394 research outputs found
High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows
We relate high-energy limits of Laplace-type and Dirac-type operators to
frame flows on the corresponding manifolds, and show that the ergodicity of
frame flows implies quantum ergodicity in an appropriate sense for those
operators. Observables for the corresponding quantum systems are matrix-valued
pseudodifferential operators and therefore the system remains non-commutative
in the high-energy limit. We discuss to what extent the space of stationary
high-energy states behaves classically.Comment: 26 pages, latex2
A comparison of full model specification and backward elimination of potential confounders when estimating marginal and conditional causal effects on binary outcomes from observational data
A common view in epidemiology is that automated confounder selection methods, such as backward elimination, should be avoided as they can lead to biased effect estimates and underestimation of their variance. Nevertheless, backward elimination remains regularly applied. We investigated if and under which conditions causal effect estimation in observational studies can improve by using backward elimination on a prespecified set of potential confounders. An expression was derived that quantifies how variable omission relates to bias and variance of effect estimators. Additionally, 3960 scenarios were defined and investigated by simulations comparing bias and mean squared error (MSE) of the conditional log odds ratio, log(cOR), and the marginal log risk ratio, log(mRR), between full models including all prespecified covariates and backward elimination of these covariates. Applying backward elimination resulted in a mean bias of 0.03 for log(cOR) and 0.02 for log(mRR), compared to 0.56 and 0.52 for log(cOR) and log(mRR), respectively, for a model without any covariate adjustment, and no bias for the full model. In less than 3% of the scenarios considered, the MSE of the log(cOR) or log(mRR) was slightly lower (max 3%) when backward elimination was used compared to the full model. When an initial set of potential confounders can be specified based on background knowledge, there is minimal added value of backward elimination. We advise not to use it and otherwise to provide ample arguments supporting its use.Clinical epidemiolog
Estimating the nuclear level density with the Monte Carlo shell model
A method for making realistic estimates of the density of levels in even-even
nuclei is presented making use of the Monte Carlo shell model (MCSM). The
procedure follows three basic steps: (1) computation of the thermal energy with
the MCSM, (2) evaluation of the partition function by integrating the thermal
energy, and (3) evaluating the level density by performing the inverse Laplace
transform of the partition function using Maximum Entropy reconstruction
techniques. It is found that results obtained with schematic interactions,
which do not have a sign problem in the MCSM, compare well with realistic
shell-model interactions provided an important isospin dependence is accounted
for.Comment: 14 pages, 3 postscript figures. Latex with RevTex. Submitted as a
rapid communication to Phys. Rev.
A geometrical origin for the covariant entropy bound
Causal diamond-shaped subsets of space-time are naturally associated with
operator algebras in quantum field theory, and they are also related to the
Bousso covariant entropy bound. In this work we argue that the net of these
causal sets to which are assigned the local operator algebras of quantum
theories should be taken to be non orthomodular if there is some lowest scale
for the description of space-time as a manifold. This geometry can be related
to a reduction in the degrees of freedom of the holographic type under certain
natural conditions for the local algebras. A non orthomodular net of causal
sets that implements the cutoff in a covariant manner is constructed. It gives
an explanation, in a simple example, of the non positive expansion condition
for light-sheet selection in the covariant entropy bound. It also suggests a
different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio
Local covariant quantum field theory over spectral geometries
A framework which combines ideas from Connes' noncommutative geometry, or
spectral geometry, with recent ideas on generally covariant quantum field
theory, is proposed in the present work. A certain type of spectral geometries
modelling (possibly noncommutative) globally hyperbolic spacetimes is
introduced in terms of so-called globally hyperbolic spectral triples. The
concept is further generalized to a category of globally hyperbolic spectral
geometries whose morphisms describe the generalization of isometric embeddings.
