Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Is there a role for axillary dissection for patients with operable breast cancer in this era of conservatism?

Background: The trend in breast cancer surgery is toward more conservative operative procedures. The new staging technique of sentinel node biopsy facilitates the identification of pathological node-negative patients in whom axillary dissection may be avoided. However, patients with a positive sentinel node biopsy would require a thorough examination of their nodal status. An axillary dissection provides good local control, and accurate staging and prognostic information to inform decisions about adjuvant therapy. In addition, the survival benefit of axillary treatment is still debated. The objectives of the present study were to examine the pattern of lymph node metastases in the axilla, and evaluate the merits of a level III axillary dissection. Methods : Between June 1997 and May 2000, 308 patients underwent a total of 320 level III dissections as part of their treatment for operable invasive breast cancer. The three axillary levels were marked intraoperatively, and the contents in each level were submitted and examined separately. The patterns of axillary lymph node (ALN) metastases were examined, and factors associated with 4 positive nodes, and level III ALN metastases were evaluated by univariate and multivariate analyses. Results: An average of 25 lymph nodes were examined per case (range: 8-54), and using strict anatomical criteria, the mean numbers of ALN found in levels I, II and III were 18 (range: 2-43), 4 (range: 0 19), and 3 ( range: 0-11), respectively. Axillary lymph node involvement was found in 45% of the cases (143/320). Of the 143 cases, 78% (n = 111) had involvement of level I nodes only, and 21% (n = 30) had positive ALN in levels II and, or, III, in addition to level I. Involvement of lymph nodes in level II or III without a level I metastasis was found in two cases only (0.6%). By including level II, in addition to level I, in the dissection, four cases (1%) were converted from one to three positive nodes to 4 positive nodes (P = 0.64). By the inclusion of level III to a level I and II dissection, three cases (1%) were converted from one to three positive nodes to 4 positive nodes (P = 0.74). Involvement of lymph nodes in level III was found in 22 cases (7%), and 51 cases (16%) had 4 positive nodes. Palpability of ALN, pathological tumour size, and lymphovascular invasion (LVI), were significantly associated with level III involvement and 4 positive nodes by univariate and multivariate analyses. The frequencies of level III involvement and 4 positive nodes in patients with palpable ALN were 22% and 42%, respectively. The corresponding frequencies in patients with a clinically negative axilla, and a primary tumour which was >20 mm and LVI positive, were over 14% and 31%, respectively. Conclusion: Level III axillary dissection is appropriate for patients with palpable ALN, and in those with a tumour which is >20 mm and LVI positive, principally to reduce the risk of axillary recurrence. Staging accuracy is achieved with a level II dissection, or even a level I dissection alone based on strict anatomical criteria. Sentinel node biopsy is a promising technique in identifying pathological node-positive patients in whom an axillary clearance provides optimal local control and staging information.

Amphitheater staging: In-the-round or to the front (and what about asides)?

When the existence in Utrecht of the DeWitt/Van Buchel drawing of the Swan Theater became known in 1888, William Poel was already seven years into his inquiries into the best means of staging the public amphitheater and great hall plays of the English Renaissance.1 I mention this to emphasize that the discourse came before the fact: the belief that Shakespeare's plays are best staged as it was then imprecisely imagined they had once been staged-simply, without elaborate settings or time-consuming scene changes, with direct actor-audience address, "in-the-round"-had as much to do with reactions against the late nineteenth-century stage's pictorialism, with its set-changing interruptions and cut-and-paste revisions to Shakespeare's texts, as it had to do with presenting the Bard "authentically." Some of the confusion caused by the uneasy mixing of historical scholarship and the assumptions and practices of our own contemporary theater profession can be glimpsed in the phenomenon of modern in-the-round staging, often claimed as a more "authentic" approach to Shakespeare in performance, but one which is then modified to make possible post-Stanislavsky acting methods and to satisfy modern audience expectations.

