Nuclear Multifragmentation Critical Exponents

We show that the critical exponents of nuclear multi-fragmentation have not been determined conclusively yet.Comment: 3 pages, LaTeX, one postscript figure appended, sub. to Phys.Rev.Lett. as a commen

Random incidence matrices: moments of the spectral density

We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the eigenvalue distribution as explicit polynomials in N and p. For large N and fixed p the spectrum contains a large eigenvalue at Np and a semi-circle of "small" eigenvalues. For large N and fixed average connectivity pN (dilute or sparse random matrices limit), we show that the spectrum always contains a discrete component. An anomaly in the spectrum near eigenvalue 0 for connectivity close to e=2.72... is observed. We develop recursion relations to compute the moments as explicit polynomials in pN. Their growth is slow enough so that they determine the spectrum. The extension of our methods to the Laplacian matrix is given in Appendix. Keywords: random graphs, random matrices, sparse matrices, incidence matrices spectrum, momentsComment: 39 pages, 9 figures, Latex2e, [v2: ref. added, Sect. 4 modified

Core percolation in random graphs: a critical phenomena analysis

We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated vertices plus an induced subgraph we call the "core". In the thermodynamic limit of an infinite random graph, we compute analytically the dynamics of leaf removal, the number of isolated vertices and the number of vertices and edges in the core. We show that a second order phase transition occurs at "alpha = e = 2.718...": below the transition, the core is small but above the transition, it occupies a finite fraction of the initial graph. The finite size scaling properties are then studied numerically in detail in the critical region, and we propose a consistent set of critical exponents, which does not coincide with the set of standard percolation exponents for this model. We clarify several aspects in combinatorial optimization and spectral properties of the adjacency matrix of random graphs. Key words: random graphs, leaf removal, core percolation, critical exponents, combinatorial optimization, finite size scaling, Monte-Carlo.Comment: 15 pages, 9 figures (color eps) [v2: published text with a new Title and addition of an appendix, a ref. and a fig.

Unbundling Policy in the United States Players, Outcomes and Effects

Building on attempts during the 1980s to establish principles of Open Network Architecture (ONA), unbundling obligations became a cornerstone of the framework for local competition devised by the Telecommunications Act of 1996. Several of the regulations developed by the Federal Communications Commission (FCC), including the impairment test to assess whether a network element had to be unbundled, the TELRIC pricing method, the obligation to re-bundle network elements to service platforms and the unbundling provisions for broadband networks were challenged repeatedly in court. In response to multiple defeats of earlier rules, the FCC had to refine its approach and define unbundling obligations more narrowly. Effective as of March 11th, 2005, unbundling obligations will essentially be limited to the local copper loop, dedicated interoffice transportation on routes connecting small markets, and high-capacity loops in small markets. Carriers presently using unbundled network elements that do not qualify under the new rules will have to transition to alternative solutions within 12-18 months. During this period, the FCC has set higher ceiling prices for these unbundled network elements. The Commission affirmed the elimination in 2003 of its unbundling obligations in broadband markets.Unbundling; voice; broadband

Bundling, Differentiation, Alliances and Mergers: Convergence Strategies in U.S. Communication Markets

Convergence is a multi-facetted phenomenon affecting the technological basis of information and communication industries, the boundaries of existing and new markets, and the organization of service providers. Convergence in substitutes will tend to increase the intensity of competition but convergence in complements may have the opposite effect. Given the economics of advanced communication industries, convergence necessitates strategies to overcome the risk of commodification at the level of networks, applications, and services. The paper examines bundling, differentiation, alliances, and merger strategies adopted by North American service providers in response to convergence. Service providers'opportunities and risks in the emerging environment differ considerably, with cable and telephone service providers presently in stronger positions than wireless service providers, broadcasters, and satellite service providers. New entrants such as Vonage, Skype, Google, and Yahoo have high disruptive potential but remain disadvantaged without their own access networks.convergence; bundling; differentiation; alliances; mergers

Why Use Sobolev Metrics on the Space of Curves

We study reparametrization invariant Sobolev metrics on spaces of regular curves. We discuss their completeness properties and the resulting usability for applications in shape analysis. In particular, we will argue, that the development of efficient numerical methods for higher order Sobolev type metrics is an extremely desirable goal

On Power Suppressed Operators and Gauge Invariance in SCET

The form of collinear gauge invariance for power suppressed operators in the soft-collinear effective theory is discussed. Using a field redefinition we show that it is possible to make any power suppressed ultrasoft-collinear operators invariant under the original leading order gauge transformations. Our manipulations avoid gauge fixing. The Lagrangians to O(lambda^2) are given in terms of these new fields. We then give a simple procedure for constructing power suppressed soft-collinear operators in SCET_II by using an intermediate theory SCET_I.Comment: 15 pages, journal versio