Computing the kk-coverage of a wireless network

Coverage is one of the main quality of service of a wirelessnetwork. $k$-coverage, that is to be covered simultaneously by $k$network nodes, is synonym of reliability and numerous applicationssuch as multiple site MIMO features, or handovers. We introduce here anew algorithm for computing the $k$-coverage of a wirelessnetwork. Our method is based on the observation that $k$-coverage canbe interpreted as $k$ layers of $1$-coverage, or simply coverage. Weuse simplicial homology to compute the network's topology and areduction algorithm to indentify the layers of $1$-coverage. Weprovide figures and simulation results to illustrate our algorithm.Comment: Valuetools 2019, Mar 2019, Palma de Mallorca, Spain. 2019. arXiv admin note: text overlap with arXiv:1802.0844

Horn conditions for quiver subrepresentations and the moment map

We give inductive conditions that characterize the Schubert positions of subrepresentations of a general quiver representation. Our results generalize Belkale’s criterion for the intersection of Schubert varieties in Grassmannians and refine Schofield’s characterization of the dimension vectors of general subrepresentations. This implies Horn type inequalities for the moment cone associated to the linear representation of the group G = ΠxGL(nx) associated to a quiver and a dimension vector n = (nx)

INTERMEDIATE SUMS ON POLYHEDRA: COMPUTATION AND REAL EHRHART THEORY

We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvi-nok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449–1466]. For a given semi-rational polytope p and a rational subspace L, we integrate a given polyno-mial function h over all lattice slices of the polytope p parallel to the subspace L and sum up the integrals. We first develop an al-gorithmic theory of parametric intermediate generating functions. Then we study the Ehrhart theory of these intermediate sums, that is, the dependence of the result as a function of a dilation of the polytope. We provide an algorithm to compute the resulting Ehrhart quasi-polynomials in the form of explicit step polynomi-als. These formulas are naturally valid for real (not just integer) dilations and thus provide a direct approach to real Ehrhart theory

Decreased levels of serum platelet-activating factor acetylhydrolase in patients with rheumatic diseases

PAF is a potent inflammatory compound known to stimulate the release of various cytokines involved in rheumatic diseases. Elevated blood PAF levels are reported in these patients. We report that serum PAF acetylhydrolase activity (AHA) levels are decreased in patients with rheumatoid arthritis or osteoarthritis as compared to healthy controls. Serum and synovial fluid AHA levels were correlated in these patients. The present study suggests the potential role of AHA in controling systemic and/or local PAF levels in patients with rheumatic diseases

Seismic velocities in Southern Tibet lower crust: a receiver function approach for eclogite detection

Beneath the Tibet plateau, the deficit of crustal thickening with respect to what is expected from the plate tectonic constraints is thought to be absorbed either by lateral extrusion or by vertical rock-mass transfer. To nourish the unsettled debate of the relative importance of these two processes, we propose a new approach, based on the S-to-P and the P-to-S wave conversions, enabling the precise determination of the seismic velocities. The weighted amplitudes of the direct conversion and of reverberations are stacked at their predicted arrival times for various values of layer thickness and v(P)/v(S) ratio separately for two sets of P- and S-receiver functions. For each set of receiver functions, coherent stack gives the v(P)/v(S) ratio and thickness for the considered layer (the grid search stacking method). The values of v(P)/v(S) ratio and layer thickness are functions of the velocity used for stacking the set of receiver functions, but using the P- and S-receiver functions allows us to solve this indetermination and to find the effective parameters of the layer: velocity v(S), v(P)/v(S) ratio and thickness. We use a bootstrap resampling of the receiver function data sets to estimate the parameters uncertainties. For the Southern Lhasa Block, the migrated sections of both P- and S-receiver functions (Hi-CLIMB experiment data) show a layer in the lower crust that may be related to the lower Indian crust underplated beneath Tibet. With the grid search stacking method, high shear wave velocities (v(S) similar to 4.73 km s(-1)) and low v(P)/v(S) ratios (similar to 1.69) are detected in this layer. Such values are typical for high-grade eclogites, and the low v(P)/v(S) ratio precludes the confusion with mafic granulites. There is no evidence for partial eclogitization near and south of the Yarlung-Tsangpo Suture, and the about 19 km thick eclogitic layer extends northwards only to about the middle of the Lhasa terrane

The 2015 Gorkha earthquake: A large event illuminating the Main Himalayan Thrust fault

International audienceThe 2015 Gorkha earthquake sequence provides an outstanding opportunity to better characterize the geometry of the Main Himalayan Thrust (MHT). To overcome limitations due to unaccounted lateral heterogeneities, we perform Centroid Moment Tensor inversions in a 3-D Earth model for the main shock and largest aftershocks. In parallel, we recompute S-toP and P-to-S receiver functions from the Hi-CLIMB data set. Inverted centroid locations fall within a low-velocity zone at 10–15 km depth and corresponding to the subhorizontal portion of the MHT that ruptured during the Gorkha earthquake. North of the main shock hypocenter, receiver functions indicate a north dipping feature that likely corresponds to the midcrustal ramp connecting the flat portion to the deep part of the MHT. Our analysis of the main shock indicates that long-period energy emanated updip of high-frequency radiation sources previously inferred. This frequency-dependent rupture process might be explained by different factors such as fault geometry and the presence of fluids

Sharp error terms for return time statistics under mixing conditions

We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S(A) the number of consecutive repetitions of A. We prove that, if the length of the string grows unbondedly, (1) the distribution of T(A), when the process starts with A, is well aproximated by a certain mixture of the point measure at the origin and an exponential law, and (2) S(A) is approximately geometrically distributed. We provide sharp error terms for each of these approximations. The errors we obtain are point-wise and allow to get also approximations for all the moments of T(A) and S(A). To obtain (1) we assume that the process is phi-mixing while to obtain (2) we assume the convergence of certain contidional probabilities

On the athermal character of structural phase transitions

The significance of thermal fluctuations on nucleation in structural first-order phase transitions has been examined. The prototype case of martensitic transitions has been experimentally investigated by means of acoustic emission techniques. We propose a model based on the mean first-passage time to account for the experimental observations. Our study provides a unified framework to establish the conditions for isothermal and athermal transitions to be observed.Comment: 5 pages, 4 figures, accepted in Phys. Rev. Let

Velocity fluctuations in forced Burgers turbulence

We propose a simple method to compute the velocity difference statistics in forced Burgers turbulence in any dimension. Within a reasonnable assumption concerning the nucleation and coalescence of shocks, we find in particular that the `left' tail of the distribution decays as an inverse square power, which is compatible with numerical data. Our results are compared to those of various recent approaches: instantons, operator product expansion, replicas.Comment: 10 pages latex, one postcript figur

Equivariant volumes of non-compact quotients and instanton counting

Motivated by Nekrasov's instanton counting, we discuss a method for calculating equivariant volumes of non-compact quotients in symplectic and hyper-K\"ahler geometry by means of the Jeffrey-Kirwan residue-formula of non-abelian localization. In order to overcome the non-compactness, we use varying symplectic cuts to reduce the problem to a compact setting, and study what happens in the limit that recovers the original problem. We implement this method for the ADHM construction of the moduli spaces of framed Yang-Mills instantons on $\R^{4}$ and rederive the formulas for the equivariant volumes obtained earlier by Nekrasov-Shadchin, expressing these volumes as iterated residues of a single rational function.Comment: 34 pages, 2 figures; minor typos corrected, to appear in Comm. Math. Phy