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How often can two independent elephant random walks on Z meet?
No full textWe show that two independent elephant random walks on the integer lattice Z meet each other finitely often or infinitely often depends on whether the memory parameter p is strictly larger than 3/4 or not. Asymptotic results for the distance between them are also obtained
Image deraining via multi-level decomposition and empirical wavelet transform
No full textImage deraining, a crucial process in image restoration, finds wide-ranging applications in computer vision. Existing state-of-the-art deraining techniques, predominantly relying on image smoothing, dictionary learning, sparse coding, and deep neural networks, often fall short in delivering desirable outputs when faced with heavy rain. In this research article, we propose an advanced approach for image deraining, employing a multilayer decomposition strategy based on Empirical Wavelet Transform (EWT) and Dual Dictionary Learning (DDL). The proposed method introduces the Dark Channel Prior (DCP) in the preprocessing stage and utilizes Frequency Discrimination (FD), Empirical Wavelet Transform, and sparse-based methods with Dual Dictionary Learning to generate one low and three high frequency (HF) decomposed image components. The rain parts are subsequently removed from each HF image component through morphological decomposition in multiple layers. The non-rain outputs are combined with the lower frequency image obtained from the bilateral filter output to produce the rain-free image. The final output is further refined by adjusting the contrast, sharpness, and color balance of the de-rained image. To validate the efficacy of our proposed algorithm, we conducted a comprehensive evaluation using both subjective (visual quality) and objective (quantitative quality metrics) approaches. Comparative analysis with state-of-the-art methods confirms that our method outperforms existing techniques, demonstrating superior image-deraining capabilities. The proposed approach showcases promising results in addressing the challenges posed by heavy rain, establishing it as a robust and effective solution for image-deraining applications in various computer vision domains
Impact of Ports on National Economy: Methodological Issues
No full textEconomic and social benefits of the economy due to port activities and associated logistics are assessed by methods like input-output (I/O) model, autoregressive distributed lag (ARDL) model, structural equation model (SEM), gravity Model, value addition, etc. However, considering limitations of each such method, and lack of access to relevant data at regional and national levels showing impacts of Ports only, the paper attempts to find impact of port performances on national economy by correlations and regression analysis with emphasis on major ports of India. Parametric tests covering narrow sub-class of possible cases have limitations to detect stationarity in time series data. Multiplier analysis assuming constant marginal propensity to consume (MPC) and no resource limitations may involve subjectivity to estimate direct, indirect and induced benefits. Economic impacts of ports by gross value addition are port specific and cannot be generalized. Multiple linear regression equations can better be fitted to the data to find empirical relationship of GDP with the chosen independent variables relating to performances of ports, logistics service providers and other service providers. Qualities of such regression equation need to be tested for linearity of error scores with zero mean and constant variance; significance of multiple correlation (R2) and relative importance of the selected independent variables. Proposed methods of rxy = 1 and R2 = C′T RXX−1 C′ = 1 may avoid the bad leverage points and correlation issues. It is recommended to go for robust multiple regression equation avoiding problems of bad leverage points and correlation issues
Machine learning algorithms on predicting the turbulent mixed convection flow in a driven-cavity with two horizontal cylinders
No full textTurbulent mixed convection flow and heat transfer properties in a driven cavity with two circular cylinders arranged one above another are analyzed numerically with the incorporation of a finite element scheme, based on the Galerkin method of weighted residuals. A comparison of streamlines, isotherms, and local, average Nusselt number is provided to illustrate how the Richardson number Ri, Reynolds number Re and the eddy viscosity ε affect the transport phenomena inside the cavity. The local and average Nusselt number have been evaluated and it is found that strong convection at the top wall causes the average Nusselt number to progressively rise with respect to Ri and ε, while steady or slightly varying profiles are seen with regard to Re. In order to predict the thermal distribution inside the cavity due to these hot cylinders, Artificial Neural Network (ANN) and Gaussian Process Regression (GPR) have been developed with these model parameters as input and average Nusselt Number as target values. Several plots have been depicted to come to a conclusion that both models have been trained very effectively with the minimal observed Mean Square Error (MSE) values of 0.0026018 and 0.0026428 for ANN and GPR, respectively. In support to these findings, the coefficient of determination R2 suggests that ANN (R2 = 0.89) outperforms GPR (R2 = 0.87) in testing accuracy, hence it is recommended for prediction task