Growth of papaya nodal and rooted shoot cultures as affected by ACC, STS, culture vessel size and incubation conditions

Nodal shoot cultures of 'Clone 003', a selected Australian papaya cultivar, were cultured on modified De Fossard medium supplemented with chemicals that either promote ethylene evolution or inhibit action while in culture. Nodal shoot cultures grown in the presence of 1-aminocyclopropane carboxylic acid (ACC, 1.0 mM) resulted in a significant reduction in percent fresh and dry weights, shoot length, leaf area, petiole length and chlorophyll content, but leaf development was significantly increased. In contrast, nodal cultures grown in the presence of silver thiosulphate (STS, 0.5 mM) significantly produced the highest percentage of fresh and dry weights, shoot length, leaf production, leaf area expansion, petiole length and leaf chlorophyll content. Nodal cultures and rooted whole plantlets placed in medium-sized (125 mL) culture vessels had significantly better growth than those cultures placed in small (70 mL) or in large (250 mL) vessels. Cultures grown in medium-sized vessels had higher fresh and dry weights, longer shoots, more leaves and larger leaf area than those cultures placed in smaller or larger vessels. Similarly, values for said growth parameters and for chlorophyll content of the nodal and rooted whole plantlets were higher when they were incubated under high light intensity of 120 mumol m(-2)s(-1) at a prevailing temperature of either 20+/-1 C or 25+/-1 C.

Li, Ruru. Shashibiya: Staging Shakespeare in China

Reviews the book "Shashibiya: Staging Shakespeare in China," by Li Ruru

Computation of bifurcation boundaries for power systems: A new Delta-plane method

This paper is devoted to the problems of finding the load flow feasibility, saddle node, and Hopf bifurcation boundaries in the space of power system parameters. The first part contains a review of the existing relevant approaches including not-so-well-known contributions from Russia. The second part presents a new robust method for finding the power system load flow feasibility boundary on the plane defined by any three vectors of dependent variables (nodal voltages), called the Delta plane. The method exploits some quadratic and linear properties of the load now equations and state matrices written in rectangular coordinates. An advantage of the method is that it does not require an iterative solution of nonlinear equations (except the eigenvalue problem). In addition to benefits for visualization, the method is a useful tool for topological studies of power system multiple solution structures and stability domains. Although the power system application is developed, the method can be equally efficient for any quadratic algebraic problem.

Prey capture and accommodation in the sandlance, Limnichthyes fasciatus (Creediidae; Teleostei)

The eyes of the sandlance, Limnichthyes fasciatus (Creediidae. Teleostei) move independently and possess a refractive cornea, a convexiclivate fovea and a non-spherical lens giving rise to a wide separation of the nodal point from the axis of rotation of the eye much like that of a chameleon. To investigate this apparent convergence of the visual optics in these phylogenetically disparate species, we examine feeding behaviour and accommodation in the sandlance with special reference to the possibility that sandlances use accommodation as a depth cue to judge strike length. Frame-by-frame analysis of over 2000 strikes show a 100% success rate. Explosive strikes are completed in 50 ms over prey distances of four body lengths. Close-up video confirms that successful strikes can be initiated monocularly (both normally and after monocular occlusion) showing that binocular cues are not necessary to judge the length of a strike. Additional means of judging prey distance may also be derived from parallax information generated by rotation of the eye as suggested for chameleons. Using photorefraction on anaesthetised sandlances, accommodative changes were induced with acetylcholine and found to range between 120 D and 180 D at a speed of 600-720 D s(-1). The large range of accommodation (25% of the total power) is also thought to be mediated by corneal accommodation where the contraction of a unique cornealis muscle acts to change the corneal curvatures.

Probability of axillary node involvement in patients with tubular carcinoma of the breast

The aim of this study was to investigate the frequency of axillary metastasis in women with tubular carcinoma (TC) of the breast. Women who underwent axillary dissection for TC in the Western Sydney area (1984-1995) were identified retrospectively through a search of computerized records. A centralized pathology review was performed and tumours were classified as pure tubular (22) or mixed tubular (nine), on the basis of the invasive component containing 90 per cent or more, or 75-90 per cent tubule formation respectively. A Medline search of the literature was undertaken to compile a collective series (20 studies with a total of 680 patients) to address the frequency of nodal involvement in TC. A quantitative meta-analysis was used to combine the results of these studies. The overall frequency of nodal metastasis was five of 31 (16 per cent); one of 22 pure tubular and four of nine mixed tumours (P = 0.019). None of the tumours with a diameter of 10 mm or less (n = 16) had nodal metastasis compared with five of 15 larger tumours (P = 0.018). The meta-analysis of 680 women showed an overall frequency of nodal metastasis in TC of 13.8 (95 per cent confidence interval 9.3-18.3) per cent. The frequency of nodal involvement was 6.6 (1.7-11.4) per cent in pure TC (n = 244) and 25.0 (12.5-37.6) per cent in mixed TC (n = 149). A case may be made for observing the clinically negative axilla in women with a small TC (10 mm or less in diameter).

