Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs

In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth

Adiabatic Quantum Computation in Open Systems

We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.Comment: v2: 4 pages, 1 figure. Published versio

Adiabatic quantum computation and quantum phase transitions

We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR

Trees with a large Laplacian eigenvalue multiplicity

In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than $1$ are simple and also the multiplicity of Laplacian eigenvalue $1$ has been well studied before. Here we consider the multiplicities of the other (non-integral) Laplacian eigenvalues. We give an upper bound and determine the trees of order $n$ that have a multiplicity that is close to the upper bound $\frac{n-3}{2}$, and emphasize the particular role of the algebraic connectivity.Comment: 11 pages, 5 figure

Experimental implementation of an adiabatic quantum optimization algorithm

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.Comment: REVTeX, 5 pages, 4 figures, improved lay-out; accepted for publication in Physical Review Letter

Return to Baseline After an Interpretation Training as a Dynamic Predictor for Treatment Response in Social Anxiety Disorder

Background: Despite considerable research efforts, consistent predictors of cognitive behavioral therapy (CBT) outcome for social anxiety disorder (SAD) are scarce. A dynamic focus on individual symptom reactivity and resilience patterns may show promise in predicting treatment response. This pilot study is the first to investigate whether rate of return to baseline after a one-session positive interpretation training indicates resilience and predicts CBT-response among individuals with SAD. Method: Participants (N = 39) completed an interpretation bias assessment before and after training, and once a day for three days after the training, followed by a six-week CBT-program. Participants completed SAD-assessments pre-treatment, during treatment, and post-treatment. Return to baseline was operationalized as the individualized slope of negative and positive interpretations across interpretation bias assessments. Results: Intention-to-treat analyses showed no significant relation between both negative and positive interpretation bias and CBT-response. Similarly, for completers-only, most analyses also showed no such relationship. Conclusion: These findings suggest that slower return to baseline as a resilience index does not have predictive value for CBT-outcome in individuals with SAD. Future studies should incorporate experience-sampling to capture subtle changes in interpretation bias.</p

Optimal parametrizations of adiabatic paths

The parametrization of adiabatic paths is optimal when tunneling is minimized. Hamiltonian evolutions do not have unique optimizers. However, dephasing Lindblad evolutions do. The optimizers are simply characterized by an Euler-Lagrange equation and have a constant tunneling rate along the path irrespective of the gap. Application to quantum search algorithms recovers the Grover result for appropriate scaling of the dephasing. Dephasing rates that beat Grover imply hidden resources in Lindblad operators.Comment: 4 pages, 2 figures; To prevent from misunderstanding, we clarified the discussion of an apparent speedup in the Grover algorithm; figures improved + minor change

Keck Observatory Laser Guide Star Adaptive Optics Discovery and Characterization of a Satellite to the Large Kuiper Belt Object 2003 EL_(61)

The newly commissioned laser guide star adaptive optics system at Keck Observatory has been used to discover and characterize the orbit of a satellite to the bright Kuiper Belt object 2003 EL_(61). Observations over a 6 month period show that the satellite has a semimajor axis of 49,500 ± 400 km, an orbital period of 49.12 ± 0.03 days, and an eccentricity of 0.050 ± 0.003. The inferred mass of the system is (4.2 ± 0.1) × 10^(21) kg, or ~32% of the mass of Pluto and 28.6% ± 0.7% of the mass of the Pluto-Charon system. Mutual occultations occurred in 1999 and will not occur again until 2138. The orbit is fully consistent neither with one tidally evolved from an earlier closer configuration nor with one evolved inward by dynamical friction from an earlier more distant configuration

Acute effects of decaffeinated coffee and the major coffee components chlorogenic acid and trigonelline on incretin hormones

Coffee consumption is associated with a lower risk of type 2 diabetes. We tested the hypothesis that this is mediated by incretin hormones by measuring the acute effects of decaffeinated coffee and coffee components on GLP-1 and GIP concentrations. A randomized cross-over trial of the effects of 12 g decaffeinated coffee, 1 g chlorogenic acid, 500 mg trigonelline, and placebo on total and intact GLP-1 and GIP concentrations during an oral glucose tolerance test took place in fifteen overweight men. No treatment significantly affected the overall GLP-1 or GIP secretion pattern following an OGTT relative to placebo. Decaffeinated coffee slightly increased total GLP-1 concentration 30 minutes after ingestion (before the OGTT) relative to placebo (2.7 pmol/L, p = 0.03), but this change did not correspond with changes in glucose or insulin secretion. These findings do not support the hypothesis that coffee acutely improves glucose tolerance through effects on the secretion of incretin hormones. Chronic effects of coffee and its major components still need to be investigated