Single-Step Quantum Search Using Problem Structure

The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT allows determining the asymptotic average behavior of these algorithms, showing they improve on quantum algorithms, such as amplitude amplification, that ignore detailed problem structure but remain exponential for hard problem instances. Compared to good classical methods, the algorithm performs better, on average, for weakly and highly constrained problems but worse for hard cases. The analytic techniques introduced here also apply to other quantum algorithms, supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of NP search problems.Comment: 39 pages, 12 figures. Revision describes further improvement with multiple steps (section 7). See also http://www.parc.xerox.com/dynamics/www/quantum.htm

Studies on the hyperplasia ('regeneration') of the rat liver following partial hepatectomy. Changes in lipid peroxidation and general biochemical aspects

Using the experimental model of partial hepatectomy in the rat, we have examined the relationship between cell division and lipid peroxidation activity. In rats entrained to a regime of 12 h light/12 h dark and with a fixed 8 h feeding period in the dark phase, partial hepatectomy is followed by a rapid regeneration of liver mass with cycles of synchronized cell division at 24 h intervals. The latter phenomenon is indicated in this study by pulses of thymidine kinase activity having maxima at 24 h, 48 h and 72 h after partial hepatectomy. Microsomes prepared from regenerating livers show changes in lipid peroxidation activity (induced by NADPH/ADP/iron or by ascorbate/iron), which is significantly decreased relative to that in microsomes from sham-operated controls, again at 24 h, 48 h and 72 h after the operation. This phenomenon has been investigated with regard to possible underlying changes in the content of microsomal fatty acids, the microsomal enzymes NADPH:cytochrome c reductase and cytochrome P-450, and the physiological microsomal antioxidant alpha-tocopherol. The cycles of decreased lipid peroxidation activity are apparently due, at least in part, to changes in microsomal alpha-tocopherol content that are closely associated in time with thymidine kinase activity

A mitotic SKAP isoform regulates spindle positioning at astral microtubule plus ends

The Astrin/SKAP complex plays important roles in mitotic chromosome alignment and centrosome integrity, but previous work found conflicting results for SKAP function. Here, we demonstrate that SKAP is expressed as two distinct isoforms in mammals: a longer, testis-specific isoform that was used for the previous studies in mitotic cells and a novel, shorter mitotic isoform. Unlike the long isoform, short SKAP rescues SKAP depletion in mitosis and displays robust microtubule plus-end tracking, including localization to astral microtubules. Eliminating SKAP microtubule binding results in severe chromosome segregation defects. In contrast, SKAP mutants specifically defective for plus-end tracking facilitate proper chromosome segregation but display spindle positioning defects. Cells lacking SKAP plus-end tracking have reduced Clasp1 localization at microtubule plus ends and display increased lateral microtubule contacts with the cell cortex, which we propose results in unbalanced dynein-dependent cortical pulling forces. Our work reveals an unappreciated role for the Astrin/SKAP complex as an astral microtubule mediator of mitotic spindle positioning.Leukemia & Lymphoma Society of America (Scholar Award)National Institute of General Medical Sciences (U.S.) (GM088313)American Cancer Society (121776

Extremal Optimization at the Phase Transition of the 3-Coloring Problem

We investigate the phase transition of the 3-coloring problem on random graphs, using the extremal optimization heuristic. 3-coloring is among the hardest combinatorial optimization problems and is closely related to a 3-state anti-ferromagnetic Potts model. Like many other such optimization problems, it has been shown to exhibit a phase transition in its ground state behavior under variation of a system parameter: the graph's mean vertex degree. This phase transition is often associated with the instances of highest complexity. We use extremal optimization to measure the ground state cost and the ``backbone'', an order parameter related to ground state overlap, averaged over a large number of instances near the transition for random graphs of size $n$ up to 512. For graphs up to this size, benchmarks show that extremal optimization reaches ground states and explores a sufficient number of them to give the correct backbone value after about $O(n^{3.5})$ update steps. Finite size scaling gives a critical mean degree value $\alpha_{\rm c}=4.703(28)$. Furthermore, the exploration of the degenerate ground states indicates that the backbone order parameter, measuring the constrainedness of the problem, exhibits a first-order phase transition.Comment: RevTex4, 8 pages, 4 postscript figures, related information available at http://www.physics.emory.edu/faculty/boettcher

NASA space station automation: AI-based technology review. Executive summary

Research and Development projects in automation technology for the Space Station are described. Artificial Intelligence (AI) based technologies are planned to enhance crew safety through reduced need for EVA, increase crew productivity through the reduction of routine operations, increase space station autonomy, and augment space station capability through the use of teleoperation and robotics

Color and gloss constancy under diverse lighting environments

When we look at an object, we simultaneously see how glossy or matte it is, how light or dark, and what color. Yet, at each point on the object's surface, both diffuse and specular reflections are mixed in different proportions, resulting in substantial spatial chromatic and luminance variations. To further complicate matters, this pattern changes radically when the object is viewed under different lighting conditions. The purpose of this study was to simultaneously measure our ability to judge color and gloss using an image set capturing diverse object and illuminant properties. Participants adjusted the hue, lightness, chroma, and specular reflectance of a reference object so that it appeared to be made of the same material as a test object. Critically, the two objects were presented under different lighting environments. We found that hue matches were highly accurate, except for under a chromatically atypical illuminant. Chroma and lightness constancy were generally poor, but these failures correlated well with simple image statistics. Gloss constancy was particularly poor, and these failures were only partially explained by reflection contrast. Importantly, across all measures, participants were highly consistent with one another in their deviations from constancy. Although color and gloss constancy hold well in simple conditions, the variety of lighting and shape in the real world presents significant challenges to our visual system's ability to judge intrinsic material properties

The Peculiar Phase Structure of Random Graph Bisection

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.Comment: substantially revised section 2, changed figures 3, 4 and 6, made minor stylistic changes and added reference