Resonance bifurcations of robust heteroclinic networks

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a long-period periodic orbit. Resonance bifurcations for heteroclinic networks are more complicated because different subcycles in the network can undergo resonance at different parameter values, but have, until now, not been systematically studied. In this article we present the first investigation of resonance bifurcations in heteroclinic networks. Specifically, we study two heteroclinic networks in $\R^4$ and consider the dynamics that occurs as various subcycles in each network change stability. The two cases are distinguished by whether or not one of the equilibria in the network has real or complex contracting eigenvalues. We construct two-dimensional Poincare return maps and use these to investigate the dynamics of trajectories near the network. At least one equilibrium solution in each network has a two-dimensional unstable manifold, and we use the technique developed in [18] to keep track of all trajectories within these manifolds. In the case with real eigenvalues, we show that the asymptotically stable network loses stability first when one of two distinguished cycles in the network goes through resonance and two or six periodic orbits appear. In the complex case, we show that an infinite number of stable and unstable periodic orbits are created at resonance, and these may coexist with a chaotic attractor. There is a further resonance, for which the eigenvalue combination is a property of the entire network, after which the periodic orbits which originated from the individual resonances may interact. We illustrate some of our results with a numerical example.Comment: 46 pages, 20 figures. Supplementary material (two animated gifs) can be found on http://www.maths.leeds.ac.uk/~alastair/papers/KPR_res_net_abs.htm

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

In vitro Growth of the Landschütz Ascites Tumour with Retention of High Mouse Virulence

ALTHOTJGH ascites tumours have been propagated for many years by regular passage in their natural host, only recently has it been possible to maintain some of these cells in continuous passage in tissue culture. The ease of adaptation to in vitro growth, the stability of cells adapted in this way with respect to morphology and chromosome constitution, and their virulence for mice have been variousl

Immunohistochemical localization of fibronectin as a tool for the age determination of human skin wounds

We analyzed the distribution of fibronectin in routinely embedded tissue specimens from 53 skin wounds and 6 postmortem wounds. In postmortem wounds a faint but focal positive staining was exclusively found at the margin of the specimens which dit not extend into the adjacent stroma. Vital wounds were classified into 3 groups. The first comprising lesions with wound ages ranging from a few seconds to 30 min, the second comprising those with wound ages upt to 3 weeks, and the third group with lesions more than 3 weeks old. Ten out of 17 lesions with a wound age up to 30 min showed a clear positive reaction within the wound area. Three specimens in this group were completely negative, while in 4 additional cases the result was not significantly different from postmortem lesions. These 7 cases were characterized by acute death with extremely short survival times (only seconds). In wounds up to 3 weeks old fibronectin formed a distinct network containing an increasing number of inflammatory cells corresponding to the wound age. In 2 cases with a survival time of 17 days and in all wounds older than 3 weeks fibronectin was restricted to the surface of fibroblasts and to parallel arranged fibers in the granulation tissue without any network structures. We present evidence that fibronectin is a useful marker for vital wounds with a survival time of more than a few minutes. Fibronectin appears before neutrophilic granulocytes migrate into the wound area. Since a faint positive fibronectin staining is seen in postmortem lesions and bleedings, we propose that only those wounds which show strong positive fibronectin staining also extending into the adjacent stroma should be regarded as vital

Exploring emotions and cognitions in hoarding: a Q-methodology analysis

Background: The cognitions and emotions of people prone to hoarding are key components of the dominant cognitive behavioural model of hoarding disorder. Aims: This study sought to use Q-methodology to explore the thoughts and feelings of people that are prone to hoarding, to identify whether distinct clusters of participants could be found. Method: A 49-statement Q-set was generated following thematic analysis of initial interviews (n = 2) and a review of relevant measures and literature. Forty-one participants with problematic hoarding met various study inclusion criteria and completed the Q-sort (either online or offline). A by-person factor analysis was conducted and subsequent participant clusters compared on psychometric measures of mood, anxiety, hoarding and time taken on the online task as proxy for impulsivity. Results: Four distinct participant clusters were found constituting 34/41 (82.92%) of the participants, as the Q-sorts of n = 7 participants failed to cluster. The four clusters found were ‘overwhelmed’ (n = 11 participants); ‘aware of consequences’ (n = 13 participants); ‘object complexity’ (n = 6 participants) and ‘object–affect fusion’ (n = 4 participants). The clusters did not markedly differ with regard to hoarding severity, anxiety, depression or impulsivity. Conclusions: Whilst the participant clusters reflect extant research evidence, they also reveal significant heterogeneity and so prompt the need for further research investigating emotional and cognitive differences between people prone to hoarding

Prevalence of hoarding disorder: A systematic review and meta-analysis

Currently there is uncertainty concerning the prevalence of Hoarding Disorder (HD) due to methodological issues in the evidence base. Estimates have widely ranged from between 1.5% and 6% of the general population. This systematic review and meta-analysis therefore aimed to summarise and reliably estimate the prevalence of HD by employing strict inclusion criteria and using studies with sufficiently large samples. A systematic literature search was conducted to identify all relevant prevalence studies. Inclusion criteria were studies that reported working age adult HD prevalence rates and had sample sizes of at least 1009 participants. Eleven studies met criteria (n = 53,378), had low risk of bias and were originally based in developed countries. A random effects meta-analysis was then conducted, with subgroup moderator analysis and meta-regression. The pooled estimated prevalence for HD was 2.5% (CI 1.7–3.6%) and subgroup analyses revealed that prevalence rates were similar for both males and females. Guidance on the manner in which HD is assessed in future prevalence studies is provided and the clinical implications of the results discussed

Enhanced formation of giant cells in common variable immunodeficiency: Relation to granulomatous disease.

Peripheral monocytes from patients with common variable immunodeficiency (CVID) had on average a 2 fold greater tendency to form giant cells in medium without additional cytokines. Giant cell formation was faster and 3 to 5 fold higher in most CVID cells compared to normal. Addition of IL4, GMCSF, IFNγ, TNFa and both T cell and monocyte conditioned media promoted monocyte fusion of some CVID individuals over 5 fold the normal average level, with combinations of cytokines and monokines acting synergistically. The reduction of normal giant cell formation by anti-IFNγ antibody and a greater tendency of CVID cells to fuse in immunoglobulin conditioned media suggests that standard IVIg treatment contributes to granuloma formation. CVID and normal giant cells expressed similar levels of phenotypic molecules and had similar phagocytic activity. Monocytes from many CVID patients have an elevated tendency to fuse which may explain the high incidence of granulomatous complications in CVID

Responses of normal and malignant cells to collagen, collagen-derived peptides and the C5-related tumor cell chemotactic peptide

Two variant subpopulations of murine fibrosarcoma cells that differ significantly in their malignant potential and normal mouse fibroblasts were compared with regard to ability to respond chemotactically to collagen, collagen-derived peptides and the C5-derived tumor cell chemotactic peptide. Two distinct patterns of responsiveness were observed. The normal fibroblasts and non-metastasizing fibrosarcoma cells responded to the collagen products but not the C5 peptide. The metastasizing fibrosarcoma cells responded to the C5 peptide but not to the collagen products. These findings emphasize the similarities between the normal fibroblasts and the non-metastasizing fibrosarcoma cells.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24181/1/0000440.pd