Distributed Optimization With Local Domains: Applications in MPC and Network Flows

In this paper we consider a network with $P$ nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector $x^\star$ minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function depends only on some components of the variable. Consequently, each node is interested in knowing only some components of $x^\star$, not the entire vector. This allows for improvement in communication-efficiency. We apply our algorithm to model predictive control (MPC) and to network flow problems and show, through experiments on large networks, that our proposed algorithm requires less communications to converge than prior algorithms.Comment: Submitted to IEEE Trans. Aut. Contro

D-ADMM: A Communication-Efficient Distributed Algorithm For Separable Optimization

We propose a distributed algorithm, named Distributed Alternating Direction Method of Multipliers (D-ADMM), for solving separable optimization problems in networks of interconnected nodes or agents. In a separable optimization problem there is a private cost function and a private constraint set at each node. The goal is to minimize the sum of all the cost functions, constraining the solution to be in the intersection of all the constraint sets. D-ADMM is proven to converge when the network is bipartite or when all the functions are strongly convex, although in practice, convergence is observed even when these conditions are not met. We use D-ADMM to solve the following problems from signal processing and control: average consensus, compressed sensing, and support vector machines. Our simulations show that D-ADMM requires less communications than state-of-the-art algorithms to achieve a given accuracy level. Algorithms with low communication requirements are important, for example, in sensor networks, where sensors are typically battery-operated and communicating is the most energy consuming operation.Comment: To appear in IEEE Transactions on Signal Processin

Distributed Basis Pursuit

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time. We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes. Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms.Comment: Preprint of the journal version of the paper; IEEE Transactions on Signal Processing, Vol. 60, Issue 4, April, 201

Different effect of mycorrhizal inoculation in direct and indirect reclamation of spoil banks

Spoil banks generated during coal mining are usually reclaimed by layering of fertile soil over original barren clay (co called indirect reclamation). This well-proven method is effective from the aspect of vegetation establishment and production, but it is very expensive. Direct reclamation of spoil bank clay promises much cheaper approach, yet its success is uncertain and the process might be rather long-term.This two-year field study aimed to assess the effect of application of commercially produced inoculum of arbuscular mycorrhizal fungi (AMF) Symbivit® on growth of two plant species commonly used for reclamation (Lotus corniculatus and Arrhenatherum elatius) sown on three different substrates: organic substrate (mixture of papermill waste, tree-bark and compost) and loess (both substrates typical for indirect reclamation) and original spoil bank clays (simulation of direct reclamation). On organic substrate and loess, A. elatius outcompeted the legume and established 100 % cover in all treatments. The effect of mycorrhizal inoculation was not observed. In contrast, on clay both species established successfully. The produced biomass and cover were, however, substantially lower compared to organic substrate and loess. In clay the positive effect of introduced AMF on plant was observed.Mycorrhizal inoculation was useful for supporting plant growth at direct reclamation. Direct reclamation in itself seems suitable for small-scale application, i.e. in patches where indirect reclamation is inconvenient or more diverse vegetation is required. Key words: arbuscular mycorrhizal fungi; inoculum; clay; papermill waste; loess; Arrhenatherum elatius; Lotus corniculatu

Radiosektion: Computertomographie-assistierte Rekonstruktion eines erweiterten Suizids

Zusammenfassung: Erweiterte Suizide durch Schusswaffen sind häufig durch eine sorgfältige Fundortanalyse zu klären. Im dargestellten Fall wurde eine 38-jährige Frau in Rückenlage auf dem Bett im Schlafzimmer aufgefunden. Im Bereich der linken Brust fand sich eine rundliche Einschusswunde. Neben dem Bett wurde eine Schusswaffe gefunden. Im Wohnzimmer lag ein 40-jähriger Mann in Bauchlage auf der Erde in einer größeren Blutlache. Ein unvollendeter Abschiedsbrief fand sich auf dem Esstisch. Nach der äußeren Leichenschau am Fundort erfolgte eine Röntgenschichtuntersuchung. Hierdurch wurde bei der Frau ein absteigender Schusskanal von der linken Brust durch die Herzspitze dargestellt. Das Projektil konnte im Rippenzwischenraum nahe der Wirbelsäule lokalisiert werden. Bei dem Mann wurden ein Schusskanal durch den harten Gaumen und ein Projektil in der Schädelhöhle festgestellt; dieses lag nicht in einer Linie mit dem Schusskanal, sodass ein "Ringelschuss" diagnostiziert wurde. Die nachfolgende Sektion beider Leichen bestätigte die Befunde. Die bei der Autopsie sichergestellten Projektile konnten durch ballistische Untersuchungen der am Ereignisort sichergestellten Waffe zugeordnet werde

An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.Comment: 10 page

A unified algorithmic approach to distributed optimization

We address general optimization problems formulated on networks. Each node in the network has a function, and the goal is to find a vec-tor x ∈ Rn that minimizes the sum of all the functions. We assume that each function depends on a set of components of x, not neces-sarily on all of them. This creates additional structure in the prob-lem, which can be captured by the classification scheme we develop. This scheme not only to enables us to design an algorithm that solves very general distributed optimization problems, but also allows us to categorize prior algorithms and applications. Our general-purpose algorithm shows a performance superior to prior algorithms, includ-ing algorithms that are application-specific. Index Terms — Distributed optimization, sensor networks 1