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In this work, we have introduced two innovative quantum algorithms: the Direct Column Algorithm and the Quantum Backtracking Algorithm to solve N-Queens problem, which involves the arrangement of $N$ queens on an $N \times N$ chessboard such that they are not under attack from each other on the same row, column and diagonal. These algorithms utilizes Controlled W-states and dynamic circuits, to efficiently address this NP-Complete computational problem. The Direct Column Algorithm strategically reduces the search space, simplifying the solution process, even with exponential circuit complexity as the problem size grows, while Quantum Backtracking Algorithm emulates classical backtracking techniques within a quantum framework which allows the possibility of solving complex problems like satellite communication, routing and VLSI testing., Comment: Accepted in Conference on COMSNETS 2024

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter $\alpha$) simultaneously, in contrast to conventional profile-likelihood technique of estimating $\alpha$. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study., Comment: 20 pages

We propose a hybrid quantum approach to threshold and binarize a grayscale image through unsharp measurements (UM) relying on image histogram. Generally, the histograms are characterized by multiple overlapping normal distributions corresponding to objects, or image features with small but significant overlaps, making it challenging to establish suitable thresholds. The proposed methodology uses peaks of the overlapping Gaussians and the distance between neighboring local minima as the variance, based on which the UM parameters are chosen, that maps the normal distribution into a localized delta function. To demonstrate its efficacy, subsequent implementation is done on noisy quantum environments in Qiskit. This process is iteratively repeated for a multimodal histogram to obtain more thresholds, which are then applied to various life-like pictures to get high-contrast images, resulting in comparable peak signal-to-noise ratio and structural similarity index measure values. The obtained thresholds are used to binarize a grayscale image by using novel enhanced quantum image representation integrated with a threshold encoder and an efficient quantum comparator (QC) that depicts the whole binarized picture. This approach significantly reduces the complexity of the proposed QC and of the whole algorithm when compared to earlier models.

In survival analysis, cure models have gained much importance due to rapid advancements in medical sciences. More recently, a subset of cure models, called destructive cure models, have been studied extensively under competing risks scenario wherein initial competing risks undergo a destructive process, such as under a chemotherapy. In this article, we study destructive cure models by assuming a flexible weighted Poisson distribution (exponentially weighted Poisson, length biased Poisson and negative binomial distributions) for the initial number of competing causes and with lifetimes of the susceptible individuals following proportional hazards. The expectation-maximization (EM) algorithm and profile likelihood approach are made use of for estimating the model parameters. An extensive simulation study is carried out under various parameter settings to examine the properties of the models, and the accuracy and robustness of the proposed estimation technique. Effects of model misspecification on the parameter estimates are also discussed in detail. Finally, for the illustration of the proposed methodology, a real-life cutaneous melanoma data set is analyzed.

The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a logistic function. This readily implies that the boundary classifying the cured and uncured subjects is linear. In this paper, we propose a new mixture cure rate model based on interval censored data that uses the support vector machine (SVM) to model the effect of covariates on the uncured or the cured probability (i.e., on the incidence part of the model). Our proposed model inherits the features of the SVM and provides flexibility to capture classification boundaries that are non-linear and more complex. Furthermore, the new model can be used to model the effect of covariates on the incidence part when the dimension of covariates is high. The latency part is modeled by a proportional hazards structure. We develop an estimation procedure based on the expectation maximization (EM) algorithm to estimate the cured/uncured probability and the latency model parameters. Our simulation study results show that the proposed model performs better in capturing complex classification boundaries when compared to the existing logistic regression based mixture cure rate model. We also show that our model's ability to capture complex classification boundaries improve the estimation results corresponding to the latency parameters. For illustrative purpose, we present our analysis by applying the proposed methodology to an interval censored data on smoking cessation.

Handling missing values plays an important role in the analysis of survival data, especially, the ones marked by cure fraction. In this paper, we discuss the properties and implementation of stochastic approximations to the expectation-maximization (EM) algorithm to obtain maximum likelihood (ML) type estimates in situations where missing data arise naturally due to right censoring and a proportion of individuals are immune to the event of interest. A flexible family of three parameter exponentiated-Weibull (EW) distributions is assumed to characterize lifetimes of the non-immune individuals as it accommodates both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub) hazard functions. To evaluate the performance of the SEM algorithm, an extensive simulation study is carried out under various parameter settings. Using likelihood ratio test we also carry out model discrimination within the EW family of distributions. Furthermore, we study the robustness of the SEM algorithm with respect to outliers and algorithm starting values. Few scenarios where stochastic EM (SEM) algorithm outperforms the well-studied EM algorithm are also examined in the given context. For further demonstration, a real survival data on cutaneous melanoma is analyzed using the proposed cure rate model with EW lifetime distribution and the proposed estimation technique. Through this data, we illustrate the applicability of the likelihood ratio test towards rejecting several well-known lifetime distributions that are nested within the wider class of EW distributions., Comment: 33 pages