Using the distribution of cells by dimension in a cylindrical algebraic decomposition

We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather, the distribution is inherent to the cylindrical structure and determined mostly by the number of variables. This insight is then combined with an algorithm that produces only full-dimensional cells to give an accurate method of predicting the number of cells in a complete CAD. Since constructing only full-dimensional cells is relatively inexpensive (involving no costly algebraic number calculations) this leads to heuristics for helping with various questions of problem formulation for CAD, such as choosing an optimal variable ordering. Our experiments demonstrate that this approach can be highly effective.Comment: 8 page

Program Verification in the presence of complex numbers, functions with branch cuts etc

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as "does the low-level arithmetic implement the high-level mathematics". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more difficult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simplification rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities

A "Piano Movers" Problem Reformulated

It has long been known that cylindrical algebraic decompositions (CADs) can in theory be used for robot motion planning. However, in practice even the simplest examples can be too complicated to tackle. We consider in detail a "Piano Mover's Problem" which considers moving an infinitesimally thin piano (or ladder) through a right-angled corridor. Producing a CAD for the original formulation of this problem is still infeasible after 25 years of improvements in both CAD theory and computer hardware. We review some alternative formulations in the literature which use differing levels of geometric analysis before input to a CAD algorithm. Simpler formulations allow CAD to easily address the question of the existence of a path. We provide a new formulation for which both a CAD can be constructed and from which an actual path could be determined if one exists, and analyse the CADs produced using this approach for variations of the problem. This emphasises the importance of the precise formulation of such problems for CAD. We analyse the formulations and their CADs considering a variety of heuristics and general criteria, leading to conclusions about tackling other problems of this form.Comment: 8 pages. Copyright IEEE 201

Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition

Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heuristics to help with the choice for this algorithm, suggest improvements and then derive a new heuristic more closely aligned with the mechanics of the new algorithm

Parallelism between the philosophy of John Dewey and the art of Dorothy Canfield

This item was digitized by the Internet Archive. Thesis (M.A.)--Boston UniversityThis study is concerned with philosophy as represented by John Dewey, America's foremost philosopher and educator, and with art as represented by Dorothy Canfield, an American writer who is intensely interested in clarifying our way of life. Philosophy is itself a phenomenon of human culture. It does not deal with eternal truths, but is significant as a revelation of the predicaments, protests, and aspirations of humanity in a changing world. We shall think of philosophy as meaning. Philosophy marks a change of culture and is additive and transforming in its place in the history of civilization. As these remarks indicate, philosophy as meaning is subject to alteration since meanings serve as tests of the values which tradition submits and for those which emotion suggests. Failure to satisfactorily meet this test denotes the necessity for change and revision. Since philosophy is the conversion of existing cultures into consciousness which is coherent and compatible with facts known, every civilization results in an imaginative formulation of itself unless it accepts unquestioningly traditions inherited from past ages. If we do not have a philosophy which is a sincere outgrowth and expression of our civilization, it is because the imagination is fettered by an intellectual timidity that reverts to the past for its ideas. It is a worship of science and a suspicion of philosophy that prevent attainment of a true philosophy which might be reconciled with science. Philosophy is an attempt to comprehend so that one may adopt an outlook on life. When we consider facts and laws of science to discover what sort of permanent disposition toward the world these laws require of us, we are approaching the philosophic. We do not thus create a ready-made, complete scheme of action, but we acquire a certain equilibrium helpful in coping with other and future experiences. Education is the vantage point from which to penetrate the significance of philosophic discussions. If we are willing to conceive education as the process of forming fundamental dispositions toward nature and fellow-beings, philosophy may be defined as the general theory of education. Another function of philosophy is criticism. This is inevitable since a search for meanings and values demands a judgment, which results in criticism. Judgment requires thoughtful inquiry, knowledge, sensitivity, and experience; it is not enough to accept the judgment of another. It is the responsibility of philosophy to appraise values by taking cognizance of their causes and consequences through an intelligent use of the logic of experience, including the conclusions of science. Art, the second term of our study, cannot be considered in isolation from esthetic perception. The true artist is not only gifted in the powers of execution but in an unusual sensitivity to the qualities of things, which makes his work satisfying to himself and to the perceiver. Before an object is perceived as a work of art, the re-creation of the object by the percipient is necessary. An understanding of the nature of elemental experience is also needed in this discussion. Experience is the interaction of an organism and environment in an attempt to come into harmony with its surroundings. The value of an experience can be judged only by worthwhile reflection of the experience on the ground of what it moves toward and into. The true work of art evokes and organizes, through imagination, an experience similar to that of the artist himself. Art is the most direct and complete manifestation of experience as experience; therefore, it particularly challenges the imaginative ventures of philosophy. Like philosophy, art presents the first dissatisfaction with existing conditions and the first intimation of a better future. Surely an art which clarifies objects otherwise dumb, inchoate, and restricted cannot be deemed "immoral." We now approach John Dewey's conception of fundamental forces in American life. The first is democracy, a name for a life of free and enriching communion. It is a means for realizing ends that lie in the wide domain of human relationships and the development of human personality. It is a way of life, social and individual. The certain way of assuring a genuine and practical democracy is through socializing intelligence so that individual efforts may unite in the accomplishment of common ends. So long as business and its outcome are private, social fulfillment must be unknown. We must substitute for private gain a cooperative effort and sharing for enrichment. Thus democracy will set free and develop the capacities of human individuals without respect to race, sex, class, or economic status. Education is an important force in American life. According to John Dewey, "getting from the present the degree and kind of growth there is in it is education." Thus education is not to be obtained merely from formal schooling. Each experience is an education and this makes learning a continuous process. It is the responsibility of the experienced to patiently guide and direct the way of the inexperienced by using methods that will develop insight, understanding, and genuine thought. There is no moral independence for child or adult; the process of growing and developing Is restricted to no age limit. It is the business of every institution, whether democratic or educational, to set the Individual free to reach the full stature of his possibility. The individual must learn complete self-reliance if he is to be happy and useful. Since society is the interactions of individuals, it is highly important that the individual attain a degree of harmony within himself that he may bring to his social relations a deeper insight and understanding. Work is a necessary element in American living. Practical activity should not be regarded as onerous and toilsome while intellectual activity is associated with leisure; nor can play and work be distinguished from one another according to the presence or absence of direct interest In what is doing. Because every occupation leaves its impress on the doer, it is important that the social condition under which it is performed should be improved so far as possible. To this view Dorothy Ganfield adds the idea of work as moral discipline, as solace in time of stress and emergency, as a life-line to which one may cling, gaining strength and courage. Intelligence in morals is a matter of supreme concern in the life of any civilization. In this discussion we do not think of morals as boxed, fixed, and final; we do think of them as the result of judgment as to what is satisfying and valuable according to experience. This Judgment is based on true thinking. This involves surrendering preconceived notions or formulae for meeting situations. Then we face the facts of the situation if we are courageous and honest, and begin the pattern of reflective thinking. The reward of such thought is to transform a situation in which there is obscurity, doubt, disturbance, conflict into a situation that is clear, coherent, settled, harmonious. These fundamental points in the philosophy of John Dewey have been used as a frame of reference by which to test the validity of the novels of Dorothy Ganfield as an art form. By means of this parallelism of philosophy with art we find that Dorothy Canfield's works perform the functions of real art as exemplified by John Dewey. Her novels, if perused by the experiential reader, constitute a challenge to modern thinking and living by presenting, in art form, the same philosophic principles as are propounded by John Dewey. The novels are stirring isn their clarification of the American way of life and deserve the whole-hearted attention and appreciation of every thinking individual

