On the heterochromatic number of hypergraphs associated to geometric graphs and to matroids

The heterochromatic number hc(H) of a non-empty hypergraph H is the smallest integer k such that for every colouring of the vertices of H with exactly k colours, there is a hyperedge of H all of whose vertices have different colours. We denote by nu(H) the number of vertices of H and by tau(H) the size of the smallest set containing at least two vertices of each hyperedge of H. For a complete geometric graph G with n > 2 vertices let H = H(G) be the hypergraph whose vertices are the edges of G and whose hyperedges are the edge sets of plane spanning trees of G. We prove that if G has at most one interior vertex, then hc(H) = nu(H) - tau(H) + 2. We also show that hc(H) = nu(H) - tau(H) + 2 whenever H is a hypergraph with vertex set and hyperedge set given by the ground set and the bases of a matroid, respectively

Comparison of averages of flows and maps

It is shown that in transient chaos there is no direct relation between averages in a continuos time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincare map. In contrast to permanent chaos, results obtained from the Poincare map can even be qualitatively incorrect. The reason is that the return time between intersections on the Poincare surface becomes relevant. However, after introducing a true-time Poincare map, quantities known from the usual Poincare map, such as conditionally invariant measure and natural measure, can be generalized to this case. Escape rates and averages, e.g. Liapunov exponents and drifts can be determined correctly using these novel measures. Significant differences become evident when we compare with results obtained from the usual Poincare map.Comment: 4 pages in Revtex with 2 included postscript figures, submitted to Phys. Rev.

Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Fast flowing populations are not well mixed

In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of individuals mixed by flows. We propose an analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.Comment: 19 pages, 8 figure

Anomalous density dependence of static friction in sand

We measured experimentally the static friction force $F_s$ on the surface of a glass rod immersed in dry sand. We observed that $F_s$ is extremely sensitive to the closeness of packing of grains. A linear increase of the grain-density yields to an exponentially increasing friction force. We also report on a novel periodicity of $F_s$ during gradual pulling out of the rod. Our observations demonstrate the central role of grain bridges and arches in the macroscopic properties of granular packings.Comment: plain tex, 6 pages, to appear in Phys.Rev.

Velocity and density profiles of granular flow in channels using lattice gas automaton

We have performed two-dimensional lattice-gas-automaton simulations of granular flow between two parallel planes. We find that the velocity profiles have non-parabolic distributions while simultaneously the density profiles are non-uniform. Under non-slip boundary conditions, deviation of velocity profiles from the parabolic form of newtonian fluids is found to be characterized solely by ratio of maximal velocity at the center to the average velocity, though the ratio depends on the model parameters in a complex manner. We also find that the maximal velocity ($u_{max}$) at the center is a linear function of the driving force (g) as $u_{max} = \alpha g - \delta$ with non-zero $\delta$ in contrast with newtonian fluids. Regarding density profiles, we observe that densities near the boundaries are higher than those in the center. The width of higher densities (above the average density) relative to the channel width is a decreasing function of a variable which scales with the driving force (g), energy dissipation parameter ($\epsilon$) and the width of the system (L) as $g^{\mu} L^{\nu}/\epsilon$ with exponents $\mu = 1.4 \pm 0.1$ and $\nu = 0.5 \pm 0.1$. A phenomenological theory based on a scaling argument is presented to interpret these findings.Comment: Latex, 15 figures, to appear in PR

Learning valued relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval

Description of diffusive and propagative behavior on fractals

The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived

The effect of iterative model reconstruction on coronary artery calcium quantification

