Institute of Mathematical Sciences, Chennai

About: Institute of Mathematical Sciences, Chennai is a facility organization based out in Chennai, India. It is known for research contribution in the topics: Parameterized complexity & Vertex cover. The organization has 478 authors who have published 1447 publications receiving 26046 citations. The organization is also known as: IMSc & Matscience.

Softly broken A(4) symmetry for nearly degenerate neutrino masses

Abstract: The leptonic Higgs doublet model of neutrino masses is implemented with an ${A}_{4}$ discrete symmetry (the even permutation of four objects or equivalently the symmetry of the tetrahedron) which has four irreducible representations: $\underset{\ifmmode\bar\else\textasciimacron\fi{}}{1},{\underset{\ifmmode\bar\else\textasciimacron\fi{}}{1}}^{\ensuremath{'}},{\underset{\ifmmode\bar\else\textasciimacron\fi{}}{1}}^{\ensuremath{''}},$ and $\underset{\ifmmode\bar\else\textasciimacron\fi{}}{3}.$ The resulting spontaneous and soft breaking of ${A}_{4}$ provides a realistic model of charged-lepton masses as well as a nearly degenerate neutrino mass matrix. The phenomenological consequences at and below the TeV scale are discussed.

Logarithmic correction to the bekenstein-hawking entropy

Abstract: The exact formula derived by us earlier for the entropy of a four dimensional nonrotating black hole within the quantum geometry formulation of the event horizon in terms of boundary states of a three dimensional Chern-Simons theory is reexamined for large horizon areas. In addition to the semiclassical Bekenstein-Hawking contribution proportional to the area obtained earlier, we find a contribution proportional to the logarithm of the area together with subleading corrections that constitute a series in inverse powers of the area.

Succinct indexable dictionaries with applications to encoding k-ary trees and multisets

Abstract: We consider the indexable dictionary problem which consists in storing a set S ⊆ {0,…, m - 1} for some integer m, while supporting the operations of rank(x), which returns the number of elements in S that are less than x if x e S, and -1 otherwise; and select(i) which returns the i-th smallest element in S.We give a structure that supports both operations in O(1) time on the RAM model and requires B(n,m) + o(n) + O(lg lg m) bits to store a set of size n, where B(n,m) = ⌈lg (nm)⌉ is the minimum number of bits required to store any n-element subset from a universe of size m. Previous dictionaries taking this space only supported (yes/no) membership queries in O(1) time. In the cell probe model we can remove the O(lg lg m) additive term in the space bound, answering a question raised by Fich and Miltersen, and Pagh.We also present two applications of our dictionary structure:• An information-theoretically optimal representation for k-ary cardinal trees (aka k-ary tries). Our structure uses C(n,k) + o(n + lg k) bits to store a k-ary tree with n nodes and can support parent, i-th child, child labeled i, and the degree of a node in constant time, where C(n,k) is the minimum number of bits to store any n-node k-ary tree. Previous space efficient representations for cardinal k-ary trees required C(n,k) + Ω(n) bits.• An optimal representation for multisets where (appropriate generalisations of) the select and rank operations can be supported in O(1) time. Our structure uses B(n, m + n) + o(n) + O(lg lg m) bits to represent a multiset of size n from an m element set; the first term is the minimum number of bits required to represent such a multiset.

The Planar k-Means Problem is NP-Hard

Abstract: In the k-means problem, we are given a finite set S of points in $\Re^m$, and integer k ≥ 1, and we want to find k points (centers) so as to minimize the sum of the square of the Euclidean distance of each point in S to its nearest center. We show that this well-known problem is NP-hard even for instances in the plane, answering an open question posed by Dasgupta [6].

General logarithmic corrections to black-hole entropy

Abstract: We compute leading-order corrections to the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form −k ln(Area). For BTZ black holes, k = 3/2, as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner–Nordstrom black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black-hole entropy and its corrections.