Multimodal fusion for anticipating human decision performance
No full textAnticipating human decisions while performing complex tasks remains a formidable challenge. This study proposes a multimodal machine-learning approach that leverages image features and electroencephalography (EEG) data to predict human response correctness in a demanding visual searching task. Notably, we extract a novel set of image features pertaining to object relationships using the Segment Anything Model (SAM), which enhances prediction accuracy compared to traditional features. Additionally, our approach effectively utilizes a combination of EEG signals and image features to streamline the feature set required for the Random Forest Classifier (RFC) while maintaining high accuracy. The findings of this research hold substantial potential for developing advanced fault alert systems, particularly in critical decision-making environments such as the medical and defence sectors
On cumulative residual information generating function: properties, inference and applications
No full textWe consider a new information generating function introduced by Kharazmi and Balakrishnan (Commun Stat Theory Methods 52(15):5260–5273, 2023), called cumulative residual information generating (CRIG) function and study some new properties. Also we find that the CRIG function has a relationship with many popular measures like Gini’s mean difference, cumulative residual Tsallis entropy and cumulative residual extropy. We obtain numerous bounds for CRIG function and study characterization in terms of CRIG of first order statistic. We propose two non-parametric estimators of CRIG function and investigate their asymptotic properties. Based on one of the proposed estimators, a new test statistic for testing equality of two distribution functions is developed. Finally, CRIG function for mixed systems is analyzed and complexity of systems is studied
On horizontal immersions of discs in fat distributions of type (4, 6)
No full textIn this paper, we discuss horizontal immersions of discs in certain corank-2 fat distributions on 6-dimensional manifolds. The underlying real distribution of a holomorphic contact distribution on a complex 3 manifold belongs to this class. The main result presented here says that the associated nonlinear PDE is locally invertible. Using this we prove the existence of germs of embedded horizontal discs
On Mathai–Haubold Past Entropy Measure
No full textIn this paper, Mathai–Haubold past entropy measure is proposed and its properties are studied. Also some generalized inequalities related to Mathai–Haubold entropy measure are discussed. A Kernel based non-parametric estimator for the proposed measure is provided when the underlying sample follows ρ-mixing dependence condition. The consistency property and asymptotic normality of the proposed estimator are established. A simulation study is conducted to assess the performance of the estimator. A data set is analyzed for illustrative purposes
Oscillations of Fourier coefficients over the sparse set of integers
No full textLet f∈Sk(Γ0(N)) be a normalized Hecke eigenforms of integral weight k and level N≥1. In the article, we establish the asymptotics of power moment associated to the sequences {λf⊗f⊗f(Q(x̲))}Q∈SD,x̲∈Z2 and {λf⊗sym2f(Q(x̲))}Q∈SD,x̲∈Z2 where SD denotes the set of inequivalent primitive integral positive-definite binary quadratic forms (reduced forms) of fixed discriminant D\u3c0. As a consequence, we prove results concerning the behaviour of sign changes associated to these sequences
Reply on the comments on the paper “evidence of fluvial to marine transition in the siwalik rocks of the itanagar area, arunachal pradesh, india: Implication for the regional paleogeography” by mullick & sinha 2024, himalayan geology, 45(1), 138-154
No full textWe welcome the comments by Chakraborty et al. on our paper and acknowledge them for their great time and effort for reading our article so thoroughly and to provide their precious suggestions. Here, we reply to the doubts and queries raised by them for clarification, most of which possibly arise due to misinterpretation of our data. We hereby respond to the queries about the technical issues, facies, drainage system and sedimentological interpretation and in reply would definitely like to answer some of their logical queries in light of sedimentological overview and our field observations, keeping in mind not to substantiate the credibility of Indian sedimentologists in front of international researchers. We would like to address the comments in a pointwise manner to make the writing more straight-forward and to-the-point