Construction of inverses with prescribed zero minors and applications to decentralized stabilization

We examine the following question: Suppose R is a principal ideal domain, and that F is an n × m matrix with elements in R, with n>m. When does there exist an m × n matrix G such that GF = Im, and such that certain prescribed minors of G equal zero? We show that there is a simple necessary condition for the existence of such a G, but that this condition is not sufficient in general. However, if the set of minors of G that are required to be zero has a certain pattern, then the condition is necessary as well as sufficient. We then show that the pattern mentioned above arises naturally in connection with the question of the existence of decentralized stabilizing controllers for a given plant. Hence our result allows us to derive an extremely simple proof of the fact that a necessary and sufficient condition for the existence of decentralized stabilizing controllers is the absence of unstable decentralized fixed modes, as well as to derive a very clean expression for these fixed modes. In addition to the application to decentralized stabilization, we believe that the result is of independent interest.

Molecular cloning and expression pattern of a Cubitus interruptus homologue from the mulberry silkworm Bombyx mori

A homologue of the segment polarity gene Cubitus interruptus from Bombyx Mori, (BmCi) has been cloned and characterized. This region harbouring Zn2+ finger motif is highly conserved across species. In B. Mori, BmCi RNA expression was first detected at stage 6 of embryogenesis, which reached maximum levels at stage 21C and was maintained until larval hatching. The segmentally reiterated striped pattern of transcript distribution in stage 21C embryos was in conformity with its predicted segment polarity nature. BmCi was expressed in the fore- and hind-wing discs, ovaries, testes and gut during fifth larval intermolt, reminiscent of its expression domains in Drosophila. Besides, BmCi expression was seen in the. anterior part of the middle silkglands in late embryonic stages, and this pattern was maintained during larval development. The transition from third to fourth and fifth larval intermolts was accompanied by an increase in the transcript levels in the middle silkglands. Our results demonstrate the presence of a novel expression domain for Ci in Bombyx. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Expression pattern of Cubitus interruptus from the mulberry silkworm Bombyx mori in late developmental stages

A partial genomic clone of Bombyx mori homologue of the segment polarity gene Cubitus interruptus (BmCi), encoding the conserved zinc finger domain and harbouring two introns, has been characterized. BmCi was expressed in the silkglands of B. mori from embryonic to the late larval stages(3rd, 4th and 5th intermoults). The expression was confined to the anterior region of the middle silkglands, overlapping with the domain of sericin-2 expression and excluding the domains of Bm invected expression, namely the middle and posterior regions of the middle silkglands. In the wing discs, the expression was restricted to the anterior compartment, which increased from 4th to 5th larval intermoults and declined later in the pupal wing buds. In gonadal tissues (both ovaries and testes) BmCi was expressed from the larval to pupal stages. The transcripts were localized to the sperm tubes containing spermatogonia in the testis of Bombyx larvae. BmCi expression, however, was not detected in any of these tissues during the moulting stages. Expression of Ci in the wing discs and gonads is evolutionarily conserved, while the silkgland represents a novel domain. Our results imply that BmCi is involved in the specification and maintenance of micro-compartment identity within the middle silkglands.

Pattern-growth based frequent serial episode discovery

Frequent episode discovery is a popular framework for pattern discovery from sequential data. It has found many applications in domains like alarm management in telecommunication networks, fault analysis in the manufacturing plants, predicting user behavior in web click streams and so on. In this paper, we address the discovery of serial episodes. In the episodes context, there have been multiple ways to quantify the frequency of an episode. Most of the current algorithms for episode discovery under various frequencies are apriori-based level-wise methods. These methods essentially perform a breadth-first search of the pattern space. However currently there are no depth-first based methods of pattern discovery in the frequent episode framework under many of the frequency definitions. In this paper, we try to bridge this gap. We provide new depth-first based algorithms for serial episode discovery under non-overlapped and total frequencies. Under non-overlapped frequency, we present algorithms that can take care of span constraint and gap constraint on episode occurrences. Under total frequency we present an algorithm that can handle span constraint. We provide proofs of correctness for the proposed algorithms. We demonstrate the effectiveness of the proposed algorithms by extensive simulations. We also give detailed run-time comparisons with the existing apriori-based methods and illustrate scenarios under which the proposed pattern-growth algorithms perform better than their apriori counterparts. (C) 2013 Elsevier B.V. All rights reserved.