Witt kernels of quadratic forms for multiquadratic extensions in characteristic 2

Let $F$ be a field of characteristic $2$ and let $K/F$ be a purely inseparable extension of exponent $1$. We show that the extension is excellent for quadratic forms. Using the excellence we recover and extend results by Aravire and Laghribi who computed generators for the kernel $W_q(K/F)$ of the natural restriction map $W_q(F)\to W_q(K)$ between the Witt groups of quadratic forms of $F$ and $K$, respectively, where $K/F$ is a finite multiquadratic extension of separability degree at most $2$.Comment: 9 page

The Symmetrical Immune Network Theory and a New HIV Vaccine Concept

The symmetrical immune network theory is based on Jerne’s network hypothesis. An improved version of the theory is presented. The theory is characterized by symmetrical stimulatory, inhibitory and killing interactions between idiotypic and antiidiotypic immune system components. In this version killing is ascribed to IgM antibodies, while IgG antibodies are stimulatory. In the symmetrical immune network theory T cells make specific T cell factors, that have a single V region, and are cytophilic for non-specific accessory cells (A cells, including macrophages and monocytes) and play a role in the system switching between stable steady states. A recurring theme in the theory is the concept of co selection. Co-selection is the mutual positive selection of individual members from within two diverse populations, such that selection of members within each population is dependent on interaction with (recognition of) one or more members within the other population. Prior to exposure to an antigen, antigen-specific and antiidiotypic T cells are equally diverse. This equality is a form of symmetry. Immune responses with the production of IgG involve co selection of the antigen-specific and antiidiotypic classes with the breaking of this diversity symmetry, while induction of unresponsiveness involves co-selection without the breaking of diversity symmetry. The theory resolves the famous I-J paradox of the 1980s, based on co selection of helper T cells with some affinity for MHC class II and suppressor T cells that are anti-anti-MHC class II. The theory leads to three experimentally testable predictions concerning I-J. The theory includes a model for HIV pathogenesis, and suggests that polyclonal IgG from many donors given in immunogenic form may be an effective vaccine for protection against infection with HIV. Surprisingly, a mathematical model that simulates the autonomous dynamics of the system is the same as one that models a previously described neural network

MHC Restriction of V-V Interactions in Serum IgG

According to Jerne’s idiotypic network hypothesis, the adaptive immune system is regulated by interactions between the variable regions of antibodies, B cells, and T cells. The symmetrical immune network theory is based on Jerne’s hypothesis, and provides a basis for understanding many of the phenomena of adaptive immunity. The theory includes the postulate that the repertoire of serum IgG molecules is regulated by T cells, with the result that IgG molecules express V region determinants that mimic V region determinants present on suppressor T cells. In this paper we describe rapid binding between purified murine serum IgG of H-2b and H-2d mice and serum IgG from the same strain and from MHC-matched mice, but not between serum IgG preparations of mice with different MHC genes. We interpret this surprising finding in terms of a model in which IgG molecules are selected to have both anti-anti-self MHC and anti-anti-anti-self MHC specificity

Witt kernels and Brauer kernels for quartic extensions in characteristic two

Let $F$ be a field of characteristic $2$ and let $E/F$ be a field extension of degree $4$. We determine the kernel $W_q(E/F)$ of the restriction map $W_qF\to W_qE$ between the Witt groups of nondegenerate quadratic forms over $F$ and over $E$, completing earlier partial results by Ahmad, Baeza, Mammone and Moresi. We also deduct the corresponding result for the Witt kernel $W(E/F)$ of the restriction map $WF\to WE$ between the Witt rings of nondegenerate symmetric bilinear forms over $F$ and over $E$ from earlier results by the first author. As application, we describe the $2$-torsion part of the Brauer kernel for such extensions