ISI Digital Commons (Indian Statistical Institute )
Not a member yet
7571 research outputs found
Sort by
Monitoring bivariate zero-inflated Poisson processes: an alternative to copula-based bivariate attribute control chart
No full textOccurrences of two (or more) types of defects are not uncommon in high quality (or zero-inflated) processes. Bivariate (or multivariate) attribute control charts are required to be developed for monitoring such processes. Fatahi et al. (2012) introduced the idea of applying copula function to derive joint distribution of two correlated zero-inflated Poisson distributions, which can be used to develop bivariate attribute control chart (BACC) for monitoring bivariate zero-inflated Poisson (BZIP) processes. However, the copula-based model often fails to represent bivariate zero-inflated data, which we come across in real-life situations. Li et al. (1999) model for BZIP distribution is quite flexible. Thus, it can overcome the limitations of Fatahi et al. (2012) model. In this paper, BACC is developed based on Li et al. (1999) model. The performances of the proposed BACC, in terms of in-control and out-of-control average run lengths, are evaluated extensively using simulations. The results show that the proposed BACC are well capable of detecting shifts in the parameters of a BZIP process. Further, two case studies on BZIP process data obtained by past researchers reveal that the BACC developed based on Li et al. (1999) model is more effective than the BACC developed based on copula-based model
Monogenity of iterates of irreducible binomials
No full textOne of the oldest problems of algebraic number theory is to find a method to determine if the ring of integers of a number field K is (Formula presented.) for some (Formula presented.); a field for which the answer to this question is affirmative is referred to as a monogenic field. Suppose (Formula presented.) is a monic irreducible polynomial and (Formula presented.) is a root of (Formula presented.), the n-fold composition of f. In this article, we prove a necessary and sufficient condition for (Formula presented.) to be monogenic for every (Formula presented.) and (Formula presented.)
More on Scarf\u27s Complementarity Problem and its Error Bounds
No full textIn this paper, we revisit Scarf\u27s complementarity problem involving a rectangular matrix, known as the vertical block matrix introduced by [Cottle, RW and GB Dantzig (1970). A generalization of the linear complementarity problem. Journal of Combinatorial Theory, 8, 79-90]. We prove that the problem has a unique solution if the underlying matrix is a vertical block P-matrix. Some results on the error bounds for the vertical block P- and R0-matrices are derived. This further extends the results on global error bounds obtained by [Mathias, R and JS Pang (1990). Error bounds for the linear complementarity problem with a P-matrix. Linear Algebra and its Applications, 132, 123-136] and [Mangasarian, OL and J Ren (1994). New improved error bounds for the linear complementarity problem. Mathematical Programming, 66, 241-255]
Multi-scale morphology-aided deep medical image segmentation
No full textMedical image segmentation serves as a critical tool for healthcare professionals, enabling the precise extraction of Regions of Interest (ROIs) from clinical images at the pixel level. The evolution of computer vision and machine learning algorithms has streamlined this labor-intensive segmentation process, which traditionally necessitates domain expertise. The intrinsic challenges posed by clinical images — such as irregular shapes, varying sizes, low contrast, and intricate details within specific areas, contribute to the intricacy of the task. In response to these complexities, we propose a solution involving three modules grounded in morphological operations: the Multi-scale Morphological Closing Module, the Multi-scale Morphological Opening Module, and the Multi-scale Morphological Gradient Module. In contrast to conventional morphological operations, our approach involves learning structuring elements through a training process, enabling effective adaptation to the irregular shapes of ROIs. To cater to the diverse range of ROI sizes in clinical images, we introduce the concept of dilation rates within the structural elements of morphological operations. Our proposal extends to Morph-UNet, a lightweight framework for medical image segmentation. This architecture integrates proposed modules with UNet, presenting a tight-coupled synergy between deep neural networks and multi-scale morphological operations. Efficacy is substantiated across diverse medical imaging datasets, spanning modalities, conditions, and ROI proportions. Extensive experimentation validated through widely recognized segmentation metrics underscores our model\u27s superiority compared to fifteen state-of-the-art segmentation methods and baseline models
Natural-neighborhood based, label-specific undersampling for imbalanced, multi-label data
