Creation of discontinuities in circle maps.

Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and 'threshold' systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake regulation, we consider how structural transitions in circle maps occur. In particular, we describe how maps evolve near the creation of a discontinuity. We show that the natural way to create discontinuities in the maps associated with both threshold systems and Cherry flows results in a singularity in the derivative of the map as the discontinuity is approached from either one or both sides. For the threshold systems, the associated maps have square root singularities and we analyse the generic properties of such maps with gaps, showing how border collisions and saddle-node bifurcations are interspersed. This highlights how the Arnold tongue picture for tongues bordered by saddle-node bifurcations is amended once gaps are present. We also show that a loss of injectivity naturally results in the creation of multiple gaps giving rise to a novel codimension two bifurcation.

Transverse instability and its long-term development for solitary waves of the (2+1)-dimensional Boussinesq equation.

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multisymplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wave number is small. The Evans function is then computed explicitly, giving the eigenvalues for the transverse instability for all transverse wave numbers. To determine the nonlinear and long-time implications of the transverse instability, numerical simulations are performed using pseudospectral discretization. The numerics confirm the analytic results, and in all cases studied, the transverse instability leads to collapse.

Encephalocytozoon intestinalis-specific monoclonal antibodies for laboratory diagnosis of microsporidiosis.

Two monoclonal antibodies which can be used for the unambiguous identification by fluorescence microscopy of Encephalitozoon intestinalis spores in clinical specimens are described. Monoclonal antibody Si91 is specific for the extruded polar filament, and Si13 recognizes the surfaces of E. intestinalis spores. No cross-reaction with spores of Encephalitozoon hellem was observed. Immunogold electron microscopy confirmed the specific reactivities of both antibodies. Combined in an indirect immunofluorescence assay, these antibodies are used to identify spores in feces. Although there was some cross-reaction with fecal bacteria and fungi, the typical morphology of the extruded polar filaments enabled proper identification of the E. intestinalis spores. Parasites could also be demonstrated to be present in urine, nasal swabs, lung brush biopsy specimens, and bronchoalveolar lavage fluid from a patient with disseminated infection with E. intestinalis. The use of these monoclonal antibodies facilitates the detection and species determination of E. intestinalis in clinical specimens.