On a Theorem by Van Vleck Regarding Sturm Sequences

In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences with pivot, and (b) incomplete Sturm sequences. Despite its importance, the Pell-Gordon Theorem for polynomials in Q[x] has been totally forgotten and, to our knowledge, it is referenced by us for the first time in the literature. In this paper we go over Van Vleck’s theorem and method, modify slightly the formula of the Pell-Gordon Theorem and present a general triangularization method, called the VanVleck-Pell-Gordon method, that correctly computes in Z[x] polynomial Sturm sequences, both complete and incomplete.

Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.

When 'listeners can't talk' : comparing active listening in opening sequences of telephone and online counselling

While there is growing use of online counselling, little is known about its interactional organisation and how it compares to telephone counselling. This is despite past research suggesting that both counsellors and clients report the impact of the different modalities on the presentation and management of the counselling interaction. This paper compares the interactional affordances of telephone and online web counselling in opening sequences on Kids Help Line, a 24-hour Australian counselling service for children and young people up to the age of 25. We examine two ways that counsellors show active listening through response tokens and formulations. The analysis describes how counsellors’ use of minimal response tokens facilitate the clients’ problem presentation and are used in the management of turn taking and sequence organisation. For example, counsellors use the response token Mm hm to show that they understand that the client’s unit of talk to is not yet complete, and to affirm or invite the client to continue speaking. Formulations in phone and web counselling are another way that counsellors display active listening to re-present stretches of the clients’ preceding talk. In phone and web counselling, however, the respective modalities can complicate matters of turn transition and sequence organisation. By examining actual phone and online counselling sessions, this paper offers empirical demonstrations of the interactional affordances of phone and online counselling, and shows how the institutional practice of active listening is accomplished across different counselling modalities

Development of a novel rolling-circle amplification technique to detect Banana streak virus which also discriminates between integrated and episomal virus sequences

Bananas are hosts to a large number of banana streak virus (BSV) species. However, diagnostic methods for BSV are inadequate because of the considerable genetic and serological diversity amongst BSV isolates and the presence of integrated BSV sequences in some banana cultivars which leads to false positives. In this study, a sequence non-specific, rolling-circle amplification (RCA) technique was developed and shown to overcome these limitations for the detection and subsequent characterisation of BSV isolates infecting banana. This technique was shown to discriminate between integrated and episomal BSV DNA, specifically detecting the latter in several banana cultivars known to contain episomal and/or integrated sequences of Banana streak Mysore virus (BSMyV), Banana streak OL virus (BSOLV) and Banana streak GF virus (BSGFV). Using RCA, the presence of BSMyV and BSOLV was confirmed in Australia, while BSOLV, BSGFV, Banana streak Uganda I virus (BSUgIV), Banana streak Uganda L virus (BSUgLV) and Banana streak Uganda M virus (BSUgMV) were detected in Uganda. This is the first confirmed report of episomally-derived BSUglV, BSUgLV and BSUgMV in Uganda. As well as its ability to detect BSV, RCA was shown to detect two other pararetroviruses, Sugarcane bacilliform virus in sugarcane and Cauliflower mosaic virus in turnip.

Interaction of NPR1 with basic leucine zipper protein transcription factors that bind sequences required for salicylic acid induction of the PR–1 gene

The Arabidopsis thaliana NPR1 has been shown to be a key regulator of gene expression during the onset of a plant disease-resistance response known as systemic acquired resistance. The npr1 mutant plants fail to respond to systemic acquired resistance-inducing signals such as salicylic acid (SA), or express SA-induced pathogenesis-related (PR) genes. Using NPR1 as bait in a yeast two-hybrid screen, we identified a subclass of transcription factors in the basic leucine zipper protein family (AHBP-1b and TGA6) and showed that they interact specifically in yeast and in vitro with NPR1. Point mutations that abolish the NPR1 function in A. thaliana also impair the interactions between NPR1 and the transcription factors in the yeast two-hybrid assay. Furthermore, a gel mobility shift assay showed that the purified transcription factor protein, AHBP-1b, binds specifically to an SA-responsive promoter element of the A. thaliana PR-1 gene. These data suggest that NPR1 may regulate PR-1 gene expression by interacting with a subclass of basic leucine zipper protein transcription factors.

Comparison of Nucleotide Sequences between Northern and Southern Philippine Isolates of Rice Grassy Stunt Virus Indicates Occurrence of Natural Genetic Reassortment

Rice grassy stunt virus is a member of the genus Tenuivirus, is persistently transmitted by a brown planthopper, and has occurred in rice plants in South, Southeast, and East Asia (similar to North and South America). We determined the complete nucleotide (nt) sequences of RNAs 1 (9760 nt), 2 (4069 nt), 3 (3127 nt), 4 (2909 nt), 5 (2704 nt), and 6 (2590 nt) of a southern Philippine isolate from South Cotabato and compared them with those of a northern Philippine isolate from Laguna (Toriyama et al., 1997, 1998). The numbers of nucleotides in the terminal untranslated regions and open reading frames were identical between the two isolates except for the 5′ untranslated region of the complementary strand of RNA 4. Overall nucleotide differences between the two isolates were only 0.08% in RNA 1, 0.58% in RNA 4, and 0.26% in RNA 5, whereas they were 2.19% in RNA 2, 8.38% in RNA 3, and 3.63% in RNA 6. In the intergenic regions, the two isolates differed by 9.12% in RNA 2, 11.6% in RNA 3, and 6.86% in RNA 6 with multiple consecutive nucleotide deletion/insertions, whereas they differed by only 0.78% in RNA 4 and 0.34% in RNA 5. The nucleotide variation in the intergenic region of RNA 6 within the South Cotabato isolate was only 0.33%. These differences in accumulation of mutations among individual RNA segments indicate that there was genetic reassortment in the two geographical isolates; RNAs 1, 4, and 5 of the two isolates came from a common ancestor, whereas RNAs 2, 3, and 6 were from two different ancestors.