Lower Bound for Convex Hull Area and Universal Cover Problems

In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.Comment: 12 pages, 9 figure

Nonconvex Cases for Carpenter\u27s Rulers

We consider the carpenter\u27s ruler folding problem in the plane, i.e., finding a minimum area shape with diameter 1 that accommodates foldings of any ruler whose longest link has length 1. An upper bound of 0.614 and a lower bound of 0.476 are known for convex cases. We generalize the problem to simple nonconvex cases: in this setting we improve the upper bound to 0.583 and establish the first lower bound of 0.073. A variation is to consider rulers with at most k links. The current best convex upper bounds are 0.486 for k = 3, 4 and 0.523 for k = 5, 6. These bounds also apply to nonconvex cases. We derive a better nonconvex upper bound of 0.296 for k = 3, 4

Bulletin of the Center for Children's Books 47 (10) 1994

published or submitted for publicatio

StrongNet: An International Network to Improve Diagnostics and Access to Treatment for Strongyloidiasis Control

Strongyloidiasis is a disease caused by an infection with a soil-transmitted helminth that affects, according to largely varying estimates, between 30 million and 370 million people worldwide [1,2]. Not officially listed as a neglected tropical disease (NTD), strongyloidiasis stands out as particularly overlooked [3]. Indeed, there is a paucity of research and public health efforts pertaining to strongyloidiasis. Hence, clinical, diagnostic, epidemiologic, treatment, and control aspects are not adequately addressed to allow for an effective management of the disease, both in clinical medicine and in public health programs [4]. The manifold signs and symptoms caused by Strongyloides stercoralis infection, coupled with the helminth’s unique potential to cause lifelong, persistent infection, make strongyloidiasis relevant beyond tropical and subtropical geographic regions, where, however, most of the disease burden is concentrated. Indeed, strongyloidiasis is acquired through contact with contaminated soil, and the infection is, thus, primarily transmitted in areas with poor sanitation, inadequate access to clean water, and lack of hygiene

Role of DNA-detection-based tools for monitoring the soil-transmitted helminth treatment response in drug-efficacy trials.

More than 1 billion people have been reported to be infected with at least one soil-transmitted helminth (STH) worldwide, according to the last published report of the World Health Organization (WHO) [1]. WHO guidelines for STH control mainly encompass periodic administration of benzimidazoles (albendazole or mebendazole) to at-risk people of the endemic areas [1]. However, extended use of benzimidazoles could entail a great selection pressure for parasitic-resistant strains. In veterinary medicine, anthelmintic resistance in gastrointestinal nematodes has been developed in response to their excessive use, and it is currently considered a serious threat to livestock health and welfare [2, 3]. In humans, the estimated efficacy of albendazole and mebendazole against Trichuris trichiura has been observed to significantly decrease over time [4]. This observed decrement in drug efficacy could be due to the development of anthelmintic resistance (among other reasons such as drug quality and administration, the increasing of drug-efficacy studies, improvements in sensitivity of diagnostic tools after treatment, etc) after years of mass drug-administration campaigns, which is one of the major concerns in STH control [5]. Monitoring anthelmintic efficacy trials have been traditionally done by microscopic approaches, although it is well known that microscopy's sensitivity may be insufficient in this context [6, 7]. We think that DNA-detection-based tools represent an accurate alternative to parasitological methods, and they should be evaluated and validated not only for monitoring worm burden before and after treatment but also for detecting genetic markers related to anthelmintic resistance