In a recent paper, Shah and Zaman proposed the rumor center as an effective rumor source estimator for rumor spreading on random graphs. They proved for a very general random tree model that the detection probability remains positive as the number of nodes to which the rumor has spread tends to infinity. Moreover, they derived explicit asymptotic formulas for the detection probability of random...

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced ce...

The so-called analytic center approach to parameter estimation has been proposed recently as an alternative to the well-known least squares approach. This new approach offers a parameter estimate that is consistent with the past data observations, has a simple geometric interpretation, and is computable sequentially. In this paper, we study the asymptotic performance of the analytic center appr...

We study the temperature profile for a semi-infinite thin layer due to a Gaussian heat source. We follow the time-dependent temperature profile at the center of the top surface of the layer, deriving the asymptotic behavior and both the short time and long time behaviors. We also show that one can estimate thermal properites from various time measurements of the temperature at the center of the...

We present a definition of angular momentum for radiative spacetimes which does not suffer from any ambiguity of supertranslations. We succeed in providing an appropriate notion of intrinsic angular momentum; and at the same time a definition of center of mass frame at future null infinity. We use the center of mass frame to present the asymptotic structure equations for vacuum spacetimes. PACS...

In a detection&#10 network, the final decision is made by fusing the decisions from local detectors. The objective of that decision is to minimize the final error probability. To implement and optimal fusion rule, the performance of each detector, i.e. its probability of false alarm and its probability of missed detection as well as the a priori probabilities of the hypotheses, must be known. H...

We prove that the (language of the) asymptotic set (and the nonwandering set) of a one-dimensional cellular automaton can be Σ11hard. We do not go into much detail, since the constructions are relatively standard.

Dana Scott’s model of λ-calculus was based on a limit construction which started from an algebra of a suitable endofunctor F and continued by iterating F . We demonstrate that this is a special case of the concept we call coalgebra relatively terminal w.r.t. the given algebra A. This means a coalgebra together with a universal coalgebra-toalgebra morphism into A. We prove that by iterating F co...

We consider a generalization of lifting modules relative to a class A of modules and a proper class E of short exact sequences of modules. These modules will be called E-A-lifting. We establish characterizations of modules with the property that every direct sum of copies of them is E-A-lifting. 2000 Mathematics Subject Classification: 16S90, 16D80.

We investigate a generalization of extending modules relative to a class of modules and a proper class of short exact sequences of modules.