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We have mapped cold atomic gas in 21cm line H i self-absorption (HISA) at arcminute resolution over more than 90% of the Milky Way's disk. To probe the formation of H2 clouds, we have compared our HISA distribution with CO J = 1-0 line emission. Few HISA features in the outer Galaxy have CO at the same position and velocity, while most inner-Galaxy HISA has overlapping CO. But many apparent inner-Galaxy HISA-CO associations can be explained as chance superpositions, so most inner-Galaxy HISA may also be CO-free. Since standard equilibrium cloud models cannot explain the very cold H i in many HISA features without molecules being present, these clouds may instead have significant CO-dark H2.
Let G be an arbitrary finite group, R be a finite associative ring with identity and RG be the group ring. We show that ℤ2Q8 is the minimal reversible group ring which is not symmetric, and we also characterise the finite rings R for which RQ8 is reversible. The first result extends a result of Gutan and Kisielewicz which shows that ℤ2Q8 is the minimal reversible group algebra over a field which is not symmetric, and it answers a question raised by Marks for the group ring case.
The aim of this project was to examine the relationships between driver behaviour and driving events during a journey and the behavioural responses of sheep to these events. Driving style can have a major influence on the welfare of the animals by affecting the risk of injury and by disturbing the ability of the sheep to rest. Two drivers each drove groups of 10 sheep in a 5·5-tonne, single-deck, non-articulated livestock vehicle on five 7-h road journeys consisting of minor roads, main single carriageways and a motorway. The driver, the driver’s view through the windscreen, the speedometer and the sheep were video recorded. Differences in driving style were identified as differences in vehicle speed, rapid braking and the number of corners taken with high cornering g-force. Differences in driving style had a slight effect on the frequency of losses of balance by the sheep and a more significant effect on the degree of disturbance to the sheep and on their ability to rest during the journey. Losses of balance were common, but falls were rare. About 80% of the losses of balance could have been caused by driving events, such as acceleration, braking, stopping, cornering, gear changes and uneven road surfaces. Only about 22% of driving events were followed by a loss of balance. It is likely that driving events were also responsible for many interruptions to both lying behaviour and rumination. Clear benefits of motorway driving compared with single carriageway driving were fewer losses of balance, more lying down, more rumination and fewer disturbances amongst the sheep. This study provides evidence that would be useful for driver training and education to promote careful driving as a means of ensuring the welfare of animals in-transit. The quality of the journey experienced by sheep during transport is dependent upon a number of factors that can be influenced by the driver of the vehicle.
If R is a ring and S ⊆ R, a mapping f:R —> R is called strong commutativity- preserving (scp) on S if [x, y] = [f(x),f(y)] for all x,y € S. We investigate commutativity in prime and semiprime rings admitting a derivation or an endomorphism which is scp on a nonzero right ideal.
This book is a collection of papers presented at a conference, “Decision Making: Descriptive, Normative, and Prescriptive Interactions,” held in Boston at the Harvard Business School during June 16–18, 1983. The conference was one of several celebrating the 75th anniversary of the Harvard Business School. It might equally have been held as a celebration of the renaissance of interest in the analysis of decision making under uncertainty that has occurred in recent years. Not since the early 1950s, in the aftermath of the pathbreaking work by von Neumann and Morgenstern, has so much intellectual enthusiasm been directed at the question of how people should, and do, behave when called upon to take action in the face of uncertainty.
When Amos Tversky visited Harvard in the spring of 1982, the three of us had long discussions about the philosophy behind the contribution made by various disciplines to research on decision making. It was clear that mathematicians (decision theorists) are interested in proposing rational procedures for decision making – how people should make decisions if they wish to obey certain fundamental laws of behavior. Psychologists are interested in how people do make decisions (whether or not rational) and in determining the extent to which their behavior is compatible with any rational model. They are also interested in learning the cognitive capacities and limitations of ordinary people to process the information required of them if they do not naturally behave rationally, but wish to.
The focus of our attention is the individual decision maker facing a choice involving uncertainty about outcomes. We will consider how people do make decisions, how “rational” people should make decisions, and how we might help less rational people, who nevertheless aspire to rationality, to do better. When we speak of nonrational people, we do not mean those with diminished capacities; we refer instead to normal people who have not given thought to the process of decision making or, even if they have, are unable, cognitively, to implement the desired process. Our decision makers are not economic automatons; they make mistakes, have remorse, suffer anxieties, and cannot make up their minds. We start with a premise, not that people have well thought out preferences, but that they may be viewed as having divided minds with different aspirations, that decision making, even for the individual, is an act of compromise among the different selves.
