Contractive idempotents on locally compact quantum groups

A general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As a consequence a one-to-one correspondence between contractive idempotents and a certain class of ternary rings of operators is established.Comment: 16 pages, v2 contains very minor changes and updates the references. The paper will appear in the Indiana University Journal of Mathematic

Methodology of a Troposphere Effect Mitigation Processor for SAR Interferometry

Troposphere effect mitigation based on numerical weather prediction (NWP) is an actual research topic in SAR interferometry (InSAR) and especially in persistent scatterer interferometry (PSI). This is the reason, a scientific troposphere effect mitigation processing system has been developed. The objective of this paper is to provide the methodology of four developed algorithms, demonstrate application examples, discuss the methods characteristic and recommend techniques for operational systems

The STUN algorithm for persistent scatterer interferometry

The Spatio-Temporal Unwrapping Network (STUN) is a new algorithm to estimate displacement and topography at Persistent Scatterer (PS) points using an interferometric single-master data stack. The STUN algorithm provides a robust method to explicitly unwrap the interferometric phase using the temporal and spatial correlations of the observed phase. Moreover, it uses alternative hypothesis tests and the integer Least-Squares estimator to optimally estimate the parameters. Key features are the ability (i) to model the displacement using a linear combination of basefunctions; (ii) to estimate the precision of each SLC image using a novel stochastic model; (iii) to obtain a description of the precision of the estimated displacements. This paper describes the STUN algorithm in detail, and demonstrates its practical application using data from a rural area nearby Marseille, France, which suffers from subsidence due to mining activities

Urban deformation monitoring in Bangkok metropolitan (Thailand) using permanent scatterer and differential interferometry techniques

Extensive ground water extraction has been identified as the principle cause of land subsidence in Bangkok and its vicinity. To mitigate major damages from large subsidence magnitudes the phenomenon must be well understood in this area. Up-to-date and reliable subsidence information is indispensable to develop this understanding. Conventionally, surface leveling has served as the primary method for measuring subsidence in Bangkok. But this is costly and time consuming. Differential SAR interferometry (DInSAR) can be an alternative means to obtain measurements of the surface displacement providing better resolution and comparable accuracy while being less time consuming. However, spatial and temporal decorrelation and atmospheric signal contributions in repeat-pass SAR interferometry often hamper the accurate measurement of surface displacements in SAR interferograms. The recently developed Permanent Scatterer (PS) technique invented by POLIMI researchers [1],[2],[3], overcomes these difficulties by interpreting time-series of interferometric phases at coherent point scatterers. In this study, we apply both DInSAR and PS techniques using two time-series of 17 and 11 ERS-SAR acquisitions for two partly overlapping image frames. This study is the first attempt to apply the PS technique to derive urban displacement information in Bangkok. We investigate the feasibility and reliability of using this technique with relatively few acquisitions and in a tropical location for deformation estimation. Using a linear deformation model and network algorithm, we estimate spatially varying displacement rates for the metropolitan area. Our first PS estimation results agree well with available ground leveling measurements

Smoothed Online Optimization with Unreliable Predictions

We examine the problem of smoothed online optimization, where a decision maker must sequentially choose points in a normed vector space to minimize the sum of per-round, non-convex hitting costs and the costs of switching decisions between rounds. The decision maker has access to a black-box oracle, such as a machine learning model, that provides untrusted and potentially inaccurate predictions of the optimal decision in each round. The goal of the decision maker is to exploit the predictions if they are accurate, while guaranteeing performance that is not much worse than the hindsight optimal sequence of decisions, even when predictions are inaccurate. We impose the standard assumption that hitting costs are globally $\alpha$-polyhedral. We propose a novel algorithm, Adaptive Online Switching (AOS), and prove that, for a large set of feasible $\delta > 0$, it is $(1+\delta)$-competitive if predictions are perfect, while also maintaining a uniformly bounded competitive ratio of $2^{\tilde{\mathcal{O}}(1/(\alpha \delta))}$ even when predictions are adversarial. Further, we prove that this trade-off is necessary and nearly optimal in the sense that \emph{any} deterministic algorithm which is $(1+\delta)$-competitive if predictions are perfect must be at least $2^{\tilde{\Omega}(1/(\alpha \delta))}$-competitive when predictions are inaccurate. In fact, we observe a unique threshold-type behavior in this trade-off: if $\delta$ is not in the set of feasible options, then \emph{no} algorithm is simultaneously $(1 + \delta)$-competitive if predictions are perfect and $\zeta$-competitive when predictions are inaccurate for any $\zeta < \infty$. Furthermore, we discuss that memory is crucial in AOS by proving that any algorithm that does not use memory cannot benefit from predictions. We complement our theoretical results by a numerical study on a microgrid application.Comment: 38 pages, 4 figure

First TerraSAR-X interferometry evaluation

The German radar satellite TerraSAR-X was launched in June 2007 [1] and is currently ending its commissioning phase. We anticipate quite different interferometric application scenarios compared to ERS- 1/2 and ASAR due to the X-band frequency, the short orbital repeat cycles of 11 days, the high range resolution and the spotlight mode of this sensor. During the commissioning phase we have scheduled a number of acquisitions over selected test sites with different characteristics to get an early quick look of TerraSAR-X's interferometric capabilities and to assess the phase quality of the sensor and DLR’s processor system [2]. Our first results are quite encouraging and the technical parameters of the system are as specified. Many spectacular image details let us expect that the high resolution will demand a different view on SAR interferometry and allow new applications in urban environments. In our paper we show interferograms and images of different test sites, coherence measurements and a first assessment of the interferometric properties. We will give hints to future scientific users on data selection and data processing. The results are of high relevance for the TanDEM-X mission scheduled for 2009, when a second compatible SAR-sensor will be launched for a joint 3 year bistatic interferometric formation flight