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.

Multi-fluid systems—Multi-Beltrami relaxed states and their implications

Abstract: We consider the non-dissipative multi-fluid equations, and demonstrate how multi-Beltrami equilibria emerge as natural relaxed states of the model, representing an evolution towards the minimum energy. General properties of these states are studied, and a wide class of solutions is obtained. We specialize to the cases of double and triple Beltrami states and highlight their connections with the appropriate physical invariants, viz., the generalized helicities and the energy. In particular, we demonstrate that different field configurations can give rise to distinct or identical values of the invariants, depending on the nature of the roots of the multi-Beltrami equation. Moreover, we also highlight equivalences between (outwardly) unconnected models allowing us to treat them in a unified manner. Some observations regarding the nature of the solutions for certain special cases of these models are presented. Potential applications for astrophysical plasmas are also highlighted.

Computing wide range of protein/peptide features from their sequence and structure

Abstract: Motivation In last three decades, a wide range of protein descriptors/features have been discovered to annotate a protein with high precision. A wide range of features have been integrated in numerous software packages (e.g., PROFEAT, PyBioMed, iFeature, protr, Rcpi, propy) to predict function of a protein. These features are not suitable to predict function of a protein at residue level such as prediction of ligand binding residues, DNA interacting residues, post translational modification etc. Results In order to facilitate scientific community, we have developed a software package that computes more than 50,000 features, important for predicting function of a protein and its residues. It has five major modules for computing; composition-based features, binary profiles, evolutionary information, structure-based features and patterns. The composition-based module allows user to compute; i) simple compositions like amino acid, dipeptide, tripeptide; ii) Properties based compositions; iii) Repeats and distribution of amino acids; iv) Shannon entropy to measure the low complexity regions; iv) Miscellaneous compositions like pseudo amino acid, autocorrelation, conjoint triad, quasi-sequence order. Binary profile of amino acid sequences provides complete information including order of residues or type of residues; specifically, suitable to predict function of a protein at residue level. Pfeature allows one to compute evolutionary information-based features in form of PSSM profile generated using PSIBLAST. Structure based module allows computing structure-based features, specifically suitable to annotate chemically modified peptides/proteins. Pfeature also allows generating overlapping patterns and feature from whole protein or its parts (e.g., N-terminal, C-terminal). In summary, Pfeature comprises of almost all features used till now, for predicting function of a protein/peptide including its residues. Availability It is available in form of a web server, named as Pfeature (https://webs.iiitd.edu.in/raghava/pfeature/), as well as python library and standalone package (https://github.com/raghavagps/Pfeature) suitable for Windows, Ubuntu, Fedora, MacOS and Centos based operating system.

Fully Dynamic Maximal Matching in $O(\log n)$ Update Time

Abstract: We present an algorithm for maintaining maximal matching in a graph under addition and deletion of edges. Our algorithm is randomized and it takes expected amortized $O(\log n)$ time for each edge update, where $n$ is the number of vertices in the graph. While there exists a trivial $O(n)$ time algorithm for each edge update, the previous best known result for this problem is due to Ivkovicź and Lloyd [Lecture Notes in Comput. Sci. 790, Springer-Verlag, London, 1994, pp. 99--111]. For a graph with $n$ vertices and $m$ edges, they gave an $O( {(n+ m)}^{0.7072})$ update time algorithm which is sublinear only for a sparse graph. For the related problem of maximum matching, Onak and Rubinfeld [Proceedings of STOC'10, Cambridge, MA, 2010, pp. 457--464] designed a randomized algorithm that achieves expected amortized $O(\log^2 n)$ time for each update for maintaining a $c$-approximate maximum matching for some unspecified large constant $c$. In contrast, we can maintain a factor 2 approximate maximum matching in expected amortized $O(\log n )$ time per update as a direct corollary of the maximal matching scheme. This in turn also implies a 2-approximate vertex cover maintenance scheme that takes expected amortized $O(\log n )$ time per update.