We present a local algorithm for model checking in a real-time extension of the modal mu-calculus. As such, the whole state space of the real-time system under investigation need not be explored, but rather only that portion necessary to determine the truthhood of the logical formula. To the best of our knowledge, this is the rst local algorithm for the veriication of real-time systems to appea...

The quotient space theory based on fuzzy tolerance relation is put forward to solve the problem of clustering in this paper. The similarity matrix does not always satisfy ultrametric inequality, theoretically and practically. We give the method to construct the hierarchical quotient space chain if the similarity matrix is only reflexive and symmetric. We consider not only the subset of data (cl...

This file contains additional information relating to the article: “A Search for Solvable Weighing Matrices,” submitted to Journal of Combinatorial Mathematics and Combinatorial Computing Feb. 25, 2005. In that article, we describe a computer search for group-developed weighing matrices of order 60 and weight 25, which we abbreviate as W (60, 25). Generally speaking, we view weighing matrices a...

In this article, we study the consistency of the template estimation with the Fréchet mean in quotient spaces. The Fréchet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distr...

The Cucker–Smale (CS) model is a velocity alignment model, and this also has been generalized on Riemannian manifolds. We modify the CS manifolds to get rid of a-priori condition particles' positions conditions communication functions. Since shortest geodesic used define an interaction between two particles, if there exist or more than geodesics, then system not well-defined. In paper, instead ...

In this article, we study the consistency of the template estimation with the Fréchet mean in quotient spaces. The Fréchet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distr...

This paper presents new alternatives to the well-known Bloom filter data structure. The Bloom filter, a compact data structure supporting set insertion and membership queries, has found wide application in databases, storage systems, and networks. Because the Bloom filter performs frequent random reads and writes, it is used almost exclusively in RAM, limiting the size of the sets it can repres...

In this short review we outline some recent developments in understanding string orbifolds. In particular, we outline the recent observation that string orbifolds do not precisely describe string propagation on quotient spaces, but rather are literally sigma models on objects called quotient stacks, which are closely related to (but not quite the same as) quotient spaces. We show how this is an...

We prove that a space is a sequentially-quotient (pseudo-sequencecovering), π-image of a separable metric space if and only if it has a point-star network consisting of countable-cs∗-covers. We also investigate spaces with count-

We characterize those classes C of separable Banach spaces for which there exists a separable Banach space Y not containing l1 and such that every space in the class C is a quotient of Y .