Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

An exceptionally rich complex of Sanguinicolidae von Graff, 1907 (Platyhelminthes : Trematoda) from Siganidae, Labridae and Mullidae (Teleostei : Perciformes) from the Indo-West Pacific Region

We describe an unprecedented radiation of sanguinicolid blood flukes ( Digenea: Sanguinicolidae) from two species of Labridae (Choerodon venustus and C. cauteroma), seven species of Mullidae (Mulloidichthys vanicolensis, Parupeneus barberinoides, P. barberinus, P. bifasciatus, P. cyclostomus, P. indicus and P. multifasciatus) and ten species of Siganidae (Siganus argenteus, S. corallinus, S. doliatus, S. fuscescens, S. lineatus, S. margaritiferus, S. puellus, S. punctatus, S. virgatus and S. vulpinus) from sites off Australia and Palau. The flukes were morphologically similar in having the combination of a long thread-like body, tegumental spines in lateral transverse rows, a vestigial oral sucker bearing concentric rows of fine spines, an H-shaped intestine, a cirrussac, a notch level with the male genital pore, a lateral or post-ovarian uterus, a uterine chamber and separate genital pores. These species are divided into two genera on the basis of testis number. Sanguinicolids from Siganus fuscescens have a single large testis between the intestinal bifurcation and the ovary and are placed in Ankistromeces Nolan & Cribb, 2004. Species from the remaining nine species of Siganidae, Labridae and Mullidae are placed in Phthinomita n. g.; these species have two testes, the anterior testis being large and between the intestinal bifurcation and the ovary whereas the small posterior testis is at the posterior end of the body and appears rudimentary or degenerate and probably non-functional. The second internal transcribed spacer (ITS2) of ribosomal DNA ( rDNA) from 29 host/parasite/location combinations (h/p/l) was sequenced together with that of Ankistromeces mariae Nolan & Cribb, 2004 for comparison. From 135 samples we found 19 distinct genotypes which were interpreted as representing at least that many species. Replicate sequences were obtained for 25 of 30 h/p/l combinations ( including A. mariae); there was no intraspecific variation between replicates sequences for any of these. Interspecific variation ranged from 1 - 41 base differences (0.3 - 12.7% sequence divergence). The 19 putative species were difficult to recognise by morphological examination. We describe 13 new species; we do not describe (= name) six species characterised solely by molecular sequences and three putative species for which morphological data is available but for which molecular data is not. We have neither morphological nor molecular data for sanguinicolids harboured in five hosts species ( Siganus margaritiferus, S. puellus, Choerodon cauteroma, Parupeneus indicus and P. multifasciatus) in which we have seen infections. Where host species were infected in different localities they almost always harboured distinct species. Some host species ( for example, S. argenteus and S. lineatus from Lizard Island) harboured two or three species in a single geographical location. This suggests that, for parts of this system, parasite speciation has outstripped host speciation. Distance analysis of ITS2 showed species from each host family ( Siganidae, Mullidae and Labridae) did not form monophyletic clades to the exclusion of species from other host families. However, a host defined clade was formed by the sequences from sanguinicolids from S. fuscescens.

Degenerate dentition of the dugong (Dugong dugon), or why a grazer does not need teeth: morphology, occlusion and wear of mouthparts

The morphology and functional occlusion of the cheekteeth of 57 dugongs Dugong dugon of both sexes were examined using reflected light and scanning electron microscopy, radiography, hardness testing and skull manipulation. The functional morphology of the horny oral pads was also described. Mouthparts and body size allometry was examined for ontogenetic and gender-related trends. We found that the worn erupted cheekteeth of the dugong are simple flat pegs composed of soft degenerative dentine. During occlusion, the mandible moves in a mainly antero-lingual direction, with the possibility of mandibular retraction in some individuals. Anterior parts of the cheektooth row may become non-functional as a dugong ages. As a function of body size, dugong cheekteeth are extremely small compared with those of other mammalian herbivores, and with other hindgut fermenters in particular. The morphology, small size and occlusal variability of the cheekteeth suggest that there has not been strong selective pressure acting to maintain an effective dentition. In contrast, great development of the horny pads and associated skull parameters and their lower size variability suggest that the horny pads may have assumed the major role in food comminution.

