Optimally Sparse Frames

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of the frame measurements of a signal typically requires a large number of additions and multiplications, and this makes a frame decomposition intractable in applications with limited computing budget. To address this problem, in this paper, we focus on frames in finite-dimensional Hilbert spaces and introduce sparsity for such frames as a new paradigm. In our terminology, a sparse frame is a frame whose elements have a sparse representation in an orthonormal basis, thereby enabling low-complexity frame decompositions. To introduce a precise meaning of optimality, we take the sum of the numbers of vectors needed of this orthonormal basis when expanding each frame vector as sparsity measure. We then analyze the recently introduced algorithm Spectral Tetris for construction of unit norm tight frames and prove that the tight frames generated by this algorithm are in fact optimally sparse with respect to the standard unit vector basis. Finally, we show that even the generalization of Spectral Tetris for the construction of unit norm frames associated with a given frame operator produces optimally sparse frames

Performance adaptive manufacturing processes

Part of: Seliger, Günther (Ed.): Innovative solutions : proceedings / 11th Global Conference on Sustainable Manufacturing, Berlin, Germany, 23rd - 25th September, 2013. - Berlin: Universitätsverlag der TU Berlin, 2013. - ISBN 978-3-7983-2609-5 (online). - http://nbn-resolving.de/urn:nbn:de:kobv:83-opus4-40276. - pp. 296-301.Energy efficiency is of increasing importance towards sustainable manufacturing in the automotive industry, in particular due to growing environment regulations and rising electricity costs. Approaches within the manufacturing planning phase are insufficient to address dynamic influences during run-time (e.g., electricity tariffs or workload). Additionally, conventional production monitoring and control systems consider the ‘Overall Equipment Effectiveness‘ of manufacturing systems, but do not include related energy efficiency. This paper introduces a novel approach that combines these both aspects and provides more effectiveness based on socalled production variants. The latter are designed during the planning phase and used to adapt manufacturing behavior when facing dynamically changes during run-time. A simulation shows how dynamic adjustments of cycle times lead to a high reduction of energy costs while maintaining high throughputs

Upper critical field pecularities of superconducting YNi2B2C and LuNi2B2C

We present new upper critical field Hc2(T) data in a broad temperature region from 0.3K to Tc for LuNi2B2C and YNi2B2C single crystals with well characterized low impurity scattering rates. The absolute values for all T, in particular Hc2(0), and the sizeable positive curvature (PC) of Hc2(T) at high and intermediate T are explained quantitatively within an effective two-band model. The failure of the isotropic single band approach is discussed in detail. Supported by de Haas van Alphen data, the superconductivity reveals direct insight into details of the electronic structure. The observed maximal PC near Tc gives strong evidence for clean limit type II superconductors.Comment: 4 pages, 2 figures, Phys. Rev. Lett. accepte

Theory of de Haas-van Alphen Effect in Type-II Superconductors

Theory of quasiparticle spectra and the de Haas-van Alphen (dHvA) oscillation in type-II superconductors are developed based on the Bogoliubov-de Gennes equations for vortex-lattice states. As the pair potential grows through the superconducting transition, each degenerate Landau level in the normal state splits into quasiparticle bands in the magnetic Brillouin zone. This brings Landau-level broadening, which in turn leads to the extra dHvA oscillation damping in the vortex state. We perform extensive numerical calculations for three-dimensional systems with various gap structures. It is thereby shown that (i) this Landau-level broadening is directly connected with the average gap at H=0 along each Fermi-surface orbit perpendicular to the field H; (ii) the extra dHvA oscillation attenuation is caused by the broadening around each extremal orbit. These results imply that the dHvA experiment can be a unique probe to detect band- and/or angle-dependent gap amplitudes. We derive an analytic expression for the extra damping based on the second-order perturbation with respect to the pair potential for the Luttinger-Ward thermodynamic potential. This formula reproduces all our numerical results excellently, and is used to estimate band-specific gap amplitudes from available data on NbSe_2, Nb_3Sn, and YNi_2B_2C. The obtained value for YNi_2B_2C is fairly different from the one through a specific-heat measurement, indicating presence of gap anisotropy in this material. C programs to solve the two-dimensional Bogoliubov-de Gennes equations are available at http://phys.sci.hokudai.ac.jp/~kita/index-e.html .Comment: 16 pages, 11 figure

Comparison of coherent and weakly incoherent transport models for the interlayer magnetoresistance of layered Fermi liquids

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport and makes use of results of semi-classical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations (AMRO) in quasi-one- and quasi-two-dimensional metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two- and quasi-one-dimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time (and thus the temperature). We point out three distinctive features of coherent interlayer transport: (i) a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, (ii) a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and (iii) a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties (i) and (ii) are compared with published experimental data for a range of quasi-two-dimensional organic metals and for Sr2RuO4.Comment: 21 pages, RevTeX + epsf, 4 figures. Published version. Subsection added. References update

Franchising as a Strategy for Combining Small and Large Group Advantages (Logics) in Social Entrepreneurship:A Hayekian Perspective

This article develops a Hayekian perspective on social franchising that distinguishes between the end-connected logic of the small group and the rule-connected logic of the big group. Our key claim is that mission-driven social entrepreneurs often draw on the small-group logic when starting their social ventures and then face difficulties when the process of scaling shifts their operations toward a big-group logic. In this situation, social franchising offers a strategy to replicate the small group despite systemwide scaling, to mobilize decentrally accessible social capital, and to reduce agency costs through mechanisms of self-selection and self-monitoring. By employing a Hayekian perspective, we are thus able to offer an explanation as to why social franchising is a suitable scaling strategy for some social entrepreneurship organizations and not for others. We illustrate our work using the Ashoka Fellow Wellcome

Time-dependent density functional study of the electronic spectra of oligoacenes in the charge states -1, 0, +1, and +2

We present a systematic theoretical study of the five smallest oligoacenes (naphthalene, anthracene, tetracene, pentacene, and hexacene) in their anionic,neutral, cationic, and dicationic charge states. We used density functional theory (DFT) to obtain the ground-state optimised geometries, and time-dependent DFT (TD-DFT) to evaluate the electronic absorption spectra. Total-energy differences enabled us to evaluate the electron affinities and first and second ionisation energies, the quasiparticle correction to the HOMO-LUMO energy gap and an estimate of the excitonic effects in the neutral molecules. Electronic absorption spectra have been computed by combining two different implementations of TD-DFT: the frequency-space method to study general trends as a function of charge-state and molecular size for the lowest-lying in-plane long-polarised and short-polarised $\pi\to\pi^\star$ electronic transitions, and the real-time propagation scheme to obtain the whole photo-absorption cross-section up to the far-UV. Doubly-ionised PAHs are found to display strong electronic transitions of $\pi\to\pi^\star$ character in the near-IR, visible, and near-UV spectral ranges, like their singly-charged counterparts. While, as expected, the broad plasmon-like structure with its maximum at about 17-18 eV is relatively insensitive to the charge-state of the molecule, a systematic decrease with increasing positive charge of the absorption cross-section between about 6 and about 12 eV is observed for each member of the class.Comment: 38 pages, 11 figures, 7 tables, accepted for publication in Chemical Physic