Discrete invariants of varieties in positive characteristic

If $S$ is a scheme of characteristic $p$, we define an $F$-zip over $S$ to be a vector bundle with two filtrations plus a collection of semi-linear isomorphisms between the graded pieces of the filtrations. For every smooth proper morphism $X\to S$ satisfying certain conditions the de Rham bundles $H^n_{{\rm dR}}(X/S)$ have a natural structure of an $F$-zip. We give a complete classification of $F$-zips over an algebraically closed field by studying a semi-linear variant of a variety that appears in recent work of Lusztig. For every $F$-zip over $S$ our methods give a scheme-theoretic stratification of $S$. If the $F$-zip is associated to an abelian scheme over $S$ the underlying topological stratification is the Ekedahl-Oort stratification. We conclude the paper with a discussion of several examples such as good reductions of Shimura varieties of PEL type and K3-surfaces.Comment: 35 pages, minor changes in exposition, major changes to introductio

Connectivity measures for internet topologies.

The topology of the Internet has initially been modelled as an undirected graph, where vertices correspond to so-called Autonomous Systems (ASs),and edges correspond to physical links between pairs of ASs. However, in order to capture the impact of routing policies, it has recently become apparent that one needs to classify the edges according to the existing economic relationships (customer-provider, peer-to-peer or siblings) between the ASs. This leads to a directed graph model in which traffic can be sent only along so-called valley-free paths. Four different algorithms have been proposed in the literature for inferring AS relationships using publicly available data from routing tables. We investigate the differences in the graph models produced by these algorithms, focussing on connectivity measures. To this aim, we compute the maximum number of vertex-disjoint valley-free paths between ASs as well as the size of a minimum cut separating a pair of ASs. Although these problems are solvable in polynomial time for ordinary graphs, they are NP-hard in our setting. We formulate the two problems as integer programs, and we propose a number of exact algorithms for solving them. For the problem of finding the maximum number of vertex-disjoint paths, we discuss two algorithms; the first one is a branch-and-price algorithm based on the IP formulation, and the second algorithm is a non LP based branch-and-bound algorithm. For the problem of finding minimum cuts we use a branch-and-cut algo rithm, based on the IP formulation of this problem. Using these algorithms, we obtain exact solutions for both problems in reasonable time. It turns out that there is a large gap in terms of the connectivity measures between the undirected and directed models. This finding supports our conclusion that economic relationships need to be taken into account when building a topology of the Internet.Research; Internet;

Software fault characteristics: A synthesis of the literature

Faults continue to be a significant problem in software. Understanding the nature of these faults is important for practitioners and researchers. There are many published fault characteristics schemes but no one scheme dominates. Consequently it is difficult for practitioners to effectively evaluate the nature of faults in their software systems, and it is difficult for researchers to compare the types of faults found by different fault detection techniques. In this paper we synthesise previous fault characteristics schemes into one comprehensive scheme. Our scheme provides a richer view of faults than the previous schemes published and presents a comprehensive, unified approach which accommodates the many previous schemes. A characteristics-based view of faults should be considered by future researchers in the analysis of software faults and in the design and evaluation of new fault detection tools. We recommend that our fault characteristics scheme be used as a benchmark scheme

Types and concept analysis for legacy systems

We combine type inference and concept analysis in order to gain insight into legacy software systems. Type inference for Cobol yields the types for variables and program parameters. These types are used to perform mathematical concept analysis on legacy systems. We have developed ConceptRefinery, a tool for interactively manipulating concepts. We show how this tools facilitates experiments with concept analysis, and lets reengineers employ their knowedge of the legacy system to refine the results of concept analysis

Square root-based multi-source early PSD estimation and recursive RETF update in reverberant environments by means of the orthogonal Procrustes problem

