From infinite ergodic theory to number theory (and possibly back)

Some basic facts of infinite ergodic theory are reviewed in a form suitable to be applied to interval maps with number theoretic significance such as the Farey map. This is an enlarged version of the lecture notes accompanying a short course on Infinite Ergodic Theory at the First meeting of the (mostly) young italian hyperbolicians (Corinaldo, Italy, June 8-12, 2009).     

Asynchronous Richardson iterations: theory and practice

Numerical Algorithms - We consider asynchronous versions of the first- and second-order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values...     

Quantum Painlevé equations: from continuous to discrete and back

We present a cascade of quantum Painlevé equations consisting in successive contiguity relations, whereupon starting form a continuous equations we obtain a discrete one, and continuous limits of the latter. We start from the quantum Painlevé V and in the process derive the quantum form of continuous PIII which was missing in previous studies.      

More Delphic theory and practice

Summary We find conditions on semigroups satisfying Kendall's [5] Delphic postulates A and B such that they then satisfy also postulate C (the central limit theorem). These conditions are of the type that the semigroup possess enough continuous homomorphisms (each into the additive reals or circle group) to separate its points. We show that the classical Delphic semigroups (of probability laws on the line, renewal sequences, and p-functions) satisfy our conditions, and thus get the classical results as consequences of the abstract theorems.We also find some curious spiral Delphic semigroups for counter-examples to do with the I ₀-problem.I am very grateful to Professor J. F. C. Kingman, for proposing, at my Ph. D. interview, the problems examined here.     

Augmented intuition: a bridge between theory and practice

Journal of Heuristics - Motivated by the celebrated paper of Hooker (J Heuristics 1(1): 33–42, 1995) published in the first issue of this journal, and by the relative lack of progress of both...     

Maximum Drawdown and Drawdown Duration of Spectrally Negative Lévy Processes Decomposed at Extremes

Journal of Theoretical Probability - Path decomposition is performed to characterize the law of the pre-/post-supremum, post-infimum and the intermediate processes of a spectrally negative...     

Classroom observations in theory and practice

This essay explores the dialectic between theorizing teachers’ decision-making and producing a workable, theoretically grounded scheme for classroom observations. One would think that a comprehensive theory of decision-making would provide the bases for a classroom observation scheme. It turns out, however, that, although the theoretical and practical enterprise are in many ways overlapping, the theoretical underpinnings for the observation scheme are sufficiently different (narrower in some ways and broader in others) and the constraints of almost real-time implementation so strong that the resulting analytic scheme is in many ways radically different from the theoretical framing that gave rise to it. This essay characterizes and reflects on the evolution of the observational scheme. It provides details of some of the failed attempts along the way, in order to document the complexities of constructing such schemes. It is hoped that the final scheme provided will be of some value, both on theoretical and pragmatic grounds. Finally, the author reflects on the relationships between theoretical and applied research on teacher behavior, and the relevant research methods.     

Social theory and system dynamics practice

This paper explores the social theories implicit in system dynamics (SD) practice. Groupings of SD practice are observed in different parts of a framework for studying social theories. Most are seen to be located within `functionalist sociology'. To account for the remainder, two new forms of practice are discussed, each related to a different paradigm. Three competing conclusions are then offered:

• 1.The implicit assumption that SD is grounded in functionalist sociology is correct and should be made explicit.
• 2.Forrester's ideas operate at the level of method not social theory so SD, though not wedded to a particular social theoretic paradigm, can be re-crafted for use within different paradigms.
• 3.SD is consistent with social theories which dissolve the individual/society divide by taking a dialectical, or feedback, stance. It can therefore bring a formal modelling approach to the `agency/structure' debate within social theory and so bring SD into the heart of social science.

The last conclusion is strongly recommended.     

Team syntegrity and democratic group decision making: theory and practice

Stafford Beer created Team Syntegrity as a methodology for social interaction that predisposes participants towards shared agreement among varied and sometimes conflicting interests, without compromising the legitimate claims and integrity of those interests. This paper outlines the methodology and the underlying philosophy, describing several applications in a variety of countries and contexts, indicating why such an approach causes us to re-think more traditional approaches to group decision processes, and relating Team Syntegrity to other systems approaches.     

Fejér processes in theory and practice: Recent results

In this paper we briefly survey the recent results of the theory of Fejér mappings and processes as applied to solving various mathematical problems, including structured systems of linear and convex inequalities, operator equations, as well as problems of linear and quadratic programming which are not necessarily solvable (improper ones).