A family of iterative methods that uses divided differences of first and second orders

The family of fourth-order Steffensen-type methods proposed by Zheng et al. (Appl. Math. Comput. 217, 9592-9597 (2011)) is extended to solve systems of nonlinear equations. This extension uses multidimensional divided differences of first and second orders. For a certain computational efficiency index, two optimal methods are identified in the family. Semilocal convergence is shown for one of these optimal methods under mild conditions. Moreover, a numerical example is given to illustrate the theoretical results.Peer ReviewedPostprint (author's final draft

Tipping the Balance: Robustness of Tip Cell Selection, Migration and Fusion in Angiogenesis

Vascular abnormalities contribute to many diseases such as cancer and diabetic retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from pre-existing vessels in response to signals, e.g., vascular endothelial growth factor (VEGF). Tip cells meet and fuse (anastomosis) to form blood-flow supporting loops. Tip cell selection is achieved by Dll4-Notch mediated lateral inhibition resulting, under normal conditions, in an interleaved arrangement of tip and non-migrating stalk cells. Previously, we showed that the increased VEGF levels found in many diseases can cause the delayed negative feedback of lateral inhibition to produce abnormal oscillations of tip/stalk cell fates. Here we describe the development and implementation of a novel physics-based hierarchical agent model, tightly coupled to in vivo data, to explore the system dynamics as perpetual lateral inhibition combines with tip cell migration and fusion. We explore the tipping point between normal and abnormal sprouting as VEGF increases. A novel filopodia-adhesion driven migration mechanism is presented and validated against in vivo data. Due to the unique feature of ongoing lateral inhibition, ‘stabilised’ tip/stalk cell patterns show sensitivity to the formation of new cell-cell junctions during fusion: we predict cell fates can reverse. The fusing tip cells become inhibited and neighbouring stalk cells flip fate, recursively providing new tip cells. Junction size emerges as a key factor in establishing a stable tip/stalk pattern. Cell-cell junctions elongate as tip cells migrate, which is shown to provide positive feedback to lateral inhibition, causing it to be more susceptible to pathological oscillations. Importantly, down-regulation of the migratory pathway alone is shown to be sufficient to rescue the sprouting system from oscillation and restore stability. Thus we suggest the use of migration inhibitors as therapeutic agents for vascular normalisation in cancer

Insects as Stem Engineers: Interactions Mediated by the Twig-Girdler Oncideres albomarginata chamela Enhance Arthropod Diversity

Background: Ecosystem engineering may influence community structure and biodiversity by controlling the availability of resources and/or habitats used by other organisms. Insect herbivores may act as ecosystem engineers but there is still poor understanding of the role of these insects structuring arthropod communities. Methodology/Principal Findings: We evaluated the effect of ecosystem engineering by the stem-borer Oncideres albomarginata chamela on the arthropod community of a tropical dry forest for three consecutive years. The results showed that ecosystem engineering by O. albomarginata chamela had strong positive effects on the colonization, abundance, species richness and composition of the associated arthropod community, and it occurred mainly through the creation of a habitat with high availability of oviposition sites for secondary colonizers. These effects cascade upward to higher trophic levels. Overall, ecosystem engineering by O. albomarginata chamela was responsible for nearly 95 % of the abundance of secondary colonizers and 82 % of the species richness. Conclusions/Significance: Our results suggest that ecosystem engineering by O. albomarginata chamela is a keystone process structuring an arthropod community composed by xylovores, predators and parasitoids. This study is the first to empirically demonstrate the effect of the ecosystem engineering by stem-boring insects on important attributes o

A new polymorphim (G->A) in the psizeta1 globin gene.

BACKGROUND AND OBJECTIVES: a-globin cluster polymorphisms are obtained with specific restriction enzymes (Xba I, Eco RI, Sac I, Apa I, Bgl II, etc) that can also have implications for genetic analysis. DESIGN AND AND METHODS: We studied three unrelated patients; one from Argentina, one from Spain and one from Australia but of Polish origin. Genomic DNA was digested with several different restriction enzymes and probes, amplified and sequenced with an ABI Prism 310 sequencer. RESULTS: In the three patients an abnormal 26 kb band appeared when they were studied with restriction enzyme Bgl II and z probe. A fragment of 944 bp was amplified with primers that cover from -280 to +714 bp of the recognition sequence of Bgl II enzyme (AGATCT) localized 5' from pseudogene z1. After digestion of this PCR product with Bgl II, two fragments of 714 and 280 bp were produced in normal controls, whereas in patient #1 the PCR fragment was undigested and in patients 2 and 3 both undigested and digested fragments were observed. Sequencing of the PCR fragment showed that in all three patients it was the same polymorphism (G->A) at nucleotide 153171 of the 16 p sequence found in the Bgl II recognition site that changed to AAATCT. INTERPRETATION AND CONCLUSIONS: We describe a new polymorphism in the yz1 first exon Bgl II restriction site (G->A). The polymorphism is associated in cis with haplotype -a3.7. The fragment obtained by PCR enabled us to corroborate the presence of the polymorphism quickly without having to use complicated sequencing techniques

A new polymorphim (G->A) in the psizeta1 globin gene.

BACKGROUND AND OBJECTIVES: a-globin cluster polymorphisms are obtained with specific restriction enzymes (Xba I, Eco RI, Sac I, Apa I, Bgl II, etc) that can also have implications for genetic analysis. DESIGN AND AND METHODS: We studied three unrelated patients; one from Argentina, one from Spain and one from Australia but of Polish origin. Genomic DNA was digested with several different restriction enzymes and probes, amplified and sequenced with an ABI Prism 310 sequencer. RESULTS: In the three patients an abnormal 26 kb band appeared when they were studied with restriction enzyme Bgl II and z probe. A fragment of 944 bp was amplified with primers that cover from -280 to +714 bp of the recognition sequence of Bgl II enzyme (AGATCT) localized 5' from pseudogene z1. After digestion of this PCR product with Bgl II, two fragments of 714 and 280 bp were produced in normal controls, whereas in patient #1 the PCR fragment was undigested and in patients 2 and 3 both undigested and digested fragments were observed. Sequencing of the PCR fragment showed that in all three patients it was the same polymorphism (G->A) at nucleotide 153171 of the 16 p sequence found in the Bgl II recognition site that changed to AAATCT. INTERPRETATION AND CONCLUSIONS: We describe a new polymorphism in the yz1 first exon Bgl II restriction site (G->A). The polymorphism is associated in cis with haplotype -a3.7. The fragment obtained by PCR enabled us to corroborate the presence of the polymorphism quickly without having to use complicated sequencing techniques