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.

     

Relating the X-band opacity of a tropical tree canopy to sapflow, rain interception and dew formation

During summer and autumn 2007, a 11 GHz microwave radiometer was deployed in an experimental tree plantation in Sardinilla, Panama. The opacity of the tree canopy was derived from incoming brightness temperatures received on the ground. A collocated eddy-covariance flux tower measured water vapor fluxes and meteorological variables above the canopy. In addition, xylem sapflow of trees was measured within the flux tower footprint. We observed considerable diurnal differences between measured canopy opacities and modeled theoretical opacities that were closely linked to xylem sapflow. It is speculated that dielectric changes in the leaves induced by the sapflow are causing the observed diurnal changes. In addition, canopy intercepted rain and dew formation also modulated the diurnal opacity cycle. With an enhanced canopy opacity model accounting for water deposited on the leaves, we quantified the influence of canopy stored water (i.e. intercepted water and dew) on the opacity. A time series of dew formation and rain interception was directly monitored during a period of two weeks. We found that during light rainfall up to 60% of the rain amount is intercepted by the canopy whereas during periods of intense rainfall only 4% were intercepted. On average, 0.17 mm of dew was formed during the night. Dew evaporation contributed 5% to the total water vapor flux measured above the canopy.     

An optical burst reordering model for time-based and random selection assembly strategies

Contention resolution schemes in optical burst switched networks (OBS) as well as contention avoidance schemes delay burst delivery and change the burst arrival sequence. The burst arrival sequence usually changes the packet arrival sequence and degrades the upper layer protocols performance, e.g., the throughput of the transmission control protocol (TCP).In this paper, we present and analyze a detailed burst reordering model for two widely applied burst assembly strategies: time-based and random selection. We apply the IETF reordering metrics and calculate explicitly three reordering metrics: the reordering ratio, the reordering extent metric and the TCP relevant metric. These metrics allow estimating the degree of reordering in a certain network scenario. They estimate the buffer space at the destination to resolve reordering and quantify the number of duplicate acknowledgements relevant for investigations on the transmission control protocol.We show that our model reflects the burst/packet reordering pattern of simulated OBS networks very well. Applying our model in a network emulation scenario, enables investigations on real protocol implementations in network emulation environments. It therefore serves as a substitute for extensive TCP over OBS network simulations with a focus on burst reordering.     

On Word Equations in One Variable

For a word equation E of length n in one variable x occurring # _x times in E a resolution algorithm of O(n+# _x log n) time complexity is presented here. This is the best result known and for the equations that feature #_x < \fracnlogn\#_{x}<\frac{n}{\log n} it yields time complexity of O(n) which is optimal. Additionally it is proven here that the set of solutions of any one-variable word equation is either of the form F or of the form F∪(uv)⁺ u where F is a set of O(log n) words and u, v are some words such that uv is a primitive word.     

Efficient Sequence Alignment with Side-Constraints by Cluster Tree Elimination

Aligning DNA and protein sequences is a core technique in molecular biology. Often, it is desirable to include partial prior knowledge and conditions in an alignment. Going beyond prior work, we aim at the integration of such side constraints in free combination into alignment algorithms. The most common and successful technique for efficient alignment algorithms is dynamic programming (DP). However, a weakness of DP is that one cannot include additional constraints without specifically tailoring a new DP algorithm. Here, we discuss a declarative approach that is based on constraint techniques and show how it can be extended by formulating additional knowledge as constraints. We take special care to obtain the efficiency of DP for sequence alignment. This is achieved by careful modeling and applying proper solving strategies. Finally, we apply our method to the scanning for RNA motifs in large sequences. This case study demonstrates how the new approach can be used in real biological problems. A prototypic implementation of the method is available at .     

Model Checking Abilities of Agents: A Closer Look

Alternating-time temporal logic (atl) is a logic for reasoning about open computational systems and multi-agent systems. It is well known that atl model checking is linear in the size of the model. We point out, however, that the size of an atl model is usually exponential in the number of agents. When the size of models is defined in terms of states and agents rather than transitions, it turns out that the problem is (1) Δ ₃ ^P -complete for concurrent game structures, and (2) Δ ₂ ^P -complete for alternating transition systems. Moreover, for “Positive atl” that allows for negation only on the level of propositions, model checking is (1) Σ ₂ ^P -complete for concurrent game structures, and (2) NP-complete for alternating transition systems. We show a nondeterministic polynomial reduction from checking arbitrary alternating transition systems to checking turn-based transition systems, We also discuss the determinism assumption in alternating transition systems, and show that it can be easily removed. In the second part of the paper, we study the model checking complexity for formulae of atl with imperfect information (atl _ir ). We show that the problem is Δ ₂ ^P -complete in the number of transitions and the length of the formula (thereby closing a gap in previous work of Schobbens in Electron. Notes Theor. Comput. Sci. 85(2), 2004). Then, we take a closer look and use the same fine structure complexity measure as we did for atl with perfect information. We get the surprising result that checking formulae of atl _ir is also Δ ₃ ^P -complete in the general case, and Σ ₂ ^P -complete for “Positive atl _ir ”. Thus, model checking agents’ abilities for both perfect and imperfect information systems belongs to the same complexity class when a finer-grained analysis is used.     

On Reduction Systems Equivalent to the Non-associative Lambek Calculus with the Empty String

The article concludes a series of results on cut-rule axiomatizabilityof the Lambek calculus. It is proved that the non-associativeproduct-free Lambek calculus with the empty string (NL₀) isnot finitely axiomatizable if the only rule of inference admittedis Lambek's cut rule. The proof makes use of the (infinitely)cut-rule axiomatized calculus NC designed by the author exactlyfor that purpose.     

Axiomatizing the Monodic Fragment of

As we can show that the two-variable monadic fragment of thefull first-order extension of the propositional branching time logic is not recursively enumerable, we show in thisarticle that the monodic fragment of can be axiomatized.     

Segmentation of microscope images of living cells

This paper describes a segmentation method combining a texture based technique with a contour based method. The technique is designed to enable the study of cell behaviour over time by segmenting brightfield microscope image sequences. The technique was tested on artificial images, based on images of living cells and on real sequences acquired from microscope observations of neutrophils and lymphocytes as well as on a sequence of MRI images. The results of the segmentation are compared with the results of the watershed and snake segmentation methods. The results show that the method is both effective and practical.