Coronary artery calcium (CAC) scoring with computed tomography (CT) is an established tool for quantifying calcified atherosclerotic plaque burden. Despite the widespread use of novel image reconstruction techniques in CT, the effect of iterative model reconstruction on CAC score remains unclear. We sought to assess the impact of iterative model based reconstruction (IMR) on coronary artery calcium quantification as compared to the standard filtered back projection (FBP) algorithm and hybrid iterative reconstruction (HIR). In addition, we aimed to simulate the impact of iterative reconstruction techniques on calcium scoring based risk stratification of a larger asymptomatic population. We studied 63 individuals who underwent CAC scoring. Images were reconstructed with FBP, HIR and IMR and CAC scores were measured. We estimated the cardiovascular risk reclassification rate of IMR versus HIR and FBP in a larger asymptomatic population (n = 504). The median CAC scores were 147.7 (IQR 9.6-582.9), 107.0 (IQR 5.9-526.6) and 115.1 (IQR 9.3-508.3) for FBP, HIR and IMR, respectively. The HIR and IMR resulted in lower CAC scores as compared to FBP (both p < 0.001), however there was no difference between HIR and IMR (p = 0.855). The CAC score decreased by 7.2 % in HIR and 7.3 % in IMR as compared to FBP, resulting in a risk reclassification rate of 2.4 % for both HIR and IMR. The utilization of IMR for CAC scoring reduces the measured calcium quantity. However, the CAC score based risk stratification demonstrated modest reclassification in IMR and HIR versus FBP

Acute hyperglycemia abolishes cardioprotection by remote ischemic perconditioning

BACKGROUND: Remote ischemic perconditioning (RIPerC) has a promising therapeutic insight to improve the prognosis of acute myocardial infarction. Chronic comorbidities such as diabetes are known to interfere with conditioning interventions by modulating cardioprotective signaling pathways, such as e.g., mTOR pathway and autophagy. However, the effect of acute hyperglycemia on RIPerC has not been studied so far. Therefore, here we investigated the effect of acute hyperglycemia on cardioprotection by RIPerC. METHODS: Wistar rats were divided into normoglycemic (NG) and acute hyperglycemic (AHG) groups. Acute hyperglycemia was induced by glucose infusion to maintain a serum glucose concentration of 15-20 mM throughout the experimental protocol. NG rats received mannitol infusion of an equal osmolarity. Both groups were subdivided into an ischemic (Isch) and a RIPerC group. Each group underwent reversible occlusion of the left anterior descending coronary artery (LAD) for 40 min in the presence or absence of acute hyperglycemia. After the 10-min LAD occlusion, RIPerC was induced by 3 cycles of 5-min unilateral femoral artery and vein occlusion and 5-min reperfusion. After 120 min of reperfusion, infarct size was measured by triphenyltetrazolium chloride staining. To study underlying signaling mechanisms, hearts were harvested for immunoblotting after 35 min in both the NG and AHG groups. RESULTS: Infarct size was significantly reduced by RIPerC in NG, but not in the AHG group (NG + Isch: 46.27 +/- 5.31 % vs. NG + RIPerC: 24.65 +/- 7.45 %, p < 0.05; AHG + Isch: 54.19 +/- 4.07 % vs. 52.76 +/- 3.80 %). Acute hyperglycemia per se did not influence infarct size, but significantly increased the incidence and duration of arrhythmias. Acute hyperglycemia activated mechanistic target of rapamycine (mTOR) pathway, as it significantly increased the phosphorylation of mTOR and S6 proteins and the phosphorylation of AKT. In spite of a decreased LC3II/LC3I ratio, other markers of autophagy, such as ATG7, ULK1 phopsphorylation, Beclin 1 and SQSTM1/p62, were not modulated by acute hyperglycemia. Furthermore, acute hyperglycemia significantly elevated nitrative stress in the heart (0.87 +/- 0.01 vs. 0.50 +/- 0.04 microg 3-nitrotyrosine/mg protein, p < 0.05). CONCLUSIONS: This is the first demonstration that acute hypreglycemia deteriorates cardioprotection by RIPerC. The mechanism of this phenomenon may involve an acute hyperglycemia-induced increase in nitrative stress and activation of the mTOR pathway