Bridges Between Subriemannian Geometry and Algebraic Geometry

We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes. Various ideas that traditionally pertain to the field of algebraic geometry emerge here organically in an attempt to elucidate the geometric structures underlying a large class of nonholonomic distributions known as Goursat constraints. Among our new results is a regularization theorem for curves stated and proved using tools exclusively from nonholonomic geometry, and a computation of topological invariants that answer a question on the global topology of our classifying space. Last but not least we present for the first time some experimental results connecting the discrete invariants of nonholonomic plane fields such as the RVT code and the Milnor number of complex plane algebraic curves.Comment: 10 pages, 2 figures, Proceedings of 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid 201

Complete spelling rules for the Monster tower over three-space

The Monster tower, also known as the Semple tower, is a sequence of manifolds with distributions of interest to both differential and algebraic geometers. Each manifold is a projective bundle over the previous. Moreover, each level is a fiber compactified jet bundle equipped with an action of finite jets of the diffeomorphism group. There is a correspondence between points in the tower and curves in the base manifold. These points admit a stratification which can be encoded by a word called the RVT code. Here, we derive the spelling rules for these words in the case of a three dimensional base. That is, we determine precisely which words are realized by points in the tower. To this end, we study the incidence relations between certain subtowers, called Baby Monsters, and present a general method for determining the level at which each Baby Monster is born. Here, we focus on the case where the base manifold is three dimensional, but all the methods presented generalize to bases of arbitrary dimension.Comment: 14 pages, 4 figures; new titl

Inactivation of Mandelate Racemase by 3-Hydroxypyruvate Reveals a Potential Mechanistic Link between Enzyme Superfamilies

Mandelate racemase (MR), a member of the enolase superfamily, catalyzes the Mg2+-dependent interconversion of the enantiomers of mandelate. Several α-keto acids are modest competitive inhibitors of MR [e.g., mesoxalate (Ki = 1.8 ± 0.3 mM) and 3-fluoropyruvate (Ki = 1.3 ± 0.1 mM)], but, surprisingly, 3-hydroxypyruvate (3-HP) is an irreversible, time-dependent inhibitor (kinact/KI = 83 ± 8 M–1 s–1). Protection from inactivation by the competitive inhibitor benzohydroxamate, trypsinolysis and electrospray ionization tandem mass spectrometry analyses, and X-ray crystallographic studies reveal that 3-HP undergoes Schiff-base formation with Lys 166 at the active site, followed by formation of an aldehyde/enol(ate) adduct. Such a reaction is unprecedented in the enolase superfamily and may be a relic of an activity possessed by a promiscuous progenitor enzyme. The ability of MR to form and deprotonate a Schiff-base intermediate furnishes a previously unrecognized mechanistic link to other α/β-barrel enzymes utilizing Schiff-base chemistry and is in accord with the sequence- and structure-based hypothesis that members of the metal-dependent enolase superfamily and the Schiff-base-forming N-acetylneuraminate lyase superfamily and aldolases share a common ancestor

DIRBE External Calibrator (DEC)

Under NASA Contract No. NAS5-28185, the Center for Space Engineering at Utah State University has produced a calibration instrument for the Diffuse Infrared Background Experiment (DIRBE). DIRBE is one of the instruments aboard the Cosmic Background Experiment Observatory (COBE). The calibration instrument is referred to as the DEC (Dirbe External Calibrator). DEC produces a steerable, infrared beam of controlled spectral content and intensity and with selectable point source or diffuse source characteristics, that can be directed into the DIRBE to map fields and determine response characteristics. This report discusses the design of the DEC instrument, its operation and characteristics, and provides an analysis of the systems capabilities and performance

A Study of Tenure and the Orderly Demotion or Dismisal of Teachers in the State of Utah

