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Perfect isometries and the Alperin-McKay conjecture
Get PDFWe give a brief survey of results and conjectures concerning the local determination of invariants of Brauer p-blocks of finite groups. We highlight the connections between the various conjectures, in particular those of Alperin-McKay and of Broue, and identify where further conjectures have to be made. We focus on the problem of generalising Broue's conjecture, and suggest a
generalisation of the idea of a perfect isometry. Finally we present evidence that such a generalised perfect isometry should exist in certain cases
Antigenicity and immunogenicity of HIV-1 consensus subtype B envelope glycoproteins
No full text“Centralized” (ancestral and consensus) HIV-1 envelope immunogens induce broadly cross-reactive T cell responses in laboratory animals; however, their potential to elicit cross-reactive neutralizing antibodies has not been fully explored. Here, we report the construction of a panel of consensus subtype B (ConB) envelopes and compare their biologic, antigenic, and immunogenic properties to those of two wild-type Env controls from individuals with early and acute HIV-1 infection. Glycoprotein expressed from full-length (gp160), uncleaved (gp160-UNC), truncated (gp145), and N-linked glycosylation site deleted (gp160-201N/S) versions of the ConB env gene were packaged into virions and, except for the fusion defective gp160-UNC, mediated infection via the CCR5 co-receptor. Pseudovirions containing ConB Envs were sensitive to neutralization by patient plasma and monoclonal antibodies, indicating the preservation of neutralizing epitopes found in contemporary subtype B viruses. When used as DNA vaccines in guinea pigs, ConB and wild-type env immunogens induced appreciable binding, but overall only low level neutralizing antibodies. However, all four ConB immunogens were significantly more potent than one wild-type vaccine at eliciting neutralizing antibodies against a panel of tier 1 and tier 2 viruses, and ConB gp145 and gp160 were significantly more potent than both wild-type vaccines at inducing neutralizing antibodies against tier 1 viruses. Thus, consensus subtype B env immunogens appear to be at least as good as, and in some instances better than, wild-type B env immunogens at inducing a neutralizing antibody response, and are amenable to further improvement by specific gene modifications
On the Definition of Two Natural Classes of Scalar Product
No full textWe identify two natural classes of scalar product, termed unitary and
orthosymmetric, which serve to unify
assumptions for the existence of
structured factorizations, iterations and mappings.
A variety of different characterizations of these scalar product classes is
given
Curve Crossing for the Reflected Levy Process at zero and infinity
Get PDFLet Rt = sup0st Xs −Xt be a L´evy process reflected in its maximum.
We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at zero and infinity. Information,
as to when the expected passage time for Rt is finite, is
given
Snaking of multiple homoclinic orbits in reversible systems
Get PDFWe study N-homoclinic orbits near a heteroclinic cycle in a reversible system. The cycle is assumed to connect two equilibria of saddle-focus type. Using Lin's method we establish the existence of infinitely many N-homoclinic orbits for each N near the cycle. In particular, these orbits exist along snaking curves, thus mirroring the behaviour one-homoclinic orbits.
The general analysis is illustrated by numerical studies for a Swift-Hohenberg system
Complex cobordism classes of homogeneous spaces
Get PDFWe consider compact homogeneous spaces of positive Euler characteristic endowed with an invariant almost complex structure and the canonical action of the maximal torus on . We obtain explicit formula for the cobordism class of such manifold through the weights of the action at the identity
fixed point by an action of the quotient group of the Weyl groups for and . In this way we show that the cobordism class for such manifolds can be computed explicitly without information on their cohomology. We also show that formula for cobordism class provides an explicit way for computing the classical Chern numbers for . As a consequence we obtain that the Chern numbers for can be computed without information on cohomology for . As an application we provide an
explicit formula for cobordism classes and characteristic numbers of the flag manifolds , Grassmann manifolds and some particular interesting examples. This paper is going to have continuation in which will be considered the stable complex structures equivariant under given torus action on homogeneous spaces of positive Euler characteristic
Optimal scaling of generalized and polynomial eigenvalue problems
Get PDFScaling is a commonly used technique for standard
eigenvalue problems to improve the sensitivity of the eigenvalues.
In this paper we investigate scaling for generalized and polynomial
eigenvalue problems (PEPs) of arbitrary degree. It is shown that an optimal diagonal
scaling of a PEP with respect to an eigenvalue can be
described by the ratio of its normwise and componentwise condition
number. Furthermore, the effect of linearization on optimally scaled polynomials is investigated.
We introduce a generalization of the diagonal scaling by Lemonnier and Van Dooren to PEPs that is especially effective if some information about the magnitude of the wanted eigenvalues is available and also discuss variable transformations of the type λ = αμ for PEPs of arbitrary degree
On Émery's Inequality and a Variation-of-Constants Formula
No full textA generalization of Émery's inequality for stochastic integrals is shown for convolution integrals of the form
, where Z is a semimartingale, Y an adapted càdlàg process, and g a deterministic function. An even more general inequality for processes with two parameters is proved. The inequality is used to prove existence and uniqueness of solutions of equations of variation-of-constants type. As a consequence, it is shown that the solution of a semilinear delay differential equation with functional Lipschitz diffusion coefficient and driven by a general semimartingale satisfies a variation-of-constants formula
On the problem of stochastic integral representations of functions of the Brownian motion II
Get PDFIn the first part of this paper [A. N. Shiryaev and M. Yor, Theory Probab. Appl., 48 (2004), pp. 304–313], a method of obtaining stochastic integral representations of functionals of Brownian motion was stated. Functionals and , where , , were considered as an illustration. In the present paper we state another derivation of representations for these functionals and two proofs of representation for functional , where (non-Markov time) are given