Then a local generally covariant quantum field theory is introduced as a
covariant functor between such a category of globally hyperbolic spectral
geometries and the category of involutive algebras (or *-algebras). Thus, a
local covariant quantum field theory over spectral geometries assigns quantum
fields not just to a single noncommutative geometry (or noncommutative
spacetime), but simultaneously to ``all'' spectral geometries, while respecting
the covariance principle demanding that quantum field theories over isomorphic
spectral geometries should also be isomorphic. It is suggested that in a
quantum theory of gravity a particular class of globally hyperbolic spectral
geometries is selected through a dynamical coupling of geometry and matter
compatible with the covariance principle.Comment: 21 pages, 2 figure
Gupta–Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times
We give a complete framework for the Gupta–Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta–Bleuler representations satisfy the time-slice axiom, and the corresponding vacuum states satisfy the microlocal spectrum condition. We also give an explicit construction of ground states on ultrastatic space-times. Unlike previous constructions, our method does not require a spectral gap or the absence of zero modes. The only requirement, the absence of zero-resonance states, is shown to be stable under compact perturbations of topology and metric. Usual deformation arguments based on the time-slice axiom then lead to a construction of Gupta–Bleuler representations on a large class of globally hyperbolic space-times. As usual, the field algebra is represented on an indefinite inner product space, in which the physical states form a positive semi-definite subspace. Gauge transformations are incorporated in such a way that the field can be coupled perturbatively to a Dirac field. Our approach does not require any topological restrictions on the underlying space-time
Topological features of massive bosons on two dimensional Einstein space-time
In this paper we tackle the problem of constructing explicit examples of
topological cocycles of Roberts' net cohomology, as defined abstractly by
Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum
field theory on the two dimensional Einstein cylinder. After deriving some
crucial results of the algebraic framework of quantization, we address the
problem of the construction of the topological cocycles. All constructed
cocycles lead to unitarily equivalent representations of the fundamental group
of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces).
The construction is carried out using only Cauchy data and related net of local
algebras on the circle.Comment: 41 pages, title changed, minor changes, typos corrected, references
added. Accepted for publication in Ann. Henri Poincare
Chromosomal instability and lack of cyclin E regulation in hCdc4 mutant human breast cancer cells
INTRODUCTION: Cyclin E, a G(1 )cyclin essential for G(1)–S phase transition, is known to have a profound effect on tumorigenesis. Elevated levels of cyclin E have been associated with breast cancer, and chromosomal instability observed in breast cancer is suggested to be associated with constitutive expression of cyclin E. It was previously demonstrated that SUM149PT human breast cancer cells show very high levels of cyclin E expression by western analysis and that they express a nonfunctional cyclin E ubiquitin ligase due to a mutation in the F-box protein hCdc4. METHODS: We examined cyclin E expression in both MCF10A and SUM149PT cells using western blot analysis and flow cytometry. Immunofluorescence was utilized for the localization of cyclin E in both normal and breast cancer cells. In addition, array comparative genomic hybridization analysis was performed to compare chromosome copy number alterations with levels of cyclin E expression among a panel of breast cancer cell lines. RESULTS: SUM149PT cells overexpress cyclin E on a cell per cell basis for the duration of the cell cycle. High cyclin E levels are maintained throughout the S phase, and SUM149PT cells exhibit an S phase delay or arrest probably due to cyclin E overexpression. In addition, comparative genomic hybridization indicated that SUM149PT cells exhibit many chromosome copy number alterations, which may reflect prior or ongoing genomic instability. However, no direct correlation was observed between cyclin E levels and genomic copy number alteration in a panel of human breast cancer cell lines. CONCLUSIONS: Cyclin E is overexpressed at high levels throughout the cell cycle in SUM149PT cells, which is in stark contrast to cyclin E degradation observed in the mid to late S phase of normal cells. SUM149PT cells are unable to regulate cyclin E and also exhibit many copy number alterations. However, there was a lack of direct correlation between cyclin E overexpression and chromosomal instability across a panel of other breast cancer cell lines examined
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