77 research outputs found
Intrinsic Localization of Anisotropic Frames II: α -Molecules
No full textThis article is a continuation of the recent paper (Appl Comput Harmon Anal 35:264–283, 2013) by the first author, where off-diagonal-decay properties (often referred to as ’localization’ in the literature) of Moore-Penrose pseudoinverses of (bi-infinite) matrices are established, whenever the latter possess similar off-diagonal-decay properties. This problem is especially interesting if the matrix arises as a discretization of an operator with respect to a frame or basis. Previous work on this problem has been restricted to wavelet- or Gabor frames. In Appl Comput Harmon Anal 35:264–283, 2013, we extended these results to frames of parabolic molecules, including curvelets or shearlets as special cases. The present paper extends and unifies these results by establishing analogous properties for frames of (Formula presented.)-molecules as introduced in recent work (Proc SPIE, 2013). Since wavelets, curvelets, shearlets, ridgelets and hybrid shearlets all constitute instances of (Formula presented.)-molecules, our results establish localization properties for all these systems simultaneously
Continuous Shearlet Tight Frames
No full textBased on the shearlet transform we present a general construction of continuous tight frames for L2(ℝ2) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From our earlier results in Grohs (Technical report, KAUST, 2009) it follows that these systems enjoy the same desirable approximation properties for directional data as the previous bandlimited and very specific constructions due to Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719-2754, 2009). We also show that the representation formulas we derive are in a sense optimal for the shearlet transform. © 2010 Springer Science+Business Media, LLC.The research for this paper has been carried out while the author was working atthe Center for Geometric Modeling and Scientific Visualization at KAUST, Saudi Arabia
Definability and stability of multiscale decompositions for manifold-valued data
No full textWe discuss multiscale representations of discrete manifold-valued data. As it turns out that we cannot expect general manifold analogs of biorthogonal wavelets to possess perfect reconstruction, we focus our attention on those constructions which are based on upscaling operators which are either interpolating or midpoint-interpolating. For definable multiscale decompositions we obtain a stability result. © 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.The authors gratefully acknowledge the support of the Austrian Science Fund. The work of Philipp Grohs has been supported by grant No. P19780. The research for this paper has been carried out while the author was working at the Center for Geometric Modeling and Scientific Visualization at KAUST, Saudi Arabia
MESA source code modifications for stable 8Be
No full text<p>MESA source code modifications for stable 8Be</p>
MESA source code modifications for unstable deuterium
No full text<p>MESA source code modifications for unstable deuterium</p>
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Self-Consistent Treatment of Neutrino Physics in Cosmology
No full textWe are developing a code to self--consistently treat beyond--standard--model physics in the early universe. This work details the calculations done with regards to the epochs of weak decoupling, weak freeze--out, big bang nucleosynthesis, recombination, and includes exploratory work on dilution and electron--positron annihilation. We assess the predictions made by the standard model, and investigate how new physics in the neutrino sector may alter or preserve those predictions. Throughout this work, we use natural units : hbar=c=k_b=
Initial Public Offerings and Venture Capital in Germany
No full textWe present a survey on the role of initial public offerings (IPOs) and venture capital (VC) in Germany after the Second World War. Between 1945 and 1983 IPOs hardly played a role at all and only a minor role thereafter. In addition, companies that chose an IPO were much older and larger than the average companies going public for the first time in the US or the UK. The level of IPO underpricing in Germany, in contrast, has not been fundamentally different from that in other countries. The picture for venture capital financing is not much different from that provided by IPOs in Germany. For a long time venture capital financing was hardly significant, particularly as a source of early stage financing. The unprecedented boom on the Neuer Markt between 1997 and 2000, when many small venture capital financed firms entered the market, provides a striking contrast to the preceding era. However, by US standards, the levels of both IPO and venture capital activities remained rather low even in this boom phase. The extent to which recent developments will have a lasting impact on the financing of German firms, the level of IPO activity, and venture capital financing, remains to be seen. At the time of writing, activity has come to a near stand still and the Neuer Markt has just been dissolved. The low number of IPOs and the fairly low volume of VC financing in Germany before the introduction of the Neuer Markt are a striking and much debated phenomenon. Understanding the reasons for these apparent peculiarities is vital to understanding the German financial system. The potential explanations that have been put forward range from differences in mentality to legal and institutional impediments and the availability of alternative sources of financing. Moreover the recent literature discusses how interest groups may have benefited and influenced the situation. These groups include politicians, unions/workers, managers/controlling-owners of established firms as well as banks.Initial Public Offering (IPO), Venture Capital, Germany
Continuous shearlet frames and resolution of the wavefront set
No full textIn recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are-unlike more traditional transforms like wavelets-able to efficiently handle data with features along edges. The main result in Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719-2754, 2009) confirming this property for shearlets is due to Kutyniok and Labate where it is shown that for very special functions ψ with frequency support in a compact conical wegde the decay rate of the shearlet coefficients of a tempered distribution f with respect to the shearlet ψ can resolve the wavefront set of f. We demonstrate that the same result can be verified under much weaker assumptions on ψ, namely to possess sufficiently many anisotropic vanishing moments. We also show how to build frames for L2(ℝ2)from any such function. To prove our statements we develop a new approach based on an adaption of the Radon transform to the shearlet structure. © 2010 Springer-Verlag.The research for this paper has been carried out while the author was working at theCenter for Geometric Modeling and Scientific Visualization at KAUST, Saudi Arabia. We thank Hans-GeorgFeichtinger for several useful comments
Thin needle aspiration biopsy. Author: Britt‐Marie Ljung Fine Needle Aspiration Technique: International Institute for Applied Cytoscience. Author: Heinz Grohs
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