Ingo Althöfer

On the evolutionary significance of the size and planarity of the proline ring

Proline is a proteinogenic amino acid in which the side chain forms a ring, the pyrrolidine ring. This is a five-membered ring made up of four carbons and one nitrogen. Here, we study the evolutionary significance of this ring size. It is shown that the size of the pyrrolidine ring has the advantage of being nearly planar and strain-free, based on a general mathematical assertion saying that the angular sum of a polygon is maximum if it is planar and convex. We also provide a sketch of the proof to this assertion. The optimality of the ring size of proline can be derived from a triangle inequality for angles. Quasi-planarity is physiologically significant because it allows an easier and evolutionarily old type of fit into binding grooves of proteins with which proline-rich proteins interact. Finally, we present a comparison with other planar, nearly planar and non-planar biomolecules such as neurotransmitters, hormones and toxins, involving, for example, aromatic rings, cyclopentanone and 1,3-dioxole.

An Analysis of Majority Systems with Dependent Agents in a Simple Subtraction Game

It is common knowledge that a majority system is typically better than its components, when the components are stochastically independent. However, in practice the independency assumption is often not justified. We investigate systems of experts which are constituted by couples of dependent agents. Based on recent theoretical work we analyse their performance in a simple 2-player subtraction game. It turns out that systems with negatively correlated couples perform better than those with positive correlation within the couples. From computer chess practice it was at least known that systems of very positively correlated bots were not too successful.

Games with arbitrary periodic moving orders

A well known two person game called Nim consists in two players, alternately taking matches from a single heap of matches. In our paper we extend this game to arbitrary periodic moving orders, for exampleAABAB, whereA andB are the players. The main result states, that the player moving more frequently always can force a win, provided there are “enough” matches in the heap initially. Thus in the exampleA will win.

Computer-Aided Go: Chess as a Role Model

Recently computers have gained strength in the Asian board game Go. The Chess community experienced some 15 to 30 years ago that teams with humans and computers may be much stronger than each of their components. This paper claims that time is ripe for computer-aided Go on a large scale, although neither most users nor the Go programmers have realized it. A central part of the paper describes successful pioneers in Go play with computer help. Progress in computer-aided Go may also lead to progress in human Go and in computer Go itself.

The problem of approach in differential–difference games

We consider the pursuit problem in 2-person differential game, one player is a pursuer and another one is an evader. The problem is given by a system of differential–difference equations with time lag. The players choose their controls in the form of measurable functions with values from certain compacts. The goal of the pursuer is to catch the evader in the shortest possible time. The goal of the evader is to avoid the meeting of the players’ trajectories on a whole semiinfinite interval of time or if it is impossible to maximally postpone the moment of meeting. For such a conflict-controlled process we derive conditions on its parameters and initial state, which are sufficient for the trajectories of the players to meet at a certain moment of time for any counteractions of the evader.

On Sliding-Block Codes

Sliding-block codes are non-block coding structures consisting of discrete time time-invariant possibly nonlinear filters.

\(\beta \)-Biased Estimators in Data Compression

In this chapter, we present the results of Krichevsky [6]. We consider the following estimation problem, which arises in the context of data compression, is discussed: For a given discrete memoryless source, we want to estimate the unknown underlying source probabilities by means of a former source output, assuming that the estimated probabilities are used to encode the letters of the source alphabet.

On \lambda -Capacities and Information Stability

In Chap. 1, we introduced \(\lambda \)-capacities with several specifications and mainly concentrated on CC.

Selected Topics of Information Theory and Mathematical Statistics

First, we notice that problems related to hypotheses testing in statistics can be viewed as extensions of source coding problems.

Algorithms for Computing Channel Capacities and Rate-Distortion Functions

Computation of the capacity \(C=C(W)\) of a DMC \(W:{\mathcal X}\rightarrow {\mathcal Y}\) involves the solution of a convex programming problem.