Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review

Sustainable management methods: performance assessment in large companies

The general objective of this study is to contribute to the understanding of the performance evaluation methods used by large companies. As specific objectives we have the following: to identify the methods used and the importance attributed to them; to analyse their implementation process and the level of success given to it. The data collection method used was a survey to the financial managers of the largest companies in Portugal, which resulted in thirty-five valid responses. The main contributions of this study were the associations found between the following variables: the method used and the level of importance assigned to it; the person in charge of implementing the method and training provided to employees; the method used and the degree of success attributed to its implementation; the degree of resistance to change and the degree of success in implementing the performance evaluation method.info:eu-repo/semantics/acceptedVersio

Soft triaxial roto-vibrational motion in the vicinity of γ=π/6\gamma=\pi/6

A solution of the Bohr collective hamiltonian for the $\beta-$soft, $\gamma-$soft triaxial rotor with $\gamma \sim \pi/6$ is presented making use of a harmonic potential in $\gamma$ and Coulomb-like and Kratzer-like potentials in $\beta$. It is shown that, while the $\gamma-$angular part in the present case gives rise to a straightforward extension of the rigid triaxial rotor energy in which an additive harmonic term appears, the inclusion of the $\beta$ part results instead in a non-trivial expression for the spectrum. The negative anharmonicities of the energy levels with respect to a simple rigid model are in qualitative agreement with general trends in the experimental data.Comment: 4 pages, 2 figures, accepted in Phys.Rev.

Outflow Dynamics in Modeling Oligopoly Markets: The Case of the Mobile Telecommunications Market in Poland

In this paper we introduce two models of opinion dynamics in oligopoly markets and apply them to a situation, where a new entrant challenges two incumbents of the same size. The models differ in the way the two forces influencing consumer choice -- (local) social interactions and (global) advertising -- interact. We study the general behavior of the models using the Mean Field Approach and Monte Carlo simulations and calibrate the models to data from the Polish telecommunications market. For one of the models criticality is observed -- below a certain critical level of advertising the market approaches a lock-in situation, where one market leader dominates the market and all other brands disappear. Interestingly, for both models the best fits to real data are obtained for conformity level $p \in (0.3,0.4)$. This agrees very well with the conformity level found by Solomon Asch in his famous social experiment

Multiresolution community detection for megascale networks by information-based replica correlations

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for community detection and O(L^{1.3} log N) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.Comment: 19 pages, 14 figures, published version with minor change

Phase diagram for a Cubic Consistent-Q Interacting Boson Model Hamiltonian: signs of triaxiality

An extension of the Consistent-Q formalism for the Interacting Boson Model that includes the cubic QxQxQ term is proposed. The potential energy surface for the cubic quadrupole interaction is explicitly calculated within the coherent state formalism using the complete chi-dependent expression for the quadrupole operator. The Q-cubic term is found to depend on the asymmetry deformation parameter gamma as a linear combination of cos(3gamma) and cos^2(3\gamma) terms, thereby allowing for triaxiality. The phase diagram of the model in the large N limit is explored, it is described the order of the phase transition surfaces that define the phase diagram, and moreover, the possible nuclear equilibrium shapes are established. It is found that, contrary to expectations, there is only a very tiny region of triaxiality in the model, and that the transition from prolate to oblate shapes is so fast that, in most cases, the onset of triaxiality might go unnoticed.Comment: 18 pages, 19 figure

Detecting modules in dense weighted networks with the Potts method

We address the problem of multiresolution module detection in dense weighted networks, where the modular structure is encoded in the weights rather than topology. We discuss a weighted version of the q-state Potts method, which was originally introduced by Reichardt and Bornholdt. This weighted method can be directly applied to dense networks. We discuss the dependence of the resolution of the method on its tuning parameter and network properties, using sparse and dense weighted networks with built-in modules as example cases. Finally, we apply the method to data on stock price correlations, and show that the resulting modules correspond well to known structural properties of this correlation network.Comment: 14 pages, 6 figures. v2: 1 figure added, 1 reference added, minor changes. v3: 3 references added, minor change

Ising model with memory: coarsening and persistence properties

We consider the coarsening properties of a kinetic Ising model with a memory field. The probability of a spin-flip depends on the persistence time of the spin in a state. The more a spin has been in a given state, the less the spin-flip probability is. We numerically studied the growth and persistence properties of such a system on a two dimensional square lattice. The memory introduces energy barriers which freeze the system at zero temperature. At finite temperature we can observe an apparent arrest of coarsening for low temperature and long memory length. However, since the energy barriers introduced by memory are due to local effects, there exists a timescale on which coarsening takes place as for the Ising model. Moreover the two point correlation functions of the Ising model with and without memory are the same, indicating that they belong to the same universality class.Comment: 10 pages, 7 figures; some figures and some comments adde

Entropy inequalities and Bell inequalities for two-qubit systems

Sufficient conditions for (the non-violation of) the Bell-CHSH inequalities in a mixed state of a two-qubit system are: 1) The linear entropy of the state is not smaller than 0.5, 2) The sum of the conditional linear entropies is non-negative, 3) The von Neumann entropy is not smaller than 0.833, 4) The sum of the conditional von Neumann entropies is not smaller than 0.280.Comment: Errors corrected. See L. Jakobcyk, quant-ph/040908