicting trend of variation in water quality at differentlocations in the Brahmani River.

There is high prevalence of hypertension and is rapidly increasing around the world, despite the intervention programme implemented, this study aimed at estimating the prevalence rate, test of association between hypertension and risk factors and model hypertension rate. Data used was obtained from the health record of Federal Medical Centre, Keffi from January 2016 – January 2019. Ordinal logistic regression model was used; Model Fitting Information, Goodness-of-Fit, Pseudo R-Square and Test of Parallel Lines are fitted to the data sets to test the accuracy and correctness of the model. The results indicated that the overall prevalence of hypertension rate is high at 36.4%, among the adult population, body mass index and gender are statistically significant, and Age is not significant in the study. Individuals that are overweight are more likely to be hypertensive compare to other weights. At age 40 – 49 years which have the highest rate of 26.5% and the odd ratio is 0.75 compared to others. One year increase in age 30 – 39, the cumulative odd of being hypertensive is 0.91 while other independent variables are held constant. The odd ratio of female being hypertensive is 0.85, therefore the females are more likely to be hypertensive with 54.4% compared to the males at 45.6% . There is no presence of multicolinearity among the variables and Logit models were formulated to calculate probabilities of the various possible outcomes.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

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

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

We present a new penalized method for estimation in sparse logistic regression models with group structure. Group sparsity suggests us to consider the Group Lasso penalty. Being different from penalized log-likelihood estimation, our method can be viewed as a penalized weighted score function method. Under some mild conditions, we provide non-asymptotic oracle inequalities promoting group sparsity of predictors. A modified block coordinate descent algorithm based on a weighted score function is also employed. The net advantage of our algorithm over the existing Group Lasso-type procedures is that the tuning parameter can be pre-specified. The simulations show that this algorithm is considerably faster and more stable than competing methods. Finally, we illustrate our methodology with two real data sets.

Computational Fluid Dynamics (CFD)-based simulation has been the traditional way to model complex industrial systems and processes. One very large and complex industrial system that has benefited from CFD-based simulations is the steel blast furnace. The problem with the CFD-based simulation approach is that it tends to be very slow to generate data. The CFD-only approach may not be fast enough for use in real-time decision-making. To address this issue, in this work, the authors propose the use of machine learning techniques to train and test models based on data generated via CFD simulation. Regression models based on neural networks are compared to tree boosting models. In particular, several areas (tuyere, raceway, and shaft) of the blast furnace are modeled using these approaches. The results of the model training and testing are presented and discussed. The obtained R2 metrics are, in general, very high. The results look promising and may help to improve the efficiency of operator and process engineer decision-making when running a blast furnace.

Training supervised machine learning models requires labeled examples. A judicious choice of examples is helpful when there is a significant cost associated with assigning labels. This article improves upon a promising extant method – Batch-mode Expected Model Change Maximization (B-EMCM) method – for selecting examples to be labeled for regression problems. Specifically, it develops and evaluates alternate strategies for adaptively selecting batch size in B-EMCM. By determining the cumulative error that occurs from the estimation of the stochastic gradient descent, a stop criteria for each iteration of the batch can be specified to ensure that selected candidates are the most beneficial to model learning. This new methodology is compared to B-EMCM via mean absolute error and root mean square error over ten iterations benchmarked against machine learning data sets. Using multiple data sets and metrics across all methods, one variation of AB-EMCM, the max bound of the accumulated error (AB-EMCM Max), showed the best results for an adaptive batch approach. It achieved better root mean squared error (RMSE) and mean absolute error (MAE) than the other adaptive and non-adaptive batch methods while reaching the result in nearly the same number of iterations as the non-adaptive batch methods.

Neither tumor growth nor regression is truly spontaneous, but both may under special circumstances be driven by similar events. We describe a sequence of processes that typically leads to tumor progression but may on occasion inadvertently result in regression. A possible procedure for reducing tumor mass through a controlled intervention is also outlined.

The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to the integer order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used.