Subgraph covers -- An information theoretic approach to motif analysis in networks

Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original network with a statistical null model. In this paper we propose an alternative approach to motif analysis where network motifs are defined to be connectivity patterns that occur in a subgraph cover that represents the network using minimal total information. A subgraph cover is defined to be a set of subgraphs such that every edge of the graph is contained in at least one of the subgraphs in the cover. Some recently introduced random graph models that can incorporate significant densities of motifs have natural formulations in terms of subgraph covers and the presented approach can be used to match networks with such models. To prove the practical value of our approach we also present a heuristic for the resulting NP-hard optimization problem and give results for several real world networks.Comment: 10 pages, 7 tables, 1 Figur

Flow Equations and Normal Ordering

In this paper we consider flow-equations where we allow a normal ordering which is adjusted to the one-particle energy of the Hamiltonian. We show that this flow converges nearly always to the stable phase. Starting out from the symmetric Hamiltonian and symmetry-broken normal ordering nearly always yields symmetry breaking below the critical temperature.Comment: 7 page

A Gravitational Redshift Determination of the Mean Mass of White Dwarfs. DBA and DB Stars

We measure apparent velocities (v_app) of absorption lines for 36 white dwarfs (WDs) with helium-dominated atmospheres -- 16 DBAs and 20 DBs -- using optical spectra taken for the European Southern Observatory SN Ia progenitor survey (SPY). We find a difference of 6.9+/-6.9 km/s in the average apparent velocity of the H-alpha lines versus that of the HeI 5876AA for our DBAs. This is a measure of the blueshift of this He line due to pressure effects. By using this as a correction, we extend the gravitational redshift method employed by Falcon et al. (2010) to use the apparent velocity of the HeI 5876AA line and conduct the first gravitational redshift investigation of a group of WDs without visible hydrogen lines. We use biweight estimators to find an average apparent velocity, _BI, (and hence average gravitational redshift, _BI) for our WDs; from that we derive an average mass, _BI. For the DBAs, we find _BI = 40.8+/-4.7 km/s and derive _BI = 0.71 +0.04 -0.05 Msun. Though different from of DAs (32.57 km/s) at the 91% confidence level and suggestive of a larger DBA mean mass than that for normal DAs derived using the same method (0.647 +0.013 -0.014 Msun; Falcon et al. 2010), we do not claim this as a stringent detection. Rather, we emphasize that the difference between _BI of the DBAs and of normal DAs is no larger than 9.2 km/s, at the 95% confidence level; this corresponds to roughly 0.10 Msun. For the DBs, we find ^He_BI = 42.9+/-8.49 km/s after applying the blueshift correction and determine _BI = 0.74 +0.08 -0.09 Msun. The difference between ^He_BI of the DBs and of DAs is less than or equal to 11.5 km/s (~0.12 Msun), at the 95% confidence level. The gravitational redshift method indicates much larger mean masses than the spectroscopic determinations of the same sample by Voss et al. (2007)...Comment: Accepted to the Astrophysical Journal, 10 pages double-column, 3 figures, 5 table

Block Diagonalization using SRG Flow Equations

By choosing appropriate generators for the Similarity Renormalization Group (SRG) flow equations, different patterns of decoupling in a Hamiltonian can be achieved. Sharp and smooth block-diagonal forms of phase-shift equivalent nucleon-nucleon potentials in momentum space are generated as examples and compared to analogous low-momentum interactions ("v_lowk").Comment: 4 pages, 9 figures (pdfLaTeX