Counting metastable states of Ising spin glasses on arbitrary graphs

Using a field-theoretical representation of the Tanaka-Edwards integral we develop a method to systematically compute the number N_s of 1-spin-stable states (local energy minima) of a glassy Ising system with nearest-neighbor interactions and random Gaussian couplings on an arbitrary graph. In particular, we use this method to determine N_s for K-regular random graphs and d-dimensional regular lattices for d=2,3. The method works also for other graphs. Excellent accuracy of the results allows us to observe that the number of local energy minima depends mainly on local properties of the graph on which the spin glass is defined.Comment: 8 pages, 4 figures (one in color), additional materials can be found under http://www.physik.uni-leipzig.de/~waclaw/glasses-data.ht

The method of data envelopment analysis as a tool for compiling a rating list

The paper presents the method of Data Envelopment Analysis (DEA) as a tool for compiling rating lists in tasks of ordering elements of assemblages. We describe the differences that result from applying a one-dimensional model and multi-dimensional model, where in the latter a so-called partial order is created for incomparable elements in the assemblage being ordered. The example used to illustrate the issues discussed is the analysis of teaching results in a student group.DEA method, ordering of assemblages, partial order, rating classes

Speckle observations of binary stars with a 0.5 m telescope

We present 36 observations of 17 visual binaries of moderate separation (range from 0.15'' to 0.79'') made with the 50 cm Cassegrain telescope of the Jagiellonian University in Cracow. The speckle interferometry technique was combined with modest optical hardware and a standard photometric CCD camera. We used broad-band V,R,I filters without a Risley prism to reduce differential colour refraction, so we performed model analysis to investigate the influence of this effect on the results of measurements. For binary components of spectral type O-F, the difference of three spectral classes between them should bias their relative positions by no more than a couple of tens of milliarcseconds (mas) for moderate zenith distances. The statistical analysis of our results confirmed this conclusion. A cross-spectrum approach was applied to resolve the quadrant ambiguity. Our separations have RMS deviations of 0.012'' and our position angles have RMS deviations of 1.8 deg. Relative photometry in V, R and I filters appeared to be the less accurately determined parameter. We discuss our errors in detail and compare them to other speckle data. This comparison clearly shows the high value of our measurements. We also present an example of the enhancement of image resolution for an extended object of angular size greater than the atmospheric coherence patch using speckle interferometry techniques.Comment: Submitted to Astronomy & Astrophysic