The defect sequence for contractive tuples

We introduce the defect sequence for a contractive tuple of Hilbert space operators and investigate its properties. The defect sequence is a sequence of numbers, called defect dimensions associated with a contractive tuple. We show that there are upper bounds for the defect dimensions. The tuples for which these upper bounds are obtained, are called maximal contractive tuples. The upper bounds are different in the non-commutative and in the commutative case. We show that the creation operators on the full Fock space and the coordinate multipliers on the Drury-Arveson space are maximal. We also study pure tuples and see how the defect dimensions play a role in their irreducibility. (C) 2012 Elsevier Inc. All rights reserved.

NUcache: an efficient multicore cache organization based on next-use distance

The effectiveness of the last-level shared cache is crucial to the performance of a multi-core system. In this paper, we observe and make use of the DelinquentPC - Next-Use characteristic to improve shared cache performance. We propose a new PC-centric cache organization, NUcache, for the shared last level cache of multi-cores. NUcache logically partitions the associative ways of a cache set into MainWays and DeliWays. While all lines have access to the MainWays, only lines brought in by a subset of delinquent PCs, selected by a PC selection mechanism, are allowed to enter the DeliWays. The PC selection mechanism is an intelligent cost-benefit analysis based algorithm that utilizes Next-Use information to select the set of PCs that can maximize the hits experienced in DeliWays. Performance evaluation reveals that NUcache improves the performance over a baseline design by 9.6%, 30% and 33% respectively for dual, quad and eight core workloads comprised of SPEC benchmarks. We also show that NUcache is more effective than other well-known cache-partitioning algorithms.

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

Sex and physiological state influence the rate of resource acquisition and monopolisation in urban free-ranging dogs, Canis familiaris

In animal populations, the constraints of energy and time can cause intraspecific variation in foraging behaviour. The proximate developmental mediators of such variation are often the mechanisms underlying perception and associative learning. Here, experience-dependent changes in foraging behaviour and their consequences were investigated in an urban population of free-ranging dogs, Canis familiaris by continually challenging them with the task of food extraction from specially crafted packets. Typically, males and pregnant/lactating (PL) females extracted food using the sophisticated `gap widening' technique, whereas non-pregnant/non-lactating (NPNL) females, the relatively underdeveloped `rip opening' technique. In contrast to most males and PL females (and a few NPNL females) that repeatedly used the gap widening technique and improved their performance in food extraction with experience, most NPNL females (and a few males and PL females) non-preferentially used the two extraction techniques and did not improve over successive trials. Furthermore, the ability of dogs to sophisticatedly extract food was positively related to their ability to improve their performance with experience. Collectively, these findings demonstrate that factors such as sex and physiological state can cause differences among individuals in the likelihood of learning new information and hence, in the rate of resource acquisition and monopolization.

On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

Quantum entropic ambiguities: Ethylene

In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are, in general, different. Therefore, one reaches the remarkable possibility that there may be many entropies for a given state R. Sorkin (private communication)]. This ambiguity in entropy can often be traced to a gauge symmetry emergent from the nontrivial topological character of the configuration space of the underlying system. It can also happen in finite-dimensional matrix models. In the present work, we discuss this entropy ambiguity and its consequences for an ethylene molecule. This is a very simple and well-known system, where these notions can be put to tests. Of particular interest in this discussion is the fact that the change of the density matrix with the corresponding entropy increase drives the system towards the maximally disordered state with maximum entropy, where Boltzman's formula applies. Besides its intrinsic conceptual interest, the simplicity of this model can serve as an introduction to a similar discussion of systems such as colored monopoles and the breaking of color symmetry.

Characterization of Birkhoff-James orthogonality

The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We investigate this notion of orthogonality when the Banach space has more structures. We start by doing so for the Banach space of square matrices moving gradually to all bounded operators on any Hilbert space, then to an arbitrary C*-algebra and finally a Hilbert C*-module.

Black holes in higher spin supergravity

We study black hole solutions in Chern-Simons higher spin supergravity based on the superalgebra sl(3 vertical bar 2). These black hole solutions have a U(1) gauge field and a spin 2 hair in addition to the spin 3 hair. These additional fields correspond to the R-symmetry charges of the supergroup sl(3 vertical bar 2). Using the relation between the bulk field equations and the Ward identities of a CFT with N = 2 super-W-3 symmetry, we identify the bulk charges and chemical potentials with those of the boundary CFT. From these identifications we see that a suitable set of variables to study this black hole is in terms of the charges present in three decoupled bosonic sub-algebras of the N = 2 super-W-3 algebra. The entropy and the partition function of these R-charged black holes are then evaluated in terms of the charges of the bulk theory as well as in terms of its chemical potentials. We then compute the partition function in the dual CFT and find exact agreement with the bulk partition function.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

On the unramified principal series of GL(3) over non-archimedean local fields

Let F be a non-archimedean local field and let O be its ring of integers. We give a complete description of the irreducible constituents of the restriction of the unramified principal series representations of GL(3)(F) to GL(3)(O). (C) 2013 Elsevier Inc. All rights reserved.

Production of syngas from steam reforming and CO removal with water gas shift reaction over nanosized Zr0.95Ru0.05O2-delta solid solution

This study presents the synthesis, characterization, and kinetics of steam reforming of methane and water gas shift (WGS) reactions over highly active and coke resistant Zr0.93Ru0.05O2-delta. The catalyst showed high activity at low temperatures for both the reactions. For WGS reaction, 99% conversion of CO with 100% H-2 selectivity was observed below 290 degrees C. The detailed kinetic studies including influence of gas phase product species, effect of temperature and catalyst loading on the reaction rates have been investigated. For the reforming reaction, the rate of reaction is first order in CH4 concentration and independent of CO and H2O concentration. This indicates that the adsorptive dissociation of CH4 is the rate determining step. The catalyst also showed excellent coke resistance even under a stoichiometric steam/carbon ratio. A lack of CO methanation activity is an important finding of present study and this is attributed to the ionic nature of Ru species. The associative mechanism involving the surface formate as an intermediate was used to correlate experimental data. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

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).

Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

STOPPING THE CCR FLOW AND ITS ISOMETRIC COCYCLES

It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e. left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.