8,596 research outputs found
Embeddings of homogeneous spaces in prime characteristics
Let be a reductive linear algebraic group. The simplest example of a
projective homogeneous -variety in characteristic , not isomorphic to a
flag variety, is the divisor in , which is modulo a non-reduced stabilizer containing the upper
triangular matrices. In this paper embeddings of projective homogeneous spaces
viewed as , where is any subgroup scheme containing a Borel subgroup,
are studied. We prove that can be identified with the orbit of the
highest weight line in the projective space over the simple -representation
of a certain highest weight . This leads to some strange
embeddings especially in characteristic , where we give an example in the
-case lying on the boundary of Hartshorne's conjecture on complete
intersections. Finally we prove that ample line bundles on are very
ample. This gives a counterexample to Kodaira type vanishing with a very ample
line bundle, answering an old question of Raynaud.Comment: 10 pages, AMS-LaTe
The Perturbed Static Path Approximation at Finite Temperature: Observables and Strength Functions
We present an approximation scheme for calculating observables and strength
functions of finite fermionic systems at finite temperature such as hot nuclei.
The approach is formulated within the framework of the Hubbard-Stratonovich
transformation and goes beyond the static path approximation and the RPA by
taking into account small amplitude time-dependent fluctuations around each
static value of the auxiliary fields. We show that this perturbed static path
approach can be used systematically to obtain good approximations for
observable expectation values and for low moments of the strength function. The
approximation for the strength function itself, extracted by an analytic
continuation from the imaginary-time response function, is not always reliable,
and we discuss the origin of the discrepancies and possible improvements. Our
results are tested in a solvable many-body model.Comment: 37 pages, 8 postscript figures included, RevTe
Role of the Pension Protection Fund in financial risk management of UK defined benefit pension sector: a multi-period economic capital study
With the advent of formal regulatory requirements for rigorous risk-based, or economic, capital quantification for the financial risk management of banking and insurance sectors, regulators and policy-makers are turning their attention to the pension sector, the other integral player in the financial markets. In this paper, we analyse the impact of applying economic capital techniques to defined benefit pension schemes in the United Kingdom. We propose two alternative economic capital quantification approaches, first, for individual defined benefit pension schemes on a stand-alone basis and then for the pension sector as a whole by quantifying economic capital of the UK’s Pension Protection Fund, which takes over eligible schemes with deficit, in the event of sponsor insolvency. We find that economic capital requirements for individual schemes are significantly high. However, we show that sharing risks through the Pension Protection Fund reduces the aggregate economic capital requirement of the entire sector
Computational aspects of DNA mixture analysis
Statistical analysis of DNA mixtures is known to pose computational
challenges due to the enormous state space of possible DNA profiles. We propose
a Bayesian network representation for genotypes, allowing computations to be
performed locally involving only a few alleles at each step. In addition, we
describe a general method for computing the expectation of a product of
discrete random variables using auxiliary variables and probability propagation
in a Bayesian network, which in combination with the genotype network allows
efficient computation of the likelihood function and various other quantities
relevant to the inference. Lastly, we introduce a set of diagnostic tools for
assessing the adequacy of the model for describing a particular dataset
Unifying Markov Properties for Graphical Models
Several types of graphs with different conditional independence
interpretations --- also known as Markov properties --- have been proposed and
used in graphical models. In this paper we unify these Markov properties by
introducing a class of graphs with four types of edges --- lines, arrows, arcs,
and dotted lines --- and a single separation criterion. We show that
independence structures defined by this class specialize to each of the
previously defined cases, when suitable subclasses of graphs are considered. In
addition, we define a pairwise Markov property for the subclass of chain mixed
graphs which includes chain graphs with the LWF interpretation, as well as
summary graphs (and consequently ancestral graphs). We prove the equivalence of
this pairwise Markov property to the global Markov property for compositional
graphoid independence models.Comment: 31 Pages, 6 figures, 1 tabl
Markov properties for mixed graphs
In this paper, we unify the Markov theory of a variety of different types of
graphs used in graphical Markov models by introducing the class of loopless
mixed graphs, and show that all independence models induced by -separation
on such graphs are compositional graphoids. We focus in particular on the
subclass of ribbonless graphs which as special cases include undirected graphs,
bidirected graphs, and directed acyclic graphs, as well as ancestral graphs and
summary graphs. We define maximality of such graphs as well as a pairwise and a
global Markov property. We prove that the global and pairwise Markov properties
of a maximal ribbonless graph are equivalent for any independence model that is
a compositional graphoid.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ502 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Discussion: Latent variable graphical model selection via convex optimization
Discussion of "Latent variable graphical model selection via convex
optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky
[arXiv:1008.1290].Comment: Published in at http://dx.doi.org/10.1214/12-AOS980 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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