Given an arbitrary ideal f on the real numbers, two topologies are denned that are both finer than the ordinary topology. There are nonmeasurable, non-Baire sets that are open in all of these topologies, independent of f . This shows why the restriction to Baire sets is necessary in the usual definition of the ./"-density topology. It appears to be difficult to find such restrictions in the cas...

We prove large deviation principles (LDP) for m-fold products of empirical measures and for U-empirical measures, where the underlying sequence of random variables is a special Markov chain, an exchangeable sequence, a mixing sequence or an independent, but not identically distributed, sequence. The LDP can be formulated on a subset of all probability measures, endowed with a topology which is ...

 The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generate...

The network topology has a significant impact on the performance of collection protocols in wireless sensor networks. In this paper, we introduce an unobtrusive methodology to quantify the impact of the topology on the performance of collection protocols. Specifically, we propose a protocol-independent metric, the Expected Network Delivery, that quantifies the delivery performance that a collec...

We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we find that the stability of the completely synchronous state in such networks only depends on the number of signals each neuron receives, independent of all other details of the network topology. This is in contrast with linea...

Given a group (G, ·), G ⊆M, definable in a first order structureM = (M, . . .) equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V ⊆ G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from M. Likewise we topologize tra...

We present a “clean-slate” design for a networklayer routing and forwarding system intended to address shortcomings of the current Internet Protocol. Our design separates routing from both forwarding and topology discovery; requires only a flat, topology-independent namespace; and allows for policies of both users and service providers to be supported. Channels serve as the primary abstraction,...

We present an algorithm for phylogenetic reconstruction using quartets that returns the correct topology for n taxa in O(n logn) time with high probability, in a probabilistic model where a quartet is not consistent with the true topology of the tree with constant probability, independent of other quartets. Our incremental algorithm relies upon a search tree structure for the phylogeny that is ...