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

A rare case of leiomyoma of the bladder

Bladder leiomyoma is a benign tumour of the bladder and constitute <0.5% of all bladder tumors. We report a clinical case of a 51‑year‑old female who presented with with symptomatic bladder leiomyoma. An ultrasound examination showed well-defined bladder leiomyoma in the right posterior bladder wall, which was excised through a transurethral resection. The pathologic diagnosis was bladder leiomyoma

Spectral geometry of κ\kappa-Minkowski space

After recalling Snyder's idea of using vector fields over a smooth manifold as `coordinates on a noncommutative space', we discuss a two dimensional toy-model whose `dual' noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its `spectral properties' and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.Comment: 23 pages, expanded versio

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

Cholinergic innervation of human mesenteric lymphatic vessels

Background: The cholinergic neurotransmission within the human mesenteric lymphatic vessels has been poorly studied. Therefore, our aim is to analyse the cholinergic nerve fibres of lymphatic vessels using the traditional enzymatic techniques of staining, plus the biochemical modifications of acetylcholinesterase (AChE) activity.Materials and methods: Specimens obtained from human mesenteric lymphatic vessels were subjected to the following experimental procedures: 1) drawing, cutting and staining of tissues; 2) staining of total nerve fibres; 3) enzymatic staining of cholinergic nerve fibres; 4) homogenisation of tissues; 5) biochemical amount of proteins; 6) biochemical amount of AChE activity; 6) quantitative analysis of images; 7) statistical analysis of data.Results: The mesenteric lymphatic vessels show many AChE positive nerve fibres around their wall with an almost plexiform distribution. The incubation time was performed at 1 h (partial activity) and 6 h (total activity). Moreover, biochemical dosage of the same enzymatic activity confirms the results obtained with morphological methods.Conclusions: The homogenates of the studied tissues contain strong AChE activity. In our study, the lymphatic vessels appeared to contain few cholinergic nerve fibres. Therefore, it is expected that perivascular nerve stimulation stimulates cholinergic nerves innervating the mesenteric arteries to release the neurotransmitter AChE, which activates muscarinic or nicotinic receptors to modulate adrenergic neurotransmission. These results strongly suggest, that perivascular cholinergic nerves have little or no effect on the adrenergic nerve function in mesenteric arteries. The cholinergic nerves innervating mesenteric arteries do not mediate direct vascular responses.

Predicting Fishing Footprint of Trawlers From Environmental and Fleet Data: An Application of Artificial Neural Networks

The increasing use of tracking devices, such as the Vessel Monitoring System (VMS) and the Automatic Identification System (AIS), have allowed, in the last decade, detailed spatial and temporal analyses of fishing footprints and of their effects on environments and resources. Nevertheless, tracking devices usually allow monitoring of the largest length classes composing different fleets, whereas fishing vessels below a regulatory threshold (i.e., 15 m in length-over-all) are not mandatorily equipped with these tools. This issue is critical, since 36% of the vessels in the European Union (EU) fleets belong to these “hidden” length classes. In this study, a model [namely, a cascaded multilayer perceptron network (CMPN)] is devised to predict the annual fishing footprints of vessels without tracking devices. This model uses information about fleet structures, environmental characteristics, human activities, and fishing effort patterns of vessels equipped with tracking devices. Furthermore, the model is able to take into account the interactions between different components of the fleets (e.g., fleet segments), which are characterized by different operating ranges and compete for the same marine space. The model shows good predictive performance and allows the extension of spatial analyses of fishing footprints to the relevant, although still unexplored, fleet segments

Quantum Bundle Description of the Quantum Projective Spaces

We realise Heckenberger and Kolb's canonical calculus on quantum projective (n-1)-space as the restriction of a distinguished quotient of the standard bicovariant calculus for Cq[SUn]. We introduce a calculus on the quantum (2n-1)-sphere in the same way. With respect to these choices of calculi, we present quantum projective (N-1)-space as the base space of two different quantum principal bundles, one with total space Cq[SUn], and the other with total space Cq[S^(2n-1)]. We go on to give Cq[CP^n] the structure of a quantum framed manifold. More specifically, we describe the module of one-forms of Heckenberger and Kolb's calculus as an associated vector bundle to the principal bundle with total space Cq[SUn]. Finally, we construct strong connections for both bundles.Comment: 33 pages; minor changes, to appear in Comm. Math. Phy