Ab initio study of reflectance anisotropy spectra of a sub-monolayer oxidized Si(100) surface

The effects of oxygen adsorption on the reflectance anisotropy spectrum (RAS) of reconstructed Si(100):O surfaces at sub-monolayer coverage (first stages of oxidation) have been studied by an ab initio DFT-LDA scheme within a plane-wave, norm-conserving pseudopotential approach. Dangling bonds and the main features of the characteristic RAS of the clean Si(100) surface are mostly preserved after oxidation of 50% of the surface dimers, with some visible changes: a small red shift of the first peak, and the appearance of a distinct spectral structure at about 1.5 eV. The electronic transitions involved in the latter have been analyzed through state-by-state and layer-by-layer decompositions of the RAS. We suggest that new interplay between present theoretical results and reflectance anisotropy spectroscopy experiments could lead to further clarification of structural and kinetic details of the Si(100) oxidation process in the sub-monolayer range.Comment: 21 pages, 8 figures. To be published in Physical Rev.

Aging in coherent noise models and natural time

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the $q$-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.Comment: 4 pages and 5 figure

Preferential attachment in the protein network evolution

The Saccharomyces cerevisiae protein-protein interaction map, as well as many natural and man-made networks, shares the scale-free topology. The preferential attachment model was suggested as a generic network evolution model that yields this universal topology. However, it is not clear that the model assumptions hold for the protein interaction network. Using a cross genome comparison we show that (a) the older a protein, the better connected it is, and (b) The number of interactions a protein gains during its evolution is proportional to its connectivity. Therefore, preferential attachment governs the protein network evolution. The evolutionary mechanism leading to such preference and some implications are discussed.Comment: Minor changes per referees requests; to appear in PR

Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamiltonian deformations of the dispersionless KdV hierarchy starting from any of its infinitesimal deformations.Comment: 43 pages. V2: the accepted version, to appear in Comm. Math. Phy

On classical finite and affine W-algebras

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.Comment: 12 page

Reflectivity Anisotropy Spectra of Cu- and Ag- (110) surfaces from {\it ab initio} theory

We are able to disentagle the effects of the intraband and interband parts of the bulk dielectric function on the bare dielectric anisotropy of the surface. We show how the position, sign and amplitude of the structures observed in such spectra depend on the above quantities. The lineshape of all the calculated structures agree very well with the ones observed experimentally for samples treated by suitable surface cleaning. In particular, we reproduce the observed single peak structure of Ag at high energy, found to represent a state of the clean surface different from the one giving the originally observed double peak structure. This results is not reproduced by the 'local field' model.Comment: 4 pages, 3 figures. submitted to Phys. Rev. Let

Feigin-Frenkel center in types B, C and D

For each simple Lie algebra g consider the corresponding affine vertex algebra V_{crit}(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev's discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras V_{crit}(g) associated with the simple Lie algebras g of types B, C and D. The construction relies on the Schur-Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra sl_2 in the context of Howe duality. This leads to explicit constructions of commutative subalgebras of the universal enveloping algebras U(g[t]) and U(g), and to higher order Hamiltonians in the Gaudin model associated with each Lie algebra g. We also introduce analogues of the Bethe subalgebras of the Yangians Y(g) and show that their graded images coincide with the respective commutative subalgebras of U(g[t]).Comment: 29 pages, constructions of Pfaffian-type Sugawara operators and commutative subalgebras in universal enveloping algebras are adde

Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the critical value $K_c =2$ in the limit of large system size $N$. How this principle could generate self-organization in natural complex systems is discussed for two examples: neural networks and regulatory networks in the genome.Comment: 4 pages RevTeX, 4 figures PostScript, revised versio

Analytical Solution of a Stochastic Content Based Network Model

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behavior to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.Comment: 13 pages, 5 figures. Rewrote conclusions regarding the relevance to gene regulation networks, fixed minor errors and replaced fig. 4. Main body of paper (model and calculations) remains unchanged. Submitted for publicatio

Avalanche dynamics in Bak-Sneppen evolution model observed with standard distribution width of fitness

We introduce the standard distribution width of fitness to characterize the global and individual features of a ecosystem in the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche dynamics, $w_{0}$ avalanche is observed. The corresponding gap equation and the self-organized threshold $w_{c}$ are obtained. The critical exponents $\tau ,$ $\gamma$and $\rho$, which describe the behavior of the avalanche size distribution, the average avalanche size and the relaxation to attractor, respectively, are calculated with numerical simulation. The exact master equation and $\gamma$ equation are derived. And the scaling relations are established among the critical exponents of this new avalanche.Comment: 14 pages, 3 figure