The holonomy groupoid of a singular foliation

We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper ([H. E. Winkelnkemper, The graph of a foliation, Ann. Glob. Anal. Geom. 1 (3) (1983), 51-75.]); the same holds in the singular cases of [J. Pradines, How to define the differentiable graph of a singular foliation, C. Top. Geom. Diff. Cat. XXVI(4) (1985), 339-381.], [B. Bigonnet, J. Pradines, Graphe d'un feuilletage singulier, C. R. Acad. Sci. Paris 300 (13) (1985), 439-442.], [C. Debord, Local integration of Lie algebroids, Banach Center Publ. 54 (2001), 21-33.], [C. Debord, Holonomy groupoids of singular foliations, J. Diff. Geom. 58 (2001), 467-500.], which from our point of view can be thought of as being "almost regular”. In the general case, the holonomy groupoid can be quite an ill behaved geometric object. On the other hand it often has a nice longitudinal smooth structure. Nonetheless, we use this groupoid to generalize to the singular case Connes' construction of the C*-algebra of the foliation. We also outline the construction of a longitudinal pseudo-differential calculus; the analytic index of a longitudinally elliptic operator takes place in the K-theory of our C*-algebra. In our construction, the key notion is that of a bi-submersion which plays the role of a local Lie groupoid defining the foliation. Our groupoid is the quotient of germs of these bi-submersions with respect to an appropriate equivalence relatio

Analysis of IPTV Channels Watching Preferences in Bosnia and Herzegovina

IPTV service is a new service which is today offered from almost every Telecom operator. One of the advantages of IPTV service stemming from its architecture is certainly the fact that it is very easy to measure what TV channels are the ones mostly watched. This papers desribes this measurement and analysis results in one Telecom operator in Bosnia and Herzegovina. They describe what TV channels are mostly watched in different time periods. We developed a simple weighting algorithm to order the channels by watching rate. Based on it we are providing extensive tables. This paper forms an industrial contribution with results important for marketing but also is scientific contribution because it introduces one new method of scoring TV channels based on previous measurements in their audience. We also developed IPTV Statistics model and described results from this research for a new statistics model. This paper is the continuous of previously published contributions from this area

Principal infinity-bundles - General theory

The theory of principal bundles makes sense in any infinity-topos, such as that of topological, of smooth, or of otherwise geometric infinity-groupoids/infinity-stacks, and more generally in slices of these. It provides a natural geometric model for structured higher nonabelian cohomology and controls general fiber bundles in terms of associated bundles. For suitable choices of structure infinity-group G these G-principal infinity-bundles reproduce the theories of ordinary principal bundles, of bundle gerbes/principal 2-bundles and of bundle 2-gerbes and generalize these to their further higher and equivariant analogs. The induced associated infinity-bundles subsume the notions of gerbes and higher gerbes in the literature. We discuss here this general theory of principal infinity-bundles, intimately related to the axioms of Giraud, Toen-Vezzosi, Rezk and Lurie that characterize infinity-toposes. We show a natural equivalence between principal infinity-bundles and intrinsic nonabelian cocycles, implying the classification of principal infinity-bundles by nonabelian sheaf hyper-cohomology. We observe that the theory of geometric fiber infinity-bundles associated to principal infinity-bundles subsumes a theory of infinity-gerbes and of twisted infinity-bundles, with twists deriving from local coefficient infinity-bundles, which we define, relate to extensions of principal infinity-bundles and show to be classified by a corresponding notion of twisted cohomology, identified with the cohomology of a corresponding slice infinity-topos. In a companion article [NSSb] we discuss explicit presentations of this theory in categories of simplicial (pre)sheaves by hyper-Cech cohomology and by simplicial weakly-principal bundles; and in [NSSc] we discuss various examples and applications of the theory.Comment: 46 pages, published versio

A Labview Based Leakage Current Monitoring System For HV Insulators

In this paper, a Labview based leakage current monitoring system for High Voltage insulators is described. The system uses a general purpose DAQ system with the addition of different current sensors. The DAQ system consists of a chassis and hot-swappable modules. Through the proper design of current sensors, low cost modules operating with a suitable input range can be employed. Fully customizable software can be developed using Labview, allowing on-demand changes and incorporation of upgrades. Such a system provides a low cost alternative to specially designed equipment with the added advantage of maximum flexibility. Further, it can be modified to satisfy the specifications (technical and economical) set under different scenarios. In fact, the system described in this paper has already been installed in the HV Lab of the TEI of Crete whereas a variation of it is currently in use in TALOS High Voltage Test Station

The holonomy of a singular foliation

We give an overview of [1], in collaboration with G. Skandalis, where we construct the holonomy groupoid and the C ∗ -algebras associated with any singular foliation (in the sense of Stefan and Sussmann)

The holonomy groupoid of a singular foliation

We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper ([H. E. Winkelnkemper, The graph of a foliation, Ann. Glob. Anal. Geom. 1 (3) (1983), 51–75.]); the same holds in the singular cases of [J. Pradines, How to define the differentiable graph of a singular foliation, C. Top. Geom. Diff. Cat. XXVI(4) (1985), 339–381.], [B. Bigonnet, J. Pradines, Graphe d'un feuilletage singulier, C. R. Acad. Sci. Paris 300 (13) (1985), 439–442.], [C. Debord, Local integration of Lie algebroids, Banach Center Publ. 54 (2001), 21–33.], [C. Debord, Holonomy groupoids of singular foliations, J. Diff. Geom. 58 (2001), 467–500.], which from our point of view can be thought of as being “almost regular”. In the general case, the holonomy groupoid can be quite an ill behaved geometric object. On the other hand it often has a nice longitudinal smooth structure. Nonetheless, we use this groupoid to generalize to the singular case Connes' construction of the C*-algebra of the foliation. We also outline the construction of a longitudinal pseudo-differential calculus; the analytic index of a longitudinally elliptic operator takes place in the K-theory of our C*-algebra. In our construction, the key notion is that of a bi-submersion which plays the role of a local Lie groupoid defining the foliation. Our groupoid is the quotient of germs of these bi-submersions with respect to an appropriate equivalence relation

Laplacians and spectrum for singular foliations

The author surveys Connes' results on the longitudinal Laplace operator along a (regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator (unbounded) and has the same spectrum in every (faithful) representation, in particular, in L 2 of the manifold and L 2 of a leaf. The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum. © 2014 Fudan University and Springer-Verlag Berlin Heidelberg

Mobile phone security and forensics: a practical approach

This new edition provides both theoretical and practical background of security and forensics for mobile phones. The author discusses confidentiality, integrity, and availability threats in mobile telephones to provide background for the rest of the book. Security and secrets of mobile phones are discussed including software and hardware interception, fraud and other malicious techniques used “against” users. The purpose of this book is to raise user awareness in regards to security and privacy threats present in the use of mobile phones while readers will also learn where forensics data reside in the mobile phone and the network and how to conduct a relevant analysis. The information on denial of service attacks has been thoroughly updated for the new edition. Also, a major addition to this edition is a section discussing software defined radio and open source tools for mobile phones

PBX Security and Forensics: A Practical Approach

PBX Security and Forensics begins with an introduction to PBXs (Private Branch Exchanges) and the scene, statistics and involved actors. This book discusses confidentiality, integrity and availability threats in PBXs. The author examines the threats and the technical background as well as security and Forensics involving PBXs. The purpose of this book is to raise user awareness in regards to security and privacy threats present in PBXs, helping both users and administrators safeguard their systems