Splittings of extensions and homological bidimension of the algebra of bounded operators on a Banach space

We show that there exists a Banach space $E$ with the following properties: the Banach algebra $\mathscr{B}(E)$ of bounded, linear operators on $E$ has a singular extension which splits algebraically, but it does not split strongly, and the homological bidimension of $\mathscr{B}(E)$ is at least two. The first of these conclusions solves a natural problem left open by Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999), while the second answers a question of Helemskii. The Banach space $E$ that we use was originally introduced by Read (J. London Math. Soc. 1989).Comment: to appear in C.R. Math. Acad. Sci. Pari

Detecting word substitutions in text

Searching for words on a watchlist is one way in which large-scale surveillance of communication can be done, for example in intelligence and counterterrorism settings. One obvious defense is to replace words that might attract attention to a message with other, more innocuous, words. For example, the sentence the attack will be tomorrow" might be altered to the complex will be tomorrow", since 'complex' is a word whose frequency is close to that of 'attack'. Such substitutions are readily detectable by humans since they do not make sense. We address the problem of detecting such substitutions automatically, by looking for discrepancies between words and their contexts, and using only syntactic information. We define a set of measures, each of which is quite weak, but which together produce per-sentence detection rates around 90% with false positive rates around 10%. Rules for combining persentence detection into per-message detection can reduce the false positive and false negative rates for messages to practical levels. We test the approach using sentences from the Enron email and Brown corpora, representing informal and formal text respectively

Mining Large Data Sets on Grids: Issues and Prospects

When data mining and knowledge discovery techniques must be used to analyze large amounts of data, high-performance parallel and distributed computers can help to provide better computational performance and, as a consequence, deeper and more meaningful results. Recently grids, composed of large-scale, geographically distributed platforms working together, have emerged as effective architectures for high-performance decentralized computation. It is natural to consider grids as tools for distributed data-intensive applications such as data mining, but the underlying patterns of computation and data movement in such applications are different from those of more conventional high-performance computation. These differences require a different kind of grid, or at least a grid with significantly different emphases. This paper discusses the main issues, requirements, and design approaches for the implementation of grid-based knowledge discovery systems. Furthermore, some prospects and promising research directions in datacentric and knowledge-discovery oriented grids are outlined

Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations

Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence {0}→W(E)→B(E)→l2~→{0}, W(E) where W(E) denotes the ideal of weakly compact operators on E, while l2~ is the unitization of the Hilbert space l2, endowed with the zero product