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

We present narrowing algorithms for the sortedness and the alldifferent constraint which achieve bound-consistency. The algorithm for the sortedness constraint takes as input 2n intervals X1, ... , Xn, Y1, ... , Yn from a linearly ordered set D. Let S denote the set of all tuples t ∈ X1 × ... × Xn × Y1 × ... × Yn such that the last n components of t are obtained by sorting the first n components. Our algorithm determines whether S is non-empty and if so reduces the intervals to bound-consistency. The running time of the algorithm is asymptotically the same as for sorting the interval endpoints. In problems where this is faster than O(n log n), this improves upon previous results.

The algorithm for the alldifferent constraint takes as input n integer intervals Z1, ... , Zn. Let T denote all tuples t ∈ Z1 × ... × Zn where all components are pairwise different. The algorithm checks whether T is non-empty and if so reduces the ranges to bound-consistency. The running time is also asymptotically the same as for sorting the interval endpoints. When the constraint is for example a permutation constraint, i.e. Zi ⊆ [1; n] for all i, the running time is linear. This also improves upon previous results.

/pdf/faster-algorithms-for-bound-consistency-of-the-sortedness-58bmclblm7.pdf

Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint

According to VLSI theory, [logn, √n] is the range of computation times for which there may exist an AT2-optimal multiplier of n-bit integers. Such networks were previously known for the time range [Ω(log2n), 0(√n)]; in this paper we settle this theoretical question, by exhibiting a-class of AT2-optimal multipliers with computation times [Ω(logn), 0(n1/2)]. Our designs are based on the DFT on a Fermat ring, whose elements are represented in a redundant radix-4 form to ensure 0(1) addition time.

Area-time optimal VLSI integer multiplier with minimum computation time

Many data structures used in computational geometry are quite involved and therefore hard to dynamize. The purpose of this paper is twofold. In section 1 we describe dynamic fractional cascading. Fractional cascading was recently introduced by Chaeelle/Cuibas as a common framework for many data structures in computational geometry. They show that it allows to derive numerous old and new results in a uniform way and thus enhance our understanding of geometric data structures tremendously. They distill a common principle which was implicitely used previously in Vaishnavi/Wood, Willard, Edelsbrunner/Guibas/ Stolfi, Imai/Asano and others. In section 2 we give an amortized analysis of update cost in fractional cascading and show that insertions take 0( 1) amortized time and insertions and deletions take 0( log log X) amortized time. The analysis is based on the technique developed in Maier/Salveter and fluddleston/Mehlhorn (cf. also Mehlhorn, Vol 1) for analyzing amortized update cost in balanced trees. The efficient set splitting algorithm of Imai/Asano (a new set splitting and union algorithm based on the O(log log N) priority queue of v. Emde Boas) is used as an auxiliary data structure in order to support efficient insertions (insertions and deletions). In section 3 we will briefiy survey two recent attempts for dynamizing the searching problem in planar subdivisions.

Dynamization of geometric data structures

We study strategies for converting randomized algorithms of the Las Vegas type into randomized algorithms with small tail probabilities.

/pdf/a-method-for-obtaining-randomized-algorithms-with-small-tail-1ui4f2fbon.pdf

A method for obtaining randomized algorithms with small tail probabilities

/pdf/the-hill-system-a-design-environment-for-the-hierarchical-28mmf6bk3q.pdf

Kurt Mehlhorn

Papers

Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint

Area-time optimal VLSI integer multiplier with minimum computation time

Dynamization of geometric data structures

A method for obtaining randomized algorithms with small tail probabilities

The HILL system : a design environment for the hierarchical specification, compaction, and simulation of integrated circuit layouts