Frames with Transitive Structures

A classical result in the theory of uniform spaces is that any topological space with a base of clopen sets admits a uniformity with a transitive base and the uniform topology of such a space has a base of clopen sets. This paper presents a pointfree generalization of this, both to uniform and quasi-uniform frames, together with various properties concerning total boundedness, compactifications and completions.     

An improved class of generalized Runge–Kutta methods for stiff problems. Part I: The scalar case

A new family of p-stage methods for the numerical integration of some scalar equations and systems of ODEs is proposed. These methods can be seen as a generalization of the explicit p-stage Runge–Kutta ones, while providing better order and stability results. We will show in this first part that, at the cost of losing linearity in the formulas, it is possible to obtain explicit A-stable and L-stable methods for the numerical integration of scalar autonomous ODEs. Scalar autonomous ODEs are of very little interest in current applications. However, be begin studying this kind of problems because most of the work can be easily extended to a more general situation. In fact, we will show in a second part (entitled ‘The separated system case'), that it is possible to generalize our methods so that they can be applied to some non-autonomous scalar ODEs and systems. We will obtain linearly implicit L-stable methods which do not require Jacobian evaluations. In both parts, some numerical examples are discussed in order to show the good performance of the new schemes.     

Optimal Paths for Symmetric Actions in the Unitary Group

Given a positive and unitarily invariant Lagrangian ${\mathcal{L}}$ defined in the algebra of matrices, and a fixed time interval ${[0,t_0]\subset\mathbb R}$ , we study the action defined in the Lie group of ${n\times n}$ unitary matrices ${\mathcal{U}(n)}$ by $$\mathcal{S}(\alpha)=\int_0^{t_0} \mathcal{L}(\dot\alpha(t))\,dt, $$ where ${\alpha:[0,t_0]\to\mathcal{U}(n)}$ is a rectifiable curve. We prove that the one-parameter subgroups of ${\mathcal{U}(n)}$ are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if ${\mathcal{L}}$ is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in ${\mathcal{U}(n)}$ as well as angular metrics in the Grassmann manifold.     

Logatom corpus for the assessment of the intelligibility in Spanish speaking environments and its relation with STI measurements

A 1000 consonant–vowel–consonant structure logatoms corpus (CVC-structure), grouped in 10 phonetically equally balanced lists of 100 words each, was developed to satisfy the need of subjective assessment of speech intelligibility in American Spanish speaking environments. This corpus was tested and correlated with the Speech Transmission Index (STI) measurements to compare its articulation intelligibility score with other lists’ scores.Through the development of this work it was determined that in two different acoustically poor rooms that have the same STI (with STI < 0.50), the intelligibility score is lower when the articulation test is performed in a quiet room with high reverberation time than when it is performed in a very noisy room with low reverberation time. The final correlation curve of the American Spanish CVC-structure corpus was around 10% points higher than the CVC_EQB curve obtained by Steeneken and Houtgast in 2002.     

The Latent Scale Covariogram: A Tool for Exploring the Spatial Dependence Structure of Nonnormal Responses

When modeling spatially distributed normal responses Y_i in terms of vectors x_i of explanatory variables, one may fit a linear model assuming independence, and then use the empirical variogram of the residuals to determine an appropriate parametric form for the autocorrelation function. Suppose, however, that the responses are not normally distributed—for example, Poisson or Bernoulli. One may model spatial dependence using a hierarchical generalized linear model in which, conditional on a latent Gaussian field Z = {Z_i}, the Y_i have independent distributions from the exponential family, with an appropriate link function connecting their conditional means with the linear predictors x^t_iβ + Z_i. The question then is how to determine an appropriate model for the autocorrelation function of Z. The empirical variogram of the Y_i is no longer appropriate, since (unless the link function is the identity) it is on the wrong scale. We propose here an alternative, the latent scale covariogram, whose graph reflects the autocorrelation structure of the underlying normal field. We illustrate its use on several real datasets, together with a simulated dataset, and obtain results quite different from those obtained using the variogram. Supplementary materials for this article are available online.     

Parkin-deficient mice are not more sensitive to 6-hydroxydopamine or methamphetamine neurotoxicity

Background  

Autosomal recessive juvenile parkinsonism (AR-JP) is caused by mutations in the parkin gene which encodes an E3 ubiquitin-protein ligase. Parkin is thought to be critical for protecting dopaminergic neurons from toxic insults by targeting misfolded or oxidatively damaged proteins for proteasomal degradation. Surprisingly, mice with targeted deletions of parkin do not recapitulate robust behavioral or pathological signs of parkinsonism. Since Parkin is thought to protect against neurotoxic insults, we hypothesized that the reason Parkin-deficient mice do not develop parkinsonism is because they are not exposed to appropriate environmental triggers. To test this possibility, we challenged Parkin-deficient mice with neurotoxic regimens of either methamphetamine (METH) or 6-hydroxydopamine (6-OHDA). Because Parkin function has been linked to many of the pathways involved in METH and 6-OHDA toxicity, we predicted that Parkin-deficient mice would be more sensitive to the neurotoxic effects of these agents.     

Variation Operators for Semigroups and Riesz Transforms on BMO in the Schrödinger Setting

In this paper we prove that the variation operators of the heat semigroup and the truncations of Riesz transforms associated to the Schrödinger operator are bounded on a suitable BMO type space.     

Nondegeneracy and uniqueness for boundary blow-up elliptic problems

In this paper, we use for the first time linearization techniques to deal with boundary blow-up elliptic problems. After introducing a convenient functional setting, we show that the problem Δu=λa(x)u^p+g(x,u) in Ω, with u=+∞ on ∂Ω, has a unique positive solution for large enough λ, and determine its asymptotic behavior as λ→+∞. Here p>1, a(x) is a continuous function which can be singular near ∂Ω and g(x,u) is a perturbation term with potential growth near zero and infinity. We also consider more general problems, obtained by replacing u^p by e^u or a “logistic type” function f(u).     

Cosmological Plebanski theory

We consider the cosmological symmetry reduction of the Plebanski action as a toy-model to explore, in this simple framework, some issues related to loop quantum gravity and spin-foam models. We make the classical analysis of the model and perform both path integral and canonical quantizations. As for the full theory, the reduced model admits two disjoint types of classical solutions: topological and gravitational ones. The quantization mixes these two solutions, which prevents the model from being equivalent to standard quantum cosmology. Furthermore, the topological solution dominates at the classical limit. We also study the effect of an Immirzi parameter in the model.     

Even-dimensional topological gravity from Chern–Simons gravity

It is shown that the topological action for gravity in 2n  -dimensions can be obtained from the (2n+1)$(2n+1)$-dimensional Chern–Simons gravity genuinely invariant under the Poincaré group. The 2n  -dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)$(2n+1)$-dimensional Chern–Simons gravity theory with suitable boundary conditions.