Synergetic Analysis of the Haeussler-von der Malsburg Equations for Manifolds of Arbitrary Geometry

We generalize a model of Haeussler and von der Malsburg which describes the self-organized generation of retinotopic projections between two one-dimensional discrete cell arrays on the basis of cooperative and competitive interactions of the individual synaptic contacts. Our generalized model is independent of the special geometry of the cell arrays and describes the temporal evolution of the connection weights between cells on different manifolds. By linearizing the equations of evolution around the stationary uniform state we determine the critical global growth rate for synapses onto the tectum where an instability arises. Within a nonlinear analysis we use then the methods of synergetics to adiabatically eliminate the stable modes near the instability. The resulting order parameter equations describe the emergence of retinotopic projections from initially undifferentiated mappings independent of dimension and geometry.Comment: Dedicated to Hermann Haken on the occasion of his 80th birthda

Disorder Effects in Superconducting Multiple Loop Quantum Interferometers

A theoretical study is presented on a number N of resistively shunted Josephson junctions connected in parallel as a disordered 1D array by superconducting wiring in such a manner that there are N-1 individual SQUID loops with arbitrary shape formed.Comment: 4 pages, 2 figure

Classification of one-dimensional quasilattices into mutual local-derivability classes

One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. Every MLD class has a finite number of quasilattices with inflation symmetries. We can choose one of them as the representative of the MLD class, and other members are given as decorations of the representative. Several MLD classes of particular importance are listed. The symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS

Mesoscopic Aharonov-Bohm oscillations in metallic rings

We study the amplitude of mesoscopic Aharonov-Bohm oscillations in quasi-one-dimensional (Q1D) diffusive rings. We consider first the low-temperature limit of a fully coherent sample. The variance of oscillation harmonics is calculated as a function of the length of the leads attaching the ring to reservoirs. We further analyze the regime of relatively high temperatures, when the dephasing due to electron-electron interaction suppresses substantially the oscillations. We show that the dephasing length L_phi^AB governing the damping factor exp(-2pi R /L_phi^AB) of the oscillations is parametrically different from the common dephasing length for the Q1D geometry. This is due to the fact that the dephasing is governed by energy transfers determined by the ring circumference 2pi R, making L_phi^AB R-dependent.Comment: 16 pages, 4 figures, to appear in proceedings of NATO/Euresco Conference "Fundamental Problems of Mesoscopic Physics: Interactions and Decoherence", Granada (Spain), September 200

Non-equilibrium electronic transport and interaction in short metallic nanobridges

We have observed interaction effects in the differential conductance $G$ of short, disordered metal bridges in a well-controlled non-equilibrium situation, where the distribution function has a double Fermi step. A logarithmic scaling law is found both for the temperature and for the voltage dependence of $G$ in all samples. The absence of magnetic field dependence and the low dimensionality of our samples allow us to distinguish between several possible interaction effects, proposed recently in nanoscopic samples. The universal scaling curve is explained quantitatively by the theory of electron-electron interaction in diffusive metals, adapted to the present case, where the sample size is smaller than the thermal diffusion length.Comment: Published version, 6 Pages, 6 postscript figures, 1 tabl

Antiferromagnetic interlayer exchange coupling across an amorphous metallic spacer layer

By means of magneto-optical Kerr effect we observe for the first time antiferromagnetic coupling between ferromagnetic layers across an amorphous metallic spacer layer. Biquadratic coupling occurs at the transition from a ferromagnetically to an antiferromagnetically coupled region. Scanning tunneling microscopy images of all involved layers are used to extract thickness fluctuations and to verify the amorphous state of the spacer. The observed antiferromagnetic coupling behavior is explained by RKKY interaction taking into account the amorphous structure of the spacer material.Comment: Typset using RevTex, 4 pages with 4 figures (.eps

Bar Evolution Over the Last Eight Billion Years: A Constant Fraction of Strong Bars in GEMS

