Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

Linear regression under fixed-rank constraints: A Riemannian approach

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms. Copyright 2011 by the author(s)/owner(s).

Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

From subspace learning to distance learning: A geometrical optimization approach

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this problem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that exploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates the subspace of the matrix and its projection onto that subspace. A proper weighting of the two iterations enables to continuously interpolate between the problem of learning a subspace and learning a distance when the subspace is fixed. © 2009 IEEE.

A PDE viewpoint on basic properties of coordination algorithms with symmetries

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. ©2009 IEEE.

Stabilization of symmetric formations to motion around convex loops

We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms. © 2007 Elsevier B.V. All rights reserved.

Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves

We provide feedback control laws to stabilize formations of multiple, unit speed particles on smooth, convex, and closed curves with definite curvature. As in previous work we exploit an analogy with coupled phase oscillators to provide controls which isolate symmetric particle formations that are invariant to rigid translation of all the particles. In this work, we do not require all particles to be able to communicate; rather we assume that inter-particle communication is limited and can be modeled by a fixed, connected, and undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. The methodology is demonstrated using a superellipse, which is a type of curve that includes circles, ellipses, and rounded rectangles. These results can be used in applications involving multiple autonomous vehicles that travel at constant speed around fixed beacons. ©2006 IEEE.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Designing climate change mitigation plans that add up.

Mitigation plans to combat climate change depend on the combined implementation of many abatement options, but the options interact. Published anthropogenic emissions inventories are disaggregated by gas, sector, country, or final energy form. This allows the assessment of novel energy supply options, but is insufficient for understanding how options for efficiency and demand reduction interact. A consistent framework for understanding the drivers of emissions is therefore developed, with a set of seven complete inventories reflecting all technical options for mitigation connected through lossless allocation matrices. The required data set is compiled and calculated from a wide range of industry, government, and academic reports. The framework is used to create a global Sankey diagram to relate human demand for services to anthropogenic emissions. The application of this framework is demonstrated through a prediction of per-capita emissions based on service demand in different countries, and through an example showing how the "technical potentials" of a set of separate mitigation options should be combined.

Warping trajectories for video synchronization

Temporal synchronization of multiple video recordings of the same dynamic event is a critical task in many computer vision applications e.g. novel view synthesis and 3D reconstruction. Typically this information is implied, since recordings are made using the same timebase, or time-stamp information is embedded in the video streams. Recordings using consumer grade equipment do not contain this information; hence, there is a need to temporally synchronize signals using the visual information itself. Previous work in this area has either assumed good quality data with relatively simple dynamic content or the availability of precise camera geometry. In this paper, we propose a technique which exploits feature trajectories across views in a novel way, and specifically targets the kind of complex content found in consumer generated sports recordings, without assuming precise knowledge of fundamental matrices or homographies. Our method automatically selects the moving feature points in the two unsynchronized videos whose 2D trajectories can be best related, thereby helping to infer the synchronization index. We evaluate performance using a number of real recordings and show that synchronization can be achieved to within 1 sec, which is better than previous approaches. Copyright 2013 ACM.

What is the weakest topology in which feedback stability is robust?

Mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations. The space of systems with transfer functions in ℋ∞, for example, has many advantages mathematically, but includes large classes of non-physical systems, and one must be careful in drawing inferences from results in that setting. Similarly, the graph topology has long been known to be the weakest, or coarsest, topology in which (1) feedback stability is a robust property (i.e. preserved in small neighbourhoods) and (2) the map from open-to-closed-loop transfer functions is continuous. However, it is not known whether continuity is a necessary part of this statement, or only required for the existing proofs. It is entirely possible that the answer depends on the underlying classes of systems used. The class of systems we concern ourselves with here is the set of systems that can be approximated, in the graph topology, by real rational transfer function matrices. That is, lumped parameter models, or those distributed systems for which it makes sense to use finite element methods. This is precisely the set of systems that have continuous frequency responses in the extended complex plane. For this class, we show that there is indeed a weaker topology; in which feedback stability is robust but for which the maps from open-to-closed-loop transfer functions are not necessarily continuous. © 2013 Copyright Taylor and Francis Group, LLC.

