On the maximum cardinality of a consistent set of arcs in a random tournament

For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if T_n denotes the random tournament on n vertices, then, $\text{P}$$\text{(h(T}{}_{\mathrm{n}}\text{) ≤}\text{1}\text{2}\text{(}{}_2{}^{\mathrm{n}}\text{) + 1.73n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) → 1}$ as n → ∞.     

Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method

Summary In this paper we develop a class of numerical methods to approximate the solutions of delay differential equations. They are essentially based on a modified version, in a predictor-corrector mode, of the one-step collocation method atn Gaussian points. These methods, applied to ODE's, provide a continuous approximate solution which is accurate of order 2n at the nodes and of ordern+1 uniformly in the whole interval. In order to extend the methods to delay differential equations, the uniform accuracy is raised to the order 2n by some a posteriori corrections. Numerical tests and comparisons with other methods are made on real-life problems.This work was supported by CNR within the Progetto Finalizzato Informatica-Sottopr. P1-SOFMAT     

Forced transverse vibrations of a submerged tensioned string

For a submerged cable, the classical equation of a vibrating string must be modified to account for added mass and damping effects. This can be done with the aid of Morison's formulae. The resulting equation is non-linear. It is solved for the case when one end of the string is forced into sinusoidal transverse motion. The first harmonic approximations for both resonant and non-resonant responses are obtained by the method of matched asymptotic expansions under the assumption that the non-dimensional damping coefficient is small.     

On some auxiliary mappings generated by nonexpansive and strictly pseudo-contractive mappings

Starting by a finite family of mappings, we define the concept of procedure with Lipschitzian dependence of the coefficients. We give seven concrete examples of such procedures and prove the strong convergence of two viscosity methods.     

The diameter of random regular graphs

We give asymptotic upper and lower bounds for the diameter of almost everyr-regular graph onn vertices (n → ∞).     

Evaluation of hydrogen chemisorption in nanostructured carbon films by near edge X-ray absorption spectroscopy

We have developed a method for the quantitative evaluation of the chemisorbed fraction of hydrogen in nanostructured carbon films using Near Edge X-ray Absorption Spectroscopy (NEXAFS). In the carbon K-edge spectrum the peak related to carbon bonded to hydrogen is assumed to be correlated with the amount of hydrogen bonded to carbon. This assumption is supported by a comparative analysis of gas-phase hydrocarbons obtained via Electron Energy Loss Spectroscopy (EELS). We applied the method to nanostructured carbon (ns-C) films synthesized by supersonic cluster beam deposition. The evaluated quantity of chemisorbed hydrogen in different samples exposed to molecular hydrogen (pressure of 0.12 MPa, for 3 hours at room temperature) is ∼1.5 wt.%.     

Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints

In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver. Research partially supported by the MIUR FIRB Project RBNE01WBBB “Large-Scale Nonlinear Optimization.”     

A Fluorescent Activatable AND‐Gate Chemokine CCL2 Enables In Vivo Detection of Metastasis‐Associated Macrophages

We report the novel chemical design of fluorescent activatable chemokines as highly specific functional probes for imaging subpopulations of immune cells in live tumours. Activatable chemokines behave as AND‐gates since they emit only after receptor binding and intracellular activation, showing enhanced selectivity over existing agents. We have applied this strategy to produce mCCL2‐MAF as the first probe for in vivo detection of metastasis‐associated macrophages in a preclinical model of lung metastasis. This strategy will accelerate the preparation of new chemokine‐based probes for imaging immune cell function in tumours.