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;

Some Statistical Issues in the LHCb Experiment

This paper describes statistical issues that are of particular importance and interest to the LHCb experiment in probing new physics beyond the Standard Model through study of CP violation and rare phenomena in B decays. A wish list for statistical methods and tools that will help LHCb to exploit its full physics potential is given at the end

Improving Usability in Procedural Modeling

This work presents new approaches and algorithms for procedural modeling geared towards user convenience and improving usability, in order to increase artists’ productivity. Procedural models create geometry for 3D models from sets of rules. Existing approaches that allow to model trees, buildings, and terrain are reviewed and possible improvements are discussed. A new visual programming language for procedural modeling is discussed, where the user connects operators to visual programs called model graphs. These operators create geometry with textures, assign or evaluate variables or control the sequence of operations. When the user moves control points using the mouse in 3D space, the model graph is executed to change the geometry interactively. Thus, model graphs combine the creativity of freehand modeling with the power of programmed modeling while displaying the program structure more clearly than textbased approaches. Usability is increased as a result of these advantages. Also, an interactive editor for botanical trees is demonstrated. In contrast to previous tree modeling systems, we propose linking rules, parameters and geometry to semantic entities. This has the advantage that problems of associating parameters and instances are completely avoided. When an entity is clicked in the viewport, its parameters are displayed immediately, changes are applied to selected entities, and viewport editing operations are reflected in the parameter set. Furthermore, we store the entities in a hierarchical data structure and allow the user to activate recursive traversal via selection options for all editing operations. The user may choose to apply viewport or parameter changes to a single entity or many entities at once, and only the geometry for the affected entities needs to be updated. The proposed user interface simplifies the modeling process and increases productivity. Interactive editing approaches for 3D models often allow more precise control over a model than a global set of parameters that is used to generate a shape. However, usually scripted procedural modeling generates shapes directly from a fixed set of parameters, and interactive editing mostly uses a fixed set of tools. We propose to use scripts not only to generate models, but also for manipulating the models. A base script would set up the state of an object, and tool scripts would modify that state. The base script and the tool scripts generate geometry when necessary. Together, such a collection of scripts forms a template, and templates can be created for various types of objects. We examine how templates simplify the procedural modeling workflow by allowing for editing operations that are context-sensitive, flexible and powerful at the same time. Many algorithms have been published that produce geometry for fictional landscapes. There are algorithms which produce terrain with minimal setup time, allowing to adapt the level of detail as the user zooms into the landscape. However, these approaches lack plausible river networks, and algorithms that create eroded terrain with river networks require a user to supervise creation and minutes or hours of computation. In contrast to that, this work demonstrates an algorithm that creates terrain with plausible river networks and adaptive level of detail with no more than a few seconds of preprocessing. While the system can be configured using parameters, this text focuses on the algorithm that produces the rivers. However, integrating more tools for user-controlled editing of terrain would be possible.Verbesserung der Usability bei prozeduraler Modellierung Ziel der vorliegenden Arbeit ist es, prozedurale Modellierung durch neue neue Ansätze und Algorithmen einfacher, bequemer und anwendungsfreundlicher zu machen, und damit die Produktivität der Künstler zu erhöhen. Diese Anforderungen werden häufig unter dem Stichwort Usability zusammengefasst. Prozedurale Modelle spezifizieren 3D-Modelle über Regeln. Existierende Ansätze für Bäume, Gebäude und Terrain werden untersucht und es werden mögliche Verbesserungen diskutiert. Eine neue visuelle Programmiersprache für prozedurale Modelle wird vorgestellt, bei der Operatoren zu Modellgraphen verschaltet werden. Die Operatoren erzeugen texturierte Geometrie, weisen Variablen zu und werten sie aus, oder sie steuern den Ablauf der Operationen. Wenn der Benutzer Kontrollpunkte im Viewport mit der Maus verschiebt, wird der Modellgraph ausgeführt, um interaktiv neue Geometrie für das Modell zu erzeugen. Modellgraphen kombinieren die kreativen Möglichkeiten des freihändigen Editierens mit der Mächtigkeit der prozeduralen Modellierung. Darüber hinaus sind Modellgraphen eine visuelle Programmiersprache und stellen die Struktur der Algorithmen deutlicher dar als textbasierte Programmiersprachen. Als Resultat dieser Verbesserungen erhöht sich die Usability. Ein interaktiver Editor für botanische Bäume wird ebenfalls vorgestellt. Im Gegensatz zu früheren Ansätzen schlagen wir vor, Regeln, Parameter und Geometrie zu semantischen Entitäten zu verschmelzen. Auf diese Weise werden Zuordnungsprobleme zwischen Parametern und deren Instanzen komplett vermieden. Wenn im Viewport eine Instanz angeklickt wird, werden sofort ihre Parameter angezeigt, alle Änderungen wirken sich direkt auf die betroffenen Instanzen aus, und Änderungen im Viewport werden sofort in den Parametern reflektiert. Darüber hinaus werden die Entitäten in einer hierarchischen Datenstruktur gespeichert und alle Änderungen können rekursiv auf der Hierarchie ausgeführt werden. Dem Benutzer werden Selektionsoptionen zur Verfügung gestellt, über die er Änderungen an den Parametern oder Änderungen im Viewport an einzelnen oder vielen Instanzen gleichzeitig vornehmen kann. Anschließend muss das System nur die Geometrie der betroffenen Instanzen aktualisieren. Auch hier ist das Ziel, das User Interface möglichst an den Bedürfnissen des Benutzers auszurichten, um Vereinfachungen und eine Erhöhung der Produktivität zu erreichen. Interaktive Editieransätze für 3D-Modelle erlauben häufig eine präzisere Kontrolle über ein Modell als ein globaler Parametersatz, der für die Erzeugung des Modells genutzt wird. Trotzdem erzeugen prozedurale Modellierskripte ihre Modelle meist direkt aus einem festen Parametersatz, während interaktive Tools meist mit hartkodierten Operationen arbeiten. Wir schlagen vor, Skripte nicht nur zur Erzeugung der Modelle zu verwenden, sondern auch um die erzeugten Modelle zu editieren. Ein Basisskript soll die Statusinformationen eines Objekts anlegen, während weitere Skripte diesen Status verändern und passende Geometrie erzeugen. Diese Skripte bilden dann ein Template zum Erzeugen einer Klasse von Objekten. Verschiedene Objekttypen können jeweils ihr eigenes Template haben. Wir zeigen, wie Templates den Workflow mit prozeduralen Modellen vereinfachen können, indem Operationen geschaffen werden, die gleichzeitig kontext-sensitiv, mächtig und flexibel sind. Es existiert eine Reihe von Verfahren, um Geometrie für synthetische Landschaften zu erzeugen. Ein Teil der Algorithmen erzeugt Geometrie mit minimaler Vorberechnung und erlaubt es, den Detailgrad der Landschaft interaktiv an die Perspektive anzupassen. Leider fehlen den so erzeugten Landschaften plausible Flussnetze. Algorithmen, die erodiertes Terrain mit Flussnetzen erzeugen, müssen aufwendig vom Benutzer überwacht werden und brauchen Minuten oder Stunden Rechenzeit. Im Gegensatz dazu stellen wir einen Algorithmus vor, der plausible Flussnetze erzeugt, während sich der Betrachter interaktiv durch die Szene bewegt. Das System kann über Parameter gesteuert werden, aber der Fokus liegt auf dem Algorithmus zur Erzeugung der Flüsse. Dennoch wäre es möglich, Tools zum benutzergesteuerten Editieren von Terrain zu integrieren

