Detecting flat normal cones using Segre classes

Given a flat, projective morphism $Y \to T$ from an equidimensional scheme to a nonsingular curve and a subscheme $Z$ of $Y$, we give conditions under which specialization of the Segre class $s(N_{Z}Y)$ of the normal cone of $Z$ in $Y$ implies flatness of the normal cone. We apply this result to study when the relative tangent star cone of a flat family is flat.Comment: LaTeX, 11 pages, no figure

Tangential Quantum Cohomology of Arbitrary Order

J. Kock has previously defined a tangency quantum product on formal power series with coefficients in the cohomology ring of any smooth projective variety, and thus a ring that generalizes the quantum cohomology ring. We further generalize Kock's construction by defining a dth-order contact product and establishing its associativity.Comment: 18 pages, LaTeX. We correct our paper to work in the correct context, viz., using numerical equivalence (rather than rational equivalence) and explicitly mentioning the Novikov rin

Computing the Loewner driving process of random curves in the half plane

We simulate several models of random curves in the half plane and numerically compute their stochastic driving process (as given by the Loewner equation). Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion. We find that just testing the normality of the process at a fixed time is not effective at determining if the process is Brownian motion. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N^1.35) rather than the usual O(N^2), where N is the number of points on the curve.Comment: 20 pages, 4 figures. Changes to second version: added new paragraph to conclusion section; improved figures cosmeticall

The Length of an SLE - Monte Carlo Studies

The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm-Loewner evolution (SLE) for a suitable value of the parameter kappa. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization (with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization.Comment: 18 pages, 10 figures. Version 2 replaced the use of "nu" for the "growth exponent" by 1/d_H, where d_H is the Hausdorff dimension. Various minor errors were also correcte

The effects of visual deprivation on adaptation to a rotating environment

Visual deprivation effects on adaptation to rotating environment - Motion sickness studie

Remarks on geometric entropy

The recently discussed notion of geometric entropy is shown to be related to earlier calculations of thermal effects in Rindler space. The evaluation is extended to de Sitter space and to a two-dimensional black hole.Comment: 7p.,uses jyTeX,MUTP/94/

A Fast Algorithm for Simulating the Chordal Schramm-Loewner Evolution

The Schramm-Loewner evolution (SLE) can be simulated by dividing the time interval into N subintervals and approximating the random conformal map of the SLE by the composition of N random, but relatively simple, conformal maps. In the usual implementation the time required to compute a single point on the SLE curve is O(N). We give an algorithm for which the time to compute a single point is O(N^p) with p<1. Simulations with kappa=8/3 and kappa=6 both give a value of p of approximately 0.4.Comment: 17 pages, 10 figures. Version 2 revisions: added a paragraph to introduction, added 5 references and corrected a few typo

Determining key research areas for healthier diets and sustainable food systems in Viet Nam

Vietnamese food systems are undergoing rapid transformation, with important implications for human and environmental health and economic development. Poverty has decreased, and diet quality and undernutrition have improved significantly since the end of the Doi Moi reform period (1986-1993) as a result of Viet Nam opening its economy and increasing its regional and global trade. Yet poor diet quality is still contributing the triple burden of malnutrition, with 25 percent stunting among children under age 5, 26 percent and 29 percent of women and children, respectively, anemic, and 21 percent of adults overweight. Agricultural production systems have shifted from predominantly diverse smallholder systems to larger more commercialized and specialized systems, especially for crops, while the ‘meatification’ of the Vietnamese diet is generating serious trade-offs between improved nutrition and sustainability of the Vietnamese food systems. The food processing industry has developed rapidly, together with food imports, resulting in new and processed food products penetrating the food retail outlets, trending towards an increase in the Westernized consumption patterns that are shifting nutrition-related problems towards overweight and obesity and, with it, an increase of non-communicable disease-related health risks. While regulatory policies exist across the food system, these are not systematically implemented, making food safety a major concern for consumers and policy makers alike. Where data exists, it is not easy to aggregate with data from across food system dimensions, making it difficult for Viet Nam to make an informed analysis of current and potential food system trade-offs. In our research, we reviewed existing literature and data, and applied a food systems framework to develop an initial food systems profile for Viet Nam and to identify a comprehensive set a of research questions to fill current data gaps identified through the review. Insights on these would provide the comprehensive evidence needed to inform policy makers on how to develop new food systems policies for Viet Nam, and further refine and improve existing policies to achieve better quality diets and more sustainable food systems in Viet Nam. Based on these, we then engaged with stakeholders to develop research priorities in the Viet Nam context and identified 25 priority research questions. This paper aims to stimulate such reflections by clearly outlining key areas for research, government policy, and development programs on priority investment to build the evidence base around inclusive food systems interventions that aim to result in healthier diets and more sustainable food systems for Viet Nam

The Woods-Saxon Potential in the Dirac Equation

The two-component approach to the one-dimensional Dirac equation is applied to the Woods-Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission resonance (when the transmission coefficient is unity) and supercriticality (when the particle bound state is at E=-m) are then derived. The square potential limit is discussed. The recent result that a finite-range symmetric potential barrier will have a transmission resonance of zero-momentum when the corresponding well supports a half-bound state at E=-m is demonstrated.Comment: 8 pages, 4 figures. Submitted to JPhys

Managing crop tradeoffs: A methodology for comparing the water footprint and nutrient density of crops for food system sustainability

The relationship between human nutrition and the use of available resources to feed the planet's growing population demands greater attention from decision makers at all levels of governance. Indicators with dual environmental sustainability and food and nutrition security goals can encourage and measure progress towards a more sustainable food system. This article proposes a methodology that supports the development of an approach to assess the water footprint of nutrient-dense foods [m3/kg]. It provides a clear explanation of the methodology, and the use of water footprint benchmark data and corresponding United States Department of Agriculture (USDA) nutrient composition data to apply the process. The study analyzed data for 17 grains, roots and tubers, 9 pulses, 10 nuts and seeds, 17 vegetables, and 27 fruits. Of these, fruits and vegetables are 85% of the bottom quartile for water footprint (i.e., highly water efficient) and 100% of the top quartile for nutrient-density (i.e., very nutrient dense). Spinach is a clear winner, with a very high nutrient-density and low water footprint. The article proposes that this approach can help to establish broad typologies to guide decision makers in distinguishing between win-win, win-lose, and lose-lose scenarios of natural resource use and nutrition security. This resource, if considered along with contributing social, environmental, and economic factors (e.g., local tastes, available water resources, soil fertility, local economies) can promote a food system that offers a diverse range of nutrient-dense foods more sustainably