Comparing Universal Covers in Polynomial Time

The universal cover T _G of a connected graph G is the unique (possibly infinite) tree covering G, i.e., that allows a locally bijective homomorphism from T _G to G. It is well-known that if a graph G covers a graph H, then their universal covers are isomorphic, and that the latter can be tested in polynomial time by checking if G and H share the same degree refinement matrix. We extend this result to locally injective and locally surjective homomorphisms by following a very different approach. Using linear programming techniques we design two polynomial time algorithms that check if there exists a locally injective or a locally surjective homomorphism, respectively, from a universal cover T _G to a universal cover T _H (both given by their degree matrices). This way we obtain two heuristics for testing the corresponding locally constrained graph homomorphisms. Our algorithm can also be used for testing (subgraph) isomorphism between universal covers, and for checking if there exists a locally injective or locally surjective homomorphism (role assignment) from a given tree to an arbitrary graph H.     

Editors’ note

Editorial Note

Editors’ note     

Continuous-time quantum Monte Carlo impurity solvers

Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states.

Program summary

Program title: dmftCatalogue identifier: AEIL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: ALPS LIBRARY LICENSE version 1.1No. of lines in distributed program, including test data, etc.: 899 806No. of bytes in distributed program, including test data, etc.: 32 153 916Distribution format: tar.gzProgramming language: C++Operating system: The ALPS libraries have been tested on the following platforms and compilers:

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  Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher)

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  MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0)

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  IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers

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  Compaq Tru64 UNIX with Compq C++ Compiler (cxx)

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  SGI IRIX with MIPSpro C++ Compiler (CC)

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  HP-UX with HP C++ Compiler (aCC)

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  Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher)

RAM: 10 MB–1 GBClassification: 7.3External routines: ALPS [1], BLAS/LAPACK, HDF5Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of “correlated electron” materials as auxiliary problems whose solution gives the “dynamical mean field” approximation to the self-energy and local correlation functions.Solution method: Quantum impurity models require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms for which we present implementations here meet this challenge. Continuous-time quantum impurity methods are based on partition function expansions of quantum impurity models that are stochastically sampled to all orders using diagrammatic quantum Monte Carlo techniques. For a review of quantum impurity models and their applications and of continuous-time quantum Monte Carlo methods for impurity models we refer the reader to [2].Additional comments: Use of dmft requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper.Running time: 60 s–8 h per iteration.References:

• [1] 

  A. Albuquerque, F. Alet, P. Corboz, et al., J. Magn. Magn. Mater. 310 (2007) 1187.

• [2] 

  http://arxiv.org/abs/1012.4474, Rev. Mod. Phys., in press.

     

Parameterized complexity of coloring problems: Treewidth versus vertex cover

We compare the fixed parameter complexity of various variants of coloring problems (including List Coloring, Precoloring Extension, Equitable Coloring, L(p,1)-Labeling and Channel Assignment) when parameterized by treewidth and by vertex cover number. In most (but not all) cases we conclude that parametrization by the vertex cover number provides a significant drop in the complexity of the problems.     

Erratum to “Dynamical Sources in Information Theory: Fundamental Intervals and Word Prefixes”

In [V] the third author studied statistical properties of words generated by dynamical sources by using generalized Ruelle operators. This erratum aims to show that a supplementary condition should be added in Definition 2.1 of dynamical sources. This supplementary condition (called (d4) below) is closely related to the so-called Bounded Distortion Property and should be used at two different stages of the paper: first in the definition of the generalized operator G_s, second in the proof of Proposition 2 that deals with the Positivity Theorem of Krasnoselskii. We also prove that this condition is actually necessary and provide an example of a source which does not satisfy condition (d4) and for which G_s is not well-defined.     

miR-16-5p Is a Stably-Expressed Housekeeping MicroRNA in Breast Cancer Tissues from Primary Tumors and from Metastatic Sites

For quantitative microRNA analyses in formalin-fixed paraffin-embedded (FFPE) tissue, expression levels have to be normalized to endogenous controls. To investigate the most stably-expressed microRNAs in breast cancer and its surrounding tissue, we used tumor samples from primary tumors and from metastatic sites. MiRNA profiling using TaqMan^® Array Human MicroRNA Cards, enabling quantification of 754 unique human miRNAs, was performed in FFPE specimens from 58 patients with metastatic breast cancer. Forty-two (72%) samples were collected from primary tumors and 16 (28%) from metastases. In a cross-platform analysis of a validation cohort of 32 FFPE samples from patients with early breast cancer genome-wide microRNA expression analysis using SurePrintG3 miRNA (8 × 60 K)^® microarrays from Agilent^® was performed. Eleven microRNAs could be detected in all samples analyzed. Based on NormFinder and geNorm stability values and the high correlation (rho ≥ 0.8) with the median of all measured microRNAs, miR-16-5p, miR-29a-3p, miR-126-3p, and miR-222-3p are suitable single gene housekeeper candidates. In the cross-platform validation, 29 human microRNAs were strongly expressed (mean log2-intensity > 10) and 21 of these microRNAs including miR-16-5p and miR-29a-3p were also stably expressed (CV < 5%). Thus, miR-16-5p and miR-29a-3p are both strong housekeeper candidates. Their Normfinder stability values calculated across the primary tumor and metastases subgroup indicate that miR-29a-3p can be considered as the strongest housekeeper in a cohort with mainly samples from primary tumors, whereas miR-16-5p might perform better in a metastatic sample enriched cohort.     

Serine Protease Inhibitors as Good Predictors of Meat Tenderness: Which Are They and What Are Their Functions?

Since years, serine proteases and their inhibitors were an enigma to meat scientists. They were indeed considered to be extracellular and to play no role in postmortem muscle proteolysis. In the 1990's, we observed that protease inhibitors levels in muscles are a better predictor of meat tenderness than their target enzymes. From a practical point of view, we therefore choose to look for serine protease inhibitors rather than their target enzymes, i.e. serine proteases and the purpose of this report was to overview the findings obtained. Fractionation of a muscle crude extract by gel filtration revealed three major trypsin inhibitory fractions designed as F1 (Mr:50–70 kDa), F2 (Mr:40–60 kDa) and F3 (Mr:10–15kD) which were analyzed separately. Besides antithrombin III, an heparin dependent thrombin inhibitor, F1 and F2 comprised a large set of closely related trypsin inhibitors encoded by at least 8 genes bovSERPINA3-1 to A3-8 and able to inhibit also strongly initiator and effector caspases. They all belong to the serpin superfamily, known to form covalent complexes with their target enzymes, were located within muscle cells and found in all tissues and fluids examined irrespective of the animal species. Potential biological functions in living and postmortem muscle were proposed for all of them. In contrast to F1 and F2 which have been more extensively investigated only preliminary findings were provided for F3. Taken together, these results tend to ascertain the onset of apoptosis in postmortem muscle. However, the exact mechanisms driving the cell towards apoptosis and how apoptosis, an energy dependent process, can be completed postmortem remain still unclear.