Training a perceptron by a bit sequence: Storage capacity

A perceptron is trained by a random bit sequence. In comparison to the corresponding classification problem, the storage capacity decreases to alpha_c=1.70\pm 0.02 due to correlations between input and output bits. The numerical results are supported by a signal to noise analysis of Hebbian weights.Comment: LaTeX, 13 pages incl. 4 figures and 1 tabl

Landschaftspläne in Europa: Status quo und Perspektiven konzeptioneller Landschaftspläne im europäischen Vergleich: Zusammenfassendes Ergebnispapier: Inspirierender Expertenaustausch über Landschaftsplanung: Expertenworkshop des BfN vom - 17.- 20.09.2008 an der Internationalen Naturschutzakademie Insel Vilm

Die Vortragenden wurden im Vorfeld gebeten folgende Aspekte zu berücksichtigen: 1. Wie sind "Landschaftspläne" in das Planungssystem ihres Landes eingebunden, d. h. wie ist ihr Verhältnis zur Raum-, Naturschutz-, Kultur- und Umweltplanung? 2. Was sind wichtige Inhalte a) der Analyse sowie b) der Entwicklungskonzeption der Pläne? Zugleich wurden die Referenten gebeten, einen guten oder erfolgreichen Landschaftsplan ihres Landes auszuwählen und diesen auf dem Workshop vorzustellen und zugänglich zu machen

Recurrent proofs of the irrationality of certain trigonometric values

We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate consequences to other values of the elementary transcendental functions are also discussed

Recursion-free solution for two-loop vacuum integrals with "collinear" masses

We investigate the structure of a particular class of massive vacuum Feynman integrals at two loops. This class enjoys the linear relation $m_1+m_2=m_3$ between its three propagator masses, corresponding to zeros of the associated K\"all\'en function. Apart from having applications in thermal field theory, the integrals can be mapped onto one-loop three-point functions with collinear external momenta, suggesting the term "collinear" masses. We present a closed-form solution for these integrals, proving that they can always be factorized into products of one-loop cases, for all integer-valued propagator powers.Comment: 34 pages, 5 figures; v2: references adde

Van der Waals Density Functional for General Geometries

A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402 (2003)]. It includes van der Waals forces in a seamless fashion. By expansion to second order in a carefully chosen quantity contained in the long range part of the correlation functional, the nonlocal correlations are expressed in terms of a density-density interaction formula. It contains a relatively simple parametrized kernel, with parameters determined by the local density and its gradient. The proposed functional is applied to rare gas and benzene dimers, where it is shown to give a realistic description.Comment: 4 pages, 4 figure

Towards a working density-functional theory for polymers: First-principles determination of the polyethylene crystal structure

Equilibrium polyethylene crystal structure, cohesive energy, and elastic constants are calculated by density-functional theory applied with a recently proposed density functional (vdW-DF) for general geometries [Phys. Rev. Lett. 92, 246401 (2004)] and with a pseudopotential-planewave scheme. The vdW-DF with its account for the long-ranged van der Waals interactions gives not only a stabilized crystal structure but also values of the calculated lattice parameters and elastic constants in quite good agreement with experimental data, giving promise for successful application to a wider range of polymers.Comment: 4 pages, 3 figure

Basal Chromospheric Flux and Maunder Minimum-type Stars: The quiet-Sun Chromosphere as a Universal Phenomenon

Aims: We demonstrate the universal character of the quiet-Sun chromosphere among inactive stars (solar-type and giants). By assessing the main physical processes, we shed new light on some common observational phenomena. Methods: We discuss measurements of the solar Mt. Wilson S-index, obtained by the Hamburg Robotic Telescope around the extreme minimum year 2009, and compare the established chromospheric basal Ca II K line flux to the Mt. Wilson S-index data of inactive ("flat activity") stars, including giants. Results: During the unusually deep and extended activity minimum of 2009, the Sun reached S-index values considerably lower than in any of its previously observed minima. In several brief periods, the Sun coincided exactly with the S-indices of inactive ("flat", presumed Maunder Minimum-type) solar analogues of the Mt. Wilson sample; at the same time, the solar visible surface was also free of any plages or remaining weak activity regions. The corresponding minimum Ca II K flux of the quiet Sun and of the presumed Maunder Minimum-type stars in the Mt. Wilson sample are found to be identical to the corresponding Ca II K chromospheric basal flux limit. Conclusions: We conclude that the quiet-Sun chromosphere is a universal phenomenon among inactive stars. Its mixed-polarity magnetic field, generated by a local, "fast" turbulent dynamo finally provides a natural explanation for the minimal soft X-ray emission observed for inactive stars. Given such a local dynamo also works for giant chromospheres, albeit on larger length scales, i.e., l ~ R/g, with R and g as stellar radius and surface gravity, respectively, the existence of giant spicular phenomena and the guidance of mechanical energy toward the acceleration zone of cool stellar winds along flux-tubes have now become traceable.Comment: 6 pages, 4 figures; Astronomy & Astrophysics (Research Note), in pres