Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

Integral inequalities for algebraic and trigonometric polynomials

Vegeu el resum a l'inici del document del fitxer adjunt.

Paranoia and post-traumatic stress disorder in the months after a physical assault: a longitudinal study examining shared and differential predictors.

Background: Being physically assaulted is known to increase the risk of the occurrence of post-traumatic stress disorder (PTSD) symptoms but it may also skew judgements about the intentions of other people. The objectives of the study were to assess paranoia and PTSD after an assault and to test whether theory-derived cognitive factors predicted the persistence of these problems. Method: At 4 weeks after hospital attendance due to an assault, 106 people were assessed on multiple symptom measures (including virtual reality) and cognitive factors from models of paranoia and PTSD. The symptom measures were repeated 3 and 6 months later. Results: Factor analysis indicated that paranoia and PTSD were distinct experiences, though positively correlated. At 4 weeks, 33% of participants met diagnostic criteria for PTSD, falling to 16% at follow-up. Of the group at the first assessment, 80% reported that since the assault they were excessively fearful of other people, which over time fell to 66%. Almost all the cognitive factors (including information-processing style during the trauma, mental defeat, qualities of unwanted memories, self-blame, negative thoughts about self, worry, safety behaviours, anomalous internal experiences and cognitive inflexibility) predicted later paranoia and PTSD, but there was little evidence of differential prediction. Conclusions: Paranoia after an assault may be common and distinguishable from PTSD but predicted by a strikingly similar range of factors.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

A note on quadrics through an algebraic curve

In this note we describe the intersection of all quadric hypersur- faces containing a given linearly normal smooth projective curve of genus n and degree 2n + 1

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

The problem of physical coordinates in predictive Hamiltonian systems

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities moduli and makes the reparametrization unnecessary.

Relaxation and derelaxation of pure and hydrogenated amorphous silicon during thermal annealing experiments

The structural relaxation of pure amorphous silicon a-Si and hydrogenated amorphous silicon a-Si:H materials, that occurs during thermal annealing experiments, has been analyzed by Raman spectroscopy and differential scanning calorimetry. Unlike a-Si, the heat evolved from a-Si:H cannot be explained by relaxation of the Si-Si network strain but it reveals a derelaxation of the bond angle strain. Since the state of relaxation after annealing is very similar for pure and hydrogenated materials, our results give strong experimental support to the predicted configurational gap between a-Si and crystalline silicon.

The Armc10/SVH gene: Genome context, regulation of mitochondrial dynamics and protection against Aβ-induced mitochondrial fragmentation

Mitochondrial function and dynamics are essential for neurotransmission, neural function and neuronal viability. Recently, we showed that the eutherian-specific Armcx gene cluster (Armcx1-6 genes), located in the X chromosome, encodes for a new family of proteins that localise to mitochondria, regulating mitochondrial trafficking. The Armcx gene cluster evolved by retrotransposition of the Armc10 gene mRNA, which is present in all vertebrates and is considered to be the ancestor gene. Here we investigate the genomic organisation, mitochondrial functions and putative neuroprotective role of the Armc10 ancestor gene. The genomic context of the Armc10 locus shows considerable syntenic conservation among vertebrates, and sequence comparisons and CHIP-data suggest the presence of at least three conserved enhancers. We also show that the Armc10 protein localises to mitochondria and that it is highly expressed in the brain. Furthermore, we show that Armc10 levels regulate mitochondrial trafficking in neurons, but not mitochondrial aggregation, by controlling the number of moving mitochondria. We further demonstrate that the Armc10 protein interacts with the KIF5/Miro1-2/Trak2 trafficking complex. Finally, we show that overexpression of Armc10 in neurons prevents A beta-induced mitochondrial fission and neuronal death. Our data suggest both conserved and differential roles of the Armc10/Armcx gene family in regulating mitochondrial dynamics in neurons, and underscore a protective effect of the Armc10 gene against A beta-induced toxicity. Overall, our findings support a further degree of regulation of mitochondrial dynamics in the brain of more evolved mammals.

The Armc10/SVH gene: Genome context, regulation of mitochondrial dynamics and protection against Aβ-induced mitochondrial fragmentation

Mitochondrial function and dynamics are essential for neurotransmission, neural function and neuronal viability. Recently, we showed that the eutherian-specific Armcx gene cluster (Armcx1-6 genes), located in the X chromosome, encodes for a new family of proteins that localise to mitochondria, regulating mitochondrial trafficking. The Armcx gene cluster evolved by retrotransposition of the Armc10 gene mRNA, which is present in all vertebrates and is considered to be the ancestor gene. Here we investigate the genomic organisation, mitochondrial functions and putative neuroprotective role of the Armc10 ancestor gene. The genomic context of the Armc10 locus shows considerable syntenic conservation among vertebrates, and sequence comparisons and CHIP-data suggest the presence of at least three conserved enhancers. We also show that the Armc10 protein localises to mitochondria and that it is highly expressed in the brain. Furthermore, we show that Armc10 levels regulate mitochondrial trafficking in neurons, but not mitochondrial aggregation, by controlling the number of moving mitochondria. We further demonstrate that the Armc10 protein interacts with the KIF5/Miro1-2/Trak2 trafficking complex. Finally, we show that overexpression of Armc10 in neurons prevents A beta-induced mitochondrial fission and neuronal death. Our data suggest both conserved and differential roles of the Armc10/Armcx gene family in regulating mitochondrial dynamics in neurons, and underscore a protective effect of the Armc10 gene against A beta-induced toxicity. Overall, our findings support a further degree of regulation of mitochondrial dynamics in the brain of more evolved mammals.

Physico-chemical analysis of Albian (Lower Cretaceous) amber from San Just (Spain): implications for palaeoenvironmental and palaeoecological studies.

Amber from a Lower Cretaceous outcrop at San Just, located in the Eastern Iberian Peninsula (Escucha Formation, Maestrat Basin), was investigated to evaluate its physico-chemical properties. Thermogravimetric (TG) and Differential Thermogravimetric (DTG) analyses, infra-red spectroscopy, elemental and C-isotope analyses were performed. Physico-chemical differences between the internal light nuclei and the peripheral darker portions of San Just amber can be attributed to processes of diagenetic alteration that preferentially took place in the external amber border colonized by microorganisms (fungi or bacteria) when the resin was still liquid or slightly polymerized. δ13Camber values of different pieces of the same sample, from the nucleus to the external part, are remarkably homogeneous, as are δ13Camber values of the darker peripheral portions and lighter inner parts of the same samples. Hence, neither invasive microorganisms, nor diagenetic alteration, changed the bulk isotopic composition of the amber. δ13C values of different amber samples range from -21.1 to -24 , as expected for C3 plant-derived material. C-isotope analysis, coupled to palaeobotanical, TG and DTG data and infra-red spectra, suggests that San Just amber was exuded by only one conifer species, belonging to either the Cheirolepidiaceae or Aracauriaceae, coniferous families probably living under stable palaeoenvironmental and palaeoecological conditions.

Relaxation and derelaxation of pure and hydrogenated amorphous silicon during thermal annealing experiments

The structural relaxation of pure amorphous silicon (a-Si) and hydrogenated amorphous silicon (a-Si:H) materials, that occurs during thermal annealing experiments, has been analyzed by Raman spectroscopy and differential scanning calorimetry. Unlike a-Si, the heat evolved from a-Si:H cannot be explained by relaxation of the Si-Si network strain but it reveals a derelaxation of the bond angle strain. Since the state of relaxation after annealing is very similar for pure and hydrogenated materials, our results give strong experimental support to the predicted configurational gap between a-Si and crystalline silicon