Classification of the monomial Cremona transformations of the plane

We classify all monomial planar Cremona maps by multidegree using recent methods developed by Aluffi. Following the main result, we prove several more properties of the set of these maps, and also extend the results to the more general `r.c. monomial' maps.Comment: Work in progress... comments are welcom

Monomial principalization in the singular setting

We generalize an algorithm by Goward for principalization of monomial ideals in nonsingular varieties to work on any scheme of finite type over a field. The normal crossings condition considered by Goward is weakened to the condition that components of the generating divisors meet as complete intersections. This leads to a substantial generalization of the notion of monomial scheme; we call the resulting schemes `c.i. monomial'. We prove that c.i. monomial schemes in arbitrarily singular varieties can be principalized by a sequence of blow-ups at codimension 2 c.i. monomial centers.Comment: 7 pages, 2 figure

The Euclidean distance degree of smooth complex projective varieties

We obtain several formulas for the Euclidean distance degree (ED degree) of an arbitrary nonsingular variety in projective space: in terms of Chern and Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an extremely simple formula equating the Euclidean distance degree of X with the Euler characteristic of an open subset of X

Segre Class Computation and Practical Applications

Let $X \subset Y$ be closed (possibly singular) subschemes of a smooth projective toric variety $T$. We show how to compute the Segre class $s(X,Y)$ as a class in the Chow group of $T$. Building on this, we give effective methods to compute intersection products in projective varieties, to determine algebraic multiplicity without working in local rings, and to test pairwise containment of subvarieties of $T$. Our methods may be implemented without using Groebner bases; in particular any algorithm to compute the number of solutions of a zero-dimensional polynomial system may be used

Design of a shim for a nanopositioner

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 37).The purpose of this thesis is to assist in the development of a low cost nanopositioner by designing a specific component - a shim that is located in the scan tip assembly of the nanopositioner. Nanopositioners must maximize precision to successfully produce features of fewer than 100 nm. The kinematic coupling used to place the tool tip is capable of producing a high level of precision across tool changes, assuming the groove mount is held in place. It is therefore very important to secure the groove mount to prevent dislocation and enhance the viability of nano-scale device fabrication. The shim developed within this thesis serves to secure the groove mount of the kinematic coupling, which was previously held in place solely with magnetic attraction. The shim secures the groove mount by applying a force to the side of the groove mount in addition to increasing the magnetic attraction between the groove mount and universal mount of the nanopositioner. It was first modeled with solid and magnetic modeling software before being manufactured and tested. With the addition of the shim, the vertical force required to displace the groove mount increased by a factor of 9.4, from 0.14 N to 1.29 N. Similarly the lateral force increased by a factor of 27.9, from 0.09 N to 2.45 N. As a result, the nanopositioner is significantly better suited to perform its function. The nanopositioner will be used to produce nano-scale devices including carbon nanotubes, molecular actuators, and transistors, with applications across several disciplines. Future work includes developing a tool to bend the shim tabs and simplify the manufacturing process.by Corey G. Harris.S.B

The Domestic Church and the Post-Nuclear Family: A Theological Analysis and Critique

This dissertation is an attempt to reconcile the Roman Catholic theological understanding that the Christian family is a domestic church (ecclesia domestica) with a realistic demographic and sociological portrait of the American family while remaining faithful to Catholic moral teaching. The first chapter analyzes several works of the Magisterium from the time of Vatican II that have specifically referenced the domestic church. These documents collectively show that the domestic church is a sacramental and ecclesial reality although the theology is commonly espoused under the subheading of marriage and referencing a specifically nuclear form of family. The following chapter analyzes the thoughts of various theologians by approaching the topic thematically. Evidence is found of two distinct schools of thought: those who believe the theology of domestic church espoused by the Magisterium is by definition too restrictive and those who agree with the Magisterium\u27s teaching that bases the domestic church within a theology of marriage excluding non-nuclear families. The following chapter analyzes demographic trends, sociology of family, and sociology of family and religion. Demographic trends show the family moving away from a standard of nuclear form. Sociological views shows that myriad family forms are valid if supported properly. Also, religion and families are shown to be mutually supportive of each other so long as religions and families perceive positive benefits in their relationship. The final chapter argues that the term domestic church is a sacramental, ecclesial, sociological, and moral term. The domestic church is sacramental because of what it is (a Church) and what it does (shares the Church\u27s mission). To that end, it is baptism which begins membership in the Church and therefore baptism that is the root of the domestic church. As such, all family forms composed of baptized members that are not inherently contrary to Catholic moral teaching can be considered domestic churches. Families that remain excluded are done so on an ecclesial basis not on a sacramental basis. Ongoing participation in the Church and conformity in lifestyle to Church teaching are the basic requirements for consideration as a domestic church

The acute effects of dietary protein at breakfast on reward driven neural activity prior to lunch

Although numerous studies have targeted the physiological, homeostatic signals altered with various dietary interventions, data are limited concerning whether the non-homeostatic, reward-driven mechanisms underlying ingestive behavior are modulated. The study purpose was to determine whether breakfast consumption would modulate the neural activity in brain regions associated with reward-driven eating in overweight `breakfast skipping' (BS) adolescent girls and to identify whether increased protein at breakfast leads to additional alterations. Ten girls (Age: 15±1y; BMI percentile 93±1%; BS 5±1x/week) completed 3 testing days. Following the BS day, the participants were provided with, in randomized order, normal protein (NP; 18±1g protein) or higher protein (HP; 50±1g protein) breakfast meals to consume at home for six days. On day 7 of each pattern, the participants came to the laboratory to consume their respective breakfast followed by pre-lunch (i.e., 3-h post-breakfast) appetite questionnaires and a functional magnetic resonance imaging (fMRI) brain scan to identify brain activation responses to viewing food vs. non-food images. Breakfast consumption led to reduced hippocampus and parahippocampus activation and increased medial frontal gyrus activation vs. BS. Between breakfast meals, HP resulted in reduced insula activation vs. NP. Parahippocampal and insula activations were correlated with appetite; insula activation was inversely correlated with satiety. Collectively, the incorporation of breakfast led to alterations in brain activation involved with reward-driven eating behavior with additional alterations following the protein-rich meal. These data suggest that increased dietary protein at breakfast might be a beneficial, modest strategy to reduce the impact of the modern food environment in overweight `breakfast skipping' adolescent girls

Senior Recital:Corey Harris, Soprano

Kemp Recital Hall Saturday Afternoon March 29, 2003 2:45p.m