Dynamics of quantum adiabatic evolution algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size $n$. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxilary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap, $g_{\rm min}={\cal O}(n 2^{-n/2})$, corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simulteneous fipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimenssional quantum diffusion in the energy space. This effect provides a general limitation on the power of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.Comment: 32 pages, 5 figures, 3 Appendices; List of additions compare to v.3: (i) numerical solution of the stationary Schroedinger equation for the adiabatic eigenstates and eigenvalues; (ii) connection between the scaling law of the minimum gap with the problem size and the shape of the coarse-grained distribution of the adiabatic eigenvalues at the avoided-crossing poin

Strong coupling of a qubit to shot noise

We perform a nonperturbative analysis of a charge qubit in a double quantum dot structure coupled to its detector. We show that strong detector-dot interaction tends to slow down and halt coherent oscillations. The transitions to a classical and a low-temperature quantum overdamping (Zeno) regime are studied. In the latter, the physics of the dissipative phase transition competes with the effective shot noise.Comment: 5 pages, 4 figure

ATXN2-CAG42 sequesters PABPC1 into insolubility and induces FBXW8 in cerebellum of old ataxic knock-in mice

Spinocerebellar Ataxia Type 2 (SCA2) is caused by expansion of a polyglutamine encoding triplet repeat in the human ATXN2 gene beyond (CAG)31. This is thought to mediate toxic gain-of-function by protein aggregation and to affect RNA processing, resulting in degenerative processes affecting preferentially cerebellar neurons. As a faithful animal model, we generated a knock-in mouse replacing the single CAG of murine Atxn2 with CAG42, a frequent patient genotype. This expansion size was inherited stably. The mice showed phenotypes with reduced weight and later motor incoordination. Although brain Atxn2 mRNA became elevated, soluble ATXN2 protein levels diminished over time, which might explain partial loss-of-function effects. Deficits in soluble ATXN2 protein correlated with the appearance of insoluble ATXN2, a progressive feature in cerebellum possibly reflecting toxic gains-of-function. Since in vitro ATXN2 overexpression was known to reduce levels of its protein interactor PABPC1, we studied expansion effects on PABPC1. In cortex, PABPC1 transcript and soluble and insoluble protein levels were increased. In the more vulnerable cerebellum, the progressive insolubility of PABPC1 was accompanied by decreased soluble protein levels, with PABPC1 mRNA showing no compensatory increase. The sequestration of PABPC1 into insolubility by ATXN2 function gains was validated in human cell culture. To understand consequences on mRNA processing, transcriptome profiles at medium and old age in three different tissues were studied and demonstrated a selective induction of Fbxw8 in the old cerebellum. Fbxw8 is encoded next to the Atxn2 locus and was shown in vitro to decrease the level of expanded insoluble ATXN2 protein. In conclusion, our data support the concept that expanded ATXN2 undergoes progressive insolubility and affects PABPC1 by a toxic gain-of-function mechanism with tissuespecific effects, which may be partially alleviated by the induction of FBXW8

On the attractors of two-dimensional Rayleigh oscillators including noise

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. For this case we provide results for the attractors and the bifurcations of the system. We show that for rational relations of the frequencies the system develops several rotational excitations with right/left symmetry, corresponding to limit cycles in the four-dimensional phase space. The corresponding noisy distributions have the form of hoops or tires in the four-dimensional space. For irrational frequency relations, as well as for increasing strength of driving or noise the periodic excitations are replaced by chaotic oscillations.Comment: 9 pages, 5 figure

The antiferromagnetic insulator Ca3FeRhO6: characterization and electronic structure calculations

We investigate the antiferromagnetic insulating nature of Ca3FeRhO6 both experimentally and theoretically. Susceptibility measurements reveal a Neel temperature T_N = 20 K, and a magnetic moment of 5.3 muB/f. u., while Moessbauer spectroscopy strongly suggests that the Fe ions, located in trigonal prismatic sites, are in a 3+ high spin state. Transport measurements display a simple Arrhenius law, with an activation energy of 0.2 eV. The experimental results are interpreted with LSDA band structure calculations, which confirm the Fe 3+ state, the high-spin/low-spin scenario, the antiferromagnetic ordering, and the value for the activation energy.Comment: 5 pages, 6 figure

Fermi surface of MoO2 studied by angle-resolved photoemission spectroscopy, de Haas-van Alphen measurements, and electronic structure calculations