Alternative teacher compensation systems: Practices and perceptions as reported by New Hampshire principals

The purpose of this study was to determine New Hampshire principal\u27s perceptions regarding alternative compensation plans for teachers. Alternative compensation plans, unlike traditional teacher pay plans, are not based exclusively on years of experience and formal educational attainment. Forms of alternative compensation plans include individually-based merit pay, career ladders, skill-and-knowledge-based pay, and group performance awards. This research was intended to provide a better understanding of how principals view the various alternatives to traditional salary schedules. An assumption of this study was that principals in the state play the primary role in formal teacher evaluations, and any new compensation plans that emerge would have the greatest chance for success if embraced and supported by principals. A survey research method of data collection was employed in this study. The entire population of 359 full-time New Hampshire public school principals was surveyed. A survey instrument consisting of a mailed questionnaire was developed to determine the perceptions held by principals regarding current evaluation and compensation practices employed by their school districts, as well as specific teacher compensation alternatives including merit pay, career ladders, skill and knowledge-based pay, and group performance awards. Completed surveys were received from 257 principals resulting in a 72% return rate. The results of the study indicate that, although New Hampshire school districts are compensating teachers according to traditional salary schedules which do not link pay to performance, a considerable number of districts are either working under or planning to implement an alternative compensation system for teachers. Although principals are largely satisfied with their ability and training in teacher evaluation, there was no correlation between this and support for the implementation of alternative systems. There is a particular reluctance to support merit pay programs which are viewed as competitive, dimly viewed by teachers, and difficult to administer. Other alternatives enjoy more favorable perceptions and merit further exploration. Based on the findings of the study, recommendations for the development of alternative compensation plans for teachers are presented

Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page

Boston Hospitality Review: Summer 2015

Boston, the Booth Brothers, and the Parker House by Susan Wilson -- Airports Hotels: Laying the Foundation for a Synergistic Relationship by Allison Fogarty -- The Pricing Effects of Heritage at an Iconic Hotel by Bradford Hudson -- The Customer is Always Right, Right? A Look at How Yelp Has Taken Hold of the Boston Restaurant Industry by Rachel DeSimone -- Search Engine Marketing (SEM): Financial & Competitive Advantages of an Effective Hotel SEM Strategy by Leora Lanz and Jovanna Fazzin

New Effort and Schedule Estimation Models for Agile Processes in the U.S. DoD

Excerpt from the Proceedings of the Nineteenth Annual Acquisition Research SymposiumThe DoD’s new software acquisition pathway prioritizes speed of delivery, advocating agile software processes. Estimating the cost and schedule of agile software projects is critical at an early phase to establish baseline budgets and to select competitive bidders. The challenge is that common ag-ile sizing measures such as story points and user stories are not practical for early estimation as these are often reported after contract award in DoD. This study provides a set of parametric effort and schedule estimation models for agile projects using a sizing measure that is available before proposal evaluation based on data from 36 DoD agile projects. The results suggest that initial software requirements, defined as the sum of functions and external interfaces, is an effective sizing measure for early estimation of effort and schedule of agile projects. The models’ accuracy improves when application domain groups and peak staff are added as inputs.Approved for public release; distribution is unlimited