Multi-channel short-time Fourier transform (STFT) domain-based processing of reverberant microphone signals commonly relies on power-spectral-density (PSD) estimates of early source images, where early refers to reflections contained within the same STFT frame. State-of-the-art approaches to multi-source early PSD estimation, given an estimate of the associated relative early transfer functions (RETFs), conventionally minimize the approximation error defined with respect to the early correlation matrix, requiring non-negative inequality constraints on the PSDs. Instead, we here propose to factorize the early correlation matrix and minimize the approximation error defined with respect to the early-correlation-matrix square root. The proposed minimization problem -- constituting a generalization of the so-called orthogonal Procrustes problem -- seeks a unitary matrix and the square roots of the early PSDs up to an arbitrary complex argument, making non-negative inequality constraints redundant. A solution is obtained iteratively, requiring one singular value decomposition (SVD) per iteration. The estimated unitary matrix and early PSD square roots further allow to recursively update the RETF estimate, which is not inherently possible in the conventional approach. An estimate of the said early-correlation-matrix square root itself is obtained by means of the generalized eigenvalue decomposition (GEVD), where we further propose to restore non-stationarities by desmoothing the generalized eigenvalues in order to compensate for inevitable recursive averaging. Simulation results indicate fast convergence of the proposed multi-source early PSD estimation approach in only one iteration if initialized appropriately, and better performance as compared to the conventional approach

Characterization of pharyngeal hypocontractility patterns during deglutition: High Resolution Impedance Manometry findings

Introduction High resolution impedance manometry (HRIM) provides an objective measure of pharyngeal pressurization and bolus flow and can be analysed using pressure flow analysis (PFA). The aim of the study is to investigate different types of pharyngeal hypocontractility and their distribution in patients with pharyngeal dysphagia. Material and Methods A cohort study was conducted on patients with dysphagia referred for HRIM. Inclusion criteria were abnormal (<5th percentile) pharyngeal contractile integral (PhCI) or abnormal regional contractile integrals (velo- or meso- or hypo-pharyngeal integrals). PFA was performed on 10ml liquid swallows using the Swallow GatewayTM open access analysis portal. Patients were classified based on a proposed HRIM scheme. The distribution of PFA metrics was compared between patients with normal and abnormal PhCI using the chi-squared test. Results In total 38 patients were studied and 137 swallows were analysed. Absent pharyngeal contractility was found in 5.3% (2/38) of the patients, ineffective pharyngeal contractility in 68.4% (26/38), and fragmented pharyngeal contractility in 26.3% (10/38). Regional weakness was mainly observed in the mesopharynx (94.7% of the patients), followed by the hypopharynx (50%) and the velopharynx (15.8%). A combined disorder of pharyngeal propulsion and UES restriction was seen in 44.7% (17/38) of the patients. Patients with a normal PhCI (fragmented pharyngeal contractility) were more likely to present an abnormal integrated relaxation pressure at the level of the upper esophageal sphincter (\u3c72=14.56, p=0.001) Conclusion Based on the pharyngeal contractile integrals, two main types of pharyngeal hypocontractility are present in the clinical population of patients: ineffective and fragmented pharyngeal contractility. Totally absent peristalsis in uncommon. In almost half of the patients, pharyngeal propulsion disorders are combined to disorders of UES restriction

Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author together with A. Ghigi [FGP] similar computations were done in the case $g'=0$. Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$ and we show that these are the only families with $g'=1$ satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.Comment: 18 pages, to appear in Geometriae Dedicat

Report on the First International Workshop on Technical Debt Analytics (TDA 2016)

This report outlines the motivation and goals of the First International Workshop on Technical Debt Analytics (TDA 2016), presents the workshop programme, introduces the work accepted for presentation, and summarizes the major results and themes that emerged from the discussion and activities undertaken during the workshop

Relations between some invariants of algebraic varieties in positive characteristic

We discuss relations between certain invariants of varieties in positive characteristic, like the a-number and the height of the Artin-Mazur formal group. We calculate the a-number for Fermat surfacesComment: 13 page