OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201

A General Model for Multilocus Epistatic Interactions in Case-Control Studies

Background: Epistasis, i.e., the interaction of alleles at different loci, is thought to play a central role in the formation and progression of complex diseases. The complexity of disease expression should arise from a complex network of epistatic interactions involving multiple genes. Methodology: We develop a general model for testing high-order epistatic interactions for a complex disease in a casecontrol study. We incorporate the quantitative genetic theory of high-order epistasis into the setting of cases and controls sampled from a natural population. The new model allows the identification and testing of epistasis and its various genetic components. Conclusions: Simulation studies were used to examine the power and false positive rates of the model under different sampling strategies. The model was used to detect epistasis in a case-control study of inflammatory bowel disease, in which five SNPs at a candidate gene were typed, leading to the identification of a significant three-locus epistasis

On the relevance of preprocessing in predictive maintenance for dynamic systems

The complexity involved in the process of real-time data-driven monitoring dynamic systems for predicted maintenance is usually huge. With more or less in-depth any data-driven approach is sensitive to data preprocessing, understood as any data treatment prior to the application of the monitoring model, being sometimes crucial for the final development of the employed monitoring technique. The aim of this work is to quantify the sensitiveness of data-driven predictive maintenance models in dynamic systems in an exhaustive way. We consider a couple of predictive maintenance scenarios, each of them defined by some public available data. For each scenario, we consider its properties and apply several techniques for each of the successive preprocessing steps, e.g. data cleaning, missing values treatment, outlier detection, feature selection, or imbalance compensation. The pretreatment configurations, i.e. sequential combinations of techniques from different preprocessing steps, are considered together with different monitoring approaches, in order to determine the relevance of data preprocessing for predictive maintenance in dynamical systems

Derandomized Evolution Strategies in Computational Neuroscience

INTRODUCTION We propose evolutionary "analysis by synthesis" guided by neurobiological knowledge as a powerful tool in computational neuroscience. The challenge is to force artificial evolution to favor solutions that are reasonable from the biological point of view. Such solutions are only likely to evolve if as much neurobiological knowledge as possible is used in the design process. This can be achieved by providing su#cient experimental data to evaluate the evolved systems and by a considerate choice of the basic structure. Additional knowledge can be incorporated into the fitness function and in constraints that ensure biological plausibility. The first step towards the design of biological systems is parameter adaptation of predefined models. In the following, we present some recent applications of the CMA-ES, an elaborated, derandomized evolution strategy [4, 5], in the field of parameter optimization of neurobiological models. 2 ADAPTATION OF MACROSCOPIC CORTICAL MODELS D

The complexity of problems on implicitly represented inputs

Abstract. Highly regular data can be represented succinctly by various kinds of implicit data structures. Many problems in P are known to be hard if their input is given as circuit or Ordered Binary Decision Diagram (OBDD). Nevertheless, in practical areas like CAD and Model Checking, symbolic algorithms using functional operations on OBDD-represented data are well-established. Their theoretical analysis has mostly been restricted to the number of functional operations yet. We show that Pcomplete problems have no symbolic algorithms using a polylogarithmic number of functional operations, unless P=NC. Moreover, we complement PSPACE-hardness results for problems on OBDD-represented inputs by fixed-parameter intractability results, where the OBDD width serves as the fixed parameter.