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

Recursive descent is for its ease of description and for its transparency one of the popular parsing methods [Gries, Knuth]. The class of languages, for which recursive descent works as a parsing method, is known as the LL-languages; their properties were studied by Lewis & Stearns, Rosenkranz & Stearns and many others (see [Aho & Ullman] for complete references).

Top Down Parsing of Macro Grammars

We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, the dynamics is governed by equations that usually describe food search of the paradigmatic Physarum polycephalum. In this work we assume that the two paths undergo damping whose relative strength is periodically modulated in time and analyse the dynamics in the presence of stochastic forces simulating Gaussian noise. We identify different responses depending on the modulation frequency and on the noise amplitude. At frequencies smaller than the mean dissipation rate, the system tends to switch to the path which minimizes dissipation. Synchronous switching occurs at an optimal noise amplitude which depends on the modulation frequency. This behaviour disappears at larger frequencies, where the dynamics can be described by the time-averaged equations. Here, we find metastable patterns that exhibit the features of noise-induced resonances.

Interplay of periodic dynamics and noise: insights from a simple adaptive system

Codes: Unequal Probabilities, Unequal Letter Costs (Extended Abstract)

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.

Kurt Mehlhorn

Papers

Top Down Parsing of Macro Grammars

Interplay of periodic dynamics and noise: insights from a simple adaptive system

Codes: Unequal Probabilities, Unequal Letter Costs (Extended Abstract)

Area-Time Optimal VLSI Integer Multiplier with Minimum Computation Time

Ten Years of LEDA Some Thoughts (Abstract)