Entanglement entropy from the holographic stress tensor

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the timetime component of the Brown-York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean actionmethods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription.

ENTANGLEMENT ENTROPY FROM SURFACE TERMS IN GENERAL RELATIVITY

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados-Teitelboim-Zanelli (BTZ) black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

On generalized gravitational entropy, squashed cones and holography

We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.

3D flat holography: entropy and logarithmic corrections

We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS(3). The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes.

Generative Maximum Entropy Learning for Multiclass Classification

Maximum entropy approach to classification is very well studied in applied statistics and machine learning and almost all the methods that exists in literature are discriminative in nature. In this paper, we introduce a maximum entropy classification method with feature selection for large dimensional data such as text datasets that is generative in nature. To tackle the curse of dimensionality of large data sets, we employ conditional independence assumption (Naive Bayes) and we perform feature selection simultaneously, by enforcing a `maximum discrimination' between estimated class conditional densities. For two class problems, in the proposed method, we use Jeffreys (J) divergence to discriminate the class conditional densities. To extend our method to the multi-class case, we propose a completely new approach by considering a multi-distribution divergence: we replace Jeffreys divergence by Jensen-Shannon (JS) divergence to discriminate conditional densities of multiple classes. In order to reduce computational complexity, we employ a modified Jensen-Shannon divergence (JS(GM)), based on AM-GM inequality. We show that the resulting divergence is a natural generalization of Jeffreys divergence to a multiple distributions case. As far as the theoretical justifications are concerned we show that when one intends to select the best features in a generative maximum entropy approach, maximum discrimination using J-divergence emerges naturally in binary classification. Performance and comparative study of the proposed algorithms have been demonstrated on large dimensional text and gene expression datasets that show our methods scale up very well with large dimensional datasets.

Higher spin entanglement entropy from CFT

We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential mu for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in mu in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated to the spin-three black hole in SL(3, R) x SL(3, R) Chern-Simons theory. Our result suggests that the order mu(2) correction to the entanglement entropy may be universal for W-algebra CFTs with spin-three chemical potential, and constitutes a check of the holographic entanglement entropy proposal for higher spin theories of gravity in AdS(3).

Parallel Flow-Sensitive Pointer Analysis by Graph-Rewriting

Precise pointer analysis is a problem of interest to both the compiler and the program verification community. Flow-sensitivity is an important dimension of pointer analysis that affects the precision of the final result computed. Scaling flow-sensitive pointer analysis to millions of lines of code is a major challenge. Recently, staged flow-sensitive pointer analysis has been proposed, which exploits a sparse representation of program code created by staged analysis. In this paper we formulate the staged flow-sensitive pointer analysis as a graph-rewriting problem. Graph-rewriting has already been used for flow-insensitive analysis. However, formulating flow-sensitive pointer analysis as a graph-rewriting problem adds additional challenges due to the nature of flow-sensitivity. We implement our parallel algorithm using Intel Threading Building Blocks and demonstrate considerable scaling (upto 2.6x) for 8 threads on a set of 10 benchmarks. Compared to the sequential implementation of staged flow-sensitive analysis, a single threaded execution of our implementation performs better in 8 of the benchmarks.

Hot deformation behaviour and microstructure control in AlCrCuNiFeCo high entropy alloy

An AlCrCuNiFeCo high entropy alloy (HEA), which has simple face centered cubic (FCC) and body centered cubic (BCC) solid solution phases as the microstructural constituents, was processed and its high temperature deformation behaviour was examined as a function of temperature (700-1030 degrees C) and strain rate (10(-3)-10(-1) s(-1)), so as to identify the optimum thermo-mechanical processing (TMP) conditions for hot working of this alloy. For this purpose, power dissipation efficiency and deformation instability maps utilizing that the dynamic materials model pioneered by Prasad and co-workers have been generated and examined. Various deformation mechanisms, which operate in different temperature-strain rate regimes, were identified with the aid of the maps and complementary microstructural analysis of the deformed specimens. Results indicate two distinct deformation domains within the range of experimental conditions examined, with the combination of 1000 degrees C/10(-3) s(-1) and 1030 degrees C/10(-2) s(-1) being the optimum for hot working. Flow instabilities associated with adiabatic shear banding, or localized plastic flow, and or cracking were found for 700-730 degrees C/10(-3)-10(-1) s(-1) and 750-860 degrees C/10(-1.4)-10(-1) s(-1) combinations. A constitutive equation that describes the flow stress of AlCrCuNiFeCo alloy as a function of strain rate and deformation temperature was also determined. (C) 2014 Elsevier Ltd. All rights reserved.

