Counting Integer flows in Networks

This paper discusses new analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory \cite{Jaeger}, representation theory \cite{kirillov}, and statistics \cite{persi}. Our methods clearly surpass traditional exhaustive enumeration and other algorithms and can even yield formulas when the input data contains some parameters. These methods are based on the study of rational functions with poles on arrangements of hyperplanes

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

From geometric quantization to Moyal quantization

We show how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic groupoid constructed by ``doubling'' the phase space.Comment: 7 two-column pages, RevTeX, UCR--FM--03--9

Computation of the highest coefficients of weighted Ehrhart quasi-polynomials of rational polyhedra

This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a polynomial function h. Our technique is based on a refinement of an algorithm of A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), pp. 1449--1466] in the unweighted case (i.e., h = 1). In contrast to Barvinok's method, our method is local, obtains an approximation on the level of generating functions, handles the general weighted case, and provides the coefficients in closed form as step polynomials of the dilation. To demonstrate the practicality of our approach we report on computational experiments which show even our simple implementation can compete with state of the art software.Comment: 34 pages, 2 figure

Organizational Adaptation

Organizational adaptation is equivocal. On the one hand, the concept is ubiquitous in management research and acts as the glue binding together the central issues of organizational change, performance, and survival. On the other hand, it lurks around in various guises (e.g., “fit,” “alignment,” “congruence,” and “strategic change”) studied from multiple theoretical streams (e.g., behavioral, resource based, and institutional) and at different levels of analysis (e.g., organization and industry levels). In a novel approach to reviewing 443 adaptation articles that leverages both computational and hand-coded analysis, we produce an interactive visual of the themes most studied by adaptation scholars. We inductively draw out a definition of adaptation as intentional decision making undertaken by organizational members, leading to observable actions that aim to reduce the distance between an organization and its economic and institutional environments. We then review the literature across three main areas of inquiry and six theoretical perspectives that surfaced from our analysis and identify 11 difficulties that have hampered adaptation research in the past 50 years. Our review suggests ways to address these difficulties to enable future research to develop and cumulate

Estimating the incidence of equine viral arteritis and the sensitivity of its surveillance in the French breeding stock

Equine viral arteritis (EVA) may have serious economic impact on the equine industry. For this reason, it is monitored in many countries, especially in breeding stock, to avoid its spread during breeding activities. In France, surveillance is mainly based on serological tests, since mares are not vaccinated, but difficulties in interpreting certain series of results may impair the estimation of the number of outbreaks. In this study, we propose specific rules for identifying seroconversion in order to estimate the number of outbreaks that were detected by the breeding stock surveillance component (BSSC) in France between 2006 and 2013. A consensus among multidisciplinary experts was reached to consider seroconversion as a change in antibody titer from negative to at least 32, or as an eight-fold or greater increase in antibody level. Using these rules, 239 cases and 177 outbreaks were identified. Subsequently, we calculated the BSSC's sensitivity as the ratio of the number of detected outbreaks to the total number of outbreaks that occurred in breeding stock (including unreported outbreaks) estimated using a capture-recapture model. The total number of outbreaks was estimated at 215 (95% credible interval 195-249) and the surveillance sensitivity at 82% (CrI95% 71-91). Our results confirm EVA circulation in French breeding stock, show that neutralizing antibodies can persist up to eight years in naturally infected mares and suggest that certain mares have been reinfected. This study shows that the sensitivity of the BSSC is relatively high and supports its relevance to prevent the disease spreading through mating

Joint inversion of teleseismic and GOCE gravity data: application to the Himalayas

Our knowledge and understanding of the 3-D lithospheric structure of the Himalayas and the Tibetan Plateau is still challenging although numerous geophysical studies have been performed in the region. The GOCE satellite mission has the ambitious goal of mapping Earth's gravity field with unprecedented precision (i.e. an accuracy of 1-2 mGal for a spatial resolution of 100 km) to observe the lithosphere and upper-mantle structure. Consequently, it gives new insights in the lithospheric structure beneath the Himalayas and the Tibetan Plateau. Indeed, the GOCE gravity data now allow us to develop a new strategy for joint gravimetry-seismology inversion. Combined with teleseismic data over a large region in a joint inversion scheme, they will lead to lithospheric velocity-density models constrained in two complementary ways. We apply this joint inversion scheme to the Hi-CLIMB (Himalayan-Tibetan Continental Lithosphere during Mountain Building) seismological network which was deployed in South Tibet and the Himalayas for a 3-yr period. The large size of the network, the high quality of the seismological data and the new GOCE gravity data set allow us to image the entire lithosphere of this active area in an innovative way. We image 3-D low velocity and density structures in the middle crust that fit the location of discontinuous low S-velocity zones revealed by receiver functions in previous geophysical studies. In the deeper parts of our velocity model we image a positive anomaly interpreted to be the heterogenous Indian lithosphere vertically descending beneath the centre of the Tibetan Platea

INTERMEDIATE SUMS ON POLYHEDRA II:BIDEGREE AND POISSON FORMULA

Abstract. We continue our study of intermediate sums over polyhedra,interpolating between integrals and discrete sums, whichwere introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449–1466]. By well-known decompositions, it is sufficient to considerthe case of affine cones s+c, where s is an arbitrary real vertex andc is a rational polyhedral cone. For a given rational subspace L,we integrate a given polynomial function h over all lattice slicesof the affine cone s + c parallel to the subspace L and sum up theintegrals. We study these intermediate sums by means of the intermediategenerating functions SL(s+c)(ξ), and expose the bidegreestructure in parameters s and ξ, which was implicitly used in thealgorithms in our papers [Computation of the highest coefficients ofweighted Ehrhart quasi-polynomials of rational polyhedra, Found.Comput. Math. 12 (2012), 435–469] and [Intermediate sums onpolyhedra: Computation and real Ehrhart theory, Mathematika 59(2013), 1–22]. The bidegree structure is key to a new proof for theBaldoni–Berline–Vergne approximation theorem for discrete generatingfunctions [Local Euler–Maclaurin expansion of Barvinokvaluations and Ehrhart coefficients of rational polytopes, Contemp.Math. 452 (2008), 15–33], using the Fourier analysis with respectto the parameter s and a continuity argument. Our study alsoenables a forthcoming paper, in which we study intermediate sumsover multi-parameter families of polytopes