ProxiMAX randomisation:a new technology for non-degenerate saturation mutagenesis of contiguous codons

Back in 2003, we published ‘MAX’ randomisation, a process of non-degenerate saturation mutagenesis using exactly 20 codons (one for each amino acid) or else any required subset of those 20 codons. ‘MAX’ randomisation saturates codons located in isolated positions within a protein, as might be required in enzyme engineering, or else on one face of an alpha-helix, as in zinc finger engineering. Since that time, we have been asked for an equivalent process that can saturate multiple, contiguous codons in a non-degenerate manner. We have now developed ‘ProxiMAX’ randomisation, which does just that: generating DNA cassettes for saturation mutagenesis without degeneracy or bias. Offering an alternative to trinucleotide phosphoramidite chemistry, ProxiMAX randomisation uses nothing more sophisticated than unmodified oligonucleotides and standard molecular biology reagents. Thus it requires no specialised chemistry, reagents nor equipment and simply relies on a process of saturation cycling comprising ligation, amplification and digestion for each cycle. The process can encode both unbiased representation of selected amino acids or else encode them in pre-defined ratios. Each saturated position can be defined independently of the others. We demonstrate accurate saturation of up to 11 contiguous codons. As such, ProxiMAX randomisation is particularly relevant to antibody engineering.

ProxiMAX Randomisation:a new technology for non-degenerate saturation mutagenesis of contiguous codons

ProxiMAX randomisation achieves saturation mutagenesis of contiguous codons without degeneracy or bias. Offering an alternative to trinucleotide phosphoramidite chemistry, it uses nothing more sophisticated than unmodified oligonucleotides and standard molecular biology reagents and as such, requires no specialised chemistry, reagents nor equipment. When particular residues are known to affect protein activity/specificity, their combinatorial replacement with all 20 amino acids, or a subset thereof, can provide a rapid route to generating proteins with desirable characteristics. Conventionally, saturation mutagenesis replaced key codons with degenerate ones. Although simple to perform, that procedure resulted in unnecessarily large libraries, termination codons and inherent uneven amino acid representation. ProxiMAX randomisation is an enzyme-based technique that can encode unbiased representation of all or selected amino acids or else can provide required codons in pre-defined ratios. Each saturated position can be defined independently of the others. ProxiMAX randomisation is achieved via saturation cycling: an iterative process comprising blunt end ligation, amplification and digestion with a Type IIS restriction enzyme. We demonstrate both unbiased saturation of a short 6-mer peptide and saturation of a hypervariable region of a scfv antibody fragment, where 11 contiguous codons are saturated with selected codons, in pre-defined ratios. As such, ProxiMAX randomisation is particularly relevant to antibody engineering. The development of ProxiMAX randomisation from concept to reality is described.

ProxiMAX randomisation:a new technology for non-degenerate saturation mutagenesis of contiguous codons

Back in 2003, we published ‘MAX’ randomisation, a process of non-degenerate saturation mutagenesis using exactly 20 codons (one for each amino acid) or else any required subset of those 20 codons. ‘MAX’ randomisation saturates codons located in isolated positions within a protein, as might be required in enzyme engineering, or else on one face of an alpha-helix, as in zinc finger engineering. Since that time, we have been asked for an equivalent process that can saturate multiple, contiguous codons in a non-degenerate manner. We have now developed ‘ProxiMAX’ randomisation, which does just that: generating DNA cassettes for saturation mutagenesis without degeneracy or bias. Offering an alternative to trinucleotide phosphoramidite chemistry, ProxiMAX randomisation uses nothing more sophisticated than unmodified oligonucleotides and standard molecular biology reagents. Thus it requires no specialised chemistry, reagents nor equipment and simply relies on a process of saturation cycling comprising ligation, amplification and digestion for each cycle. The process can encode both unbiased representation of selected amino acids or else encode them in pre-defined ratios. Each saturated position can be defined independently of the others. We demonstrate accurate saturation of up to 11 contiguous codons. As such, ProxiMAX randomisation is particularly relevant to antibody engineering.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Bifurcation and stability in a low-dimensional model for multiple-frequency mode-locked lasers

Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels. © 2010 The American Physical Society.

Bifurcation and dynamic response analysis of a rotating blade excited by upstream vortices

Acknowledgements The authors acknowledge the projects supported by the National Basic Research Program of China (973 Project)(No. 2015CB057405) and the National Natural Science Foundation of China (No. 11372082) and the State Scholarship Fund of CSC. DW thanks for the hospitality of the University of Aberdeen.

Équations différentielles à retard et leur application en hématopoïèse, avec étude du cas de la neutropénie cyclique

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Analyse des bifurcations dans un modèle du flutter auriculaire

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Characterizing the transition dynamics for multi-pulsing in mode-locked lasers

We consider experimentally and theoretically a refined parameter space near the transition to multi-pulse modelocking. Near the transition, the onset of instability is initiated by a Hopf (periodic) bifurcation. As cavity energy is increased, the band of unstable, oscillatory modes generates a chaotic behavior between single- and multi-pulse operation. Both theory and experiment are in good qualitative agreement and they suggest that the phenomenon is of a universal nature in mode-locked lasers at the onset of multi-pulsing from N to N + 1 pulses per round trip. This is the first theoretical and experimental characterization of the transition behavior, made possible by a highly refined tuning of the gain pump level. © 2010 Copyright SPIE - The International Society for Optical Engineering.