Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

Closing the window on strongly interacting dark matter with IceCube

We use the recent results on dark matter searches of the 22-string IceCube detector to probe the remaining allowed window for strongly interacting dark matter in the mass range 10(4) < m(X) < 10(15) GeV. We calculate the expected signal in the 22-string IceCube detector from the annihilation of such particles captured in the Sun and compare it to the detected background. As a result, the remaining allowed region in the mass versus cross section parameter space is ruled out. We also show the expected sensitivity of the complete IceCube detector with 86 strings.

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J, and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices, and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.

Skewness, splitting number and vertex deletion of some toroidal meshes

The skewness sk(G) of a graph G = (V, E) is the smallest integer sk(G) >= 0 such that a planar graph can be obtained from G by the removal of sk(C) edges. The splitting number sp(G) of C is the smallest integer sp(G) >= 0 such that a planar graph can be obtained from G by sp(G) vertex splitting operations. The vertex deletion vd(G) of G is the smallest integer vd(G) >= 0 such that a planar graph can be obtained from G by the removal of vd(G) vertices. Regular toroidal meshes are popular topologies for the connection networks of SIMD parallel machines. The best known of these meshes is the rectangular toroidal mesh C(m) x C(n) for which is known the skewness, the splitting number and the vertex deletion. In this work we consider two related families: a triangulation Tc(m) x c(n) of C(m) x C(n) in the torus, and an hexagonal mesh Hc(m) x c(n), the dual of Tc(m) x c(n) in the torus. It is established that sp(Tc(m) x c(n)) = vd(Tc(m) x c(n) = sk(Hc(m) x c(n)) = sp(Hc(m) x c(n)) = vd(Hc(m) x c(n)) = min{m, n} and that sk(Tc(m) x c(n)) = 2 min {m, n}.

Adaptations in autonomic function during exercise training in heart failure

Although neurohumoral excitation is the hallmark of heart failure (HF), the mechanisms underlying this alteration are not entirely known. Abnormalities in several systems contribute to neurohumoral excitation in HF, including arterial and cardiopulmonary baroreceptors, central and peripheral chemoreceptors, cardiac chemoreceptors, and central nervous system abnormalities. Exercise intolerance is characteristic of chronic HF, and growing evidence strongly suggests that exercise limitation in patients with chronic HF is not due to elevated filling pressures or inadequate cardiac output during exercise, but instead due to skeletal myopathy. Several lines of evidence suggest that sympathetic excitation contributes to the skeletal myopathy of HF, since sympathetic activity mediates vasoconstriction at rest and during exercise likely restrains muscle blood flow, arteriolar dilatation, and capillary recruitment, leading to underperfused areas of working muscle, and areas of muscle ischemia, release of reactive oxygen species (ROS), and inflammation. Although controversial, either unmyelinated, metabolite-sensitive afferent fibers, and/or myelinated, mechanosensitive afferent fibers in skeletal muscle underlie the exaggerated sympathetic activity in HF. Exercise training has emerged as a unique non-pharmacological strategy for the treatment of HF. Regular exercise improves functional capacity and quality of life, and perhaps prognosis in chronic HF patients. Recent studies have provided convincing evidence that these benefits in chronic HF patients are mediated by significant reduction in central sympathetic outflow as a consequence of improvement in arterial and chemoreflex controls, and correction of central nervous system abnormalities, and increase in peripheral blood flow with reduction in cytokines and increase in mass muscle.

Treatment of vitamin D deficiency increases lower limb muscle strength in institutionalized older people independently of regular physical activity: a randomized double-blind controlled trial

Aims: To investigate the effects of a 6-month supplementation with calcium and cholecalciferol on biochemical parameters and muscle strength of institutionalized elderly. Methods: This prospective, double-blind, placebo-controlled, randomized trial included Brazilian institutionalized people 6 60 years of age receiving a 6-month supplementation ( December to May) of daily calcium plus monthly placebo (calcium/placebo group) or daily calcium plus oral cholecalciferol (150,000 IU once a month during the first 2 months, followed by 90,000 IU once a month for the last 4 months; calcium/vitamin D group). Fasting blood samples for 25-(OH) D, PTH and calcium determination were collected (n = 56) and muscle tests were performed ( n = 46) to measure the strength of hip flexors (SHF) and knee extensors (SKE) before ( baseline) and after the 6-month intervention ( 6 months). Results: Due to seasonal variations, serum 25( OH) D significantly enhanced in both groups after treatment, but the calcium/vitamin D group had significantly higher 25-(OH) D levels than the calcium/placebo group (84 vs. 33%, respectively; p < 0.0001). No cases of hypercalcemia were observed. While the calcium/placebo group showed no improvement in SHF and SKE at 6 months (p = 0.93 and p = 0.61, respectively), SHF was increased in the calcium/vitamin D group by 16.4% (p = 0.0001) and SKE by 24.6% (p = 0.0007). Conclusions: The suggested cholecalciferol supplementation was safe and efficient in enhancing 25(OH)D levels and lower limb muscle strength in the elderly, in the absence of any regular physical exercise practice. Copyright (C) 2009 S. Karger AG, Basel

Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

Concentration inequalities and laws of large numbers under epistemic and regular irrelevance

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda`s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance. (C) 2010 Elsevier Inc. All rights reserved.

