Singularities of bi-Hamiltonian systems

We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with a fixed 2-cocycle. In terms of such linearizations, we give a criterion for non-degeneracy of singular points of bi-Hamiltonian systems and describe their types

Rapid entry and downregulation of T Cells in the central nervous system During the reinduction of experimental autoimmune encephalomyelitis

We investigated the mechanisms whereby a previous attack of experimental autoimmune encephalomyelitis (EAE) modifies a subsequent attack in the Lewis rat. Active immunization with myelin basic protein (MBP) and complete Freund's adjuvant 28 days after the passive transfer of MBP-sensitized spleen cells induced a second episode of EAE, which occurred earlier than in naive control animals, but was less severe overall. The pattern of neurological signs was also different in rechallenged rats, which had less severe tail and hindlimb weakness but more severe forelimb weakness. In rechallenged rats, inflammation was more severe in the cervical spinal cord, cerebellum, brainstem and cerebrum, but less severe in the lumbar spinal cord, than in controls. The early onset of EAE in rechallenged rats was explained by a memory T cell response to MBP72-89 in the draining lymph node and spleen, and by the enhanced entry of T cells into the central nervous system (CNS). However, the number of alpha beta T cells in the spinal cord of rechallenged rats declined faster than in controls, especially in the lumbosacral cord, where the number of V beta 8.2+ T cells and the frequency of T cells reactive to MBP72-89 rapidly decreased, indicating rapid downregulation of the immune response in the previously inflamed spinal cord. Apoptosis of inflammatory cells in the CNS was increased in the rechallenged rats and is likely to contribute to this downregulation. Furthermore, during the disease course the generation of encephalitogenic T cells in the peripheral lymphoid organs was limited compared with controls. Thus, a previous attack of EAE modifies a subsequent attack through the interaction of the following processes: a memory T cell response to MBP; facilitated T cell entry into the CNS; downregulation of the immune response in the CNS, including increased apoptosis of inflammatory cells; and a limited generation of encephalitogenic T cells in the peripheral lymphoid organs

Hybrid gap plasmon GaAs nanolasers

Compact semiconductor lasers with sub-wavelength-scale dimensions rely heavily on materials with low surface recombination due to the large surface area to volume ratios of their nano-cavities. Furthermore, the reliance on semiconductor nanostructures has led to predominantly bottom-up fabrication approaches, which has hindered scalable and practical applications. In this letter, we present lithographically constructed hybrid gap plasmon nanolasers using the gain of bulk GaAs operating at room temperature. The nanolasers are built on GaAs suspended membranes with InGaP passivation layers. Laser resonators are defined only by patterning gold on top of these GaAs membranes, thus eliminating the need to etch the semiconductor for optical confinement, which would intro duce additional surface recombination. An analysis of the modal gain and losses in these devices suggests that threshold carrier densities in the range of 4-5×1018 cm -3 are necessary - potentially achievable with current densities as low as 6-8 kA cm-2

Rapid hepatic clearance of full length CCN-2/CTGF: a putative role for LRP1-mediated endocytosis

CCN-2 (connective tissue growth factor; CTGF) is a key factor in fibrosis. Plasma CCN-2 has biomarker potential in numerous fibrotic disorders, but it is unknown which pathophysiological factors determine plasma CCN-2 levels. The proteolytic amino-terminal fragment of CCN-2 is primarily eliminated by the kidney. Here, we investigated elimination and distribution profiles of full length CCN-2 by intravenous administration of recombinant CCN-2 to rodents. After bolus injection in mice, we observed a large initial distribution volume (454 mL/kg) and a fast initial clearance (120 mL/kg/min). Immunosorbent assay and immunostaining showed that CCN-2 distributed mainly to the liver and was taken up by hepatocytes. Steady state clearance in rats, determined by continuous infusion of CCN-2, was fast (45 mL/kg/min). Renal CCN-2 clearance, determined by arterial and renal vein sampling, accounted for only 12 % of total clearance. Co-infusion of CCN-2 with receptor-associated protein (RAP), an antagonist of LDL-receptor family proteins, showed that RAP prolonged CCN-2 half-life and completely prevented CCN-2 internalization by hepatocytes. This suggests that hepatic uptake of CCN-2 is mediated by a RAP-sensitive mechanism most likely involving LRP1, a member of the LDL-receptor family involved in hepatic clearance of various plasma proteins. Surface plasmon resonance binding studies confirmed that CCN-2 is an LRP1 ligand. Co-infusion of CCN-2 with an excess of the heparan sulphate-binding protamine lowered the large initial distribution volume of CCN-2 by 88 % and reduced interstitial staining of CCN-2, suggesting binding of CCN-2 to heparan sulphate proteoglycans (HSPGs). Protamine did not affect clearance rate, indicating that RAP-sensitive clearance of CCN-2 is HSPG independent. In conclusion, unlike its amino-terminal fragment which is cleared by the kidney, fu

