Chaos in the Takens-Bogdanov bifurcation with O(2) symmetry

The Takens–Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation invariant in one spatial dimension with no left-right preference the imposition of periodic boundary conditions leads to the Takens–Bogdanov bifurcation with O(2) symmetry. This bifurcation, analyzed by G. Dangelmayr and E. Knobloch, Phil. Trans. R. Soc. London A 322, 243 (1987), describes the interaction between steady states and traveling and standing waves in the nonlinear regime and predicts the presence of modulated traveling waves as well. The analysis reveals the presence of several global bifurcations near which the averaging method (used in the original analysis) fails. We show here, using a combination of numerical continuation and the construction of appropriate return maps, that near the global bifurcation that terminates the branch of modulated traveling waves, the normal form for the Takens–Bogdanov bifurcation admits cascades of period-doubling bifurcations as well as chaotic dynamics of Shil’nikov type. Thus chaos is present arbitrarily close to the codimension two point

ANCA-associated vasculitis.

The anti-neutrophil cytoplasmic antibody (ANCA)-associated vasculitides (AAVs) are a group of disorders involving severe, systemic, small-vessel vasculitis and are characterized by the development of autoantibodies to the neutrophil proteins leukocyte proteinase 3 (PR3-ANCA) or myeloperoxidase (MPO-ANCA). The three AAV subgroups, namely granulomatosis with polyangiitis (GPA), microscopic polyangiitis and eosinophilic GPA (EGPA), are defined according to clinical features. However, genetic and other clinical findings suggest that these clinical syndromes may be better classified as PR3-positive AAV (PR3-AAV), MPO-positive AAV (MPO-AAV) and, for EGPA, by the presence or absence of ANCA (ANCA+ or ANCA-, respectively). Although any tissue can be involved in AAV, the upper and lower respiratory tract and kidneys are most commonly and severely affected. AAVs have a complex and unique pathogenesis, with evidence for a loss of tolerance to neutrophil proteins, which leads to ANCA-mediated neutrophil activation, recruitment and injury, with effector T cells also involved. Without therapy, prognosis is poor but treatments, typically immunosuppressants, have improved survival, albeit with considerable morbidity from glucocorticoids and other immunosuppressive medications. Current challenges include improving the measures of disease activity and risk of relapse, uncertainty about optimal therapy duration and a need for targeted therapies with fewer adverse effects. Meeting these challenges requires a more detailed knowledge of the fundamental biology of AAV as well as cooperative international research and clinical trials with meaningful input from patients

Learning on a torus

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Empathic-like responding by domestic dogs (Canis familiaris) to distress in humans: An exploratory study

Empathy covers a range of phenomena from cognitive empathy involving metarepresentation to emotional contagion stemming from automatically triggered reflexes. An experimental protocol first used with human infants was adapted to investigate empathy in domestic dogs. Dogs oriented toward their owner or a stranger more often when the person was pretending to cry than when they were talking or humming. Observers, unaware of experimental hypotheses and the condition under which dogs were responding, more often categorized dogs’ approaches as submissive as opposed to alert, playful or calm during the crying condition. When the stranger pretended to cry, rather than approaching their usual source of comfort, their owner, dogs sniffed, nuzzled and licked the stranger instead. The dogs’ pattern of response was behaviorally consistent with an expression of empathic concern, but is most parsimoniously interpreted as emotional contagion coupled with a previous learning history in which they have been rewarded for approaching distressed human companions