Eigenvectors

This work is related to the damage detection problem in a homogeneous rod and consists of finding the location and severity of damage in the rod. It is shown that a finite element model based on the geometric parameters of the rod can be reconstructed from one eigenpair, that is, one eigenvalue and its respective eigenvector. This reconstruction permits development of an inverse eigenvalue procedure for damage detection. The procedure is sensitive to perturbations for a large order model. The use of overdetermined data decreases sensitivity, although this may lead to a more expensive procedure. Therefore, we use a new technique for filtering the information from a single eigenpair to obtain a realizable and less expensive procedure. (~)

In this paper we offer a topology-driven ('natural') definition of subclusters of an undirected graph or network. In addition we find rules for assigning unique roles (from a small set of possible roles) to each node in the network. Our approach is based on the use of a 'smooth' index for wellconnectedness (eigenvector centrality) which is computed for each node. This index, viewed as a height function, then guides the decomposition of the graph into regions (associated with local peaks of the index), and borders (valleys) between regions. We propose and compare two rules for assigning nodes to regions. We illustrate our approach with simple test graphs, and also by applying it to snapshots of the Gnutella peer-to-peer network from late 2001. This latter analysis suggests that our method implies novel ways of interpreting the notion of well-connectedness for a graph, as these snapshots represent very well connected networks. We argue that our approach is well suited for analyzing computer networks, towards the goal of enhancing their security.

For most unsymmetric matrices it is difficult to compute many accurate eigenvalues using the prim- itive form of the unsymmetric Lanczos algorithm (ULA). In this paper we propose a modification of the ULA. It is related to ideas used in (J. Chem. Phys. 122 (2005), 244107 (11 pages)) to compute resonance lifetimes. Using the refined ULA we suggest, the calculation

The Davidson method is a popular preconditioned variant of the Arnoldi method for solving large eigenvalue problems. For theoretical, as well as practical reasons the two methods are often used with restarting. Frequently, information is saved through approximated eigenvectors to compensate for the convergence impairment caused by restarting. We call this scheme of retaining more eigenvectors than needed`thick restarting', and prove that thick restarted, non-preconditioned Davidson is equivalent to the implicitly restarted Arnoldi. We also establish a relation between thick restarted Davidson, and a Davidson method applied on a de ated system. The theory is used to address the question of which and how many eigenvectors to retain and motivates the development of a dynamic thick restarting scheme for the symmetric case, which can be used in both Davidson and implicit restarted Arnoldi. Several experiments demonstrate the e ciency and robustness of the scheme.

Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species' distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing

A new database of weather and circulation type catalogs is presented comprising 17 automated classification methods and five subjective classifications. It was compiled within COST Action 733 ''Harmonisation and Applications of Weather Type Classifications for European regions" in order to evaluate different methods for weather and circulation type classification. This paper gives a technical description of the included methods using a new conceptual categorization for classification methods reflecting the strategy for the definition of types. Methods using predefined types include manual and threshold based classifications while methods producing types derived from the input data include those based on eigenvector techniques, leader algorithms and optimization algorithms. In order to allow direct comparisons between the methods, the circulation input data and the methods' configuration were harmonized for producing a subset of standard catalogs of the automated methods. The harmonization includes the data source, the climatic parameters used, the classification period as well as the spatial domain and the number of types. Frequency based characteristics of the resulting catalogs are presented, including variation of class sizes, persistence, seasonal and inter-annual variability as well as trends of the annual frequency time series. The methodological concept of the classifications is partly reflected by these properties of the resulting catalogs. It is shown that the types of subjective classifications compared to automated methods show higher persistence, inter-annual variation and long-term trends. Among the automated classifications optimization methods show a tendency for longer persistence and higher seasonal variation. However, it is also concluded that the distance metric used and the data preprocessing play at least an equally important role for the properties of the resulting classification compared to the algorithm used for type definition and assignment.

In this paper we empirically assess the evolution for the EU regions of both employment and unemployment before and after the Global Crisis. After a review of the literature on the theories and key determinants of regional unemployment, we shall overview the main findings concerning the labour market impact of the Global Crisis. The empirical analysis will initially be carried out at the national level including all EU countries; subsequently, we shall focus on the EU regions (at the NUTS-2 level), in order to detect possible changes in the dispersion of regional unemployment rates after the crisis. Our econometric investigations aim to assess the effect, on labour market performance, of previous developments in regional labour markets time series, as well as the importance of structural characteristics of the labour markets, in terms of the sectoral specialization of the regional economies. In fact, the local industry mix may have played a crucial role in shaping labour market performance in response to the crisis. In addition, we consider further characteristics of the regional labour markets, by including indicators of the level of precarization of labour and of the share of long-term unemployed, as indicators of the efficiency of the local labour markets. From a methodological viewpoint, we exploit eigenvector decomposition-based spatial filtering techniques, which allow us to greatly reduce unobserved variable bias -a significant problem in cross-sectional models -by including indicators of latent unobserved spatial patterns. Finally, we render a geographical description of the heterogeneity influence of past labour market performance over the crisis period, showing that the past performance has a differentiated impact on recent labour market developments.