There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

https://www.bioinf.uni-leipzig.de/Leere/WS1516/SeqAnalGen/T-Coffee.pdf

T-Coffee: A novel method for fast and accurate multiple sequence alignment.

The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

/pdf/the-quickhull-algorithm-for-convex-hulls-ug134bwaff.pdf

The quickhull algorithm for convex hulls

In this article, we propose a family of efficient kernels for large graphs with discrete node labels. Key to our method is a rapid feature extraction scheme based on the Weisfeiler-Lehman test of isomorphism on graphs. It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information. A family of kernels can be defined based on this Weisfeiler-Lehman sequence of graphs, including a highly efficient kernel comparing subtree-like patterns. Its runtime scales only linearly in the number of edges of the graphs and the length of the Weisfeiler-Lehman graph sequence. In our experimental evaluation, our kernels outperform state-of-the-art graph kernels on several graph classification benchmark data sets in terms of accuracy and runtime. Our kernels open the door to large-scale applications of graph kernels in various disciplines such as computational biology and social network analysis.

/pdf/weisfeiler-lehman-graph-kernels-2mc1fyeygq.pdf

Weisfeiler-Lehman Graph Kernels

Combinatorial and geometric computing is a core area of computer science (CS). In fact, most CS curricula contain a course in data structures and algorithms. The area deals with objects such as graphs, sequences, dictionaries, trees, shortest paths, flows, matchings, points, segments, lines, convex hulls, and Voronoi diagrams and forms the basis for application areas such as discrete optimization, scheduling, traffic control, CAD, and graphics. There is no standard library of the data structures and algorithms of combinatorial and geometric computing. This is in sharp contrast to many other areas of computing. There are, for example, packages in statistics (SPSS), numerical analysis (LINPACK, EISPACK), symbolic computation (MAPLE, MATHEMATICA), and linear programming (CPLEX).

/pdf/leda-a-platform-for-combinatorial-and-geometric-computing-3jn6ktiem9.pdf

LEDA: A Platform for Combinatorial and Geometric Computing

State-of-the-art graph kernels do not scale to large graphs with hundreds of nodes and thousands of edges. In this article we propose to compare graphs by counting graphlets, i.e., subgraphs with k nodes where k ∈ {3, 4, 5}. Exhaustive enumeration of all graphlets being prohibitively expensive, we introduce two theoretically grounded speedup schemes, one based on sampling and the second one specifically designed for bounded degree graphs. In our experimental evaluation, our novel kernels allow us to efficiently compare large graphs that cannot be tackled by existing graph kernels.

/pdf/efficient-graphlet-kernels-for-large-graph-comparison-18g172jjlp.pdf

Efficient Graphlet Kernels for Large Graph Comparison

Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C, a one-level form of radix heap gives a time bound for Dijkstra's algorithm of O(m + n log C). A two-level form of radix heap gives a bound of O(m + n log C/log log C). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O(m + na

/pdf/faster-algorithms-for-the-shortest-path-problem-4y13u2dyi6.pdf

Faster Algorithms for the Shortest Path Problem

We give an overview of the LEDA platform for combinatorial and geometric computing and an account of its development. We discuss our motivation for building LEDA and to what extent we have reached our goals. We also discuss some recent theoretical developments. This paper contains no new technical material. It is intended as a guide to existing publications about the system. We refer the reader also to our web-pages for more information.

/pdf/the-leda-platform-of-combinatorial-and-geometric-computing-4r8e0w0sj0.pdf

Kurt Mehlhorn

Papers

Weisfeiler-Lehman Graph Kernels

LEDA: A Platform for Combinatorial and Geometric Computing

Efficient Graphlet Kernels for Large Graph Comparison

Faster Algorithms for the Shortest Path Problem

The LEDA Platform of Combinatorial and Geometric Computing