240 research outputs found
Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities
We survey our recently proposed method for constructing biholomorphic
invariants of quasihomogeneous isolated hypersurface singularities and, more
generally, invariants of graded Artinian Gorenstein algebras. The method
utilizes certain polynomials associated to such algebras, called
nil-polynomials, and we compare them with two other classes of polynomials that
have also been used to produce invariants.Comment: 13 page
Cosmology, cohomology, and compactification
Ashtekar and Samuel have shown that Bianchi cosmological models with compact
spatial sections must be of Bianchi class A. Motivated by general results on
the symmetry reduction of variational principles, we show how to extend the
Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as
defined, e.g., by Singer and Thurston. In particular, it is shown that any
m-dimensional homogeneous space G/K admitting a G-invariant volume form will
allow a compact discrete quotient only if the Lie algebra cohomology of G
relative to K is non-vanishing at degree m.Comment: 6 pages, LaTe
Gravitational Waves: Just Plane Symmetry
We present some remarkable properties of the symmetry group for gravitational
plane waves. Our main observation is that metrics with plane wave symmetry
satisfy every system of generally covariant vacuum field equations except the
Einstein equations. The proof uses the homothety admitted by metrics with plane
wave symmetry and the scaling behavior of generally covariant field equations.
We also discuss a mini-superspace description of spacetimes with plane wave
symmetry.Comment: 10 pages, TeX, uses IOP style file
The Principle of Symmetric Criticality in General Relativity
We consider a version of Palais' Principle of Symmetric Criticality (PSC)
that is applicable to the Lie symmetry reduction of Lagrangian field theories.
PSC asserts that, given a group action, for any group-invariant Lagrangian the
equations obtained by restriction of Euler-Lagrange equations to
group-invariant fields are equivalent to the Euler-Lagrange equations of a
canonically defined, symmetry-reduced Lagrangian. We investigate the validity
of PSC for local gravitational theories built from a metric. It is shown that
there are two independent conditions which must be satisfied for PSC to be
valid. One of these conditions, obtained previously in the context of
transverse symmetry group actions, provides a generalization of the well-known
unimodularity condition that arises in spatially homogeneous cosmological
models. The other condition seems to be new. The conditions that determine the
validity of PSC are equivalent to pointwise conditions on the group action
alone. These results are illustrated with a variety of examples from general
relativity. It is straightforward to generalize all of our results to any
relativistic field theory.Comment: 46 pages, Plain TeX, references added in revised versio
Semiclassical States in Quantum Cosmology: Bianchi I Coherent States
We study coherent states for Bianchi type I cosmological models, as examples
of semiclassical states for time-reparametrization invariant systems. This
simple model allows us to study explicitly the relationship between exact
semiclassical states in the kinematical Hilbert space and corresponding ones in
the physical Hilbert space, which we construct here using the group averaging
technique. We find that it is possible to construct good semiclassical physical
states by such a procedure in this model; we also discuss the sense in which
the original kinematical states may be a good approximation to the physical
ones, and the situations in which this is the case. In addition, these models
can be deparametrized in a natural way, and we study the effect of time
evolution on an "intrinsic" coherent state in the reduced phase space, in order
to estimate the time for this state to spread significantly.Comment: 21 pages, 1 figure; Version to be published in CQG; The discussion
has been slightly reorganized, two references added, and some typos correcte
Differential effects of long-term aerobic versus cognitively-engaging physical activity on children's visuospatial working memory related brain activation:A cluster RCT
Different types of physical activity are thought to differentially affect children's brain activation, via physiological mechanisms, or by activating similar brain areas during physical and cognitive tasks. Despite many behavioral studies relying on these mechanisms, they have been rarely studied. This study looks at both mechanisms simultaneously, by examining effects of two physical activity interventions (aerobic vs. cognitively-engaging) on children's brain activation. Functional Magnetic Resonance Imaging (fMRI) data of 62 children (48.4% boys, mean age 9.2 years) was analyzed. Children's visuospatial working memory related brain activity patterns were tested using a Spatial Span Task before and after the 14-week interventions consisting of four physical education lessons per week. The control group followed their regular program of two lessons per week. Analyses of activation patterns in SPM 12.0 revealed no activation changes between pretest and posttest (p > .05), and no differences between the three conditions in pretest-posttest changes in brain activation (p > .05). Large inter-individual differences were found, suggesting that not every child benefited from the interventions in the same way. To get more insight into the assumed mechanisms, further research is needed to understand whether, when, for whom, and how physical activity results in changed brain activation patterns
Cardiovascular Fitness and Executive Functioning in Primary School-aged Children
Previous research in children has shown that higher cardiovascular fitness is related to better executive functioning. However, the available literature is hampered by methodological limitations. The present study investigates the relationship between cardiovascular fitness and executive functioning in a large sample of healthy children (N = 814). Cardiovascular fitness was assessed with estimated VO2Max from 20 m Shuttle Run Test performance. Executive functioning was assessed using a set of computerized neurocognitive tasks aimed at executive functions (working memory, motor inhibition, interference control) and lower-level neurocognitive functions (information processing and attention). Dependent measures derived from the neurocognitive tests were subjected to principal component analysis. Mixed model analyses tested the relation between cardiovascular fitness and neurocognitive functioning components. Results showed that children with higher cardiovascular fitness performed better on the neurocognitive function components Information Processing and Control, Visuospatial Working Memory and Attention Efficiency. The following measures contained in these components contributed to the observed relations: information processing measures, visuospatial working memory, and speed of alerting attention. No relationship was found between cardiovascular fitness and the other components: Verbal Working Memory, Attention Accuracy, and Interference Control. The present study suggests that there is a relationship between cardiovascular fitness and a specific set of executive functions and lower level neurocognitive functions. These findings highlight the importance of cardiovascular fitness for the overall health of school-aged children
Quantization of Midisuperspace Models
We give a comprehensive review of the quantization of midisuperspace models.
Though the main focus of the paper is on quantum aspects, we also provide an
introduction to several classical points related to the definition of these
models. We cover some important issues, in particular, the use of the principle
of symmetric criticality as a very useful tool to obtain the required
Hamiltonian formulations. Two main types of reductions are discussed: those
involving metrics with two Killing vector fields and spherically symmetric
models. We also review the more general models obtained by coupling matter
fields to these systems. Throughout the paper we give separate discussions for
standard quantizations using geometrodynamical variables and those relying on
loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit
A Novel Fluorescent Imaging Agent for Diffuse Optical Tomography of the Breast: First Clinical Experience in Patients
Purpose: This is the first clinical evaluation of a novel fluorescent imaging agent (Omocianine) for breast cancer detection with diffuse optical tomography (DOT). Procedures: Eleven women suspected of breast cancer were imaged with DOT at multiple time points (up to 24 h) after receiving an intravenous injection of Omocianine (doses 0.01 to 0.1 mg/kg bodyweight). Breast MRI was obtained for comparison. Results: Histopathology showed invasive cancer in ten patients and fibroadenoma in one patient. With the lowest dose of Omocianine, two of three lesions were detected; with the second dose, three of three lesions were detected; with the two highest doses, none of five lesions were detected. Lesion location on DOT showed excellent agreement with MRI. Optimal lesion-tobackground signals were obtained after 8 h. No adverse events occurred. Conclusions: Lowest doses of Omocianine performed best in lesion detection; DOT using a lowdose fluorescent agent is feasible and safe for breast cancer visualization in patients
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