One-dimensional point interaction with three complex parameters

For a pair of non-Hermitian Hamiltonian H and its Hermitian adjoint H(dagger), there are situations in which their eigenfunctions form a biorthogonal system. We illustrate such a situation by means of a one-particle system with a one-dimensional point interaction in the form of the Fermi pseudo-potential. The interaction consists of three terms with three strength parameters g(i) (i = 1, 2 and 3), which are all complex. This complex point interaction is neither Hermitian nor PT-invariant in general. The S-matrix for the transmission reflection problem constructed with H (or with H(dagger)) in the usual manner is not unitary, but it conforms to the pseudo-unitarity that we define. The pseudounitarity is closely related to the biorthogonality of the eigenfunctions. The eigenvalue spectrum of H with the complex interaction is generally complex but there are cases where the spectrum is real. In such a case H and H(dagger) form a pseudo-Hermitian pair.

Humoral responses and immune protection in mice immunized with irradiated T. gondii tachyzoites and challenged with three genetically distinct strains of T. gondii

Toxoplasma gondii is an obligate intracellular parasite that infects a variety of mammals and birds. T. gondii also causes human toxoplasmosis; although toxoplasmosis is generally a benign disease, ocular, congenital or reactivated disease is associated with high numbers of disabled people. Infection occurs orally through the ingestion of meat containing cysts or by the intake of food or water contaminated with oocysts. Although the immune system responds to acute infection and mediates the clearance of tachyzoites, parasite cysts persist for the lifetime of the host in tissues such as the eye, muscle, and CNS. However, T. gondii RH strain tachyzoites irradiated with 255 Gy do not cause residual infection and induce the same immunity as a natural infection. To assess the humoral response in BALB/c and C57BL/6J mice immunized with irradiated tachyzoites either by oral gavage (p.o.) or intraperitoneal (i.p.) injection, we analyzed total and high-affinity IgG and IgA antibodies in the serum. High levels of antigen-specific IgG were detected in the serum of parenterally immunized mice, with lower levels in mice immunized via the oral route. However, most serum antibodies exhibited low affinity for antigen in both mice strain. We also found antigen specific IgA antibodies in the stools of the mice, especially in orally immunized BALB/c mice. Examination of bone marrow and spleen cells demonstrated that both groups of immunized mice clearly produced specific lgG, at levels comparable to chronic infection, suggesting the generation of IgG specific memory. Next, we challenged i.p. or p.o. immunized mice with cysts from ME49. VEG or P strains of T. gondii. Oral immunization resulted in partial protection as compared to challenged naive mice: these findings were more evident in highly pathogenic ME49 strain challenge. Additionally, we found that while mucosal IgA was important for protection against infection, antigen-specific IgG antibodies were involved with protection against disease and disease pathogenesis. Most antigen responsive cells in culture produced specific high-affinity IgG after immunization, diverse of the findings in serum IgG or from cells after infection, which produced low proportion of high-avidity IgG. (C) 2011 Elsevier B.V. All rights reserved.