Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions

A language L over a finite alphabet is growth-sensitive (or entropy sensitive) if forbidding any set of subwords F yields a sub-language L^F whose exponential growth rate (entropy) is smaller than that of L. Let (X, E, l) be an infinite, oriented, labelled graph. Considering the graph as an (infinite) automaton, we associate with any pair of vertices x,y in X the language consisting of all words that can be read as the labels along some path from x to y. Under suitable, general assumptions we prove that these languages are growth-sensitive. This is based on using Markov chains with forbidden transitions.Comment: to appear in Theoretical Computer Science, 201

On Left and Right Dislocation: A Dynamic Perspective

The paper argues that by modelling the incremental and left-right process of interpretation as a process of growth of logical form (representing logical forms as trees), an integrated typology of left-dislocation and right-dislocation phenomena becomes available, bringing out not merely the similarities between these types of phenomena, but also their asymmetry. The data covered include hanging topic left dislocation, clitic left dislocation, left dislocation, pronoun doubling, expletives, extraposition, and right node raising, with each set of data analysed in terms of general principles of tree growth. In the light of the success in providing a characterisation of the asymmetry between left and right periphery phenomena, a result not achieved in more wellknown formalisms, the paper concludes that grammar formalisms should model the dynamics of language processing in time.Articl

Growth Tight Actions of Product Groups

A group action on a metric space is called growth tight if the exponential growth rate of the group with respect to the induced pseudo-metric is strictly greater than that of its quotients. A prototypical example is the action of a free group on its Cayley graph with respect to a free generating set. More generally, with Arzhantseva we have shown that group actions with strongly contracting elements are growth tight. Examples of non-growth tight actions are product groups acting on the $L^1$ products of Cayley graphs of the factors. In this paper we consider actions of product groups on product spaces, where each factor group acts with a strongly contracting element on its respective factor space. We show that this action is growth tight with respect to the $L^p$ metric on the product space, for all $1<p\leq \infty$. In particular, the $L^\infty$ metric on a product of Cayley graphs corresponds to a word metric on the product group. This gives the first examples of groups that are growth tight with respect to an action on one of their Cayley graphs and non-growth tight with respect to an action on another, answering a question of Grigorchuk and de la Harpe.Comment: 13 pages v2 15 pages, minor changes, to appear in Groups, Geometry, and Dynamic

Recent research on child language brokering in the United Kingdom

Recent patterns of migration and population change in the UK have led in some places to a need for child language brokering (CLB). Although there is only limited evidence on CLB in the UK, the research that has been published indicates the diversity of the phenomenon and suggests its frequency and significance in the lives of some families. In this paper we review a range of small scale studies from different research centres to illustrate that diversity. The research has highlighted ways in which language brokering often elides into cultural brokering with young children playing a brokering role within as well as outside their families. An important line of enquiry has been research on the CLB process itself, but detailed studies of how children and young people respond to the challenges of translation in different settings remain elusive, as do studies of the impact that the activity has on their interactions with others. A key issue for the children and parents involved is others’ perceptions of and reaction to CLB, including not only the professionals and officials with whom they deal but also their peers at school and elsewhere who are not involved in language brokering. Ultimately CLB is of theoretical interest not only for the light it throws on children’s language learning and acculturation but also for the challenge it presents to traditional notions of child development and family role

archiTECTONICS: Pre- and Trans-Disciplinary Reference in Beginning Design

This presentation was part of the session : Pedagogy: Procedures, Scaffolds, Strategies, Tactics24th National Conference on the Beginning Design StudentPedagogical approaches to beginning design in architecture often assume trans-disciplinary modes of exploration to filter problem parameters and sculpt perceptual outlook for iterative potential. A closer look suggests moments within the architectural design process that come before, or around, the discipline itself in the form of other disciplines accompanied by basic principles, such as Visual Literacy. Iterating and perceiving through every disciplinary dynamic, instance, and/or action in the process of designing transcends, builds, and structures its neighbor for explorative sequencing, intention, and growth of sensibilities in design resolution. An acute awareness of disciplinary state, in a maturing design process, can alleviate obscurity of ideological foundation and facilitate growth for trans-disciplinary thinking, making, and communicating in a root discipline such as architecture. How can beginning design instructors guide young designers to keep ideas and concepts for design in focus, recognizing that root disciplines transcend pre- and trans-disciplinary processes? Does recognizing variation in pace, induced by digital and analog tools, and intention of design iteration, by discipline, instill clarity by pre-disciplinary thinking, perception, and operation? Trans-disciplinary exercise provokes awareness of pre-disciplinary foundations furthering possibilities for unique root-disciplinary understandings and results. The developed exercise, archiTECTONIC, recognizes and cycles through reasoning, conceptualization, and iteration in a trans-disciplinary sequence, allowing the beginning design student to recognize pre-disciplinary ideology, pace, and purpose when processing ideas through fundamentals of architectural design. Engaging this as a strategy for seeing, thinking, and maneuvering through a dynamic process provides design liberty and clarity for processing and communicating in a root discipline, in this case architecture