On the rooted Tutte polynomial

The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph. The connection with the Potts model is also reviewed.Comment: plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut Fourier (1999

Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6

Kondo insulator samarium hexaboride (SmB6) has been intensely studied in recent years as a potential candidate of a strongly correlated topological insulator. One of the most exciting phenomena observed in SmB6 is the clear quantum oscillations appearing in magnetic torque at a low temperature despite the insulating behavior in resistance. These quantum oscillations show multiple frequencies and varied effective masses. The origin of quantum oscillation is, however, still under debate with evidence of both two-dimensional Fermi surfaces and three-dimensional Fermi surfaces. Here, we carry out angle-resolved torque magnetometry measurements in a magnetic field up to 45 T and a temperature range down to 40 mK. With the magnetic field rotated in the (010) plane, the quantum oscillation frequency of the strongest oscillation branch shows a four-fold rotational symmetry. However, in the angular dependence of the amplitude of the same branch, this four-fold symmetry is broken and, instead, a twofold symmetry shows up, which is consistent with the prediction of a two-dimensional Lifshitz-Kosevich model. No deviation of Lifshitz-Kosevich behavior is observed down to 40 mK. Our results suggest the existence of multiple light-mass surface states in SmB6, with their mobility significantly depending on the surface disorder level.Comment: 15 pages, 9 figure

A probabilistic model checking approach to analysing reliability, availability, and maintainability of a single satellite system

Satellites now form a core component for space based systems such as GPS and GLONAS which provide location and timing information for a variety of uses. Such satellites are designed to operate in-orbit and have lifetimes of 10 years or more. Reliability, availability and maintainability (RAM) analysis of these systems has been indispensable in the design phase of satellites in order to achieve minimum failures or to increase mean time between failures (MTBF) and thus to plan maintainability strategies, optimise reliability and maximise availability. In this paper, we present formal modelling of a single satellite and logical specification of its reliability, availability and maintainability properties. The probabilistic model checker PRISM has been used to perform automated quantitative analyses of these properties

Closed-form Absorption Probability of Certain D=5 and D=4 Black Holes and Leading-Order Cross-Section of Generic Extremal p-branes

We obtain the closed-form absorption probabilities for minimally-coupled massless scalars propagating in the background of D=5 single-charge and D=4 two-charge black holes. These are the only two examples of extremal black holes with non-vanishing absorption probabilities that can be solved in closed form for arbitrary incident frequencies. In both cases, the absorption probability vanishes when the frequency is below a certain threshold, and we discuss the connection between this phenomenon and the behaviour of geodesics in these black hole backgrounds. We also obtain leading-order absorption cross-sections for generic extremal p-branes, and show that the expression for the cross-section as a function of frequency coincides with the leading-order dependence of the entropy on the temperature in the corresponding near-extremal p-branes.Comment: Latex (3 times), 20 page

Antrodia cinnamomea reduces obesity and modulates the gut microbiota in high-fat diet-fed mice.

BackgroundObesity is associated with gut microbiota dysbiosis, disrupted intestinal barrier and chronic inflammation. Given the high and increasing prevalence of obesity worldwide, anti-obesity treatments that are safe, effective and widely available would be beneficial. We examined whether the medicinal mushroom Antrodia cinnamomea may reduce obesity in mice fed with a high-fat diet (HFD).MethodsMale C57BL/6J mice were fed a HFD for 8 weeks to induce obesity and chronic inflammation. The mice were treated with a water extract of A. cinnamomea (WEAC), and body weight, fat accumulation, inflammation markers, insulin sensitivity and the gut microbiota were monitored.ResultsAfter 8 weeks, the mean body weight of HFD-fed mice was 39.8±1.2 g compared with 35.8±1.3 g for the HFD+1% WEAC group, corresponding to a reduction of 4 g or 10% of body weight (P<0.0001). WEAC supplementation reduced fat accumulation and serum triglycerides in a statistically significant manner in HFD-fed mice. WEAC also reversed the effects of HFD on inflammation markers (interleukin-1β, interleukin-6, tumor necrosis factor-α), insulin resistance and adipokine production (leptin and adiponectin). Notably, WEAC increased the expression of intestinal tight junctions (zonula occludens-1 and occludin) and antimicrobial proteins (Reg3g and lysozyme C) in the small intestine, leading to reduced blood endotoxemia. Finally, WEAC modulated the composition of the gut microbiota, reducing the Firmicutes/Bacteroidetes ratio and increasing the level of Akkermansia muciniphila and other bacterial species associated with anti-inflammatory properties.ConclusionsSupplementation with A. cinnamomea produces anti-obesogenic, anti-inflammatory and antidiabetic effects in HFD-fed mice by maintaining intestinal integrity and modulating the gut microbiota

Parallel processing architecture for computing inverse differential kinematic equations of the PUMA arm

In advanced robot control problems, on-line computation of inverse Jacobian solution is frequently required. Parallel processing architecture is an effective way to reduce computation time. A parallel processing architecture is developed for the inverse Jacobian (inverse differential kinematic equation) of the PUMA arm. The proposed pipeline/parallel algorithm can be inplemented on an IC chip using systolic linear arrays. This implementation requires 27 processing cells and 25 time units. Computation time is thus significantly reduced

Gamma-ray emission from the globular clusters Liller 1, M80, NGC 6139, NGC 6541, NGC 6624, and NGC 6752

Globular clusters (GCs) are emerging as a new class of gamma-ray emitters, thanks to the data obtained from the Fermi Gamma-ray Space Telescope. By now, eight GCs are known to emit gamma-rays at energies >100~MeV. Based on the stellar encounter rate of the GCs, we identify potential gamma-ray emitting GCs out of all known GCs that have not been studied in details before. In this paper, we report the discovery of a number of new gamma-ray GCs: Liller 1, NGC 6624, and NGC 6752, and evidence for gamma-ray emission from M80, NGC 6139, and NGC 6541, in which gamma-rays were found within the GC tidal radius. With one of the highest metallicity among all GCs in the Milky Way, the gamma-ray luminosity of Liller 1 is found to be the highest of all known gamma-ray GCs. In addition, we confirm a previous report of significant gamma-ray emitting region next to NGC 6441. We briefly discuss the observed offset of gamma-rays from some GC cores. The increasing number of known gamma-ray GCs at distances out to ~10 kpc is important for us to understand the gamma-ray emitting mechanism and provides an alternative probe to the underlying millisecond pulsar populations of the GCs.Comment: 22 pages, 7 figures, 2 tables; ApJ, in pres