Present and Future CP Measurements

We review theoretical and experimental results on CP violation summarizing the discussions in the working group on CP violation at the UK phenomenology workshop 2000 in Durham.Comment: 104 pages, Latex, to appear in Journal of Physics

The scaling limits of the Minimal Spanning Tree and Invasion Percolation in the plane

We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invariant under rotations, scalings, and, in the case of the MST, also under translations. However, they are not expected to be conformally invariant. We also prove some geometric properties of the limiting MST. The topology of convergence is the space of spanning trees introduced by Aizenman, Burchard, Newman & Wilson (1999), and the proof relies on the existence and conformal covariance of the scaling limit of the near-critical percolation ensemble, established in our earlier works.Comment: 56 pages, 21 figures. A thoroughly revised versio

Parallelizing Maximal Clique Enumeration on GPUs

We present a GPU solution for exact maximal clique enumeration (MCE) that performs a search tree traversal following the Bron-Kerbosch algorithm. Prior works on parallelizing MCE on GPUs perform a breadth-first traversal of the tree, which has limited scalability because of the explosion in the number of tree nodes at deep levels. We propose to parallelize MCE on GPUs by performing depth-first traversal of independent subtrees in parallel. Since MCE suffers from high load imbalance and memory capacity requirements, we propose a worker list for dynamic load balancing, as well as partial induced subgraphs and a compact representation of excluded vertex sets to regulate memory consumption. Our evaluation shows that our GPU implementation on a single GPU outperforms the state-of-the-art parallel CPU implementation by a geometric mean of 4.9x (up to 16.7x), and scales efficiently to multiple GPUs. Our code has been open-sourced to enable further research on accelerating MCE

Boosting Higgs pair production in the bbˉbbˉb\bar{b}b\bar{b} final state with multivariate techniques

The measurement of Higgs pair production will be a cornerstone of the LHC program in the coming years. Double Higgs production provides a crucial window upon the mechanism of electroweak symmetry breaking and has a unique sensitivity to the Higgs trilinear coupling. We study the feasibility of a measurement of Higgs pair production in the $b\bar{b}b\bar{b}$ final state at the LHC. Our analysis is based on a combination of traditional cut-based methods with state-of-the-art multivariate techniques. We account for all relevant backgrounds, including the contributions from light and charm jet mis-identification, which are ultimately comparable in size to the irreducible $4b$ QCD background. We demonstrate the robustness of our analysis strategy in a high pileup environment. For an integrated luminosity of $\mathcal{L}=3$ ab$^{-1}$, a signal significance of $S/\sqrt{B}\simeq 3$ is obtained, indicating that the $b\bar{b}b\bar{b}$ final state alone could allow for the observation of double Higgs production at the High-Luminosity LHC.Comment: 47 pages, 22 figures. v2: updated references, added comparison of post-MVA kinematic distributions. v3: matches published version in EPJ