358 research outputs found
Subalgebras with Converging Star Products in Deformation Quantization: An Algebraic Construction for \complex \mbox{\LARGE P}^n
Based on a closed formula for a star product of Wick type on \CP^n, which
has been discovered in an earlier article of the authors, we explicitly
construct a subalgebra of the formal star-algebra (with coefficients contained
in the uniformly dense subspace of representative functions with respect to the
canonical action of the unitary group) that consists of {\em converging} power
series in the formal parameter, thereby giving an elementary algebraic proof of
a convergence result already obtained by Cahen, Gutt, and Rawnsley. In this
subalgebra the formal parameter can be substituted by a real number :
the resulting associative algebras are infinite-dimensional except for the case
, a positive integer, where they turn out to be isomorphic to
the finite-dimensional algebra of linear operators in the th energy
eigenspace of an isotropic harmonic oscillator with degrees of freedom.
Other examples like the -torus and the Poincar\'e disk are discussed.Comment: 16 pages, LaTeX with AMS Font
A Boolean Gene Regulatory Model of heterosis and speciation
Modelling genetic phenomena affecting biological traits is important for the
development of agriculture as it allows breeders to predict the potential of
breeding for certain traits. One such phenomenon is heterosis or hybrid vigor:
crossing individuals from genetically distinct populations often results in
improvements in quantitative traits, such as growth rate, biomass production
and stress resistance. Heterosis has become a very useful tool in global
agriculture, but its genetic basis remains controversial and its effects hard
to predict. We have taken a computational approach to studying heterosis,
developing a simulation of evolution, independent reassortment of alleles and
hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework.
Fitness is measured as the ability of a network to respond to external inputs
in a pre-defined way. Our model reproduced common experimental observations on
heterosis using only biologically justified parameters. Hybrid vigor was
observed and its extent was seen to increase as parental populations diverged,
up until a point of sudden collapse of hybrid fitness. We also reproduce, for
the first time in a model, the fact that hybrid vigor cannot easily be fixed by
within a breeding line, currently an important limitation of the use of hybrid
crops. The simulation allowed us to study the effects of three standard models
for the genetic basis of heterosis and the level of detail in our model allows
us to suggest possible warning signs of the impending collapse of hybrid vigor
in breeding. In addition, the simulation provides a framework that can be
extended to study other aspects of heterosis and alternative evolutionary
scenarios.Comment: See online version for supplementary materia
Purification and analytical characterization of an anti- CD4 monoclonal antibody for human therapy
A purification process for the monclonal anti-CD4 antibody MAX.16H5 was developed on an analytical scale using (NH&SO,
precipitation, anion-exchange chromatography on MonoQ or Q-Sepharose, hydrophobic interaction chromatography on phenyl-
Sepharose and gel filtration chromatography on Superdex 200. The purification schedule was scaled up and gram amounts of
MAX.16H5 were produced on corresponding BioPilot columns. Studies of the identity, purity and possible contamination by a
broad range of methods showed that the product was highly purified and free from contaminants such as mouse DNA, viruses,
pyrogens and irritants. Overall, the analytical data confirm that the monoclonal antibody MAX.16H5 prepared by this protocol is
suitable for human therapy
Phase Space Reduction for Star-Products: An Explicit Construction for CP^n
We derive a closed formula for a star-product on complex projective space and
on the domain using a completely elementary
construction: Starting from the standard star-product of Wick type on and performing a quantum analogue of Marsden-Weinstein
reduction, we can give an easy algebraic description of this star-product.
Moreover, going over to a modified star-product on ,
obtained by an equivalence transformation, this description can be even further
simplified, allowing the explicit computation of a closed formula for the
star-product on \CP^n which can easily transferred to the domain
.Comment: LaTeX, 17 page
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