Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship

This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or indecisive, in the presence of a continuity hypothesis that is, in principle, non-testable. It identifies topological connectedness of the (choice) set over which the continuous binary relation is defined as being crucial to this question. Referring to the two-way relationship as the Eilenberg-Sonnenschein (ES) research program, it presents four synthetic, and complete, characterizations of connectedness, and its natural extensions; and two consequences that only stem from it. The six theorems are novel to both the economic and the mathematical literature: they generalize pioneering results of Eilenberg (1941), Sonnenschein (1965), Schmeidler (1971) and Sen (1969), and are relevant to several applied contexts, as well as to ongoing theoretical work.Comment: 47 pages, 4 figure

Strategies for Consistency Checking

Viewpoint models of system development are becoming increasingly important. A major requirement for viewpoints modelling is to be able to check that the multiple viewpoint specifications are consistent with one another. The work presented in this report makes a contribution to this task. Our work is particularly influenced by the viewpoints model used in the ISO standardisation architecture for Open Distributed Processing. This report focuses on the issue of strategies for consistency checking. In particular, it considers how global consistency (between any arbitrary number of viewpoints) can be obtained from binary consistency (between two viewpoints). The report documents a number of different classes of consistency checking, from those that are very poorly behaved to those that are very well behaved. The report is intended as a companion to the work presented in [1] and it should be read in association with this document. In particular, the body of this report is a single chapter which should be viewed as additional to the chapters included in [1]. This report contains complete proofs of all relevant results, even though some of the results are obvious and some of the proofs are trivial. A much compressed version of the report is being submitted for publication. Thus, the main value of this report is as a reference document for readers who require a complete presentation of the technical. [1] E. Boiten, H. Bowman, J. Derrick and M. Steen ''Cross Viewpoint Consistency in Open Distributed Processing (Intra Language Consistency)'', Technical Report, Computing Laboratory, University of Kent at Canterbury, report No. 8-95, 1995. Phone: +44 1227 827913, Fax: 44 1227 762811 Email: H.Bowman,E.A.Boiten,J.Derrick,[email protected]

Феномен синкретизма в украинской лингвистике

У сучасній лінгвістиці вивчення складних системних зв’язків та динамізму мови навряд чи буде завершеним без урахування синкретизму. Традиційно явища транзитивності трактуються як поєднання різних типів утворень як результат процесів трансформації або відображення проміжних, синкретичних фактів, що характеризують мовну систему в синхронному аспекті.In modern linguistics, the study of complex systemic relations and language dynamism is unlikely to be complete without considering the transitivity. Traditionally, transitivity phenomena are treated as a combination of different types of entities, formed as a result of the transformation processes or the reflection of the intermediate, syncretic facts that characterize the language system in the synchronous aspect.В современной лингвистике изучение сложных системных отношений и языкового динамизма вряд ли будет полным без учета синкретизма. Традиционно явления транзитивности трактуются как совокупность различных типов сущностей, сформированных в результате процессов преобразования или отражения промежуточных синкретических фактов, которые характеризуют языковую систему в синхронном аспекте

A mission for grammar writing : early approaches to Inuit (Eskimo) languages

The Inuit inhabit a vast area of--from a European point of view--most inhospitable land, stretching from the northeastern tip of Asia to the east coast of Greenland. Inuit peoples have never been numerous, their settlements being scattered over enormous distances. But nevertheless, from an ethnological point of view, all Inuit peoples shared a distinct culture, featuring sea mammal and caribou hunting, sophisticated survival skills, technical and social devices, including the sharing of essential goods and strategies for minimizing and controlling aggression

Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm (Liu \textit{et al.,} Phys. Rev. E \textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatment disregarding the intrinsic non-stationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for non-stationary stochastic processes like fBm.Comment: 8 pages, 6 figure