Markus Maucher

Variations on an Ordering Theme with Constraints

We investigate the problem of finding a total order of a finite set that satisfies various local ordering constraints. Depending on the admitted constraints, we provide an efficient algorithm or prove NP-completeness. We discuss several generalisations and systematically classify the problems.

Inferring Boolean network structure via correlation

MOTIVATION Accurate, context-specific regulation of gene expression is essential for all organisms. Accordingly, it is very important to understand the complex relations within cellular gene regulatory networks. A tool to describe and analyze the behavior of such networks are Boolean models. The reconstruction of a Boolean network from biological data requires identification of dependencies within the network. This task becomes increasingly computationally demanding with large amounts of data created by recent high-throughput technologies. Thus, we developed a method that is especially suited for network structure reconstruction from large-scale data. In our approach, we took advantage of the fact that a specific transcription factor often will consistently either activate or inhibit a specific target gene, and this kind of regulatory behavior can be modeled using monotone functions. RESULTS To detect regulatory dependencies in a network, we examined how the expression of different genes correlates to successive network states. For this purpose, we used Pearson correlation as an elementary correlation measure. Given a Boolean network containing only monotone Boolean functions, we prove that the correlation of successive states can identify the dependencies in the network. This method not only finds dependencies in randomly created artificial networks to very high percentage, but also reconstructed large fractions of both a published Escherichia coli regulatory network from simulated data and a yeast cell cycle network from real microarray data.

An empirical assessment of local and population based search methods with different degrees of pseudorandomness

When designing and analyzing randomized algorithms, one usually assumes that a sequence of uniformly distributed, independent random variables is available as a source of randomness. Implementing these algorithms, however, one has to use pseudorandom numbers. The quality of the used pseudorandom number generator may severely influence the quality of an algorithm’s output. We examined the effect of using low quality pseudorandom numbers on the performance of different search heuristics like Simulated Annealing and a basic evolutionary algorithm.

On the different notions of pseudorandomness

This article explains the various notions of pseudorandomness, like Martin-Lof randomness, Kolmogorov complexity, Shannon entropy and quasi-randomness. We describe interconnections between these notions and describe how the non-computable notions among them are relaxed and used in practice, for example in statistics or cryptography. We give examples for pseudorandom generators relating to these notions and list some dependancies between the quality of pseudorandom numbers and its impact on some properties of randomized algorithms using them.

Extended pairwise local alignment of wild card DNA/RNA sequences using dynamic programming

Optimal string alignment is used to discover evolutionary relationships or mutations in DNA/RNA or protein sequences. Errors, missing parts or uncertainty in such a sequence can be covered with wild cards, so-called wild bases. This makes an alignment possible even when the data are corrupted or incomplete. The extended pairwise local alignment of wild card DNA/RNA sequences requires additional calculations in the dynamic programming algorithm and necessitates a subsequent best- and worst-case analysis for the wild card positions. In this paper, we propose an algorithm which solves the problem of input data wild cards, offers a highly flexible set of parameters and displays a detailed alignment output and a compact representation of the mutated positions of the alignment. An implementation of the algorithm can be obtained at https://github.com/sysbio-bioinf/swat+ and http://sysbio.uni-ulm.de/?Software:Swat+.

Group-based ant colony optimization

We introduce Group-Based Ant Colony Optimization which uses a parallel construction principle on group-structured solution encodings. We compare the parallel construction method with the classical sequential one. In this context we also perform simulation experiments for the Vehicle Routing Problem with Time Windows using the Solomon [8] and the Homberger & Gehring [5] instances.

Randomized quicksort and the entropy of the random source

The worst-case complexity of an implementation of Quicksort depends on the random source that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function of the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from nlog n to n2, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy and the geometrical distribution, as well as an upper bound when using a δ-random source.

Information Theoretic Measures for Ant Colony Optimization

We survey existing measures to analyze the search behavior of Ant Colony Optimization (ACO) algorithms and introduce a new uncertainty measure for characterizing three ACO variants. Unlike previous measures, the group uncertainty allows for quantifying the exploration of the search space with respect to the group assignment. We use the group uncertainty to analyze the search behavior of Group-Based Ant Colony Optimization.

Ant colony optimization with group learning

We introduce Group Learning for Ant Colony Optimization applied to combinatorial optimization problems with group-structured solution encodings. In contrast to the common assignment of one pheromone value per solution component in Group Learning each solution component has one pheromone value per group. Hence, the algorithm has the possibility to learn the optimal group membership of the components. We present different strategies for Group Learning and evaluate these in simulation experiments for the Vehicle Routing Problem with Time Windows using the problem instances of Solomon. We describe a revised Ant Colony System (ACS) algorithm which does not use a local pheromone update while maintaining the general ideas of ACS. We evaluate the revised ACS experimentally comparing it to the original ACS. Our experimental results show that Group Learning is a valuable modification for Ant Colony Optimization. Additionally, the results indicate that the revised ACS performs at least as well as the original algorithms.

Fuzzy Boolean Network Reconstruction

Genes interact with each other in complex networks that enable the processing of information inside the cell. For an understanding of the cellular functions, the identification of the gene regulatory networks is essential. We present a novel reverse-engineering method to recover networks from gene expression measurements. Our approach is based on Boolean networks, which require the assignment of the label “expressed” or “not expressed” to an individual gene. However, techniques like microarray analyses provide real-valued expression values, consequently the continuous data have to be binarized. Binarization is often unreliable, since noise on gene expression data and the low number of temporal measurement points frequently lead to an uncertain binarization of some values. Our new approach incorporates this uncertainty in the binarized data for the inference process. We show that this new reconstruction approach is less influenced by noise which is inherent in these biological systems.