One third of present-day spirals host optically visible strong bars that drive their dynamical evolution. However, the fundamental question of how bars evolve over cosmological times has yet to be addressed, and even the frequency of bars at intermediate redshifts remains controversial. We investigate the frequency of bars out to z~1.0 drawing on a sample of 1590 galaxies from the GEMS survey, which provides morphologies from HST ACS two-color images, and highly accurate redshifts from the COMBO-17 survey. We identify spiral galaxies using the Sersic index, concentration parameter, and rest-frame color. We characterize bars and disks by fitting ellipses to F606W and F850LP images, taking advantage of the two bands to minimize bandpass shifting. We exclude highly inclined (i>60 deg) galaxies to ensure reliable morphological classifications, and apply completeness cuts of M_v <= -19.3 and -20.6. More than 40% of the bars that we detect have semi major axes a<0.5" and would be easily missed in earlier surveys without the small PSF of ACS. The bars that we can reliably detect are fairly strong (with ellipticities e>=0.4) and have a in the range ~1.2-13 kpc. We find that the optical fraction of such strong bars remains at ~(30% +- 6%) from the present-day out to look-back times of 2-6 Gyr (z~0.2-0.7) and 6-8 Gyr (z~0.7-1.0); it certainly shows no sign of a drastic decline at z>0.7. Our findings of a large and similar bar fraction at these three epochs favor scenarios in which cold gravitationally unstable disks are already in place by z~1, and where on average bars have a long lifetime (well above 2 Gyr). The distributions of structural bar properties in the two slices are, however, not statistically identical and therefore allow for the possibility that the bar strengths and sizes may evolve over time.Comment: Accepted by ApJ Letters, to appear in Nov 2004 issue. Minor revisions,updated reference

Cluster Performance reconsidered: Structure, Linkages and Paths in the German Biotechnology Industry, 1996-2003

This paper addresses the evolution of biotechnology clusters in Germany between 1996 and 2003, paying particular attention to their respective composition in terms of venture capital, basic science institutions and biotechnology firms. Drawing upon the significance of co-location of "money and ideas", the literature stressing the importance of a cluster's openness and external linkages, and the path dependency debate, the paper aims to analyse how certain cluster characteristics correspond with its overall performance. After identifying different cluster types, we investigate their internal and external interconnectivity in comparative manner and draw on changes in cluster composition. Our results indicate that the structure, i.e. to which group the cluster belongs, and the openness towards external knowledge flows deliver merely unsystematic indications with regard to a cluster's overall success. Its ability to change composition towards a more balanced ratio of science and capital over time, on the other hand, turns out as a key explanatory factor. Hence, the dynamic perspective proves effective illuminating cluster growth and performance, where our explorative findings provide a promising avenue for further evolutionary research

CANDELS Observations of the Structural Properties and Evolution of Galaxies in a Cluster at z=1.62

We discuss the structural and morphological properties of galaxies in a z=1.62 proto-cluster using near-IR imaging data from Hubble Space Telescope Wide Field Camera 3 data of the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS). The cluster galaxies exhibit a clear color-morphology relation: galaxies with colors of quiescent stellar populations generally have morphologies consistent with spheroids, and galaxies with colors consistent with ongoing star formation have disk-like and irregular morphologies. The size distribution of the quiescent cluster galaxies shows a deficit of compact (< 1kpc), massive galaxies compared to CANDELS field galaxies at z=1.6. As a result the cluster quiescent galaxies have larger average effective sizes compared to field galaxies at fixed mass at greater than 90% significance. Combined with data from the literature, the size evolution of quiescent cluster galaxies is relatively slow from z~1.6 to the present, growing as (1+z)^(-0.6+/-0.1). If this result is generalizable, then it implies that physical processes associated with the denser cluster region seems to have caused accelerated size growth in quiescent galaxies prior to z=1.6 and slower subsequent growth at z<1.6 compared to galaxies in the lower density field. The quiescent cluster galaxies at z=1.6 have higher ellipticities compared to lower redshift samples at fixed mass, and their surface-brightness profiles suggest that they contain extended stellar disks. We argue the cluster galaxies require dissipationless (i.e., gas-poor or "dry") mergers to reorganize the disk material and to match the relations for ellipticity, stellar mass, size, and color of early-type galaxies in z<1 clusters.Comment: Accepted for publication in ApJ. 14 pages in emulateapj format. Replacement includes improvements from referee report, and updates and additions to reference

Detailed Decomposition of Galaxy Images. II. Beyond Axisymmetric Models

We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting algorithms by allowing for irregular, curved, logarithmic and power-law spirals, ring and truncated shapes in otherwise traditional parametric functions like the Sersic, Moffat, King, Ferrer, etc., profiles. One can mix and match these new shape features freely, with or without constraints, apply them to an arbitrary number of model components and of numerous profile types, so as to produce realistic-looking galaxy model images. Yet, despite the potential for extreme complexity, the meaning of the key parameters like the Sersic index, effective radius or luminosity remain intuitive and essentially unchanged. The new features have an interesting potential for use to quantify the degree of asymmetry of galaxies, to quantify low surface brightness tidal features beneath and beyond luminous galaxies, to allow more realistic decompositions of galaxy subcomponents in the presence of strong rings and spiral arms, and to enable ways to gauge the uncertainties when decomposing galaxy subcomponents. We illustrate these new features by way of several case studies that display various levels of complexity.Comment: 41 pages, 22 figures, AJ accepted. Minor changes. Full resolution version of this paper is available at: http://users.obs.carnegiescience.edu/peng/work/galfit/galfit3.pd