Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.Comment: 4 pages, 3 figure

On Nonzero Kronecker Coefficients and their Consequences for Spectra

A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A, r^B, r^{AB}). How can we characterise such triples? It turns out that the admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means that the irreducible representation V_lambda is contained in the tensor product of V_mu and V_nu. Here, we show that such triples form a finitely generated semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a complete information-theoretic proof of the correspondence between triples of spectra and representations. Finally, we show that spectral triples form a convex polytope.Comment: 13 page

Wightman function and vacuum fluctuations in higher dimensional brane models

Wightman function and vacuum expectation value of the field square are evaluated for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two codimension one parallel branes located on $(D+1)$-dimensional background spacetime $AdS_{D_1+1}\times \Sigma$ with a warped internal space $\Sigma$. The general case of different Robin coefficients on separate branes is considered. The application of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions allows us to extract manifestly the part due to the bulk without boundaries. Unlike to the purely AdS bulk, the vacuum expectation value of the field square induced by a single brane, in addition to the distance from the brane, depends also on the position of the brane in the bulk. The brane induced part in this expectation value vanishes when the brane position tends to the AdS horizon or AdS boundary. The asymptotic behavior of the vacuum densities near the branes and at large distances is investigated. The contribution of Kaluza-Klein modes along $\Sigma$ is discussed in various limiting cases. As an example the case $\Sigma =S^1$ is considered, corresponding to the $AdS_{D+1}$ bulk with one compactified dimension. An application to the higher dimensional generalization of the Randall-Sundrum brane model with arbitrary mass terms on the branes is discussed.Comment: 25 pages, 2 figures, discussion added, accepted for publication in Phys.Rev.

Wightman function and vacuum densities for a Z_2-symmetric thick brane in AdS spacetime

Positive frequency Wightman function, vacuum expectation values of the field square and the energy-momentum tensor induced by a Z_{2}-symmetric brane with finite thickness located on (D+1)- dimensional AdS background are evaluated for a massive scalar field with general curvature coupling parameter. For the general case of static plane symmetric interior structure the expectation values in the region outside the brane are presented as the sum of free AdS and brane induced parts. For a conformally coupled massless scalar the brane induced part in the vacuum energy-momentum tensor vanishes. In the limit of strong gravitational fields the brane induced parts are exponentially suppressed for points not too close to the brane boundary. As an application of general results a special model is considered in which the geometry inside the brane is a slice of the Minkowski spacetime orbifolded along the direction perpendicular to the brane. For this model the Wightman function, vacuum expectation values of the field square and the energy-momentum tensor inside the brane are evaluated as well and their behavior is discussed in various asymptotic regions of the parameters. It is shown that for both minimally and conformally coupled scalar fields the interior vacuum forces acting on the brane boundaries tend to decrease the brane thickness.Comment: 25 pages, 6 figures, discussion adde

Flavor changing interactions mediated by scalars at the weak scale

The quark and lepton mass matrices possess approximate flavor symmetries. Several results follow if the interactions of new scalars possess these approximate symmetries. Present experimental bounds allow these exotic scalars to have a weak scale mass. The Glashow-Weinberg criterion is rendered unnecessary. Finally, rare leptonic B meson decays provide powerful probes of these scalars, especially if they are leptoquarks.Comment: 13 pages, report LBL-3234

Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs

We theoretically study semi-supervised clustering in sparse graphs in the presence of pairwise constraints on the cluster assignments of nodes. We focus on bi-cluster graphs, and study the impact of semi-supervision for varying constraint density and overlap between the clusters. Recent results for unsupervised clustering in sparse graphs indicate that there is a critical ratio of within-cluster and between-cluster connectivities below which clusters cannot be recovered with better than random accuracy. The goal of this paper is to examine the impact of pairwise constraints on the clustering accuracy. Our results suggests that the addition of constraints does not provide automatic improvement over the unsupervised case. When the density of the constraints is sufficiently small, their only impact is to shift the detection threshold while preserving the criticality. Conversely, if the density of (hard) constraints is above the percolation threshold, the criticality is suppressed and the detection threshold disappears.Comment: 8 pages, 4 figure

