Efficient Wiener filtering without preconditioning

We present a new approach to calculate the Wiener filter solution of general data sets. It is trivial to implement, flexible, numerically absolutely stable, and guaranteed to converge. Most importantly, it does not require an ingenious choice of preconditioner to work well. The method is capable of taking into account inhomogeneous noise distributions and arbitrary mask geometries. It iteratively builds up the signal reconstruction by means of a messenger field, introduced to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently. Using cosmic microwave background (CMB) radiation data as a showcase, we demonstrate the capabilities of our scheme by computing Wiener filtered WMAP7 temperature and polarization maps at full resolution for the first time. We show how the algorithm can be modified to synthesize fluctuation maps, which, combined with the Wiener filter solution, result in unbiased constrained signal realizations, consistent with the observations. The algorithm performs well even on simulated CMB maps with Planck resolution and dynamic range.Comment: 5 pages, 2 figures. Submitted to Astronomy and Astrophysics. Replaced to match published versio

ARKCoS: Artifact-Suppressed Accelerated Radial Kernel Convolution on the Sphere

We describe a hybrid Fourier/direct space convolution algorithm for compact radial (azimuthally symmetric) kernels on the sphere. For high resolution maps covering a large fraction of the sky, our implementation takes advantage of the inexpensive massive parallelism afforded by consumer graphics processing units (GPUs). Applications involve modeling of instrumental beam shapes in terms of compact kernels, computation of fine-scale wavelet transformations, and optimal filtering for the detection of point sources. Our algorithm works for any pixelization where pixels are grouped into isolatitude rings. Even for kernels that are not bandwidth limited, ringing features are completely absent on an ECP grid. We demonstrate that they can be highly suppressed on the popular HEALPix pixelization, for which we develop a freely available implementation of the algorithm. As an example application, we show that running on a high-end consumer graphics card our method speeds up beam convolution for simulations of a characteristic Planck high frequency instrument channel by two orders of magnitude compared to the commonly used HEALPix implementation on one CPU core while maintaining at typical a fractional RMS accuracy of about 1 part in 10^5.Comment: 10 pages, 6 figures. Submitted to Astronomy and Astrophysics. Replaced to match published version. Code can be downloaded at https://github.com/elsner/arkco

Fast calculation of the Fisher matrix for cosmic microwave background experiments

The Fisher information matrix of the cosmic microwave background (CMB) radiation power spectrum coefficients is a fundamental quantity that specifies the information content of a CMB experiment. In the most general case, its exact calculation scales with the third power of the number of data points N and is therefore computationally prohibitive for state-of-the-art surveys. Applicable to a very large class of CMB experiments without special symmetries, we show how to compute the Fisher matrix in only O(N^2 log N) operations as long as the inverse noise covariance matrix can be applied to a data vector in time O(l_max^3 log l_max). This assumption is true to a good approximation for all CMB data sets taken so far. The method takes into account common systematics such as arbitrary sky coverage and realistic noise correlations. As a consequence, optimal quadratic power spectrum estimation also becomes feasible in O(N^2 log N) operations for this large group of experiments. We discuss the relevance of our findings to other areas of cosmology where optimal power spectrum estimation plays a role.Comment: 4 pages, 1 figures. Accepted for publication in Astronomy and Astrophysics Letters. Replaced to match published versio

Using hybrid GPU/CPU kernel splitting to accelerate spherical convolutions

We present a general method for accelerating by more than an order of magnitude the convolution of pixelated functions on the sphere with a radially-symmetric kernel. Our method splits the kernel into a compact real-space component and a compact spherical harmonic space component. These components can then be convolved in parallel using an inexpensive commodity GPU and a CPU. We provide models for the computational cost of both real-space and Fourier space convolutions and an estimate for the approximation error. Using these models we can determine the optimum split that minimizes the wall clock time for the convolution while satisfying the desired error bounds. We apply this technique to the problem of simulating a cosmic microwave background (CMB) anisotropy sky map at the resolution typical of the high resolution maps produced by the Planck mission. For the main Planck CMB science channels we achieve a speedup of over a factor of ten, assuming an acceptable fractional rms error of order 1.e-5 in the power spectrum of the output map.Comment: 9 pages, 11 figures, 1 table, accepted by Astronomy & Computing w/ minor revisions. arXiv admin note: substantial text overlap with arXiv:1211.355

Revisiting Entrepreneurial Orientation and its Contributions to Business Performance: An Industry Type Comparison employing Computer-Aided Text Analysis under Consideration of Configurational, Contingency, Environmental, and Temporal Aspects

