Stein's Method and Characters of Compact Lie Groups

Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the trace into irreducible components. This is illustrated for Lie groups of classical type and Dyson's circular ensembles. The approach in this paper will be useful for the study of higher dimensional characters, where normal approximations need not hold.Comment: 22 pages; same results, but more efficient exposition in Section 3.

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Stein's method on Wiener chaos

We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. We also prove results concerning random variables admitting a possibly infinite Wiener chaotic decomposition. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-It\^o integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We apply our techniques to prove Berry-Ess\'een bounds in the Breuer-Major CLT for subordinated functionals of fractional Brownian motion. By using the well-known Mehler's formula for Ornstein-Uhlenbeck semigroups, we also recover a technical result recently proved by Chatterjee, concerning the Gaussian approximation of functionals of finite-dimensional Gaussian vectors.Comment: 39 pages; Two sections added; To appear in PTR

The effect of a high-polyphenol Mediterranean diet (Green-MED) combined with physical activity on age-related brain atrophy: The Dietary Intervention Randomized Controlled Trial Polyphenols Unprocessed Study (DIRECT PLUS)

Background: The effect of diet on age-related brain atrophy is largely unproven. Objectives: We aimed to explore the effect of a Mediterranean diet (MED) higher in polyphenols and lower in red/processed meat (Green-MED diet) on age-related brain atrophy. Methods: This 18-mo clinical trial longitudinally measured brain structure volumes by MRI using hippocampal occupancy score (HOC) and lateral ventricle volume (LVV) expansion score as neurodegeneration markers. Abdominally obese/dyslipidemic participants were randomly assigned to follow 1) healthy dietary guidelines (HDG), 2) MED, or 3) Green-MED diet. All subjects received free gym memberships and physical activity guidance. Both MED groups consumed 28 g walnuts/d (+440 mg/d polyphenols). The Green-MED group consumed green tea (3-4 cups/d) and Mankai (Wolffia-globosa strain, 100 g frozen cubes/d) green shake (+800 mg/d polyphenols). Results: Among 284 participants (88% men; mean age: 51 y; BMI: 31.2 kg/m2; APOE-ε4 genotype = 15.7%), 224 (79%) completed the trial with eligible whole-brain MRIs. The pallidum (-4.2%), third ventricle (+3.9%), and LVV (+2.2%) disclosed the largest volume changes. Compared with younger participants, atrophy was accelerated among those ≥50 y old (HOC change: -1.0% ± 1.4% compared with -0.06% ± 1.1%; 95% CI: 0.6%, 1.3%; P Conclusions: A Green-MED (high-polyphenol) diet, rich in Mankai, green tea, and walnuts and low in red/processed meat, is potentially neuroprotective for age-related brain atrophy.This trial was registered at clinicaltrials.gov as NCT03020186

The effect of high-polyphenol Mediterranean diet on visceral adiposity: the DIRECT PLUS randomized controlled trial

Background Mediterranean (MED) diet is a rich source of polyphenols, which benefit adiposity by several mechanisms. We explored the effect of the green-MED diet, twice fortified in dietary polyphenols and lower in red/processed meat, on visceral adipose tissue (VAT). Methods In the 18-month Dietary Intervention Randomized Controlled Trial PoLyphenols UnproceSsed (DIRECT-PLUS) weight-loss trial, 294 participants were randomized to (A) healthy dietary guidelines (HDG), (B) MED, or (C) green-MED diets, all combined with physical activity. Both isocaloric MED groups consumed 28 g/day of walnuts (+ 440 mg/day polyphenols). The green-MED group further consumed green tea (3–4 cups/day) and Wolffia globosa (duckweed strain) plant green shake (100 g frozen cubes/day) (+ 800mg/day polyphenols) and reduced red meat intake. We used magnetic resonance imaging (MRI) to quantify the abdominal adipose tissues. Results Participants (age = 51 years; 88% men; body mass index = 31.2 kg/m2; 29% VAT) had an 89.8% retention rate and 79.3% completed eligible MRIs. While both MED diets reached similar moderate weight (MED: − 2.7%, green-MED: − 3.9%) and waist circumference (MED: − 4.7%, green-MED: − 5.7%) loss, the green-MED dieters doubled the VAT loss (HDG: − 4.2%, MED: − 6.0%, green-MED: − 14.1%; p < 0.05, independent of age, sex, waist circumference, or weight loss). Higher dietary consumption of green tea, walnuts, and Wolffia globosa; lower red meat intake; higher total plasma polyphenols (mainly hippuric acid), and elevated urine urolithin A polyphenol were significantly related to greater VAT loss (p < 0.05, multivariate models). Conclusions A green-MED diet, enriched with plant-based polyphenols and lower in red/processed meat, may be a potent intervention to promote visceral adiposity regression

