Emergence of Zipf's Law in the Evolution of Communication

Zipf's law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and hearer in a communication system, we introduce evolution by means of a variational approach to the problem based on Kullback's Minimum Discrimination of Information Principle. Therefore, using a formalism fully embedded in the framework of information theory, we demonstrate that Zipf's law is the only expected outcome of an evolving, communicative system under a rigorous definition of the communicative tension described by Zipf.Comment: 7 pages, 2 figure

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.Comment: 7 pages, 4 figure

Nonlinear Jaynes-Cummings model of atom-field interaction

Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of the elements of a closed algebra, which has SU(1,1) and Heisenberg-Weyl algebras as limiting cases. Eigenstates and eigenvalues of the Hamiltonian are constructed. With the field being in a coherent state initially, the dynamical behaviour of atomic-inversion, field-statistics and uncertainties in the field quadratures are studied. The appearance of nonclassical features during the evolution of the field is shown. Further, we explore the overlap of initial and time-evolved field states.Comment: 14 pages, 6 figures is PS forma

Solid hydrogen structure

The J=0{minus}>2 Raman signal from solid J=0 D{sub 2} or H{sub 2} reveals HCP structure when deposited at a rate 0.1 {le} R({mu}/min) {le} 40 onto MgF{sub 2} at T{sub d}/T{sub tp} > 0.3, a mixture of HCP and FCC crystals at 0.2 < T{sub d}/T{sub tp} < 0.3 and possibly a randomly stacked close packed structure at T{sub d}/T{sub tp} < 0.2, where T{sub tp} is the triple point temperature. Non-HCP crystals transform to HCP continuously and irreversibly with increasing T. Finally, the crystal size decreases with decreasing T{sub d} and increasing R, from {approximately} 1 mm at T{sub d} {approximately} 0.8 T{sub tp} and R {approximately} 2 {mu}/min to {approximately} 1 {mu}m at 0.25 T{sub tp} and R {approximately} 40 {mu}/min

Nanosecond spin lifetimes in single- and few-layer graphene-hBN heterostructures at room temperature

We present a new fabrication method of graphene spin-valve devices which yields enhanced spin and charge transport properties by improving both the electrode-to-graphene and graphene-to-substrate interface. First, we prepare Co/MgO spin injection electrodes onto Si$^{++}$/SiO$_2$. Thereafter, we mechanically transfer a graphene-hBN heterostructure onto the prepatterned electrodes. We show that room temperature spin transport in single-, bi- and trilayer graphene devices exhibit nanosecond spin lifetimes with spin diffusion lengths reaching 10$\mu$m combined with carrier mobilities exceeding 20,000 cm$^2$/Vs.Comment: 15 pages, 5 figure

Topological reversibility and causality in feed-forward networks

Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths defines a feed-forward, acyclic network. A key problem associated with these systems involves characterizing their intrinsic degree of path reversibility: given an end node in the graph, what is the uncertainty of recovering the process backwards until the origin? Here we propose a novel concept, \textit{topological reversibility}, which rigorously weigths such uncertainty in path dependency quantified as the minimum amount of information required to successfully revert a causal path. Within the proposed framework we also analytically characterize limit cases for both topologically reversible and maximally entropic structures. The relevance of these measures within the context of evolutionary dynamics is highlighted.Comment: 9 pages, 3 figure

Expansion history and f(R) modified gravity

We attempt to fit cosmological data using $f(R)$ modified Lagrangians containing inverse powers of the Ricci scalar varied with respect to the metric. While we can fit the supernova data well, we confirm the $a\propto t^{1/2}$ behaviour at medium to high redshifts reported elsewhere and argue that the easiest way to show that this class of models are inconsistent with the data is by considering the thickness of the last scattering surface. For the best fit parameters to the supernova data, the simplest 1/R model gives rise to a last scattering surface of thickness $\Delta z\sim 530$, inconsistent with observations.Comment: accepted in JCAP, presentation clarified, results and conclusions unchange