Algorithmic approach to adiabatic quantum optimization

It is believed that the presence of anticrossings with exponentially small gaps between the lowest two energy levels of the system Hamiltonian, can render adiabatic quantum optimization inefficient. Here, we present a simple adiabatic quantum algorithm designed to eliminate exponentially small gaps caused by anticrossings between eigenstates that correspond with the local and global minima of the problem Hamiltonian. In each iteration of the algorithm, information is gathered about the local minima that are reached after passing the anticrossing non-adiabatically. This information is then used to penalize pathways to the corresponding local minima, by adjusting the initial Hamiltonian. This is repeated for multiple clusters of local minima as needed. We generate 64-qubit random instances of the maximum independent set problem, skewed to be extremely hard, with between 10^5 and 10^6 highly-degenerate local minima. Using quantum Monte Carlo simulations, it is found that the algorithm can trivially solve all the instances in ~10 iterations.Comment: 7 pages, 3 figure

Consistent Quantum Counterfactuals

An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum reasoning together with the ``one framework'' rule prevents a logical contradiction, and there is no evidence for any mysterious nonlocal influences. Counterfactual reasoning can support a realistic interpretation of standard quantum theory (measurements reveal what is actually there) under appropriate circumstances.Comment: Minor modifications to make it agree with published version. Latex 8 pages, 2 figure

Early Effects on the Morphology of Mouse Small Intestine of Single or Combined Modality Treatment with Hyperthermia and X-Irradiation

This study describes the effects of hyperthermia and X-irradiation on the morphological appearance of normal, at risk tissues in the ileum of the mouse. The early morphological effects day after a combined modality treatment are compared with those due to either hyperthermia or X-irradiation given alone. The response was assessed qualitatively and semiquantitatively using scanning electron microscopy and a villous scoring technique. Early post-irradiation effects on topography did not differ significantly from those observed after small intestine exteriorisation without treatment. The villous scores for the combined modality treatments reflected greater damage than would be expected from the sum of villous scores for each modality treatment on its own. This suggests that the combined modality treatment had a synergistic or enhancing effect. A 4 hour time interval between the two treatments did not seem to reduce the enhancing effect. Further studies are required to investigate the effects of fractionated combined treatment

On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

Algebro-Geometric Solutions of the Boussinesq Hierarchy

We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes associated Burchnall-Chaundy curves, Baker-Akhiezer functions and Dubrovin-type equations for analogs of Dirichlet and Neumann divisors. The principal aim of this paper is a detailed theta function representation of all algebro-geometric quasi-periodic solutions and related quantities of the Bsq hierarchy.Comment: LaTeX, 48 page

Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory

MUBs inequivalence and affine planes

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes "old" results that do not appear to be well-known concerning known families of complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical Physics 53, 032204 (2012) except for format changes due to the journal's style policie

Ionization state, excited populations and emission of impurities in dynamic finite density plasmas: I. The generalized collisional-radiative model for light elements

The paper presents an integrated view of the population structure and its role in establishing the ionization state of light elements in dynamic, finite density, laboratory and astrophysical plasmas. There are four main issues, the generalized collisional-radiative picture for metastables in dynamic plasmas with Maxwellian free electrons and its particularizing to light elements, the methods of bundling and projection for manipulating the population equations, the systematic production/use of state selective fundamental collision data in the metastable resolved picture to all levels for collisonal-radiative modelling and the delivery of appropriate derived coefficients for experiment analysis. The ions of carbon, oxygen and neon are used in illustration. The practical implementation of the methods described here is part of the ADAS Project

Self-consistent symmetries in the proton-neutron Hartree-Fock-Bogoliubov approach

Symmetry properties of densities and mean fields appearing in the nuclear Density Functional Theory with pairing are studied. We consider energy functionals that depend only on local densities and their derivatives. The most important self-consistent symmetries are discussed: spherical, axial, space-inversion, and mirror symmetries. In each case, the consequences of breaking or conserving the time-reversal and/or proton-neutron symmetries are discussed and summarized in a tabulated form, useful in practical applications.Comment: 26 RevTex pages, 1 eps figure, 9 tables, submitted to Physical Review

Individualised pelvic floor muscle training in women with pelvic organ prolapse: a multicentre randomised controlled trial

<br>Background: Pelvic organ prolapse is common and is strongly associated with childbirth and increasing age. Women with prolapsed are often advised to do pelvic floor muscle exercises, but supporting evidence is limited. Our aim was to establish if one-to-one individualised pelvic floor muscle training (PFMT) is effective in reducing prolapse symptoms.</br> <br>Methods: A parallel‐group multicentre randomised controlled trial (ISRCTN35911035) in female outpatients with newly-diagnosed, symptomatic stage I, II or III prolapse, comparing five PFMT appointments over 16 weeks (n=225) versus a lifestyle advice leaflet (n=222). Treatment allocation was by remote computer allocation using minimisation. Our primary endpoint was participants’ self-report of prolapsed symptoms at 12 months. Group assignment was masked from outcome assessors. We compared outcomes between trial groups in an intention-to-treat analysis. The cost of PFMT and savings on subsequent treatments were calculated to estimate cost-effectiveness.</br> <br>Findings: Compared to the control group, the intervention group reported fewer prolapse symptoms at 12 months (mean difference between groups in change score 1.52, 95% CI [0.46, 2.59], p=0.0053); reported their prolapse to be “better” more often (57.2% versus 44.7%, difference 12.6%, 95% CI [1.1%, 24.1%], p=0.0336); and had an increased but non-significant odds of having less severe stage of prolapse at their 6-month clinical examination, (OR 1.47, 95% CI [0.97, 2.27], p=0.07). The control group had a greater uptake of other prolapse treatment (49.6% versus 24.1%, difference 25.5%, 95% CI [14.5%, 36.0%], p <0.0001). Findings were robust to missing data. The net cost of the 25 intervention was £131.61 per woman and the cost per one-point reduction in the symptom score was £86.59, 95% CI [£50.81, £286.11]. </br&gt