REPRESENTING A CUBIC GRAPH AS THE INTERSECTION GRAPH OF AXIS-PARALLEL BOXES IN THREE DIMENSIONS

We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if their corresponding vertices are adjacent. In fact, we construct a representation in which any two intersecting boxes touch just at their boundaries.

Hall viscosity to entropy ratio in higher derivative theories

In this paper based on the basic principles of gauge/gravity duality we compute the hall viscosity to entropy ratio in the presence of various higher derivative corrections to the dual gravitational description embedded in an asymptotically AdS(4) space time. As the first step of our analysis, considering the back reaction we impose higher derivative corrections to the abelian gauge sector of the theory where we notice that the ratio indeed gets corrected at the leading order in the coupling. Considering the probe limit as a special case we compute this leading order correction over the fixed background of the charged black brane solution. Finally we consider higher derivative (R-2) correction to the gravity sector of the theory where we notice that the above ratio might get corrected at the sixth derivative level.

Temperature-Induced Reversible First-Order Single Crystal to Single Crystal Phase Transition in Boc-gamma(4)(R)Val-Val-OH: Interplay of Enthalpy and Entropy

Crystals of Boc-gamma y(4)(R)Val-Val-OH undergo a reversible first-order single crystal to single crystal phase transition at T-c approximate to 205 K from the orthorhombic space group P22(1)2(1) (Z' = 1) to the monoclinic space group P2(1) (Z' = 2) with a hysteresis of similar to 2.1 K. The low-temperature monoclinic form is best described as a nonmerohedral twin with similar to 50% contributions from its two components. The thermal behavior of the dipeptide crystals was characterized by differential scanning calorimetry experiments. Visual changes in birefringence of the sample during heating and cooling cycles on a hot-stage microscope with polarized light supported the phase transition. Variable-temperature unit cell check measurements from 300 to 100 K showed discontinuity in the volume and cell parameters near the transition temperature, supporting the first-order behavior. A detailed comparison of the room-temperature orthorhombic form with the low-temperature (100 K) monoclinic form revealed that the strong hydrogen-bonding motif is retained in both crystal systems, whereas the non-covalent interactions involving side chains of the dipeptide differ significantly, leading to a small change in molecular conformation in the monoclinic form as well as a small reorientation of the molecules along the ac plane. A rigid-body thermal motion analysis (translation, libration, screw; correlation of translation and libration) was performed to study the crystal entropy. The reversible nature of the phase transition is probably the result of an interplay between enthalpy and entropy: the low-temperature monoclinic form is enthalpically favored, whereas the room-temperature orthorhombic form is entropically favored.

BELIEF PROPAGATION FOR OPTIMAL EDGE COVER IN THE RANDOM COMPLETE GRAPH

We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (2) limit of the random assignment problem. A proof via the objective method is useful because it provides us with more information on the nature of the edge's incident on a typical root in the minimum-cost edge cover. We further show that a belief propagation algorithm converges asymptotically to the optimal solution. This can be applied in a computational linguistics problem of semantic projection. The belief propagation algorithm yields a near optimal solution with lesser complexity than the known best algorithms designed for optimality in worst-case settings.

Rainbow Connection Number of Graph Power and Graph Products

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely the Cartesian product, the lexicographic product and the strong product) and the operation of taking the power of a graph. In this direction, we show that if G is a graph obtained by applying any of the operations mentioned above on non-trivial graphs, then rc(G) a parts per thousand currency sign 2r(G) + c, where r(G) denotes the radius of G and . In general the rainbow connection number of a bridgeless graph can be as high as the square of its radius 1]. This is an attempt to identify some graph classes which have rainbow connection number very close to the obvious lower bound of diameter (and thus the radius). The bounds reported are tight up to additive constants. The proofs are constructive and hence yield polynomial time -factor approximation algorithms.

On entanglement entropy functionals in higher-derivative gravity theories

In arXiv:1310.5713 1] and arXiv:1310.6659 2] a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926 3]. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the R-2 case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

Logarithmic corrections to extremal black hole entropy in N=2, 4 and 8 supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter-BPS black holes in N = 4 supergravity and one-eighth BPS black holes in N = 8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half-BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of sl (2, R), a result which is of possible mathematical interest.