Shiv Nadar University

About: Shiv Nadar University is a education organization based out in Dadri, Uttar Pradesh, India. It is known for research contribution in the topics: Population & Graphene. The organization has 1015 authors who have published 1924 publications receiving 18420 citations.

Solution of Linear and Non Linear Regression Problem by K Nearest Neighbour Approach: By Using Three Sigma Rule

Abstract: K Nearest Neighbor is one of the simplest method for classification as well as regression problem. That is the reason it is widely adopted. KNN is a supervised method that uses estimation based on values of neighbors. Though KNN came into existence in decade of 1990, it still demands improvements based on domain in which it is being used. Now the researchers have invented methods in which multiple techniques can be combined in some order such that advantages of each technique covers the disability of techniques being combined for example, KNN-Kernel based algorithms are being used for clustering. Though heavy applicability of KNN in classification problems, it is not that much used in function estimation problems. This paper is an attempt in using KNN as function estimation problem. The approach is made for linear as well as nonlinear regression problem. We have made an assumption that supervisor data given is reliable. We have considered here two dimensional data to illustrate the idea which is equally applicable to n-dimensional data for some large but finite n.

Exact distribution of spacing ratios for random and localized states in quantum chaotic systems

Abstract: Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra are modeled through an appropriate ensemble described by random matrix theory. However, a small subset of states violates this principle and displays eigenstate localization, a counterintuitive feature known to arise due to purely quantum or semiclassical effects. In the spectrum of chaotic systems, the localized and random states interact with one another and modify the spectral statistics. In this work, a 3×3 random matrix model is used to obtain exact results for the ratio of spacing between a generic and localized state. We consider time-reversal-invariant as well as noninvariant scenarios. These results agree with the spectra computed from realistic physical systems that display localized eigenmodes.