Laguerre-Gaussian wave propagation in parabolic media

We report a new set of Laguerre-Gaussian wave-packets that propagate with periodical self-focusing and finite beam width in weakly guiding inhomogeneous media. These wave-packets are solutions to the paraxial form of the wave equation for a medium with parabolic refractive index. The beam width is defined as a solution of the Ermakov equation associated to the harmonic oscillator, so its amplitude is modulated by the strength of the medium inhomogeneity. The conventional Laguerre-Gaussian modes, available for homogenous media, are recovered as a particular case.Comment: 11 pages, 5 figure

Moderate exercise and chronic stress produce counteractive effects on different areas of the brain by acting through various neurotransmitter receptor subtypes: A hypothesis

BACKGROUND: Regular, "moderate", physical exercise is an established non-pharmacological form of treatment for depressive disorders. Brain lateralization has a significant role in the progress of depression. External stimuli such as various stressors or exercise influence the higher functions of the brain (cognition and affect). These effects often do not follow a linear course. Therefore, nonlinear dynamics seem best suited for modeling many of the phenomena, and putative global pathways in the brain, attributable to such external influences. HYPOTHESIS: The general hypothesis presented here considers only the nonlinear aspects of the effects produced by "moderate" exercise and "chronic" stressors, but does not preclude the possibility of linear responses. In reality, both linear and nonlinear mechanisms may be involved in the final outcomes. The well-known neurotransmitters serotonin (5-HT), dopamine (D) and norepinephrine (NE) all have various receptor subtypes. The article hypothesizes that 'Stress' increases the activity/concentration of some particular subtypes of receptors (designated nt(s)) for each of the known (and unknown) neurotransmitters in the right anterior (RA) and left posterior (LP) regions (cortical and subcortical) of the brain, and has the converse effects on a different set of receptor subtypes (designated nt(h)). In contrast, 'Exercise' increases nt(h )activity/concentration and/or reduces nt(s )activity/concentration in the LA and RP areas of the brain. These effects may be initiated by the activation of Brain Derived Neurotrophic Factor (BDNF) (among others) in exercise and its suppression in stress. CONCLUSION: On the basis of this hypothesis, a better understanding of brain neurodynamics might be achieved by considering the oscillations caused by single neurotransmitters acting on their different receptor subtypes, and the temporal pattern of recruitment of these subtypes. Further, appropriately designed and planned experiments will not only corroborate such theoretical models, but also shed more light on the underlying brain dynamics

Consensus Statement on Vitamin D Status Assessment and Supplementation: Whys, Whens, and Hows.

The 6th International Conference, "Controversies in Vitamin D," was convened to discuss controversial topics, such as vitamin D metabolism, assessment, actions, and supplementation. Novel insights into vitamin D mechanisms of action suggest links with conditions that do not depend only on reduced solar exposure or diet intake and that can be detected with distinctive noncanonical vitamin D metabolites. Optimal 25-hydroxyvitamin D (25(OH)D) levels remain debated. Varying recommendations from different societies arise from evaluating different clinical or public health approaches. The lack of assay standardization also poses challenges in interpreting data from available studies, hindering rational data pooling and meta-analyses. Beyond the well-known skeletal features, interest in vitamin D's extraskeletal effects has led to clinical trials on cancer, cardiovascular risk, respiratory effects, autoimmune diseases, diabetes, and mortality. The initial negative results are likely due to enrollment of vitamin D-replete individuals. Subsequent post hoc analyses have suggested, nevertheless, potential benefits in reducing cancer incidence, autoimmune diseases, cardiovascular events, and diabetes. Oral administration of vitamin D is the preferred route. Parenteral administration is reserved for specific clinical situations. Cholecalciferol is favored due to safety and minimal monitoring requirements. Calcifediol may be used in certain conditions, while calcitriol should be limited to specific disorders in which the active metabolite is not readily produced in vivo. Further studies are needed to investigate vitamin D effects in relation to the different recommended 25(OH)D levels and the efficacy of the different supplementary formulations in achieving biochemical and clinical outcomes within the multifaced skeletal and extraskeletal potential effects of vitamin D