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 paper we describe and discuss a kernel for higher-dimensional computational geometry and we present its application in the calculation of convex hulls and Delaunay triangulations. The kernel is available in form of a software library module programmed in C++ extending LEDA. We introduce the basic data types like points, vectors, directions, hyperplanes, segments, rays, lines, spheres, affine transformations, and operations connecting these types. The description consists of a motivation for the basic class layout as well as topics like layered software design, runtime correctness via checking routines and documentation issues. Finally we shortly describe the usage of the kernel in the application domain.

A computational basis for higher-dimensional computational geometry and applications

We present four results on the complexity of VLSI computations:
a) We further justify the Boolean circuit model [Vu, Sa, LS] by showing that it is able to model multi-directional VLSI devices (eg pass transistors, pre-charged bus drivers)
b) We prove a general cutting theorem for compact regions in R^{d} (d\geq2) that allows us to drop the convexity assumption in lower bound proofs based on the crossing sequence argument
c) We exhibit an \Omega(n^{1/3}) asymptotically tight lower bound on the area of strongly where-oblivious chips for transitive functions
d) We prove a lower bound on the switching energy needed for computing transitive functions

Four results on the complexity of VLSI computations

Proceedings of the 16th annual European symposium on Algorithms

Cache-Oblivious and Cache-Aware Algorithms

We show that the point containment problem in the integer hull of a polyhedron, which is defined by m inequalities, with coefficients of at most φ bits can be solved in time O(m + φ) in the two-dimensional case and in expected time O(m + φ2 log m) in any fixed dimension. This improves on the algorithm which is based on the equivalence of separation and optimization in the general case and on a direct algorithm (SODA 97) for the two-dimensional case.

Kurt Mehlhorn

Papers

A computational basis for higher-dimensional computational geometry and applications

Four results on the complexity of VLSI computations

Proceedings of the 16th annual European symposium on Algorithms

Cache-Oblivious and Cache-Aware Algorithms

Point containment in the integer hull of a polyhedron