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

Deep Reinforcement Learning for Autonomous Inspection System

The objective of the group is to investigate the application of Reinforced Deep Learning to autonomously complete damage inspection on buildings after natural disasters. By using Reinforced Deep Learning with Convolutional Neural Networks performing image processing, the drone will be trained to navigate itself towards buildings and perform building inspection without scanning the whole structure. The algorithms for Reinforced Deep Learning can be used to drive drones autonomously and perform inspections currently done by humans. The stability of the structure of buildings are unknown when these inspections are performed. This application would greatly reduce the risk of individuals involved in inspecting the building structures and provide greater insight into the stability of these structures

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

A travel guide to the canonical bundle formula

We survey known results on the canonical bundle formula and its applications in algebraic geometry.Comment: 17 pages, to appear in the Proceedings of the conference Birational Geometry and Moduli Space

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