This paper investigates the asymptotic power of a Spearman's rank correlation-based test for assessing independence between the joint regressors and the error term in a generalized partially linear logistic regression model. The proposed test statistic is constructed using general order differences of the observed binary responses and their fitted probabilities, leveraging the property that independence between joint covariates and the error term implies asymptotic independence between these order differences under mild regularity conditions. We introduce a sequence of contiguous alternatives to derive the limiting distribution of the test and to compute its asymptotic power. Simulation studies demonstrate strong finite-sample performance and confirm the theoretical power results. A real-data application further highlights the practical usefulness of the proposed method.
Survival analysis involves modeling time-to-event data using multiple models, such as the Accelerated Failure Time (AFT) model. Choosing the most appropriate model is crucial. Various model selection criteria are available in the literature. This study examines the performance of new model selection criteria based on Kullback's Symmetric Divergence within the Parametric AFT model framework. Simulations and real data were used to compare the Kullback Information Criterion (KIC) and its corrected version (KICc) with traditional information criteria, such as the Akaike Information Criterion (AIC), corrected AIC (AIC(c)), improved AIC (AIC(sur)), and Bayesian Information Criterion. Results showed that KICc outperforms other criteria in selecting the true model order in small samples and maintains competitive predictive accuracy across conditions. KIC and KICc outperform the AIC family criteria for moderate and large sample sizes. The real data shows that AIC and AIC(sur) tend to select overfitted models, while KICc and AIC(c) favor underfitted models.
Partial Multi-Label Learning (PML) is a weakly supervised learning framework in which each instance is associated with a set of candidate labels, among which only a subset are correct. The presence of noisy labels in the candidate set poses significant challenges for accurate classification and effective feature selection. Existing methods often overlook either the noise in the feature space or the structural relationships within the label space, limiting their robustness and generalizability. In this paper, we propose a novel PML approach based on Shared Subspace Representation, which jointly learns a low-dimensional latent space for both feature and label information. Our method decomposes the noisy candidate label matrix into a low-rank ground-truth label component and a sparse noise component, leveraging the inherent structure and sparsity of label noise. Simultaneously, a feature correlation matrix maps original features into a compact subspace, enhancing discriminative power while mitigating the impact of feature noise. To preserve the geometric structure of the data, manifold regularization is incorporated via a graph Laplacian constructed from the feature space, enforcing local consistency between similar instances. We formulate the overall objective as a unified optimization problem, which is efficiently solved using block coordinate descent and gradient-based methods. Extensive experiments on benchmark datasets demonstrate that our approach outperforms state-of-the-art methods in both label recovery and feature selection, confirming the effectiveness of shared subspace modeling in partial multi-label learning.
We established the complete solution set for a specific exponential Diophantine equation involving polynomial bases with three unknown exponents (k, m, n). Our analysis demonstrated that the equation possesses a unique positive integer solution for the exponents (k, m, n), namely (1, 1, 2), which holds true for every positive integer value of the parameter 'w', subject to a set of arithmetic constraints. The proof is constructed through a rigorous synthesis of established arithmetic methods (such as modular congruences and the Quadratic Reciprocity Law) and advanced analytic tools derived from transcendental number theory, specifically leveraging a powerful bound on p-adic measurement of logarithmic sums developed by Bugeaud. The proof's numerical bounds and specific calculations were performed and confirmed using Python code.
Retinography is a non-invasive medical imaging technique for analyzing the human visual system. As one of the top three global causes of blindness, diabetic retinopathy's early identification is critical, with exudates often being the initial visible indicator. The presence of the optic disc can interfere with the detection of bright lesions, particularly exudates. For this reason, accurate detection of the optic disc is considered essential. The primary goal of this research is the detection and segmentation of the optic disc. This work presents a new model for the automatic localization of the optic disc in retinal images from a South African patient cohort.. The method utilized images sourced from the Eye Centre fundus photo database. An efficient method for segmenting the optic disc for retinal image analysis is described. This approach integrates wavelet and wavelet packet denoising techniques with morphological operations. The algorithm was tested on a set of 100 images, which included 60 normal images and 40 images presenting exudates. The roundness metric was measured, achieving values of 0.8 or higher in 90% of the normal images and in 87.5% of the images with exudates. The algorithm demonstrated a high degree of accuracy in detecting the optic disc in the majority of cases. In contrast to other methods found in the literature, this algorithm's effectiveness is not compromised by the presence of exudates in retinal images.
