The termination of rewrite systems for parameter recursion, simple nested recursion and unnested multiple recursion is shown by using monotone interpretations both on the ordinals below the first primitive recursively closed ordinal and on the natural numbers. We show that the resulting derivation lengths are primitive recursive. As a corollary we obtain transparent and illuminating proofs of the facts that the schemata of parameter recursion, simple nested recursion and unnested multiple recursion lead from primitive recursive functions to primitive recursive functions.

Let F be a signature and R a strictly orthogonal rewrite system on ground terms of F . We give an effective proof of a bounding condition for R , based on a detailed analysis of how terms are transformed during the rewrite process, which allows us to give recursive bounds on the derivation lengths of terms. We give a syntactic characterisation of the Grzegorczyk hierarchy and a rewriting schema for calculating its functions. As a consequence of this, using results (...) of Elias Tahhan–Bittar, it can be shown that, for n⩾3 , the derivation length functions for functions in Grzegorczyk class E n belong to Grzegorczyk class E n+1 . We also give recursive bounds for the derivation lengths of functions defined by parameter recursion. (shrink)

Standard models of adolescent risk taking posit that the cognitive abilities of adolescents and adults are equivalent, and that increases in risk taking that occur during adolescence are the result of socio emotional differences in impulsivity, sensation seeking, and lack of self-control. Fuzzy-trace theory incorporates these socio emotional differences. However, it predicts that there are also cognitive differences between adolescents and adults, specifically that there are developmental increases in gist-based intuition that reflects understanding. Gist understanding, as opposed to verbatim-based analysis, (...) generally has been hypothesized to have a protective effect on risk taking in adolescence. Gist understanding is also an essential element of informed consent regarding risks in medical decision- making. Evidence thus supports the argument that adolescents’ status as mature minors should be treated as an exception rather than a presumption, because accuracy in verbatim analysis is not mature gist understanding. Use of the exception should be accompanied by medical experts’ input on the bottom-line gist of risks involved in treatment. (shrink)

Plato is one of the key ancient authors studied by both classicists and philosophers. This long-awaited new edition contains seven of the dialogues of Plato, and is the first in the five-volume complete edition of his works in the Oxford Classical Texts series. The result of many years of painstaking scholarship, the new volume will replace the now nearly 100 year old original edition, and is destined to become just as long-lasting a classic.

Using payment to recruit research subjects is a common practice, but it raises ethical concerns that coercion or undue inducement could potentially compromise participants’ informed consent. This is the first national study to explore the attitudes of IRB members and other human subjects protection professionals concerning whether payment of research participants constitutes coercion or undue influence, and if so, why. The majority of respondents expressed concern that payment of any amount might influence a participant’s decisions or behaviors regarding research participation. (...) Respondents expressed greater acceptance of payment as reimbursement or compensation than as an incentive to participate in research, and most agreed that subjects are coerced if the offer of payment makes them participate when they otherwise would not or when the offer of payment causes them to feel that they have no reasonable alternative but to participate . Views about undue influence were similar. We conclude that human subjects protection professionals hold expansive and inconsistent views about coercion and undue influence that may interfere with the recruitment of research participants and impede valuable research. (shrink)

I think that to Lord Kelvin is attributed the saying that the scientific attitude to a thing, if you can't do anything else with it, is to measure it. This is the attitude I propose to adopt towards Time . The situation is to some extent analogous to the situation with regard to electricity . Science is unable to say what electricity is, and so it almost denies the word any entrance into a treatise on the subject. It replaces it (...) by the word charge , which is something that can be measured. It is important to avoid hypostatizing time into a thing-in-itself. Instead of trying to say what time is we try to find a way of measuring it. (shrink)

When I agreed to lecture to-night I stipulated that I might be allowed to interpret the subject announced so as to let my treatment relate less to the subject in general than to some particular aspects which happen to have been interesting me lately. Professor Whitehead, Sir Arthur Eddington, and Sir James Jeans have given to the world brilliant accounts of the present position of physics in relation to mathematics and philosophy. What I have to say bears to their writings, (...) the humble relation of an example to a piece of book-work, or of an application of a theorem to the theorem itself. (shrink)

Although the equally pervasive and abstract concept of space has generated a vast body of disciplines, time, and the related idea of "becoming" (transforming, ...

