Stage progression and neurological symptoms in Trypanosoma brucei rhodesiense sleeping sickness: role of the CNS inflammatory response

Background: Human African trypanosomiasis progresses from an early (hemolymphatic) stage, through CNS invasion to the late (meningoencephalitic) stage. In experimental infections disease progression is associated with neuroinflammatory responses and neurological symptoms, but this concept requires evaluation in African trypanosomiasis patients, where correct diagnosis of the disease stage is of critical therapeutic importance. Methodology/Principal Findings: This was a retrospective study on a cohort of 115 T.b.rhodesiense HAT patients recruited in Eastern Uganda. Paired plasma and CSF samples allowed the measurement of peripheral and CNS immunoglobulin and of CSF cytokine synthesis. Cytokine and immunoglobulin expression were evaluated in relation to disease duration, stage progression and neurological symptoms. Neurological symptoms were not related to stage progression (with the exception of moderate coma). Increases in CNS immunoglobulin, IL-10 and TNF-α synthesis were associated with stage progression and were mirrored by a reduction in TGF-β levels in the CSF. There were no significant associations between CNS immunoglobulin and cytokine production and neurological signs of disease with the exception of moderate coma cases. Within the study group we identified diagnostically early stage cases with no CSF pleocytosis but intrathecal immunoglobulin synthesis and diagnostically late stage cases with marginal CSF pleocytosis and no detectable trypanosomes in the CSF. Conclusions: Our results demonstrate that there is not a direct linkage between stage progression, neurological signs of infection and neuroinflammatory responses in rhodesiense HAT. Neurological signs are observed in both early and late stages, and while intrathecal immunoglobulin synthesis is associated with neurological signs, these are also observed in cases lacking a CNS inflammatory response. While there is an increase in inflammatory cytokine production with stage progression, this is paralleled by increases in CSF IL-10. As stage diagnostics, the CSF immunoglobulins and cytokines studied do not have sufficient sensitivity to be of clinical value

Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $\Omega_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deformations of (N-1)-dimensional linear subspaces. For the class of solutions which are Laurent polynomials in one variable these systems coincide with N-dimensional integrable systems such as Liouville equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3), dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4) and others. Gauge invariant part of the forms $\Omega_{N-1}$ provides us with the compact form of the corresponding hierarchies. Dual quasi-linear systems associated with the projectively dual Grassmannians Gr(2,N+1) are defined via the requirement of the closedness of the dual forms $\Omega_{N-1}^{\star}$. It is shown that at N=3 the self-dual quasi-linear system, which is associated with the harmonic (closed and co-closed) form $\Omega_{2}$, coincides with the Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde

Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group

The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we firstly consider the needed general theory and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.Comment: 35 pages, REVTEX, 1 figure, Phys. Rev. E, submitte

Phase transition curves for mesoscopic superconducting samples

We compute the phase transition curves for mesoscopic superconductors. Special emphasis is given to the limiting shape of the curve when the magnetic flux is large. We derive an asymptotic formula for the ground state of the Schr\"odinger equation in the presence of large applied flux. The expansion is shown to be sensitive to the smoothness of the domain. The theoretical results are compared to recent experiments.Comment: 8 pages, 1 figur

Onset of Superconductivity in Decreasing Fields for General Domains

Ginzburg–Landau theory has provided an effective method for understanding the onset of superconductivity in the presence of an external magnetic field. In this paper we examine the instability of the normal state to superconductivity with decreasing magnetic field for a closed smooth cylindrical region of arbitrary cross-section subject to a vertical magnetic field. We examine the problem asymptotically in the boundary layer limit (i.e., when the Ginzburg–Landau parameter, k, is large). We demonstrate that instability first occurs in a region exponentially localized near the point of maximum curvature on the boundary. The transition occurs at a value of the magnetic field associated with the half-plane at leading order, with a small positive correction due to the curvature (which agrees with the transition problem for the disc), and a smaller correction due to the second derivative of the curvature at the maximum