We consider the Burau and Gassner representations of the braid groups B„ . A sufficient condition for faithfulness, involving just a pair of arcs, is shown to be necessary as well for all but at most two values of n. In the Burau case, this implies nonfaithfulness for n > 10 . Alexander showed in [6] that any knot K can be made by connecting the ends of some braid b. The Alexander polynomial A(...

This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that almost all the regular Gaussian distributions that factorize with respect to a chain graph are faithful to it. This result has three important consequences. First, chain graphs are more powerful than undirected graphs and acyclic directed graphs for representing regular Gaussian distr...

The paper presents a critical examination of the way certain central aspects of concurrent programs are formally modeled. The main formal model examined is the operational model of fair transition system which represents concurrency by interleaving of actions considered atomic. Several questions concerning the faithfulness of this representation naturally arise. The paper considers some of thes...

A main question in graphical models and causal inference is whether, given a probability distribution P (which is usually an underlying distribution of data), there is a graph (or graphs) to which P is faithful. The main goal of this paper is to provide a theoretical answer to this problem. We work with general independence models, which contain probabilistic independence models as a special ca...

In the dialects of Japanese spoken in the city of Fukuoka, there are two ways in which the prosodic phonology of nouns differs from that of verbs and adjectives. First, verbs have an obligatory pitch accent, while nouns may be accented or unaccented. These dialects thus differ from dialects such as Tôkyô (McCawley 1968; Poser 1984), in which a word of any category may be either accented or unac...

This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the strictly positive discrete probability distributions with the prescribed sample space that factorize according to a chain graph G with dimension d have positive Lebesgue measure wrt R, whereas those that factorize according to G but are not faithful to it have zero Lebesgue measur...

Farrah J. Mateen, MD Ascending the steps of the Pink Palace, it is easy to imagine the land of the old Nawabs. Their doughfaced, proud faces, now confined to mere portraits, are still poised to overlook Old Dhaka. Below, on the Sadarghat, the palatial park is crowded with people of all ages: sellers, schoolchildren, rickshaw drivers, peddlers, beggars, artisans, businesswomen, and many people, ...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...