Recent results in kinematics, obtained by myself and those working with me, have convinced me that the philosophical status of physics, as it has come down to us from Renaissance days, requires reconsideration. The reason can be stated in a couple of sentences: it has been found possible to establish certain laws of physics—laws of motion, the law of gravitation, the laws known under the name of the Lorentz transformation, and some others—purely deductively, without specific assumptions, and without empirical appeals (...) save only to the empirical awareness of something we call “the passage of time.” Yet physicists have claimed ad nauseam that the ultimate sanction for “laws of nature” is observation and experiment, that this is what distinguishes physics from other branches of exact inquiry. The contrast in these two conceptions of natural law needs no emphasis. It is the purpose of this article to attempt to clarify this confused situation. (shrink)

"Of all the economic bubbles that have been pricked," the editors of The Economist recently observed, "few have burst more spectacularly than the reputation of economics itself." Indeed, the financial crisis that crested in 2008 destroyed the credibility of the economic thinking that had guided policymakers for a generation. But what will take its place? In How the Economy Works, one of our leading economists provides a jargon-free exploration of the current crisis, offering a powerful argument for how economics must (...) change to get us out of it. Roger E. A. Farmer traces the swings between classical and Keynesian economics since the early twentieth century, gracefully explaining the elements of both theories. During the Great Depression, Keynes challenged the longstanding idea that an economy was a self-correcting mechanism; but his school gave way to a resurgence of classical economics in the 1970s-a rise that ended with the current crisis. Rather than simply allowing the pendulum to swing back, Farmer writes, we must synthesize the two. From classical economics, he takes the idea that a sound theory must explain how individuals behave-how our collective choices shape the economy. From Keynesian economics, he adopts the principle that markets do not always work well, that capitalism needs some guidance. The goal, he writes, is to correct the excesses of a free-market economy without stifling entrepreneurship and instituting central planning.Recent events have shown that we cannot afford to treat economics as an ivory-tower abstraction. It has a direct impact on our lives by guiding regulators and policymakers as they make decisions with far-reaching practical consequences. Written in clear, accessible language, How the Economy Works makes an argument that no one should ignore. (shrink)

Air transport is playing an increasing role in the world economy every year. This is facilitated by technological development and the latest developments in the aviation industry, globalization. This paper provides an overview of artificial neural network training methods for airfare predicting. The articles for 2017-2019 were analyzed in order to determine the model with the most accurate prediction. The researchers conducted research on open data collected by themselves and set themselves the goal of creating a model that would advise (...) a user the best time to buy a ticket when the price would be the lowest. The review of the papers by similar themes revealed that the Bagging Regression Tree model has the highest results with an accuracy of 88% and the random forest method has an accuracy of 87%. Civil aviation plays an important role in the economy of each country. Aviation is the best way to cover long distances in comfort in the shortest time. Airlines offer customers a variety of opportunities to travel both within the country and abroad. The main problem of interaction between airlines and customers is the airfare: the former want to sell more at the higher price, and the latter want to buy cheaper. Therefore, companies use their own private algorithms for dynamic pricing and constantly monitor the market situation, responsive to changes in demand and the actions of competitors. This behavior allows them to achieve a balance between the desires of airlines and customers. Scientists are trying to invent a way to predict airfare so that air travelers can buy them at the lowest price. The results of the work in this area provide general rules for the best purchase. For example, according to the article thebest day to buy a ticket by expedia.com for a domestic flight on the United States is Sunday, and the best period is 57 days before departure. This article provides an overview of the works, the authors of which compared the models of machine learning. Achievements in this area are limited to direct flights of a certain domestic market and 88% accuracy of the forecast. The Bagging Regression Tree model described in the article can be considered the best result. This trained model can make predictions based only on two parameters: the number of free cargo and the number of days left before departure and has an accuracy of 88%. (shrink)

In this paper we briefly expose a project which could be summed up as ‘doing justice to Mario Pieri’. The main result of the project will be the publication of a book on him, in which we will mainl...

In his article on “The Nature and the Status of the Study of Politics” 1 Professor White raises, whether explicitly or by implication, some of the most important and, probably permanent problems of the subject. The solutions that he attempts to provide seem to me, however, to be less satisfying than might be expected.