A firm’s entrepreneurial orientation (EO) refers to a firm-level strategic orientation that reflects its strategic choices, managerial styles, and organisational behaviours that are entrepreneurial in their basis. The majority of previous studies on a firm’s EO investigate its three most common characteristics – innovativeness, risk-taking, and proactiveness – attempting to measure and analyse their effects on business performance on a unidimensional basis while claiming a generally and overall positive impact. However, this approach is different from Lumpkin and Dess’ (1996) superior development of the conceptualisation of EO as being driven by five (not three) dimensions (they added autonomy and competitive aggressiveness). These five dimensions were conceived to vary on an independent basis, each potentially relating differently to various firm performance measures (such as sales growth, gross-profit-margin, market share, and return on assets), while being determined by both internal and external factors. Consequently, even though Lumpkin and Dess’ (1996) EO theory has rarely been previously considered empirically in the literature on the subject, it has presented a more plausible development of the conceptualisation of EO, making it highly relevant to the current entrepreneurial research. Therefore, this thesis employs the five-dimensional approach with the aim to investigate four research questions: (1) whether and how a firm can achieve an ideal profile of EO dimensions and the manner in which this fit may vary across industrial contexts, (2) whether and which dimensions may be more beneficial towards the contingency of firm performance as opposed to their counterparts when considering factors such as different industry types (high-tech versus less-tech intensive firms) as well as (3) environmental conditions (industry turbulence and munificence), and, ultimately, (4) whether the effects of EO may last longer than their initial investment period. In brief, the proposed hypotheses were tested across a sample of US companies drawn from the Standard & Poor 500 that were selected to provide a relatively equal representation of high-technology and less-technology intensive companies, as determined by their industry types. This study pioneers a new research approach by examining the levels of the five EO dimensions through computer-aided text analysis along with a set of keywords advanced from Short et al.’s (2009) paper to extract values from the letters to shareholders and 10-K filings in the firms’ annual reports. Performance indicators and information related to the moderator and control variables were sourced from COMPUSTAT. In describing an EO’s contextuality regarding configurational, contingency, environmental, and temporal aspects, this thesis contributes to the current knowledge of EO in the following ways. Firstly, relating to research question 1, this study found that EO is associated with high performance in the set of ideal profile firms whereas deviance is associated with mediocre outcomes in the remaining group. Inconsistencies in the EO-performance linkage, therefore, are perceived to be driven by a poorer configuration of the EO multi-dimensions. Furthermore, it was examined to what extent the configuration associated with optimal performance remains the same across both the industry types. Herein, it was discovered that the ideal profiles do not differ across the two industry types of high-tech and less-tech. Secondly, relating to research question 2, within the context of this study, it was discovered that EO is, in fact, to be conceived as a multi-dimensional construct comprising of five dimensions as each has either a positive or a negative impact on individual performance measures (here under consideration of the contingency approach). However, such a linkage generally does not differ with respect to the industry types of high-tech and less-tech (except for two dimensions related to the market share measure). Thirdly, pertaining to research question 3, it was discovered that industry turbulence regarding employee stability positively moderates the EO-performance linkage for the performance indicator of market share. In contrast, for industry munificence, characterised by employee growth, a negatively moderating effect on the EO-performance relationship was observed for the same performance indicator. Thus, both employee variables are considered as central environmental influencers towards the EO-firm performance linkage regarding market share. Even so, with respect to the remaining studied performance indicators, no such effect was observed. Lastly, relating to research question 4, innovativeness was the sole dimension that positively affected the performance indicator of gross-profit-margin over a period of two years. Moreover, an adverse effect for risk-taking on return on assets was also found over the same time-span. As a consequence, EO, when considering the nuanced research within this thesis (cross-sectional of firms and/or industry types and conditions), was neither linked with generally positive nor superior firm performance as has been assumed across earlier studies but was instead associated with varying levels of the EO-performance linkage over time. Implications for scholarship, firms and top-level managers, limitations of this study, as well as recommendations and directions for future EO-based research close the work