No full textThis work presents a novel undersampling scheme to tackle the imbalance problem in multi-label datasets. We use the principles of the natural nearest neighborhood and follow a paradigm of label-specific undersampling. Natural-nearest neighborhood is a parameter-free principle. Our scheme’s novelty lies in exploring the parameter-optimization-free natural nearest neighborhood principles. The class imbalance problem is particularly challenging in a multi-label context, as the imbalance ratio and the majority–minority distributions vary from label to label. Consequently, the majority–minority class overlaps also vary across the labels. Working on this aspect, we propose a framework where a single natural neighbor search is sufficient to identify all the label-specific overlaps. Natural neighbor information is also used to find the key lattices of the majority class (which we do not undersample). The performance of the proposed method, NaNUML, indicates its ability to mitigate the class-imbalance issue in multi-label datasets to a considerable extent. We could also establish a statistically superior performance over other competing methods several times. An empirical study involving twelve real-world multi-label datasets, seven competing methods, and four evaluating metrics—shows that the proposed method effectively handles the class-imbalance issue in multi-label datasets. In this work, we have presented a novel label-specific undersampling scheme, NaNUML, for multi-label datasets. NaNUML is based on the parameter-free natural neighbor search and the key factor, neighborhood size ‘k’ is determined without invoking any parameter optimization
nhanesA: achieving transparency and reproducibility in NHANES research
No full textThe National Health and Nutrition Examination Survey provides comprehensive data on demographics, sociology, health and nutrition. Conducted in 2-year cycles since 1999, most of its data are publicly accessible, making it pivotal for research areas like studying social determinants of health or tracking trends in health metrics such as obesity or diabetes. Assembling the data and analyzing it presents a number of technical and analytic challenges. This paper introduces the nhanesA R package, which is designed to assist researchers in data retrieval and analysis and to enable the sharing and extension of prior research efforts. We believe that fostering community-driven activity in data reproducibility and sharing of analytic methods will greatly benefit the scientific community and propel scientific advancements. Database URL: https://github.com/cjendres1/nhanes
On rigidity of Pham-Brieskorn surfaces
No full textIt is well known that, over an algebraically closed field k of characteristic zero, for any three integers a,b,c≥2, any Pham-Brieskorn surface B(a,b,c):=k[X,Y,Z]/(Xa+Yb+Zc) is rigid when at most one of a,b,c is 2 and stably rigid when [Formula presented]. In this paper we consider Pham-Brieskorn domains over an arbitrary field k of characteristic p≥0 and give sufficient conditions on (a,b,c) for which any Pham-Brieskorn domain B(a,b,c) is rigid. This gives an alternative approach to showing that there does not exist any non-trivial exponential map on k[X,Y,Z,T]/(XmY+Tprq+Zpe)=k[x,y,z,t], for m,q\u3e1, p∤mq and e\u3er≥1, fixing y, a crucial result used in [10] to show that the Zariski Cancellation Problem (ZCP) does not hold for the affine 3-space in positive characteristic. We also provide a sufficient condition for B(a,b,c) to be stably rigid. Along the way we prove that for integers a,b,c≥2 with gcd(a,b,c)=1 and for F(Y)∈k[Y], the ring k[X,Y,Z]/(XaYb+Zc+F(Y)) is a rigid domain
ON THE MÖBIUS INVARIANT PRINCIPAL FUNCTIONS OF PINCUS
No full textIn this semi-expository short note, we prove that the only homogeneous pure hyponormal operator T with rank(T∗T − TT∗) = 1, modulo unitary equivalence, is the unilateral shift
Optimal diagnosis interval for online quality control methods
No full textOnline quality control methods emphasize manufacturing processes to attain maximum conformance with respect to the specifications of the concerned quality characteristics of a product. One key factor that affects the effectiveness of these methods is the diagnosis interval. In this paper, the existing cost model along with its cost components for online quality control methods has been revisited and modified by incorporating new variables like the rate of production, the loss due to false alarm, the loss due to non-detection of process abnormalities, and considering a workable break-up of diagnosis cost for finding the optimal diagnosis interval from the perspective of present-day manufacturing engineering. As already mentioned, the proposed cost model has not ignored the loss due to the generation of defective items as well as the adjustment cost available in the pertinent literature. The modified cost function thus proposed has been appropriately minimized to obtain the corresponding optimal diagnosis interval. The proposed methodology has been compared numerically with other methodologies to establish its effectiveness. The cornerstone of the proposed methodology lies in reinforcing its effectiveness through a real-life case example in manufacturing. Sensitivity analysis has also been carried out for the real-life case example to fortify the proposed methodology
Orderings of extremes among dependent extended Weibull random variables
No full textIn this work, we consider two sets of dependent variables {X1, ..., Xn} and {Y1, ..., Yn}, where Xi ∼ EW(αi, λi, ki) and Yi ∼ EW(βi, μi, li), for i = 1, ..., n, which are coupled by Archimedean copulas having different generators. We then establish different inequalities between two extremes, namely, X1:n and Y1:n and Xn:n and Yn:n, in terms of the usual stochastic, star, Lorenz, hazard rate, reversed hazard rate and dispersive orders. Several examples and counterexamples are presented for illustrating all the results established here. Some of the results here extend the existing results of [5] (Barmalzan, G., Ayat, S.M., Balakrishnan, N., & Roozegar, R. (2020). Stochastic comparisons of series and parallel systems with dependent heterogeneous extended exponential components under Archimedean copula. Journal of Computational and Applied Mathematics 380: Article No. 112965)