Apoptosis in the Nervous System in Experimental Allergic Encephalomyelitis

We report here for the first time the occurrence of apoptosis of cells in the spinal cord in experimental allergic encephalomyelitis (EAE), an autoimmune, T-cell-mediated demyelinating disease. Four different forms of EAE were studied in the Lewis rat: (i) acute EAE induced by inoculation with whole spinal cord and adjuvants; (ii) acute EAE induced by inoculation with myelin basic protein (MBP) and adjuvants; (iii) acute EAE induced by the passive transfer of MBP-sensitized spleen cells; (iv) chronic relapsing EAE induced by inoculation with whole spinal cord and adjuvants followed by treatment with low-dose cyclosporin A. Cells undergoing apoptosis were recognized at light and electron microscopy by the presence of either crescentic masses of condensed chromatin lying against the nuclear envelope or rounded masses of uniformly dense chromatin. They were found in both the white and grey matter of the spinal cord in all 4 forms of this disease. Although it was not possible to identify definitively the types of cells undergoing apoptosis, the size and location of some of the affected cells suggested that they were oligodendrocytes. As there is now a large body of evidence that T-cell-induced target cell death takes the form of apoptosis, it is attractive to hypothesize that oligodendrocyte apoptosis is occurring in EAE as a result of oligodendrocyte-directed T-cell cytotoxicity. However, other apoptotic cells were located within the myelin sheath, meninges and perivascular spaces and were clearly not oligodendrocytes but were most likely blood-derived mononuclear cells. The sparsity of their cytoplasm and the absence of phagocytosed material suggested that they were mainly lymphocytes rather than macrophages. Apoptosis has been shown to be involved in deleting autoreactive T-cells during the normal development of tolerance. Thus apoptotic deletion of myelin/oligodendrocyte-specific lymphocytes in the central nervous system in EAE might explain both the subsidence of inflammation and the acquisition of tolerance in this autoimmune disease

Helicoidal surfaces rotating/translating under the mean curvature flow

We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.Comment: 21 pages, 22 figures, final versio

Random Exchange Quantum Heisenberg Chains

The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite size systems.Comment: 13 pages, RevTex, 12 figures available on request ([email protected]

The Effects of Prophylactic Cyclosporin A on Experimental Allergic Neuritis (EAN) in the Lewis Rat: Induction of Relapsing EAN Using Low Dose Cyclosporin A

Experimental allergic neuritis (EAN) was induced in Lewis rats by inoculation with bovine intradural root myelin plus adjuvants. Animals treated with high dose (30 mg/kg) cyclosporin A (CsA) 3 times per week did not develop clinical EAN during the period of CsA treatment, but had an episode of EAN after cessation of CsA treatment. Animals treated with low dose (4 mg/kg) CsA 3 times per week developed EAN during the period of treatment, and after cessation of CsA treatment all of these animals developed relapsing EAN with disease continuing for up to four episodes. In contrast, 30-40% of untreated animals had a mild second episode of EAN but no further attacks. Histological studies performed in treated and untreated animals at the time of clinical episodes revealed inflammation and demyelination in the spinal roots and dorsal root ganglia. When animals were challenged with a second inoculation at age 7 months, one of 15 untreated control animals but none of the CsA treated animals developed an episode of EAN