Thoughts on Barnette's Conjecture

We prove a new sufficient condition for a cubic 3-connected planar graph to be Hamiltonian. This condition is most easily described as a property of the dual graph. Let $G$ be a planar triangulation. Then the dual $G^*$ is a cubic 3-connected planar graph, and $G^*$ is bipartite if and only if $G$ is Eulerian. We prove that if the vertices of $G$ are (improperly) coloured blue and red, such that the blue vertices cover the faces of $G$, there is no blue cycle, and every red cycle contains a vertex of degree at most 4, then $G^*$ is Hamiltonian. This result implies the following special case of Barnette's Conjecture: if $G$ is an Eulerian planar triangulation, whose vertices are properly coloured blue, red and green, such that every red-green cycle contains a vertex of degree 4, then $G^*$ is Hamiltonian. Our final result highlights the limitations of using a proper colouring of $G$ as a starting point for proving Barnette's Conjecture. We also explain related results on Barnette's Conjecture that were obtained by Kelmans and for which detailed self-contained proofs have not been published.Comment: 12 pages, 7 figure

Energy dependence of transverse mass spectra of kaons produced in p+p and p+pbar interactions.A compilation

The data on m_T spectra of K0S K+ and K- mesons produced in all inelastic p+p and p+pbar interactions in the energy range sqrt(s)NN=4.7-1800GeV are compiled and analyzed. The spectra are parameterized by a single exponential function, dN/(m_T*dm_T)=C exp(-m_T/T), and the inverse slope parameter T is the main object of study. The T parameter is found to be similar for K0S, K+ and K- mesons. It increases monotonically with collision energy from T~30MeV at sqrt(s)NN=4.7GeV to T~220MeV at sqrt(s)NN=1800GeV. The T parameter measured in p+p and p+pbar interactions is significantly lower than the corresponding parameter obtained for central Pb+Pb collisions at all studied energies. Also the shape of the energy dependence of $T$ is different for central Pb+Pb collisions and p+p(pbar) interactions.Comment: more differential analysis adde

Bayesian feedback control of a two-atom spin-state in an atom-cavity system

We experimentally demonstrate real-time feedback control of the joint spin-state of two neutral Caesium atoms inside a high finesse optical cavity. The quantum states are discriminated by their different cavity transmission levels. A Bayesian update formalism is used to estimate state occupation probabilities as well as transition rates. We stabilize the balanced two-atom mixed state, which is deterministically inaccessible, via feedback control and find very good agreement with Monte-Carlo simulations. On average, the feedback loops achieves near optimal conditions by steering the system to the target state marginally exceeding the time to retrieve information about its state.Comment: 4 pages, 4 figure

Podoplanin immunopositive lymphatic vessels at the implant interface in a rat model of osteoporotic fractures

Insertion of bone substitution materials accelerates healing of osteoporotic fractures. Biodegradable materials are preferred for application in osteoporotic patients to avoid a second surgery for implant replacement. Degraded implant fragments are often absorbed by macrophages that are removed from the fracture side via passage through veins or lymphatic vessels. We investigated if lymphatic vessels occur in osteoporotic bone defects and whether they are regulated by the use of different materials. To address this issue osteoporosis was induced in rats using the classical method of bilateral ovariectomy and additional calcium and vitamin deficient diet. In addition, wedge-shaped defects of 3, 4, or 5 mm were generated in the distal metaphyseal area of femur via osteotomy. The 4 mm defects were subsequently used for implantation studies where bone substitution materials of calcium phosphate cement, composites of collagen and silica, and iron foams with interconnecting pores were inserted. Different materials were partly additionally functionalized by strontium or bisphosphonate whose positive effects in osteoporosis treatment are well known. The lymphatic vessels were identified by immunohistochemistry using an antibody against podoplanin. Podoplanin immunopositive lymphatic vessels were detected in the granulation tissue filling the fracture gap, surrounding the implant and growing into the iron foam through its interconnected pores. Significant more lymphatic capillaries were counted at the implant interface of composite, strontium and bisphosphonate functionalized iron foam. A significant increase was also observed in the number of lymphatics situated in the pores of strontium coated iron foam. In conclusion, our results indicate the occurrence of lymphatic vessels in osteoporotic bone. Our results show that lymphatic vessels are localized at the implant interface and in the fracture gap where they might be involved in the removal of lymphocytes, macrophages, debris and the implants degradation products. Therefore the lymphatic vessels are involved in implant integration and fracture healing

Evidence for an exotic S=-2, Q=-2 baryon resonance in proton-proton collisions at the CERN SPS