The problem of this study is to determine, so far as possible, the conditions, reasons, and underlying motives which have led to the dismissal, demotion, or non-issuance of contracts to teachers in the state of Utah during a recent five-year period, 1943-1947, and also what methods have been used in terminating the tenure of those teachers who have been considered undesriable by their employers. The study will seek to reveal the extent to which the professional education associations are influential in determining policies for the dismissal of teachers. It is hoped that from this study some suggestions may emerge which will aid in establishing principles for the orderly dismissal of teachers. More specifically, these are the problems for which answers will be attempted: 1. What existing conditions contributed to the demotion or dismissal of teachers; and what conditions seemed to permit, encourage, or cause employers to act adversely toward teachers? 2. What reasons were advanced as for grounds or action taken to demote or dismiss teachers? 3. What were the underlying motives given by those responsible for the demoting or removing of teachers from their positions? 4. To what extent and in what ways have professional education associations exerted influence where teachers have been dismissed or demoted? 5. Is there an evident trend indicating an increase in the influence professional organizations are having on the tenure of their members? 6. What are some principles and procedures based on the data collected which may be incorporated in a plan for the orderly demotion and/or dismissal of incompetent and unsatisfactory teachers

Mother-child relationships and stuttering in children

Thesis (Ph.D.)--Boston UniversityThe Problem. Theories concerning the origin and treatment of stuttering have varied widely. Older theories have been highly speculative, while a more systematic clinical and experimental approach has been prevalent lately. A major weakness of research studies has been the lack of adequate conceptual schemes for systematizing the data and the absence of specific hypotheses to be tested. In this study recent findings in genetic psychology, in the psychology of language, and in the psychoanalytic study of ego development have been utilized for the formulation of a "developmental crisis" theory of stuttering. The onset of stuttering has been interpreted as the result of a crisis in language learning coincident with a crisis in the relationship between mother and child. [TRUNCATED

Divine Intervention: Designed for Social Evolution by Integrating Natural Order

There is a long tradition in architecture of using ordering systems found in nature and science to create built space. This thesis builds upon such line of thought to propose new design methods based on ordering systems with a particular focus on social relations. It focuses on the design of a community center in the city of Atlanta which is considered as a catalyst for jumpstarting the betterment of society through improvement of social bonds, community involvement, activism, meditation, and the integration of nature in the community. The design is situated on the Bellwood Quarry site and creates an ecological balance by combining the man-made and natural environment where man and nature co-exist in a mutual symbiotic relationship neither having adverse effects on the other, and the reconstitution of public realm by finding order in the chaotic behavior of the site. The design methods aim to augment existing ordering systems based on geometrical elements with new ordering systems based on topological qualities that depict social relations. The thesis questions is it necessary to first understand order within nature, to achieve order within ourselves and the built environments that surround us; proposing that when natural ordering systems are used in a spatial context, an architecture can be created that will help enhance the socio-economic development, and place of underserved people, making architecture a direct solution to the many problems that face disadvantaged and impoverished communities today

How accessible and acceptable are current GP referral mechanisms for IAPT for low-income patients? Lay and primary care perspectives

Background: Improving Access to Psychological Therapies (IAPT) constitutes a key element of England’s national mental health strategy. Accessing IAPT usually requires patients to self-refer on the advice of their GP. Little is known about how GPs perceive and communicate IAPT services with patients from low-income communities, nor how the notion of self-referral is understood and responded to by such patients. Aims: This paper examines how IAPT referrals are made by GPs and how these referrals are perceived and acted on by patients from low-income backgrounds Method: Findings are drawn from in-depth interviews with low-income patients experiencing mental distress (n = 80); interviews with GPs (n = 10); secondary analysis of video-recorded GP-patient consultations for mental health (n = 26). Results: GPs generally supported self-referral, perceiving it an important initial step towards patient recovery. Most patients however, perceived self-referral as an obstacle to accessing IAPT, and felt their mental health needs were being undermined. The way that IAPT was discussed and the pathway for referral appears to affect uptake of these services. Conclusions: A number of factors deter low-income patients from self-referring for IAPT. Understanding these issues is necessary in enabling the development of more effective referral and support mechanisms within primary care