A narrative review of the potential pharmacological influence and safety of ibuprofen on coronavirus disease 19 (COVID-19), ACE2, and the immune system: a dichotomy of expectation and reality

The coronavirus disease 19 (COVID-19) pandemic is currently the most acute healthcare challenge in the world. Despite growing knowledge of the nature of Severe Acute Respiratory Syndrome coronavirus-2 (SARS-CoV-2), treatment options are still poorly defined. The safety of non-steroidal anti-inflammatory drugs (NSAIDs), specifically ibuprofen, has been openly questioned without any supporting evidence or clarity over dose, duration, or temporality of administration. This has been further conflicted by the initiation of studies to assess the efficacy of ibuprofen in improving outcomes in severe COVID-19 patients. To clarify the scientific reality, a literature search was conducted alongside considerations of the pharmacological properties of ibuprofen in order to construct this narrative review. The literature suggests that double-blind, placebo-controlled study results must be reported and carefully analysed for safety and efficacy in patients with COVID-19 before any recommendations can be made regarding the use of ibuprofen in such patients. Limited studies have suggested: (i) no direct interactions between ibuprofen and SARS-CoV-2 and (ii) there is no evidence to suggest ibuprofen affects the regulation of angiotensin-converting-enzyme 2 (ACE2), the receptor for COVID-19, in human studies. Furthermore, in vitro studies suggest ibuprofen may facilitate cleavage of ACE2 from the membrane, preventing membrane-dependent viral entry into the cell, the clinical significance of which is uncertain. Additionally, in vitro evidence suggests that inhibition of the transcription factor nuclear factor-κB (NF-kB) by ibuprofen may have a role in reducing excess inflammation or cytokine release in COVID-19 patients. Finally, there is no evidence that ibuprofen will aggravate or increase the chance of infection of COVID-19

Generalizations of the General Lotto and Colonel Blotto Games

In this paper, we generalize the General Lotto game (budget constraints satisfied in expectation) and the Colonel Blotto game (budget constraints hold with probability one) to allow for battlefield valuations that are heterogeneous across battlefields and asymmetric across players, and for the players to have asymmetric resource constraints. We completely characterize Nash equilibrium in the generalized version of the General Lotto game and then show how this characterization can be applied to identify equilibria in the Colonel Blotto version of the game. In both games, we find that there exist sets of non-pathological parameter configurations of positive Lebesgue measure with multiple payoff nonequivalent equilibria

Stochastic loss and gain of symmetric divisions in the C. elegans epidermis perturbs robustness of stem cell number

Biological systems are subject to inherent stochasticity. Nevertheless, development is remarkably robust, ensuring the consistency of key phenotypic traits such as correct cell numbers in a certain tissue. It is currently unclear which genes modulate phenotypic variability, what their relationship is to core components of developmental gene networks, and what is the developmental basis of variable phenotypes. Here, we start addressing these questions using the robust number of Caenorhabditis elegans epidermal stem cells, known as seam cells, as a readout. We employ genetics, cell lineage tracing, and single molecule imaging to show that mutations in lin-22, a Hes-related basic helix-loop-helix (bHLH) transcription factor, increase seam cell number variability. We show that the increase in phenotypic variability is due to stochastic conversion of normally symmetric cell divisions to asymmetric and vice versa during development, which affect the terminal seam cell number in opposing directions. We demonstrate that LIN-22 acts within the epidermal gene network to antagonise the Wnt signalling pathway. However, lin-22 mutants exhibit cell-to-cell variability in Wnt pathway activation, which correlates with and may drive phenotypic variability. Our study demonstrates the feasibility to study phenotypic trait variance in tractable model organisms using unbiased mutagenesis screens