Joerg Fliege

Machine learning approaches for the discovery of gene–gene interactions in disease data

Because of the complexity of gene-phenotype relationships machine learning approaches have considerable appeal as a strategy for modelling interactions. A number of such methods have been developed and applied in recent years with some modest success. Progress is hampered by the challenges presented by the complexity of the disease genetic data, including phenotypic and genetic heterogeneity, polygenic forms of inheritance and variable penetrance, combined with the analytical and computational issues arising from the enormous number of potential interactions. We review here recent and current approaches focusing, wherever possible, on applications to real data (particularly in the context of genome-wide association studies) and looking ahead to the further challenges posed by next generation sequencing data.

Stochastic Multiobjective Optimization: Sample Average Approximation and Applications

We investigate one stage stochastic multiobjective optimization problems where the objectives are the expected values of random functions. Assuming that the closed form of the expected values is difficult to obtain, we apply the well known Sample Average Approximation (SAA) method to solve it. We propose a smoothing infinity norm scalarization approach to solve the SAA problem and analyse the convergence of efficient solution of the SAA problem to the original problem as sample sizes increase. Under some moderate conditions, we show that, with probability approaching one exponentially fast with the increase of sample size, an ϵ-optimal solution to the SAA problem becomes an ϵ-optimal solution to its true counterpart. Moreover, under second order growth conditions, we show that an efficient point of the smoothed problem approximates an efficient solution of the true problem at a linear rate. Finally, we describe some numerical experiments on some stochastic multiobjective optimization problems and report preliminary results.

Support Vector Machine Classifier for Estrogen Receptor Positive and Negative Early-Onset Breast Cancer

Two major breast cancer sub-types are defined by the expression of estrogen receptors on tumour cells. Cancers with large numbers of receptors are termed estrogen receptor positive and those with few are estrogen receptor negative. Using genome-wide single nucleotide polymorphism genotype data for a sample of early-onset breast cancer patients we developed a Support Vector Machine (SVM) classifier from 200 germline variants associated with estrogen receptor status (p<0.0005). Using a linear kernel Support Vector Machine, we achieved classification accuracy exceeding 93%. The model indicates that polygenic variation in more than 100 genes is likely to underlie the estrogen receptor phenotype in early-onset breast cancer. Functional classification of the genes involved identifies enrichment of functions linked to the immune system, which is consistent with the current understanding of the biological role of estrogen receptors in breast cancer.

Predicting Directed Links Using Nondiagonal Matrix Decompositions

We present a method for trust prediction based on no diagonal decompositions of the asymmetric adjacency matrix of a directed network. The method we propose is based on a no diagonal decomposition into directed components (DEDICOM), which we use to learn the coefficients of a matrix polynomial of the networks adjacency matrix. We show that our method can be used to compute better low-rank approximations to a polynomial of a networks adjacency matrix than using the singular value decomposition, and that a higher precision can be achieved at the task of predicting directed links than by undirected or bipartite methods.

Operations research in the space industry

Operations research techniques have been used in the space industry since its infancy, and various competing methods and codes, with widely varying characteristics, have been used over time. This survey is intended to give an overview of current application cases of different operations research techniques and methodologies in the domain of space engineering and space science.

A modelling framework for solving restricted planar location problems using phi-objects

This paper presents a general modelling framework for restricted facility location problems with arbitrarily shaped forbidden regions or barriers, where regions are modelled using phi-objects. Phi-objects are an efficient tool in mathematical modelling of 2D and 3D geometric optimization problems, and are widely used in cutting and packing problems and covering problems. The paper shows that the proposed modelling framework can be applied to both median and centre facility location problems, either with barriers or forbidden regions. The resulting models are either mixed-integer linear or non-linear programming formulations, depending on the shape of the restricted region and the considered distance measure. Using the new framework, all instances from the existing literature for this class of problems are solved to optimality. The paper also introduces and optimally solves a realistic multi-facility problem instance derived from an archipelago vulnerable to earthquakes. This problem instance is significantly more complex than any other instance described in the literature.

The Unmanned Aerial Vehicle Routing and Trajectory Optimisation Problem, a Taxonomic Review

Abstract Over the past few years, Unmanned Aerial Vehicles (UAVs) have become more and more popular. The complexity of routing UAVs has not been fully investigated in the literature. In this paper, we provide a formal definition of the UAV Routing and Trajectory Optimisation Problem (UAVRTOP). Next, we introduce a taxonomy and review recent contributions in UAV trajectory optimisation, UAV routing and articles addressing these problems, and their variants, simultaneously. We conclude with the identification of future research opportunities.

An active constraint method for distributed routing, and power control in wireless networks

Efficiently transmitting data in wireless networks requires joint optimization of routing, scheduling, and power control. As opposed to the universal dual decomposition we present a method that solves this optimization problem by fully exploiting our knowledge of active constraints. The method still maintains main requirements such as optimality, distributed implementation, multiple path routing and per-hop error performance. To reduce the complexity of the whole problem, we separate scheduling from routing and power control, including it instead in the constraint set of the joint optimization problem. Apart from the mathematical framework we introduce a routing and power control decomposition algorithm that uses the active constraint method, and we give further details on its distributed application. For verification, we apply the distributed RPCD algorithm to examples of wireless mesh backhaul networks with fixed nodes. Impressive convergence results indicate that the distributed RPCD algorithm calculates the optimum solution in one decomposition step only.