A comprehensive study of the electronic properties of monoclinic MoO2 from both an experimental and a theoretical point of view is presented. We focus on the investigation of the Fermi body and the band structure using angle resolved photoemission spectroscopy, de Haas-van Alphen measurements, and electronic structure calculations. For the latter, the new full-potential augmented spherical wave (ASW) method has been applied. Very good agreement between the experimental and theoretical results is found. In particular, all Fermi surface sheets are correctly identified by all three approaches. Previous controversies concerning additional hole-like surfaces centered around the Z- and B-point could be resolved; these surfaces were an artefact of the atomic-sphere approximation used in the old calculations. Our results underline the importance of electronic structure calculations for the understanding of MoO2 and the neighbouring rutile-type early transition-metal dioxides. This includes the low-temperature insulating phases of VO2 and NbO2, which have crystal structures very similar to that of molybdenum dioxide and display the well-known prominent metal-insulator transitions.Comment: 17 pages, 21 figures, more information at http://www.physik.uni-augsburg.de/~eyert

Просвещение как форма популяризации культурно- художественных достижений этнических меньшинств Украины: тенденции 1990-2000-х годов

У статті розглянуто місце і роль просвітництва у популяризації культурно- мистецьких надбань етноменшин. На основі специфічного методологічного інструментарію проаналізовано відповідність популяризації культурно-мистецьких надбань – стратегічними цілями – визнання поліетнічного характеру українського суспільства, розбудові соціокультурного середовища і духовному розвитку етносів. Підкреслено, що в Україні діяла розгалужена мережа музеїв, де діяли спеціальні підрозділи – відділи, центри, експозиції тощо. Проаналізовані напрямки науково – дослідної роботи музеїв та виокремлена її просвітницької складової.В статье рассмотрены место и роль просвещения в популяризации культурно - художественных достижений этнических меньшинств. На основе специфического методологического инструментария проанализированы соответствие популяризации культурно - художественных достижений - стратегическими целями - признание полеэтнического характера украинского общества, развитии социокультурной среды и духовном развитии этносов. Подчеркнуто, что в Украине действовала разветвленная сеть музеев, в которых действовали специальные подразделения - отделы, центры, экспозиции и т.д. Проанализованы направления научно - исследовательской работы музеев с выделением ее просветительской составляющей.On the basis of archival, statistical materials, analytical inputs predecessors considered the place and role of education in promoting cultural - artistic achievements of ethnic minorities. Nonfiction includes the problems of cultural heritage of the Ukrainian people is partly considered problem areas, shapes, nature education. Importance designated problem is primarily due to the need to have a clear understanding of the mechanism solutions independent state problems of interethnic relations. Found that in Ukraine there and operated an extensive network of structures that were engaged in the popularization of cultural - artistic achievements of Ukraine’s ethnic groups: governments, national - cultural societies, cultural institutions. We considered the prospect of continuity and the protection and conservation of heritage. Considerable attention is given to finding areas of education: conducting scientific - practical conferences, advocacy through the museums, the publication of the relevant literature. First in the historiography on the basis of specific methodological tools to analyze the relevant promotion of cultural - artistic achievements - the strategic objectives - recognition of the field of an ethnic nature of Ukrainian society, the development of social and cultural environment and spiritual development of ethnic groups. Particular attention is given to explaining participation in the process of popularizing the achievements of local history museums in Ukraine. Stress that Ukraine had an extensive network of museums that had special units - departments, centers, exposure, etc.. Directions of scientific - research museums and highlighted its educational component. Significant place in the article devoted to subjects found clarification of the regional museum

The Role of Bilayer Tilt Difference in Equilibrium Membrane Shapes

Lipid bilayer membranes below their main transition have two tilt order parameters, corresponding to the two monolayers. These two tilts may be strongly coupled to membrane shape but only weakly coupled to each other. We discuss some implications of this observation for rippled and saddle phases, bilayer tubules, and bicontinuous phases. Tilt difference introduces a length scale into the elastic theory of tilted fluid membranes. It can drive an instability of the flat phase; it also provides a simple mechanism for the spontaneous breaking of inversion symmetry seen in some recent experiments.Comment: Latex file; .ps available at http://dept.physics.upenn.edu/~nelson/saddle.p

Escape from a metastable well under a time-ramped force

Thermally activated escape of an over-damped particle from a metastable well under the action of a time-ramped force is studied. We express the mean first passage time (MFPT) as the solution to a partial differential equation, which we solve numerically for a model case. We discuss two approximations of the MFPT, one of which works remarkably well over a wide range of loading rates, while the second is easy to calculate and can provide a valuable first estimate.Comment: 9 pages, including 2 figure