Endomorphism algebras of Abelian varieties with special reference to superelliptic Jacobians

This is (mostly) a survey article. We use an information about Galois properties of points of small order on an Abelian variety in order to describe its endomorphism algebra over an algebraic closure of the ground field. We discuss in detail applications to jacobians of cyclic covers of the projective line

White noise approach to parabolic stochastic partial differential equations

A certain dass of stochastic partial differential equations of parabolic type is studied within white noise analysis

Multimodal Management of Atrophic Acne Scarring in the Aging Face

Atrophic facial acne scarring is a widely prevalent condition that can have a negative impact on a patient’s quality of life. The appearance of these scars is often worsened by the normal effects of aging. A number of options are available for the treatment of acne scarring, including chemical peeling, dermabrasion, ablative or nonablative laser resurfacing, dermal fillers, and surgical techniques such as subcision or punch excision. Depending on the type and extent of scarring, a multimodal approach is generally necessary to provide satisfactory results. Resurfacing techniques correct surface irregularities, long-lasting dermal fillers address the volume loss resulting from acne, and sub-superficial musculoaponeurotic system (SMAS) face-lift procedures counter the soft tissue laxity and ptosis associated with aging. This article briefly reviews the evolution of individual approaches to treating atrophic acne scarring, followed by case examples illustrating results that can be achieved using a multimodal approach. Representative cases from patients in their 30s, 40s, and 50s are presented. In the author’s clinical practice, multimodal approaches incorporating fractionated laser, injectable poly-l-lactic acid, and sub-SMAS face-lift procedures have achieved optimal aesthetic outcomes, high patient satisfaction, and durability of aesthetic effect over time

Diet rapidly and reproducibly alters the human gut microbiome

Long-term diet influences the structure and activity of the trillions of microorganisms residing in the human gut1–5, but it remains unclear how rapidly and reproducibly the human gut microbiome responds to short-term macronutrient change. Here, we show that the short-term consumption of diets composed entirely of animal or plant products alters microbial community structure and overwhelms inter-individual differences in microbial gene expression. The animal-based diet increased the abundance of bile-tolerant microorganisms (Alistipes, Bilophila, and Bacteroides) and decreased the levels of Firmicutes that metabolize dietary plant polysaccharides (Roseburia, Eubacterium rectale, and Ruminococcus bromii). Microbial activity mirrored differences between herbivorous and carnivorous mammals2, reflecting trade-offs between carbohydrate and protein fermentation. Foodborne microbes from both diets transiently colonized the gut, including bacteria, fungi, and even viruses. Finally, increases in the abundance and activity of Bilophila wadsworthia on the animal-based diet support a link between dietary fat, bile acids, and the outgrowth of microorganisms capable of triggering inflammatory bowel disease6. In concert, these results demonstrate that the gut microbiome can rapidly respond to altered diet, potentially facilitating the diversity of human dietary lifestyles