Counting Simplices in Hypergraph Streams

We consider the problem of space-efficiently estimating the number of simplices in a hypergraph stream. This is the most natural hypergraph generalization of the highly-studied problem of estimating the number of triangles in a graph stream. Our input is a $k$-uniform hypergraph $H$ with $n$ vertices and $m$ hyperedges. A $k$-simplex in $H$ is a subhypergraph on $k+1$ vertices $X$ such that all $k+1$ possible hyperedges among $X$ exist in $H$. The goal is to process a stream of hyperedges of $H$ and compute a good estimate of $T_k(H)$, the number of $k$-simplices in $H$. We design a suite of algorithms for this problem. Under a promise that $T_k(H) \ge T$, our algorithms use at most four passes and together imply a space bound of $O( \epsilon^{-2} \log\delta^{-1} \text{polylog} n \cdot \min\{ m^{1+1/k}/T, m/T^{2/(k+1)} \} )$ for each fixed $k \ge 3$, in order to guarantee an estimate within $(1\pm\epsilon)T_k(H)$ with probability at least $1-\delta$. We also give a simpler $1$-pass algorithm that achieves $O(\epsilon^{-2} \log\delta^{-1} \log n\cdot (m/T) ( \Delta_E + \Delta_V^{1-1/k} ))$ space, where $\Delta_E$ (respectively, $\Delta_V$) denotes the maximum number of $k$-simplices that share a hyperedge (respectively, a vertex). We complement these algorithmic results with space lower bounds of the form $\Omega(\epsilon^{-2})$, $\Omega(m^{1+1/k}/T)$, $\Omega(m/T^{1-1/k})$ and $\Omega(m\Delta_V^{1/k}/T)$ for multi-pass algorithms and $\Omega(m\Delta_E/T)$ for $1$-pass algorithms, which show that some of the dependencies on parameters in our upper bounds are nearly tight. Our techniques extend and generalize several different ideas previously developed for triangle counting in graphs, using appropriate innovations to handle the more complicated combinatorics of hypergraphs

Julia: A Fresh Approach to Numerical Computing

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia questions notions generally held as "laws of nature" by practitioners of numerical computing: 1. High-level dynamic programs have to be slow. 2. One must prototype in one language and then rewrite in another language for speed or deployment, and 3. There are parts of a system for the programmer, and other parts best left untouched as they are built by the experts. We introduce the Julia programming language and its design --- a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming. Julia shows that one can have machine performance without sacrificing human convenience.Comment: 37 page

Cash Box, November 14, 1964

The international music record weeklyPublication ceased with Nov. 199

Représentation d'un grand réseau à partir d'une classification hiérarchique de ses sommets

International audienceGraph visualization is an important tool to understand the main features of a network but, when the number of nodes in the graph exceeds few hundreds, standard visualization methods are computationally expensive. Moreover, force directed algorithms do not help the understanding of the community structure of the newtork, if is exists. In this paper, a new visualization method based on a hierarchical clustering of the nodes of the graph is proposed. It can handle graphs having several thousands nodes in a few seconds. Several simplified representations of the graph are accessible, giving the user the opportunity to understand the macroscopic organization of the network and then, to focus on some particular parts of the graph. This refining process is controlled as follows. Partitions under consideration are evaluated via the classical modularity quality measure. A distribution of the quality measure in the case of graphs without structure is obtained by applying the proposed method to random graphs with the same degree distribution as the graph under study. Then only significant partitions are shown during the refining process. This approach is illustrated on several public datasets and compared with other visualization methods meant to emphasize the graph communities. It is also tested on a large network built from a corpus of medieval land charters

Earthquake Engineering

The book Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures contains fifteen chapters written by researchers and experts in the fields of earthquake and structural engineering. This book provides the state-of-the-art on recent progress in the field of seimology, earthquake engineering and structural engineering. The book should be useful to graduate students, researchers and practicing structural engineers. It deals with seismicity, seismic hazard assessment and system oriented emergency response for abrupt earthquake disaster, the nature and the components of strong ground motions and several other interesting topics, such as dam-induced earthquakes, seismic stability of slopes and landslides. The book also tackles the dynamic response of underground pipes to blast loads, the optimal seismic design of RC multi-storey buildings, the finite-element analysis of cable-stayed bridges under strong ground motions and the acute psychiatric trauma intervention due to earthquakes