Mitochondrial genome data alone are not enough to unambiguously resolve the relationships of Entognatha, Insecta and Crustacea sensu lato (Arthropoda)

An analysis of the relationships of the major arthropod groups Was undertaken using mitochondrial genome data to examine the hypotheses that Hexapoda is polyphyletic and that Collembola is more closely related to branchiopod crustaceans than insects. We sought to examine the sensitivity of this relationship to outgroup choice, data treatment. gene choice and optimality criteria used in the phylogenetic analysis of mitochondrial genome data. Additionally we sequenced the mitochondrial genome of ail archaeognathan, Nesomachilis australica. to improve taxon selection in the apterygote insects, a group poorly represented in previous mitochondrial phylogenies. The sister group of the Collembola was rarely resolved in our analyses with a significant level of support. The use of different outgroups (myriapods, nematodes, or annelids + mollusks) resulted in many different placements of Collembola. The way in which the dataset was coded for analysis (DNA, DNA with the exclusion of third codon position and as amino acids) also had marked affects on tree topology. We found that nodal Support was spread evenly throughout the 13 mitochondrial genes and the exclusion of genes resulted in significantly less resolution in the inferred trees. Optimality criteria had a much lesser effect on topology than the preceding factors; parsimony and Bayesian trees for a given data set and treatment were quite similar. We therefore conclude that the relationships of the extant arthropod groups as inferred by mitochondrial genomes are highly vulnerable to outgroup choice, data treatment and gene choice, and no consistent alternative hypothesis of Collembola's relationships is supported. Pending the resolution of these identified problems with the application of mitogenomic data to basal arthropod relationships, it is difficult to justify the rejection of hexapod monophyly, which is well supported on morphological grounds. (c) The Willi Hennig Society 2004.

Cited2 is required both for heart morphogenesis and establishment of the left-right axis in mouse development

Establishment of the left-right axis is a fundamental process of vertebrate embryogenesis. Failure to develop left-right asymmetry leads to incorrect positioning and morphogenesis of numerous internal organs, and is proposed to underlie the etiology of several common cardiac malformations. The transcriptional modulator Cited2 is essential for embryonic development: Cited2-null embryos die during gestation with profound developmental abnormalities, including cardiac malformations, exencephaly and adrenal agenesis. Cited2 is also required for normal establishment of the left-right axis; we demonstrate that abnormal heart looping and right atrial and pulmonary isomerism are consistent features of the left-right-patterning defect. We show by gene expression analysis that Cited2 acts upstream of Nodal, Lefty2 and Pitx2 in the lateral mesoderm, and of Lefty1 in the presumptive floor plate. Although abnormal left-right patterning has a major impact on the cardiac phenotype in Cited2-null embryos, laterality defects are only observed in a proportion of these embryos. We have therefore used a combination of high-resolution imaging and three-dimensional (3D) modeling to systematically document the full spectrum of Cited2-associated cardiac defects. Previous studies have focused on the role of Cited2 in cardiac neural crest cell development, as Cited2 can bind the transcription factor Tfap2, and thus affect the expression of Erbb3 in neural crest cells. However, we have identified Cited2-associated cardiac defects that cannot be explained by laterality or neural crest abnormalities. In particular, muscular ventricular septal defects and reduced cell density in the atrioventricular (AV) endocardial cushions are evident in Cited2-null embryos. As we found that Cited2 expression tightly correlated with these sites, we believe that Cited2 plays a direct role in development of the AV canal and cardiac septa. We therefore propose that, in addition to the previously described reduction of cardiac neural crest cells, two other distinct mechanisms contribute to the spectrum of complex cardiac defects in Cited2-null mice; disruption of normal left-right patterning and direct loss of Cited2 expression in cardiac tissues.