Trust-Level Risk Evaluation and Risk Control Guidance in the NHS East of England

In recent years, the healthcare sector has adopted the use of operational risk assessment tools to help understand the systems issues that lead to patient safety incidents. But although these problem-focused tools have improved the ability of healthcare organizations to identify hazards, they have not translated into measurable improvements in patient safety. One possible reason for this is a lack of support for the solution-focused process of risk control. This article describes a content analysis of the risk management strategies, policies, and procedures at all acute (i.e., hospital), mental health, and ambulance trusts (health service organizations) in the East of England area of the British National Health Service. The primary goal was to determine what organizational-level guidance exists to support risk control practice. A secondary goal was to examine the risk evaluation guidance provided by these trusts. With regard to risk control, we found an almost complete lack of useful guidance to promote good practice. With regard to risk evaluation, the trusts relied exclusively on risk matrices. A number of weaknesses were found in the use of this tool, especially related to the guidance for scoring an event's likelihood. We make a number of recommendations to address these concerns. The guidance assessed provides insufficient support for risk control and risk evaluation. This may present a significant barrier to the success of risk management approaches in improving patient safety. © 2013 Society for Risk Analysis.

Durability indicators of SCC towards performance-based specifications for the durability of SCC

The fundamental principle behind the development of SCC has been the nanoscale tailoring of cementitious matrices. Although self-compacting concrete (SCC) is currently used in many countries, there is a fundamental lack of the intrinsic durability of the material itself. The scope of the current paper is to present the outcomes of a research study on some principal indicators (porosity and capillary absorption) that define the durability of SCC, and how these are compared with the corresponding parameters of conventional concrete. Furthermore, this paper investigates the addition of industrial by-products, such as fly-ash or lime powder, to SCC mixtures and their effect on the durability indicators.

Combined effects of polyfluorinated and perfluorinated compounds on primary cultured hepatocytes from rare minnow (Gobiocypris rarus) using toxicogenomic analysis

Polyfluorinated and perfluorinated compounds (PFCs) are used in numerous commercial products and have been ubiquitously detected in the environment as well as in the blood of humans and wildlife. To assess the combined effects caused by PFCs in mixtures, gene expression profiles were generated using a custom cDNA microarray to detect changes in primary cultured hepatocytes of rare minnows exposed to six individual PFCs (perfluorooctanoic acid, perfluorononanoic acid, perfluorodecanoic acid, perfluorododecanoic acid, perfluorooctane sulfonate, and 8:2 fluorotelomer alcohol) and four formulations of the PFCs mixtures. Mixtures as well as individual compounds consistently regulated a particular gene set, which suggests that these conserved genes may play a central role in the toxicity mediated by PFCs. Specifically, a number of genes regulated by the mixtures were identified in this study, which were not affected by exposure to any single component. These genes are implicated in multiple biological functions and processes, including fatty acid metabolism and transport, xenobiotic metabolism, immune responses, and oxidative stress. More than 80% of the altered genes in the PFOA- and PFOS-dominant mixture groups were of the same gene set, while the gene expression profiles from single PFOA and PFOS exposures were not as similar. This work contributes to the development of toxicogenomic approaches in combined toxicity assessment and allows for comprehensive insights into the combined action of PFCs mixtures in multiple environmental matrices. (C) 2009 Elsevier B.V. All rights reserved.

Rapid quantification of total microcystins in cyanobacterial samples by periodate-permanganate oxidation and reversed-phase liquid chromatography

Microcystins (MCs) comprise a family of more than 80 related cyclic hepatotoxic heptapeptides. Oxidation of MCs causes cleavage of the chemically unique C-20 beta-amino acid (2S, 3S, 8S, 9S)-3-amino-9-methoxy-2,6,8-trimethyl-10-phenyldeca-4,6-dienoic acid (Adda) amino to form 2-methyl-3-methoxy-4-phenylbutanoic acid (MMPB), which has been exploited to enable analysis of the entire family. In the present study, the reaction conditions (e.g. concentration of the reactants. temperature and pH) used in the production of MMPB by oxidation of cyanobacterial samples with permanganate-periodate were optimized through a series of well-controlled batch experiments. The oxidation product (MMPB) was then directly analyzed by high-performance liquid chromatography with diode array detection. The results of this study provided insight into the influence of reaction conditions on the yield of MMPB. Specifically, the optimal conditions, including a high dose of permanganate (>= 50 mM) in saturated periodate solution at ambient temperature under alkaline conditions (pH similar to 9) over 1-4 h were proposed, as indicated by a MMPB yield of greater than 85%. The technique developed here was applied to determine the total concentration of MCs in cyanobacterial bloom samples, and indicated that the MMPB technique was a highly sensitive and accurate method of quantifying total MCs. Additionally, these results will aid in development of a highly effective analytical method for detection of MMPB as an oxidation product for evaluation of total MCs in a wide range of environmental sample matrices, including natural waters, soils (sediments) and animal tissues. (C) 2009 Elsevier B.V. All rights reserved.