Generalized statistical models of voids and hierarchical structure in cosmology

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution which contains a parameter "a". The parameter is related to the Levy index alpha and the Fisher critical exponent tau, the latter describing the power law fall off of clumps of matter around a phase transition. The parameter"a", exponent tau, or index alpha can be obtained from properties of a void scaling function. A stochastic probability variable "p" is introduced into a statistical model which represent the adhesive growth of galaxy structure. For p<1/2, the galaxy count distribution decays exponential fast with size. For p>1/2, an adhesive growth can go on indefinitely thereby forming an infinite supercluster. At p=1/2 a scale free power law distribution for the galaxy count distribution is present. The stochastic description also leads to consequences that have some parallels with cosmic string results, percolation theory and phase transitions.Comment: 25 page

Efficacy of Thermotherapy to Treat Cutaneous Leishmaniasis Caused by Leishmania tropica in Kabul, Afghanistan: A Randomized, Controlled Trial

BACKGROUND: Pentavalent antimony is the agent recommended for treatment of cutaneous leishmaniasis (CL). Its use is problematic, because it is expensive and because of the potential for drug-associated adverse effects during a lengthy and painful treatment course. METHODS: We tested the efficacy of thermotherapy for the treatment of CL due to Leishmania tropica in a randomized, controlled trial in Kabul, Afghanistan. We enrolled 401 patients with a single CL lesion and administered thermotherapy using radio-frequency waves (1 treatment of ≥1 consecutive application at 50°C for 30 s) or sodium stibogluconate (SSG), administered either intralesionally (a total of 5 injections of 25 mL every 57 days, depending on lesion size) or intramuscularly (20 mg/kg daily for 21 days). RESULTS: Cure, defined as complete reepithelialization at 100 days after treatment initiation, was observed in 75 (69.4%) of 108 patients who received thermotherapy, 70 (75.3%) of 93 patients who received intralesional SSG, and 26 (44.8%) of 58 patients who received intramuscular SSG. The OR for cure with thermotherapy was 2.80 (95% confidence interval [CI], 1.455.41), compared with intramuscular SSG treatment (P = .002). No statistically significant difference was observed in the odds of cure in comparison of intralesional SSG and thermotherapy treatments. The OR for cure with intralesional SSG treatment was 3.75 (95% CI, 1.867.54), compared with intramuscular SSG treatment (P 100 days, respectively; P = .003). CONCLUSIONS: Thermotherapy is an effective, comparatively well-tolerated, and rapid treatment for CL, and it should be considered as an alternative to antimony treatment

Provider Stakeholders’ Perceived Benefit from a Nascent Health Information Exchange: A Qualitative Analysis

We sought to better understand the perceived costs and benefits of joining a nascent health information exchange (HIE) from the perspective of potential provider organization participants. We therefore conducted semi-structured interviews with organizational representatives. Interview transcriptions were thematically coded, and coded text was subsequently aggregated to summarize the breadth and depth of responses. Although no respondents expected HIE to result in net financial benefit to their organization, all respondents recognized some potential benefits, and some respondents expected HIE to result in overall organizational benefit. Disproportionate benefit was expected for the poorest, sickest patients. Many respondents had concerns about HIE increasing the risk of data security breaches, and these concerns were most pronounced at larger organizations. We found little evidence of organizational concern regarding loss of patients to other organizations or publication of unfavorable quality data. If HIE’s greatest benefactors are indeed the poorest, sickest patients, our current health care financing environment will make it difficult to align HIE costs with benefits. To sustain HIE, state and federal governments may need to consider ongoing subsidies. Furthermore, these governments will need to ensure that policies regulating data exchange have sufficient nationwide coordination and liability limitations that the perceived organizational risks of joining HIEs do not outweigh perceived benefits. HIE founders can address organizational concerns by attempting to coordinate HIE policies with those of their largest founding organizations, particularly for data security policies. Early HIE development and promotional efforts should not only focus on potential benefits, but should also address organizational concerns

Adaptive Boolean Networks and Minority Games with Time--Dependent Capacities

In this paper we consider a network of boolean agents that compete for a limited resource. The agents play the so called Generalized Minority Game where the capacity level is allowed to vary externally. We study the properties of such a system for different values of the mean connectivity $K$ of the network, and show that the system with K=2 shows a high degree of coordination for relatively large variations of the capacity level.Comment: 4 pages, 4 figure