Kodaira Dimension of Subvarieties

In this article we study how the birational geometry of a normal projective variety $X$ is influenced by a normal subvariety $A \subset X.$ One of the most basic examples in this context is provided by the following situation. Let $f:X\to Y$ be a surjective holomorphic map with connected fibers between compact connected complex manifolds. It is well known that given a general fiber $A$ of $f$ we have $$\kappa(X)\le \kappa(A)+\dim Y.$$ This article grew out of the realization that this result should be true with $\dim Y$ replaced by the codimension \cod_X A for a pair $(X,A)$ consisting of a normal subvariety $A$ of a compact normal variety $X$ under weak semipositivity conditions on the normal sheaf of $A$ and the weak singularity condition \cod_A (A\cap\sing X)\ge 2. We shall now state our main results in the special case of a submanifold $A$ in a projective manifold $X$ and we also simplify the semipositivity notion

Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations

Climate projections continue to be marred by large uncertainties, which originate in processes that need to be parameterized, such as clouds, convection, and ecosystems. But rapid progress is now within reach. New computational tools and methods from data assimilation and machine learning make it possible to integrate global observations and local high-resolution simulations in an Earth system model (ESM) that systematically learns from both. Here we propose a blueprint for such an ESM. We outline how parameterization schemes can learn from global observations and targeted high-resolution simulations, for example, of clouds and convection, through matching low-order statistics between ESMs, observations, and high-resolution simulations. We illustrate learning algorithms for ESMs with a simple dynamical system that shares characteristics of the climate system; and we discuss the opportunities the proposed framework presents and the challenges that remain to realize it.Comment: 32 pages, 3 figure

Superluminal Caustics of Close, Rapidly-Rotating Binary Microlenses

The two outer triangular caustics (regions of infinite magnification) of a close binary microlens move much faster than the components of the binary themselves, and can even exceed the speed of light. When $\epsilon > 1$, where $\epsilon c$ is the caustic speed, the usual formalism for calculating the lens magnification breaks down. We develop a new formalism that makes use of the gravitational analog of the Li\'enard-Wiechert potential. We find that as the binary speeds up, the caustics undergo several related changes: First, their position in space drifts. Second, they rotate about their own axes so that they no longer have a cusp facing the binary center of mass. Third, they grow larger and dramatically so for $\epsilon >> 1$. Fourth, they grow weaker roughly in proportion to their increasing size. Superluminal caustic-crossing events are probably not uncommon, but they are difficult to observe.Comment: 12 pages, 7 ps figures, submitted to Ap

Financial Advisors' Role in Influencing Social Security Claiming

For millions of Americans, financial advisors are a trusted source of financial and retirement preparation information. This includes providing advice and information on Social Security benefits, a critical component of most Americans’ retirement finances. To gain greater insight into what financial advisors say to their clients about Social Security, an online survey of over 400 professional financial advisors was conducted in the Spring of 2011. The results reveal that a majority of advisors believe that they are responsible for educating their clients on the role Social Security will play in their retirement income. Moreover, advisors have the ability to influence their clients’ decisions about when to claim their Social Security retirement benefits. Three-quarters advise the majority of their clients on when to claim. In addition, the study finds that the Social Security Administration (SSA) is the leading and preferred source of information and education for financial advisors and their clients. Over half of advisors say it is a major source of Social Security-related information, more than any other source. However, advisors are critical of the job SSA does in educating advisors and the public, and are interested in additional resources from the Agency. Financial advisors also indicate that the financial services companies they work with could improve their communication and education efforts as it relates to Social Security. The research findings uncover a need for improved methods of educating and disseminating information to financial advisors and the public on Social Security.

Noise Pollution? What\u27s the solution?: Understanding Traffic Noise Pollution in Gettysburg, Pennsylvania

Noise pollution can be damaging to a community by impacting its atmosphere as well as the health of its residents, local quality of life, and local economy. Our study sought to gain insight into the level of noise pollution in Gettysburg, both in-town and on the Gettysburg College campus, and how noise pollution may be affecting the local residents and students. We selected 9 sampling sites, 6 in-town and 3 on the college campus, and measured the noise pollution in dBA with portable sound meters three days a week and three times a day over a three week period. Our data showed no major trends in terms of time of day or day of the week, but there were clear differences in noise pollution levels between the different sites in that town sites were generally louder than on campus sites. Noise pollution in town was often louder than 70 dBA, the noise threshold that indicates possible hearing damage overtime set by the World Health Organization. Gettysburg has recently enacted a noise ordinance; our study suggests the Borough possibly could do more to mitigate traffic noise by repairing roads and manipulating road design

Language Policy and Planning in A Church-Sponsored ESL Program

The purpose of this qualitative study is to examine language policy in privately funded church-sponsored adult English as a Second Language (ESL) programs in the United States. Specifically, this study focuses on one church and how its policy prohibiting proselytization in the classroom is interpreted by its volunteer instructors. The aim of this study is not to critique the success or failure of these policies but instead attempt to observe, describe, and report the spectrum of resistance and acceptance of restrictions (indeed, if it is perceived as such) on the types of language permitted to be used in ESL classrooms. Findings show that volunteers have different interpretations about how the Christian faith should or should not be integrated into curriculum. These beliefs stem from their theological interpretations about religious conversion as well as the volunteers’ self-reported depth of religious beliefs. No evidence of proselytization or religious activities was observed, showing that this locally-created policy was effective in its goal of separating the teaching of faith and language during ESL classes. This is significant because it represents, to date, the only example of the impact of explicit language policies studied in adult ESL church-sponsored programs

Projections from Subvarieties

Let $X\subset P^N$ be an n-dimensional connected projective submanifold of projective space. Let $p : P^N\to P^{N-q-1}$ denote the projection from a linear $P^q\subset P^N$. Assuming that $X\not\subset P^q$ we have the induced rational mapping $\psi:=p_X: X\to P^{N-q-1}$. This article started as an attempt to understand the structure of this mapping when $\psi$ has a lower dimensional image. In this case of necessity we have $Y := X\cap P^q$ is nonempty. We have in this article studied a closely related question, which includes many special cases including the case when the center of the projection \pn q is contained in $X$. PROBLEM. Let $Y$ be a proper connected k-dimensional projective submanifold of an $n$-dimensional projective manifold $X$. Assume that $k>0$. Let $L$ be a very ample line bundle on $X$ such that $L\otimes I_Y$ is spanned by global sections, where $I_Y$ denotes the ideal sheaf of $Y$ in $X$. Describe the structure of $(X,Y,L)$ under the additional assumption that the image of $X$ under the mapping $\psi$ associated to $| L\otimes I_Y|$ is lower dimensional