In this paper Walter Christaller's Central Place Theory is used to examine the spatial relationship between urbanization and infrastructure across five regions of India: NCR, Southern, Eastern, Western, and Central (Mitra, Mukherji, and Bose, 1980). Using the largest city in each region as the core, multiple ring buffers (0-50 km, 50-100 km, and beyond 100 km) were generated using ArcGIS 10.8.1. The study analyses city size classes and infrastructure indicators such as number of latrines, electricity connections, and hospitals within these buffers using Census 2011 data from District Census Handbooks and HL-14 tables. Statistical methods including descriptive, correlation, and regression analyses were employed. Findings reveal regional disparities in infrastructure quality. The National Capital Region (NCR), Southern, and Eastern regions exhibit better infrastructure within the 50 km ring, while the Western region shows higher quality beyond 100 km. The Central region displays mixed outcomes across all rings. A strong positive correlation is observed between urbanization and infrastructure within the 0-50 km and 50-100 km rings, but the correlation weakens positively beyond 100 km. Regression analysis identifies latrines, electricity connections, and hospitals as significant predictors of urban growth, with exceptions: electricity is not a significant factor in the 50 km and beyond 100 km rings of NCR and in the Southern region's 50-100 km ring. This study underscores the spatial variation in urban infrastructure development and its alignment with urban population distribution in India.
In nonparametric regression statistical relationship between covariate and random error is a matter of interest. For a traditional nonparametric regression model, Y = m(X) + is an element of with Y the response, X the covariate, is an element of the random error and m() a suitably chosen smooth function the null hypothesis of interest is X and is an element of are independent against all possible alternatives citing dependence between X and is an element of. A valid extension is if for an incomplete data set with several missing responses, similar testing of independence is applicable. In the present article, some observations on Y are missing at random whereas X possesses complete set of observations. Thereafter, in this missing at random (MAR) type data, test of independence between X and is an element of is investigated. Test statistics, based on some available or modified measures of association are constructed to develop consistent test procedures against a sequence of contiguous alternatives. The asymptotic powers of the test statistics are further determined through a finite sample simulation study. Finally, real data analysis is executed to examine the usefulness of the proposed test statistics.
Sombor index is a novel topological index, which was introduced by Gutman and defined fora graph G as S(G) = Sigma(uv is an element of EG) root d(u)(2) + d(v)(2), where d(u) = d(G)(u) and d(v)=d(G)(v) denote the degree of vertex u and v in G. Liu et al. investigated extremal problems concerning the Sombor indices of unicyclic graphs under diameter constraints. Extending their findings, we apply inductive reasoning to derive the extremal Sombor indices for bicyclic graphs with prescribed order and diameter.
We consider the semiparametric proportional hazards model for the cause-specific hazard function in analysis of competing risks data with missing cause of failure. The inverse probability weighting equation is well used for estimating the regression parameters under the missing at random (MAR), provided the model for the nonmissing cause case is correctly specified. In this study, we consider a parametric logistic regression, discriminant analysis, and neural network for the model of missingness probability. Simulation studies demonstrate that the inverse probability weighted (IPW) estimators by a correctly specified logistic regression model and by discriminant analysis perform well and are appropriate for practical use. The IPW estimator by neural network works considerably well for a sufficient large sample. The application of the proposed methods are illustrated with data from a bone marrow transplant study and Women's Interagency HIV study.
The online portfolio selection has gained significant interest in recent years. It involves allocating capital among assets and updating the portfolio to maximize long-term return. This research presents an online portfolio selection algorithm incorporating fuzzy returns, dual-beta risk measure, and trading volume. The algorithm employs dual-beta to achieve maximum utility by exploiting positive market movements while avoiding negative ones. To make the model more realistic, each day's return is represented as a fuzzy number, which avoids the simplifying assumption of trading at the stock's closing price. Another key feature of this study is using trading volume to identify similar time windows. The algorithm presented in this study follows the pattern-matching principle. Fuzzy clustering is used in the sample selection step to cluster fuzzy returns and trading volumes. This helps identify time windows similar to the recent one, using Manhattan and Canberra distance criteria. In the portfolio optimization step, an optimal logarithmic objective function with the dual-beta risk measure incorporating transaction costs is employed. The algorithm underwent evaluation by testing it on five datasets of different time intervals and characteristics. The evaluation results demonstrate a substantial enhancement in returns and risk-adjusted returns compared to prior algorithms in the literature.
