In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random k–regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the max...

We present a generalization of Renyi's [A. Renyi, Trans. Math. Stat. Prob. 4, 205 (1963)] classical solution to the one-dimensional random sequential adsorption (RSA) problem, to the case where particle sizes are drawn from an arbitrary distribution, a process known as competitive RSA. We formulate the process using recursive relations, and without explicitly solving the equations, we extract l...

Shannon entropy used in standard top-down decision trees does not guarantee the best generalization. Split criteria based on generalized entropies offer different compromise between purity of nodes and overall information gain. Modified C4.5 decision trees based on Tsallis and Renyi entropies have been tested on several high-dimensional microarray datasets with interesting results. This approac...

Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. The present paper demonstrates that Kolmogorov’s (1933) formulation of probability theory admits a minimal generalization which includes improper priors and a general Bayes theorem. The resulting theory is closely related to the theory of conditional probability spaces formulated by Renyi...

Following a review of the probe optimization of Slutsky, Rao, Sun, and Fainman @Phys. Rev. A 57, 2383 ~1998!# for the standard four-state protocol of quantum key distribution, I generalize the optimization to a variable angle between the signal bases. I calculate the corresponding maximum Renyi information gain by the probe, and determine the optimum probe parameters. A larger set of optimum pr...

Using a Wigner-function-based approach, we study the Renyi entropy of subsystem $A$ system bosons interacting with local repulsive potential. The full is assumed to be in thermal equilibrium at temperature $T$ and density $\ensuremath{\rho}$. For $\mathcal{U}(N)$-symmetric model, show that large-$N$ limit can understood terms an effective noninteracting spatially varying mean field potential, w...