Some algebraic properties of differential operators

First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that the Dieudonne' determinant of a matrix pseudodifferential operator with coefficients in a differential subring A of K lies in the integral closure of A in K, and we give an example of a 2x2 matrix differential operator with coefficients in A whose Dieudonne' determiant does not lie in A.Comment: 15 page

Scale Radii and Aggregation Histories of Dark Haloes

Relaxed dark-matter haloes are found to exhibit the same universal density profiles regardless of whether they form in hierarchical cosmologies or via spherical collapse. Likewise, the shape parameters of haloes formed hierarchically do not seem to depend on the epoch in which the last major merger took place. Both findings suggest that the density profile of haloes does not depend on their aggregation history. Yet, this possibility is apparently at odds with some correlations involving the scale radius r_s found in numerical simulations. Here we prove that the scale radius of relaxed, non-rotating, spherically symmetric haloes endowed with the universal density profile is determined exclusively by the current values of four independent, though correlated, quantities: mass, energy and their respective instantaneous accretion rates. Under this premise and taking into account the inside-out growth of haloes during the accretion phase between major mergers, we build a simple physical model for the evolution of r_s along the main branch of halo merger trees that reproduces all the empirical trends shown by this parameter in N-body simulations. This confirms the conclusion that the empirical correlations involving r_s do not actually imply the dependence of this parameter on the halo aggregation history. The present results give strong support to the explanation put forward in a recent paper by Manrique et al. (2003) for the origin of the halo universal density profile.Comment: 13 pages, 8 figures, accepted for publication in MNRA

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

Reconstruction of Network Evolutionary History from Extant Network Topology and Duplication History

Genome-wide protein-protein interaction (PPI) data are readily available thanks to recent breakthroughs in biotechnology. However, PPI networks of extant organisms are only snapshots of the network evolution. How to infer the whole evolution history becomes a challenging problem in computational biology. In this paper, we present a likelihood-based approach to inferring network evolution history from the topology of PPI networks and the duplication relationship among the paralogs. Simulations show that our approach outperforms the existing ones in terms of the accuracy of reconstruction. Moreover, the growth parameters of several real PPI networks estimated by our method are more consistent with the ones predicted in literature.Comment: 15 pages, 5 figures, submitted to ISBRA 201

The variational Poisson cohomology

It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the two Hamiltonian operators. In the first part of the paper we explain how to introduce various cohomology complexes, including Lie superalgebra and Poisson cohomology complexes, and basic and reduced Lie conformal algebra and Poisson vertex algebra cohomology complexes, by making use of the corresponding universal Lie superalebra or Lie conformal superalgebra. The most relevant are certain subcomplexes of the basic and reduced Poisson vertex algebra cohomology complexes, which we identify (non-canonically) with the generalized de Rham complex and the generalized variational complex. In the second part of the paper we compute the cohomology of the generalized de Rham complex, and, via a detailed study of the long exact sequence, we compute the cohomology of the generalized variational complex for any quasiconstant coefficient Hamiltonian operator with invertible leading coefficient. For the latter we use some differential linear algebra developed in the Appendix.Comment: 130 pages, revised version with minor changes following the referee's suggestion

Benchmarking and viability assessment of optical packet switching for metro networks

Optical packet switching (OPS) has been proposed as a strong candidate for future metro networks. This paper assesses the viability of an OPS-based ring architecture as proposed within the research project DAVID (Data And Voice Integration on DWDM), funded by the European Commission through the Information Society Technologies (IST) framework. Its feasibility is discussed from a physical-layer point of view, and its limitations in size are explored. Through dimensioning studies, we show that the proposed OPS architecture is competitive with respect to alternative metropolitan area network (MAN) approaches, including synchronous digital hierarchy, resilient packet rings (RPR), and star-based Ethernet. Finally, the proposed OPS architectures are discussed from a logical performance point of view, and a high-quality scheduling algorithm to control the packet-switching operations in the rings is explained

Dirac operators and the Very Strange Formula for Lie superalgebras

Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.Comment: Latex file, 25 pages. A few misprints corrected. To appear in the forthcoming volume "Advances in Lie Superalgebras", Springer INdAM Serie