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

Emotive Captioning and Access to Television

Closed captioning has been enabling access to television for people who are deaf and hard of hearing since the early 1970s. Since that time, technology and people’s demands have been steadily improving and increasing. Closed captioning has not kept up with these changes. We present the results of a study that used graphics, colour, icons and animation as well as text, emotive captions, to capture more of the sound information contained in television content. deaf and hard of hearing participants compared emotive and conventional captions for two short video segments. The results showed that there was a significant difference between deaf and hard of hearing viewers in their reaction to the emotive captions. Hard of hearing viewers seemed to enjoy them and find them interesting. deaf viewers had a strong dislike for them although they did see some potential for intermittent use of emotive captions or for use with children’s programs

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

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

Covariants,joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature

The invariant theory of Killing tensors (ITKT) is extended by introducing the new concepts of covariants and joint invariants of (product) vector spaces of Killing tensors defined in pseudo-Riemannian spaces of constant curvature. The covariants are employed to solve the problem of classification of the orthogonal coordinate webs generated by non-trivial Killing tensors of valence two defined in the Euclidean and Minkowski planes. Illustrative examples are provided.Comment: 60 pages. to appear in J. Math. Phy

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

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

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