In this article, we study the Thakur et al. (Thakur, Thakur and Postolache, 2014) iterative process for finding the best proximity pair for noncyclic relatively nonexpansive mappings. Using this iterative process, we establish the convergence results in uniformly convex Banach spaces. We support our main result by a numerical example in which, we approximate the best proximity pair using MATLAB program.
This study investigates two forms of exponential Diophantine equations that are built upon special numerical structures: centered tetradecagonal numbers and pronic numbers. The primary focus lies in determining the existence of integer solutions for each equation. It is shown that for one of the equations, there exists a unique solution in the set of whole numbers for all values of the parameter greater than one. In contrast, the second equation exhibits a consistent pattern of solutions across all positive integers. Additionally, several particular instances are examined to further support and illustrate the general results.
The present paper discusses a two-state single server retrial queueing model with feedback and batch departures. If an arriving customer finds the server free, it is served immediately else it joins the orbit. Both type of customers follow the Poisson arrival process. The customers depart from the system in batches of random size. Also, if a departing batch has unsatisfied customers, it may join the orbit with a certain probability to receive a satisfied service. The transient state probabilities are obtained by solving the difference-differential equations recursively. Numerical and graphical illustrations are also given.
In this paper, the aim is to examine population and economic variables using the Exponential Smoothing, ARIMA, FTS, NNAR, and BSTS models. We have to forecast for the next ten years using these models to determine which is the best model based on the MAE, RMSE, and MAPE values, whose values are lower than the best prediction model. For population variables, the ARIMA model is best fitted as compared to other models, and the Total and Urban populations have well fitted in the ARIMA model as compared to other models and the Rural population has well fitted in the ARIMA and FTS models as compared to other models. For economic variables, the ARIMA model has the best performance as compared to other models in the Age dependency ratio variable, and the NNAR model has good performance as compared to other models in the GDP variable. Based on RMSE, MAE, and MAPE values, the ARIMA model performs better than other models like Holt's Exponential Smoothing, ANN, Fuzzy Time Series, and Bayesian Time Series Models. Except for the ARIMA model, the NNAR model has better fits than other models.
This study uses statistical methodologies to investigate the relationship between signature features and behavioral and psychological traits among undergraduate students. The research analyzes signature attributes such as size. pressure. slant, and zone utilization to determine their association with specific personality characteristics like confidence, introversion. emotional intensity and analytical thinking. Through statistical modeling and hypothesis testing, significant correlations are identified. underscoring the potential of signature analysis in behavioral profiling. This paper contributes to the field by utilizing a data-driven approach to validate graphological insights through quantitative methods, emphasizing the integration of statistical analysis with personality profiling.
In this work we discribe new technical approxmations for numerical solution of Volterra and Fredholm integro-differential equations using a modified Taylor series method and modified integration method with Lagrange polynomials. For each method we present some numerical examples compared with other known methods in order to illustrate accuracy and efficiency of our two methods.
Bayesian analysis provides a distinctive approach to forecasting by allowing the integration of current data with existing predictions. This method improves the reliability of predictions by effectively addressing uncertainties, offering an edge over traditional forecasting techniques. In this study, we denve the predictive density using the Lindley distribution under various prior assumptions, including conjugate. quasi, uniform. and non-informative priors. The results underscore the effectiveness of Bayesian predictive methods in generating more accurate and credible predictions.
The present study is an attempt to understand the role of temperature of an urban area in shaping the dispersion of air pollutants. We know that there are certain gases in the form of air pollutants which are highly reactive and temperature dependent and converted into the secondary pollutants. In the present model, we considered that the inter-conversion process takes place dunng the urban heat island effect while taking the rate of reaction as temperature dependent in the form of Arrhenius equation. Urban heat island intensity is taken into an account while considering the temperature. The overall structure is divided into two intervals where the first interval reflects the inter-conversion process while the second interval is the non-existence of inter-conversion process. The twodimensional advective diffusion equations along with the appropriate boundary conditions are used to define the phenomenon. It was observed that not only the temperature but also the urban length plays a vital role in shaping the distribution of pollutants in both intervals_
We study stability and stabilization issue for a time delays continuously distributed on a specified duration of time system of integro-differential equations, under introduced certain conditions. Characteristics of global stability of these systems subject to with hybrid impulse conditions in the continuous -time case investigated.
The aim of our work is to solve numerically a Generalized Volterra Abel-Fredholm integral equations using a new spectral method based on a shifted first kind Chebyshev Polynomials, this method leads us to convert the equation to a system of a linear algebraic equations in the unknown expansion coefficients. The numerical solutions obtained in some examples by our technical show its high accuracy and efficiency compared with others methods.