Optimization and Complexity Reduction of Switch-Reconfigured Antennas Using Graph Models

This letter addresses the optimization and complexity reduction of switch-reconfigured antennas. A new optimization technique based on graph models is investigated. This technique is used to minimize the redundancy in a reconfigurable antenna structure and reduce its complexity. A graph modeling rule for switch-reconfigured antennas is proposed, and examples are presented.

Relating MODIS vegetation index time-series with structure, light absorption and stem production of fast-growing Eucalyptus plantations

By allowing the estimation of forest structural and biophysical characteristics at different temporal and spatial scales, remote sensing may contribute to our understanding and monitoring of planted forests. Here, we studied 9-year time-series of the Normalized Difference Vegetation Index (NDVI) from the Moderate Resolution Imaging Spectroradiometer (MODIS) on a network of 16 stands in fast-growing Eucalyptus plantations in Sao Paulo State, Brazil. We aimed to examine the relationships between NDVI time-series spanning entire rotations and stand structural characteristics (volume, dominant height, mean annual increment) in these simple forest ecosystems. Our second objective was to examine spatial and temporal variations of light use efficiency for wood production, by comparing time-series of Absorbed Photosynthetically Active Radiation (APAR) with inventory data. Relationships were calibrated between the NDVI and the fractions of intercepted diffuse and direct radiation, using hemispherical photographs taken on the studied stands at two seasons. APAR was calculated from the NDVI time-series using these relationships. Stem volume and dominant height were strongly correlated with summed NDVI values between planting date and inventory date. Stand productivity was correlated with mean NDVI values. APAR during the first 2 years of growth was variable between stands and was well correlated with stem wood production (r(2) = 0.78). In contrast, APAR during the following years was less variable and not significantly correlated with stem biomass increments. Production of wood per unit of absorbed light varied with stand age and with site index. In our study, a better site index was accompanied both by increased APAR during the first 2 years of growth and by higher light use efficiency for stem wood production during the whole rotation. Implications for simple process-based modelling are discussed. (C) 2009 Elsevier B.V. All rights reserved.

Eight-state supersymmetric U model of strongly correlated fermions

An integrable eight-state supersymmetric U model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has a gl(3/1) supersymmetry and contains one symmetry-preserving free parameter. The model is solved and the Bethe ansatz equations are obtained. [S0163-1829(98)00616-X].

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

A new two-parameter integrable model of strongly correlated fermions with quantum superalgebra symmetry

A new two-parameter integrable model with quantum superalgebra U-q[gl(3/1)] symmetry is proposed, which is an eight-state fermions model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. The model is solved and the Bethe ansatz equations are obtained.

Growth hormone binding protein correlates strongly with leptin and percentage body fat in GH-deficient adults, is increased by GH replacement but does not predict IGF-I response

GH-binding protein (GHBP) corresponds to the extracellular domain of the GH receptor (GHR) and has been shown to be closely related to body fat. This study aimed to examine the inter-relationship between GHBP, leptin and body fat, and to test the hypothesis that GHBP is modified by GH replacement in GH-deficient adults and predicts IGF-I response. Twenty adults, mean age 47 years (range 20-69) with proven GH deficiency were randomly allocated to either GH (up to 0.25 U/kg/week in daily doses) or placebo for 3 months before cross-over to the opposite treatment. Plasma GHBP and leptin were measured at baseline and 2, 4, 8 and 12 weeks after each treatment. Whole body composition was measured at baseline by dual-energy X-ray absorptiometry (DEXA). There was a strong correlation between baseline leptin and GHBP (r = 0.88, P < 0.0001) and between baseline GHBP and percentage body fat, (r = 0.83, P < 0.0001). Mean GHBP levels were higher on GH compared with placebo, 1.53 +/- 0.28 vs 1.41 +/- 0.25 nM, P = 0.049. There was no correlation between baseline IGF-I and GHBP (r = -0.049, P = 0.84), and GHBP did not predict IGF-I response to GH replacement. The close inter-relationship between GHBP, leptin and body fat suggests a possible role for GHBP in the regulation of body composition. GHBP is increased by GH replacement in GH-deficient adults, but does not predict biochemical response to GH replacement. (C) 1999 Churchill Livingstone.

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.