A Scale-Invariant Spatial Graph Model

Information wird räumlich genannt, wenn sie Referenzen zum Raum beinhaltet. Die vorliegende Dissertation zielt darauf ab, die Charakterisierung räumlicher Information auf ein strukturelles Level zu heben. Toblers erstes Gesetz der Geographie und die Skaleninvarianz werden weithin zur Charakterisierung räumlicher Information verwendet. Ihre formale Beschreibung basiert jedoch auf expliziten Referenzen zum Raum, was einer Verwendung für die strukturelle Charakterisierung räumlicher Information entgegensteht. Der Autor führt daher ein Graphenmodell ein, welches im Falle einer Einbettung des Graphen in einen Raum typische Eigenschaften räumlicher Information aufweist, d.h. unter anderem Toblers Gesetz befolgt und skaleninvariant ist. Das Graphenmodell weist die Auswirkungen dieser typischen Eigenschaften auf seine Struktur auch dann auf, wenn es als abstrakter Graph interpretiert wird. Daher ist es zur Diskussion dieser typischen Eigenschaften auf einem strukturellen Level geeignet. Ein Vergleich des Modells mit verschiedenen räumlichen und nicht-räumlichen Datensätzen in der vorliegenden Dissertation legt nahe, dass räumliche Datensätze durch eine gemeinsame Struktur gekennzeichnet sind, weil die betrachteten räumlichen Datensätze im Gegensatz zu den nicht-räumlichen Gemeinsamkeiten mit dem Modell aufweisen. Dies lässt das Konzept einer räumlichen Struktur sinnvoll erscheinen. Das eingeführte Modell ist ein Modell dieser räumlichen Struktur. Die Dimension des Raumes wirkt sich auf räumliche Information und somit auch auf die räumliche Struktur aus. Die Dissertation untersucht, wie die Eigenschaften des Modells, insbesondere im Falle einer Gleichverteilung der Knoten im Raum, von der Dimension des Raumes abhängen und zeigt, wie eine Schätzung der Dimension aus der räumlichen Struktur eines Datensatzes gefolgert werden kann. Die Ergebnisse der Dissertation, insbesondere das Konzept einer räumlichen Struktur und das Graphenmodell, stellen einen grundlegenden Beitrag für die Diskussion räumlicher Information auf einem strukturellen Level dar: Auf räumlichen Daten operierende Algorithmen können unter Berücksichtigung der räumlichen Struktur verbessert werden; eine statistische Evaluation von Überlegungen zu räumlichen Daten wird möglich, da das Graphenmodell beliebig viele Testdatensätze mit kontrollierbaren Eigenschaften generieren kann; und das Erkennen von räumlichen Strukturen sowie die Schätzung der Dimension und weiterer Parameter kann zum langfristigen Ziel beitragen, Daten mit unvollständiger oder fehlender Semantik zu verwenden.Information is called spatial if it contains references to space. The thesis aims at lifting the characterization of spatial information to a structural level. Tobler's first law of geography and scale invariance are widely used to characterize spatial information, but their formal description is based on explicit references to space, which prevents them from being used in the structural characterization of spatial information. To overcome this problem, the author proposes a graph model that exposes, when embedded in space, typical properties of spatial information, amongst others Tobler's law and scale invariance. The graph model, considered as an abstract graph, still exposes the effect of these typical properties on the structure of the graph and can thus be used for the discussion of these typical properties at a structural level. A comparison of the proposed model to several spatial and non-spatial data sets in this thesis suggests that spatial data sets can be characterized by a common structure, because the considered spatial data sets expose structural similarities to the proposed model but the non-spatial data sets do not. This proves the concept of a spatial structure to be meaningful, and the proposed model to be a model of spatial structure. The dimension of space has an impact on spatial information, and thus also on the spatial structure. The thesis examines how the properties of the proposed graph model, in particular in case of a uniform distribution of nodes in space, depend on the dimension of space and shows how to estimate the dimension from the structure of a data set. The results of the thesis, in particular the concept of a spatial structure and the proposed graph model, are a fundamental contribution to the discussion of spatial information at a structural level: algorithms that operate on spatial data can be improved by paying attention to the spatial structure; a statistical evaluation of considerations about spatial data is rendered possible, because the graph model can generate arbitrarily many test data sets with controlled properties; and the detection of spatial structures as well as the estimation of the dimension and other parameters can contribute to the long-term goal of using data with incomplete or missing semantics.von Franz-Benjamin MocnikZusammenfassung in deutscher SpracheAbweichender Titel nach Übersetzung der Verfasserin/des VerfassersTechnische Universität Wien, Dissertation, 2016OeBB(VLID)164200

Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics

Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface which partitions the domain and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that to accurately compute variances using the PBD simulation requires the overlap region. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented.Comment: submitted to SIAM Journal on Applied Mathematic