Path-Fault-Tolerant Approximate Shortest-Path Trees

Let $G=(V,E)$ be an $n$-nodes non-negatively real-weighted undirected graph. In this paper we show how to enrich a {\em single-source shortest-path tree} (SPT) of $G$ with a \emph{sparse} set of \emph{auxiliary} edges selected from $E$, in order to create a structure which tolerates effectively a \emph{path failure} in the SPT. This consists of a simultaneous fault of a set $F$ of at most $f$ adjacent edges along a shortest path emanating from the source, and it is recognized as one of the most frequent disruption in an SPT. We show that, for any integer parameter $k \geq 1$, it is possible to provide a very sparse (i.e., of size $O(kn\cdot f^{1+1/k})$) auxiliary structure that carefully approximates (i.e., within a stretch factor of $(2k-1)(2|F|+1)$) the true shortest paths from the source during the lifetime of the failure. Moreover, we show that our construction can be further refined to get a stretch factor of $3$ and a size of $O(n \log n)$ for the special case $f=2$, and that it can be converted into a very efficient \emph{approximate-distance sensitivity oracle}, that allows to quickly (even in optimal time, if $k=1$) reconstruct the shortest paths (w.r.t. our structure) from the source after a path failure, thus permitting to perform promptly the needed rerouting operations. Our structure compares favorably with previous known solutions, as we discuss in the paper, and moreover it is also very effective in practice, as we assess through a large set of experiments.Comment: 21 pages, 3 figures, SIROCCO 201

The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere

Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one on the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton' projection. We also introduce a real structure which satisfies all required properties modulo smoothing operators.Comment: 40 pages, no figures, Latex. v2: Title changed. Sect. 9 on real structure completely rewritten and results strengthened. Additional minor changes throughout the pape

Fully-dynamic Approximation of Betweenness Centrality

Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in evolving networks. In previous work we proposed the first semi-dynamic algorithms that recompute an approximation of betweenness in connected graphs after batches of edge insertions. In this paper we propose the first fully-dynamic approximation algorithms (for weighted and unweighted undirected graphs that need not to be connected) with a provable guarantee on the maximum approximation error. The transfer to fully-dynamic and disconnected graphs implies additional algorithmic problems that could be of independent interest. In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs. For both weighted and unweighted graphs, we also propose the first fully-dynamic algorithms that keep track of such upper bound. In addition, we extend our former algorithm for semi-dynamic BFS to batches of both edge insertions and deletions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in fully-dynamic networks with millions of edges feasible. Our experiments show that they can achieve substantial speedups compared to recomputation, up to several orders of magnitude

Open and / or laparoscopic surgical treatment of liver hydatic cysts

Hydatid disease is a severe parasitic disease with a widely ranging distribution. In the human being the liver is the most frequent organ affected. 1 The treatment should be individualized to the morphology, size, number and location of the cysts, that is why a variety of surgical operations have been advocated from complete resection like total pericystectomy or partial hepatectomy to laparoscopy to a minimally invasive procedures like percutaneous aspiration of cysts to conservative drug therapy. 3-4 This study compares laparoscopic versus open management of the hydatid cyst of liver the surgical approach to liver echinococcosis is still a controversial issue and shows our results of surgical treatment of liver hydatid cysts during a 3-years period

Quantum Isometries of the finite noncommutative geometry of the Standard Model

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.Comment: 29 pages, no figures v3: minor change

Quantized algebras of functions on homogeneous spaces with Poisson stabilizers

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman and Dijkhuizen-Stokman we classify the irreducible representations of C(G_q/K_q) and obtain a composition series for C(G_q/K_q). We describe closures of the symplectic leaves of G/K refining the well-known description in the case of flag manifolds in terms of the Bruhat order. We then show that the same rules describe the topology on the spectrum of C(G_q/K_q). Next we show that the family of C*-algebras C(G_q/K_q), 0<q\le1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra \C[G/K]. Finally, extending a result of Nagy, we show that C(G_q/K_q) is canonically KK-equivalent to C(G/K).Comment: 23 pages; minor changes, typos correcte

A Hypothetical New Challenging Use for Indocyanine Green Fluorescence during Laparoscopic Appendectomy: A Mini-Series of Our Experience and Literary Review

Laparoscopic appendectomy (LA) is a well-standardized surgical procedure, but there are still controversies about the different devices to be used for the appendiceal stump closure and the related postoperative complications. Indocyanine green (ICG) fluorescence angiography (FA) has already been shown to be helpful in elective and emergency surgery, providing intraoperative information on tissue and organ perfusion, thus guiding the surgical decisions and the technical strategies. According to these two aspects, we report a mini-series of the first five patients affected by gangrenous and flegmonous acute appendicitis intraoperatively evaluated with ICG-FA during LA. The patients were admitted to the Emergency Department with an usual range of symptoms for acute appendicitis. The patients were successfully managed by fully LA with the help of a new hypothetical challenging use of ICG-FA

Teaching mathematics for search using a tutorial style of delivery

Understanding of mathematics is needed to underpin the process of search, either explicitly with Exact Match (Boolean logic, adjacency) or implicitly with Best match natural language search. In this paper we outline some pedagogical challenges in teaching mathematics for information retrieval (IR) to postgraduate information science students. The aim is to take these challenges either found by experience or in the literature, to identify both theoretical and practical ideas in order to improve the delivery of the material and positively affect the learning of the target audience by using a tutorial style of teaching. Results show that there is evidence to support the notion that a more pro-active style of teaching using tutorials yield benefits both in terms of assessment results and student satisfaction