Bad communities with high modularity

In this paper we discuss some problematic aspects of Newman and Girvan’s modularity function Q _N . Given a graph G, the modularity of G can be written as Q _N = Q _f ? Q ₀, where Q _f is the intracluster edge fraction of G and Q ₀ is the expected intracluster edge fraction of the null model, i.e., a randomly connected graph with same expected degree distribution as G. It follows that the maximization of Q _N must accomodate two factors pulling in opposite directions:Q _f favors a small number of clusters and Q ₀ favors many balanced (i.e., with approximately equal degrees) clusters. In certain cases the Q ₀ term can cause overestimation of the true cluster number; this is the opposite of the well-known underestimation effect caused by the “resolution limit” of modularity. We illustrate the overestimation effect by constructing families of graphs with a “natural” community structure which, however, does not maximize modularity. In fact, we show there exist graphs G with a “natural clustering” V of G and another, balanced clustering U of G such that (i) the pair (G, U) has higher modularity than (G, V) and (ii) V and U are arbitrarily different.     

Free energy landscape from path-sampling: application to the structural transition in LJ38

We introduce a path-sampling scheme that allows equilibrium state-ensemble averages to be computed by means of a biased distribution of non-equilibrium paths. This non-equilibrium method is applied to the case of the 38-atom Lennard-Jones atomic cluster, which has a double-funnel energy landscape. We calculate the free energy profile along the Q₄ bond orientational order parameter. At high or moderate temperature the results obtained using the non-equilibrium approach are consistent with those obtained using conventional equilibrium methods, including parallel tempering and Wang-Landau Monte Carlo simulations. At lower temperatures, the non-equilibrium approach becomes more efficient in exploring the relevant inherent structures. In particular, the free energy agrees with the predictions of the harmonic superposition approximation.     

Optical behaviour of cobalt and nickel ions in different media

The absorption and diffusion of different solutions and crystals of NaCl and KCl containing bivalent cobalt and níckel ions were measured. The kinds of complexes are determined from the results and their importance in the luminescence process is discussed.The experimental part of this work was completed in December 1961 during his stay in the Inst. Sol. State Physics, Prague.The authors would like to thank Dr. J. Trnka, M. Lébl and J. Kunzl, Dr. J. Dolejí and M. Závtová for their effective help in preparing the samples and valuable discussions and K. Listoová for carrying out some of the experiments.     

An example of L-fuzzy join space

On a generalized deMorgan lattice (X, ≤, ∨, ∧,′) we introduce a family of join hyperoperations * _p , parametrized by a parameterp εX. As a result we obtain a family of join spaces (X, * _p ). We show that: for everya,b εX the family {a*_pb} _pεX can be considered as thep-cuts of aL-fuzzy seta*b; in this manner we synthesize aL-fuzzy hyperoperation * which takes pairs fromX toL-fuzzy subsets ofX. We then show that (X, * _p ) is aL-fuzzy hypergroup (in the sense of Corsini) and can be considered as aL-fuzzy join space. Furthermore,a*b is aL-fuzzy interval for alla,b εX.     

A path-sampling scheme for computing thermodynamic properties of a many-body system in a generalized ensemble

We propose to compute the thermodynamic properties of many-body systems using a path-sampling Monte Carlo scheme implemented in a generalized path ensemble. Trial paths are generated through an expanded ensemble using a reversible discretization of Langevins equation of motion. We also show how the systematic errors resulting from the use of a finite time step can rigorously be taken into account in the path-sampling scheme. We find that the degree of convergence of the estimated thermodynamic quantity towards the exact value correlates with the mean acceptance rates of the path-sampling scheme. An application of the path method for simulating glassy systems is finally suggested.Received: 28 January 2004, Published online: 8 June 2004PACS: 82.60.Lf Thermodynamics of solutions - 07.05.Tp Computer modeling and simulation - 64.70.Pf Glass transitions     

Bioinspired Synthesis of Pulvinic Acids Including Xerocomic Acid and Fluorescence Properties of Bis-lactone Intermediates

A set of representative pulvinic acids were synthesised using a bioinspired strategy. Terphenyl-quinones (polyporic acid scaffold) were prepared via sequential Suzuki-Miyaura couplings allowing access to unsymmetrically substituted derivatives in a one-pot protocol. Subjected to the action of acetic anhydride and DMSO, quinones were converted into bis-lactone intermediates. Methanolysis and deprotection achieved the total syntheses of the corresponding pulvinic acids. Following this general strategy, symmetrical pulvinic, atromentic, variegatic acids and unsymmetrical congener pinastric, iso-pinastric, xerocomic and iso-xerocomic acids were prepared in fair yields. Fluorescence properties were observed for the bis-lactone intermediates and, as a complement to this synthetic work, optical properties were measured, and fluorescence quantum yields were determined for the bis-lactone pigments.     

Multiple‐Replica Exchange with Information Retrieval

The parallel tempering simulation method was recently extended to allow for possible exchanges between non‐adjacent replicas. We introduce a multiple‐exchange variant which naturally incorporates the information from all replicas when calculating statistical averages, building on the related virtual‐move method of Coluzza and Frenkel (ChemPhysChem 2005 , 6, 1779). The method is extensively tested on three model systems, namely, a Lennard‐Jones cluster exhibiting a finite size phase transition, the Lennard‐Jones fluid, and the 2D ferromagnetic Ising model. In all cases, the present method performs significantly better and converges faster than conventional parallel tempering Monte Carlo simulations. The standard deviations are also systematically decreased with respect to virtual moves.