Results of resonance searches in the Xi - pi -, Xi - pi +, Xi -bar+ pi -, and Xi -bar+ pi + invariant mass spectra in proton-proton collisions at sqrt[s]=17.2 GeV are presented. Evidence is shown for the existence of a narrow Xi - pi - baryon resonance with mass of 1.862±0.002 GeV/c2 and width below the detector resolution of about 0.018 GeV/c2. The significance is estimated to be above 4.2 sigma . This state is a candidate for the hypothetical exotic Xi --3/2 baryon with S=-2, I=3 / 2, and a quark content of (dsdsu-bar). At the same mass, a peak is observed in the Xi - pi + spectrum which is a candidate for the Xi 03/2 member of this isospin quartet with a quark content of (dsusd-bar). The corresponding antibaryon spectra also show enhancements at the same invariant mass

Does presence of a mid-ocean ridge enhance biomass and biodiversity?

In contrast to generally sparse biological communities in open-ocean settings, seamounts and ridges are perceived as areas of elevated productivity and biodiversity capable of supporting commercial fisheries. We investigated the origin of this apparent biological enhancement over a segment of the North Mid-Atlantic Ridge (MAR) using sonar, corers, trawls, traps, and a remotely operated vehicle to survey habitat, biomass, and biodiversity. Satellite remote sensing provided information on flow patterns, thermal fronts, and primary production, while sediment traps measured export flux during 2007-2010. The MAR, 3,704,404 km 2 in area, accounts for 44.7% lower bathyal habitat (800-3500 m depth) in the North Atlantic and is dominated by fine soft sediment substrate (95% of area) on a series of flat terraces with intervening slopes either side of the ridge axis contributing to habitat heterogeneity. The MAR fauna comprises mainly species known from continental margins with no evidence of greater biodiversity. Primary production and export flux over the MAR were not enhanced compared with a nearby reference station over the Porcupine Abyssal Plain. Biomasses of benthic macrofauna and megafauna were similar to global averages at the same depths totalling an estimated 258.9 kt C over the entire lower bathyal north MAR. A hypothetical flat plain at 3500 m depth in place of the MAR would contain 85.6 kt C, implying an increase of 173.3 kt C attributable to the presence of the Ridge. This is approximately equal to 167 kt C of estimated pelagic biomass displaced by the volume of the MAR. There is no enhancement of biological productivity over the MAR; oceanic bathypelagic species are replaced by benthic fauna otherwise unable to survive in the mid ocean. We propose that globally sea floor elevation has no effect on deep sea biomass; pelagic plus benthic biomass is constant within a given surface productivity regime.Peer reviewe

Microwave study of quantum n-disk scattering

We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin 2-D microwave cavities. Two, three, and four-disk scattering are investigated in detail. The experiments, which are able to probe the stationary Green's function of the system, yield both frequencies and widths of the low-lying quantum resonances. The observed spectra are found to be in good agreement with calculations based on semiclassical periodic orbit theory. Wave-vector autocorrelation functions are analyzed for various scattering geometries, the small wave-vector behavior allowing one to extract the escape rate from the quantum repeller. Quantitative agreement is found with the value predicted from classical scattering theory. For intermediate energies, non-universal oscillations are detected in the autocorrelation function, reflecting the presence of periodic orbits.Comment: 13 pages, 8 eps figures include

Oncogenic transformation in the absence of Xrcc4 targets peripheral B cells that have undergone editing and switching

Nonhomologous end-joining (NHEJ) repairs DNA double-strand breaks (DSBs) during V(D)J recombination in developing lymphocytes and during immunoglobulin (Ig) heavy chain (IgH) class switch recombination (CSR) in peripheral B lymphocytes. We now show that CD21-cre–mediated deletion of the Xrcc4 NHEJ gene in p53-deficient peripheral B cells leads to recurrent surface Ig-negative B lymphomas (“CXP lymphomas”). Remarkably, CXP lymphomas arise from peripheral B cells that had attempted both receptor editing (secondary V[D]J recombination of Igκ and Igλ light chain genes) and IgH CSR subsequent to Xrcc4 deletion. Correspondingly, CXP tumors frequently harbored a CSR-based reciprocal chromosomal translocation that fused IgH to c-myc, as well as large chromosomal deletions or translocations involving Igκ or Igλ, with the latter fusing Igλ to oncogenes or to IgH. Our findings reveal peripheral B cells that have undergone both editing and CSR and show them to be common progenitors of CXP tumors. Our studies also reveal developmental stage-specific mechanisms of c-myc activation via IgH locus translocations. Thus, Xrcc4/p53-deficient pro–B lymphomas routinely activate c-myc by gene amplification, whereas Xrcc4/p53-deficient peripheral B cell lymphomas routinely ectopically activate a single c-myc copy