Landscape statistics of the p-spin Ising model

The statistical properties of the local optima (metastable states) of the infinite range Ising spin glass with p-spin interactions in the presence of an external magnetic field h are investigated analytically. The average number of optima as well as the typical overlap between pairs of identical optima are calculated for general p. Similarly to the thermodynamic order parameter, for p>2 and small h the typical overlap q_t is a discontinuous function of the energy. The size of the jump in q_t increases with p and decreases with h, vanishing at finite values of the magnetic field.Comment: 12 pages,te

Teleportation, Braid Group and Temperley--Lieb Algebra

We explore algebraic and topological structures underlying the quantum teleportation phenomena by applying the braid group and Temperley--Lieb algebra. We realize the braid teleportation configuration, teleportation swapping and virtual braid representation in the standard description of the teleportation. We devise diagrammatic rules for quantum circuits involving maximally entangled states and apply them to three sorts of descriptions of the teleportation: the transfer operator, quantum measurements and characteristic equations, and further propose the Temperley--Lieb algebra under local unitary transformations to be a mathematical structure underlying the teleportation. We compare our diagrammatical approach with two known recipes to the quantum information flow: the teleportation topology and strongly compact closed category, in order to explain our diagrammatic rules to be a natural diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version of the preprint, quant-ph/0601050, which includes details of calculation, more topics such as topological diagrammatical operations and entanglement swapping, and calls the Temperley--Lieb category for the collection of all the Temperley--Lieb algebra with physical operations like local unitary transformation

Evaporation of a packet of quantized vorticity

A recent experiment has confirmed the existence of quantized turbulence in superfluid He3-B and suggested that turbulence is inhomogenous and spreads away from the region around the vibrating wire where it is created. To interpret the experiment we study numerically the diffusion of a packet of quantized vortex lines which is initially confined inside a small region of space. We find that reconnections fragment the packet into a gas of small vortex loops which fly away. We determine the time scale of the process and find that it is in order of magnitude agreement with the experiment.Comment: figure 1a,b,c and d, figure2, figure

Properties of Galactic Outflows: Measurements of the Feedback from Star Formation

Properties of starburst-driven outflows in dwarf galaxies are compared to those in more massive galaxies. Over a factor of roughly 10 in galactic rotation speed, supershells are shown to lift warm ionized gas out of the disk at rates up to several times the star formation rate. The amount of mass escaping the galactic potential, in contrast to the disk, does depend on the galactic mass. The temperature of the hottest extended \x emission shows little variation around $\sim 10^{6.7}$ K, and this gas has enough energy to escape from the galaxies with rotation speed less than approximately 130 km/s.Comment: 11 pages + 3 figues. Accepted for publication in the Astrophysical Journa

Differential Cross Sections for Higgs Production

We review recent theoretical progress in evaluating higher order QCD corrections to Higgs boson differential distributions at hadron-hadron colliders

Spacetime Embedding Diagrams for Black Holes

We show that the 1+1 dimensional reduction (i.e., the radial plane) of the Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how features of this spacetime can be seen from the embedding diagram. The purpose of this work is educational: The associated embedding diagrams may be useful for explaining aspects of black holes to students who are familiar with special relativity, but not general relativity.Comment: 22 pages, 21 figures, RevTex. To be submitted to the American Journal of Physics. Experts will wish only to skim appendix A and to look at the pictures. Suggested Maple code is now compatible with MapleV4r

On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants

It is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of +/-J Ising spin glasses a particular instance of certain simple sums known as quadratically signed weight enumerators (QWGTs). On the other hand it is known that quantum computing is polynomially equivalent to classical probabilistic computing with an oracle for estimating QWGTs. This suggests a connection between the partition function estimation problem for spin glasses and quantum computation. This connection extends to knots and graph theory via the equivalence of the Kauffman polynomial and the partition function for the Potts model.Comment: 8 pages, incl. 2 figures. v2: Substantially rewritte

Analysis of multiply spliced transcripts in lymphoid tissue reservoirs of rhesus macaques infected with RT-SHIV during HAART.

Highly active antiretroviral therapy (HAART) can reduce levels of human immunodeficiency virus type 1 (HIV-1) to undetectable levels in infected individuals, but the virus is not eradicated. The mechanisms of viral persistence during HAART are poorly defined, but some reservoirs have been identified, such as latently infected resting memory CD4⁺ T cells. During latency, in addition to blocks at the initiation and elongation steps of viral transcription, there is a block in the export of viral RNA (vRNA), leading to the accumulation of multiply-spliced transcripts in the nucleus. Two of the genes encoded by the multiply-spliced transcripts are Tat and Rev, which are essential early in the viral replication cycle and might indicate the state of infection in a given population of cells. Here, the levels of multiply-spliced transcripts were compared to the levels of gag-containing RNA in tissue samples from RT-SHIV-infected rhesus macaques treated with HAART. Splice site sequence variation was identified during development of a TaqMan PCR assay. Multiply-spliced transcripts were detected in gastrointestinal and lymphatic tissues, but not the thymus. Levels of multiply-spliced transcripts were lower than levels of gag RNA, and both correlated with plasma virus loads. The ratio of multiply-spliced to gag RNA was greatest in the gastrointestinal samples from macaques with plasma virus loads <50 vRNA copies per mL at necropsy. Levels of gag RNA and multiply-spliced mRNA in tissues from RT-SHIV-infected macaques correlate with plasma virus load

Computing a Knot Invariant as a Constraint Satisfaction Problem

We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides an algorithm to find the solution. The method also allows one to get some deeper insight into the structural complexity of knots, which is expected to be related with the landscape structure of constraint satisfaction problem.Comment: 6 pages, 3 figures, submitted to short note in Journal of Physical Society of Japa

Hamming distance kernelisation via topological quantum computation

We present a novel approach to computing Hamming distance and its kernelisation within Topological Quantum Computation. This approach is based on an encoding of two binary strings into a topological Hilbert space, whose inner product yields a natural Hamming distance kernel on the two strings. Kernelisation forges a link with the field of Machine Learning, particularly in relation to binary classifiers such as the Support Vector Machine (SVM). This makes our approach of potential interest to the quantum machine learning community