Compactness in Groups of Group-Valued Mappings

We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Frechet-Smulian and Ascoli-Arzela compactness criteria found in the literature

Rearrangement and Convergence in Spaces of Measurable Functions

We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space , and also on Orlicz spaces with respect to a finitely additive extended real-valued set function. In the space and in the space , of finite elements of an Orlicz space of a -additive set function, we introduce some parameters which estimate the Hausdorff measure of noncompactness. We obtain some relations involving these parameters when passing from a bounded set of , or , to the set of rearrangements

Massless Interacting Scalar Fields in de Sitter space

We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\sqrt\lambda$ and in $1/N$. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large $N$ limit. The new method allows for a systematic calculation of higher order corrections both in $\sqrt\lambda$ and in $1/N$.Comment: 8 pages. Summarized version of JHEP 09 (2016) 117 [arXiv:1606.03481]. Published in the Proceedings of the 19th International Seminar on High Energy Physics (QUARKS-2016

O(N)O(N) model in Euclidean de Sitter space: beyond the leading infrared approximation

We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling constant $\sqrt\lambda$ and in 1/N. We explicitly perform the calculation up to the next-to-next-to-leading order in $\sqrt\lambda$ and up to next-to-leading order in 1/N. The results reduce to those known in the leading infrared approximation. We also show that they coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit, provided the same renormalization scheme is used.Comment: 31 pages, 5 figures. Minor changes. Published versio

The Effects of Diethyldithiocarbamate (DDC) on the Astrocytic Cytoskeleton

The dithiocarbamates are a group of compounds that are used extensively in industry, agriculture and medicine. Exposure to these compounds has caused deleterious effects to both the central and peripheral nervous systems. Cultured rat hippocampal astroglia treated with 35 μg/ml diethyldithiocarbamate (DDC) in media were studied for alterations to the cytoskeleton. Examination by both immunohistochemistry and scanning electron microscopy revealed disruption of the cytoskeletal elements. This occurred in a progressive time-dependent manner. Electrophoretic patterns demonstrated two cytoskeletal protein alterations. The microtubular protein, β-tubulin, appeared to have an altered mobility while the major intermediate filament protein, glial fibrillary acidic protein (GF AP), was decreased. The cytoskeleton appears to be an important cellular target for injury by DDC exposure. This study has demonstrated that DDC induces alterations in the architecture of the cytoskeleton of astroglia and suggests that these changes involve microtubular and intermediate filament proteins

Stochastic particle creation: from the dynamical Casimir effect to cosmology

We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic particle creation with the deterministic counterpart. Then we go beyond the perturbative evaluation using a stochastic version of the multiple scale analysis, that takes into account stochastic parametric resonance. We stress the relevance of the coupling between the different modes induced by the stochastic motion. In the single-mode approximation, the equations are formally analogous to those that describe the stochastic particle creation in a cosmological context, that we rederive using multiple scale analysis.Comment: 23 pages, no figure

The application of structural retinal biomarkers to evaluate the effect of intravitreal ranibizumab and dexamethasone intravitreal implant on treatment of diabetic macular edema

Background: The aim of this study was to compare the therapeutic effect of intravitreal treatment with ranibizumab and dexamethasone using specific swept-source optical coherence tomography retinal biomarkers in patients with diabetic macular edema (DME). Methods: 156 treatment-naïve patients with DME were divided in two groups: 75 patients received 3 monthly intravitreal injections of ranibizumab 0.5 mg (Lucentis®) (Group 1) and 81 patients received an intravitreal implant of dexamethasone 0.7 mg (Ozurdex®) (Group 2). Patients were evaluated at baseline (V1), at three months post-treatment in Group 1, and at two months post-treatment in Group 2 (V2). Best-corrected visual acuity (BCVA) and swept source-OCT were recorded at each interval. Changes between V1 and V2 were analyzed using the Wilcoxon test and differences between the two groups of treatment were assessed using the Mann-Whitney test. Multiple regression analysis was performed to evaluate the possible OCT biomarker (CRT, ICR, CT, SND, HRS) as predictive factors for final visual acuity improvement. Results: In both groups, BCVA improved (p-value < 0.0001), and a significant reduction in central retinal thickness, intra-retinal cysts, red dots, hyper-reflective spots (HRS), and serous detachment of neuro-epithelium (SDN) was observed. A superiority of dexamethasone over ranibizumab in reducing the SDN height (p-value = 0.03) and HRS (p-value = 0.01) was documented. Conclusions: Ranibizumab and dexamethasone are effective in the treatment of DME, as demonstrated by functional improvement and morphological biomarker change. DME associated with SDN and HRS represents a specific inflammatory pattern for which dexamethasone appears to be more effective