For our purposes we shall augment the usual dichotomy that distinguishes between the normative and descriptive sides (the “ought” and the “is”) of decision making, by adding a third component: the prescriptive side. We do this because much of our concern in this paper addresses the question: “How can real people – as opposed to imaginary, idealized, super-rational people without psyches – make better choices in a way that does not do violence to their deep cognitive concerns?” And we find that much that we have to say on these matters does not fit conveniently into the usual normative or descriptive niches.
The analysis of decision making under uncertainty has again become a major focus of interest. This volume presents contributions from leading specialists in different fields and provides a summary and synthesis of work in this area. It is based on a conference held at the Harvard Business School. The book brings together the different approaches to decision making - normative, descriptive, and prescriptive - which largely correspond to different disciplinary interests. Mathematicians have concentrated on rational procedures for decision making - how people should make decisions. Psychologists have examined how poeple do make decisions, and how far their behaviour is compatible with any rational model. Operations researchers study the application of decision models to actual problems. Throughout, the aim is to present the current state of research and its application and also to show how the different disciplinary approaches can inform one another and thus lay the foundations for the integrated analysis of decision making. The book will be of interest to researchers, teachers - for use as background reading for a decision theory course - students, and consultants and others involved in the practical application of the analysis of decision making. It will be of interest to specialists and students in statistics, mathematics, economics, psychology and the behavioural sciences, operations research, and management science.
Imagine that you will shortly be asked to consciously select one of several urns and from this urn you will then be asked to randomly select one ball. For the moment, we assume that each urn contains exactly N balls (say, 1,000), and each ball in the selected urn is equally likely to be chosen. Each ball has a number on it which specifies the incremental monetary return to you for drawing that ball.
Suppose that you have the opportunity to examine the balls and their numbers in all the urns before deciding upon your choice of urn. How would you use that opportunity? A useful answer to this question would have to take some account of the length of time available for your examination. Here we will adopt the view that time is available for any extensive analysis that you would care to make.
We will present three different but related techniques for choosing among urns. In order to decide when and for whom these techniques are appropriate, we shall discuss various behavioral assumptions that underlie each of these techniques. In mathematical parlance, we shall discuss necessary and sufficient behavioral assumptions that justify each of these techniques.
The papers in this volume are organized according to a few guiding principles.
The first dichotomy is between theory (20 papers) and application (8 papers).
Within the domain of theory we organized the papers into the following trichotomy:
(a) conceptions of choice (9 papers)
(b) beliefs and judgments about uncertainties (4 papers)
(c) values and utilities (7 papers)
Within each of these categories we arranged the papers according to the following sequence:
(a) decisions people make and how they decide
(b) logically consistent decision procedures and proposals of how people should decide
(c) behavioral objections to normative proposals
(d) how to help people to make better decisions in the light of behavioral realities and normative ideals
(e) how to train people to make better decisions, for example, by providing heuristics and, possibly, therapy
This sequence is motivated and elaborated in the overview paper by the editors (chapter 1).
In the application section, the papers are arranged by fields: economics, management, education, and medicine.
We, the organizers of this conference and its proceedings, in discussions among ourselves about our domain of concern – individual decision making under uncertainty – have found the following taxonomy helpful:
Decisions people make
How people decide
Logically consistent decision procedures
How people should decide
How to help people to make good decisions
How to train people to make better decisions
Observe that we have moved from the usual dichotomy (descriptive and normative) to a trichotomy by adding a “prescriptive” category.
We examine the connection between, and distinction between, decreasing marginal value (whatever that may mean) and risk aversion (from Pratt, 1964). When a decision maker (DM henceforth) declares indifference between $1,500 for certain and a 50–50 lottery with payoffs $0 and $5,000, the DM may have two concerns: (1) a feeling that going from $0 to $2,500 is “worth far more” than going from $2,500 to $5,000, and (2) being “nervous” about the uncertainty in the gamble. We will call the first concern “strength of preference” and the second concern “intrinsic risk aversion.” How much of the $1,000 difference between the arithmetical average of the gamble payoffs and the certainty equivalent is due to each of these concerns? Apart from a natural curiosity about such things we have other motivations:
(a) Many utility-assessment procedures currently rely heavily on answers to questions about gambles (e.g., Keeney and Raiffa, 1976); but decision makers are often uncomfortable with making choices among risky alternatives. Can alternative procedures that do not rely heavily on gambling questions be used justifiably?
(b) Many value-assessment procedures rely exclusively on strength-of-preference protocols (e.g., by comparing increments of gain or loss) and never confront subjects with risky choices. But some of these studies are then used to guide risky-choice options. […]
Let R be an arbitrary near-ring and define the multiplicative centre Z(R) by
In previous papers (2,3,5) we have established additive or multiplicative commutativity for various near-rings R in which selected elements were restricted to lie in Z(R); the near-rings involved were usually distributively-generated (d-g) and were frequently assumed to have a multiplicative identity element as well.