Finger Search in Grammar-Compressed Strings

Grammar-based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. Given a grammar, the random access problem is to compactly represent the grammar while supporting random access, that is, given a position in the original uncompressed string report the character at that position. In this paper we study the random access problem with the finger search property, that is, the time for a random access query should depend on the distance between a specified index $f$, called the \emph{finger}, and the query index $i$. We consider both a static variant, where we first place a finger and subsequently access indices near the finger efficiently, and a dynamic variant where also moving the finger such that the time depends on the distance moved is supported. Let $n$ be the size the grammar, and let $N$ be the size of the string. For the static variant we give a linear space representation that supports placing the finger in $O(\log N)$ time and subsequently accessing in $O(\log D)$ time, where $D$ is the distance between the finger and the accessed index. For the dynamic variant we give a linear space representation that supports placing the finger in $O(\log N)$ time and accessing and moving the finger in $O(\log D + \log \log N)$ time. Compared to the best linear space solution to random access, we improve a $O(\log N)$ query bound to $O(\log D)$ for the static variant and to $O(\log D + \log \log N)$ for the dynamic variant, while maintaining linear space. As an application of our results we obtain an improved solution to the longest common extension problem in grammar compressed strings. To obtain our results, we introduce several new techniques of independent interest, including a novel van Emde Boas style decomposition of grammars

Fast Dynamic Arrays

We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of $n$ elements supporting access in time $O(1)$ and insertion and deletion in time $O(n^\epsilon)$ for $\epsilon > 0$ while using $o(n)$ extra space. We consider several different implementation optimizations in C++ and compare their performance to that of vector and multiset from the standard library on sequences with up to $10^8$ elements. Our fastest implementation uses much less space than multiset while providing speedups of $40\times$ for access operations compared to multiset and speedups of $10.000\times$ compared to vector for insertion and deletion operations while being competitive with both data structures for all other operations

Tramp Ship Scheduling Problem with Berth Allocation Considerations and Time-dependent Constraints

This work presents a model for the Tramp Ship Scheduling problem including berth allocation considerations, motivated by a real case of a shipping company. The aim is to determine the travel schedule for each vessel considering multiple docking and multiple time windows at the berths. This work is innovative due to the consideration of both spatial and temporal attributes during the scheduling process. The resulting model is formulated as a mixed-integer linear programming problem, and a heuristic method to deal with multiple vessel schedules is also presented. Numerical experimentation is performed to highlight the benefits of the proposed approach and the applicability of the heuristic. Conclusions and recommendations for further research are provided.Comment: 16 pages, 3 figures, 5 tables, proceedings paper of Mexican International Conference on Artificial Intelligence (MICAI) 201

Pride, prejudice and pragmatism: family language policies in the UK

In this study, we examine how mobility and on-going changes in sociocultural contexts impact family language policy (FLP) in the UK. Using a questionnaire and involving 470 transnational families across the UK, our study provides a descriptive analysis of different family language practices in England and establishes how attitudes influence the different types of FLP in these families. Complementing the descriptive analysis, we use interview data to understand the driving forces behind the different types of language practices and language management activities, and explore how ideological constructs of ‘pride’, ‘prejudice’ and ‘pragmatism’ are directly related to negative or positive attitudes towards the development of children’s heritage language. The findings indicate that migration trajectories, social values, raciolinguistic policing in schools, and linguistic loyalty have shaped family decisions about what languages to keep and what languages to let go. Our paper responds to the linguistic and demographic changes in British society, and makes an important contribution to our knowledge about multilingual development of children in transnational families. Critically, this study shows that FLPs alone cannot save the minority languages; institutionally sanctioned language practices and ideologies have to make a move from limiting the use of these languages in educational contexts to legitimising them as what they are: linguistic resources and languages of pride

Pride, prejudice and pragmatism:family language policies in the UK

In this study, we examine how mobility and on-going changes in sociocultural contexts impact family language policy (FLP) in the UK. Using a questionnaire and involving 470 transnational families across the UK, our study provides a descriptive analysis of different family language practices in England and establishes how attitudes influence the different types of FLP in these families. Complementing the descriptive analysis, we use interview data to understand the driving forces behind the different types of language practices and language management activities, and explore how ideological constructs of ‘pride’, ‘prejudice’ and ‘pragmatism’ are directly related to negative or positive attitudes towards the development of children’s heritage language. The findings indicate that migration trajectories, social values, raciolinguistic policing in schools, and linguistic loyalty have shaped family decisions about what languages to keep and what languages to let go. Our paper responds to the linguistic and demographic changes in British society, and makes an important contribution to our knowledge about multilingual development of children in transnational families. Critically, this study shows that FLPs alone cannot save the minority languages; institutionally sanctioned language practices and ideologies have to make a move from limiting the use of these languages in educational contexts to legitimising them as what they are: linguistic resources and languages of pride.<br/

Introduction:The changing faces of transnational communities in Britain

In this editorial introduction, we outline the key conceptualisations andoverarching questions of this collection of studies on the changing faces of thetransnational communities in Britain. Using the nexus of migration and languageas our critical lens, we examine the internal diversities within the transnationalcommunities in Britain, evident in the emergence of groups differing on migrationtrajectories, social and educational backgrounds, linguistic repertories and statusassigned to community languages. We also explore how language shapes, and isshaped by, these internal diversities and wider socio-cultural-political dynamicsand pay particular attention to the multilingual and translanguaging practices inthese communities. We demonstrate how these communities function as sites forcontestation of language and identity that can be conflictual as well as a source ofothering. The introduction concludes with an outline of the contributions made bythe studies in this special issue, highlighting the key claims put forward by thecontributors

Pride, prejudice and pragmatism:family language policies in the UK

In this study, we examine how mobility and on-going changes in sociocultural contexts impact family language policy (FLP) in the UK. Using a questionnaire and involving 470 transnational families across the UK, our study provides a descriptive analysis of different family language practices in England and establishes how attitudes influence the different types of FLP in these families. Complementing the descriptive analysis, we use interview data to understand the driving forces behind the different types of language practices and language management activities, and explore how ideological constructs of ‘pride’, ‘prejudice’ and ‘pragmatism’ are directly related to negative or positive attitudes towards the development of children’s heritage language. The findings indicate that migration trajectories, social values, raciolinguistic policing in schools, and linguistic loyalty have shaped family decisions about what languages to keep and what languages to let go. Our paper responds to the linguistic and demographic changes in British society, and makes an important contribution to our knowledge about multilingual development of children in transnational families. Critically, this study shows that FLPs alone cannot save the minority languages; institutionally sanctioned language practices and ideologies have to make a move from limiting the use of these languages in educational contexts to legitimising them as what they are: linguistic resources and languages of pride.<br/

‘来来, 大家一起玩’ (C’mon, let’s play together):grassroots planning from a Bourdieusian perspective

This paper presents an on-going study of grassroots language-planning engagement in the Chinese transnational communities in the UK. It explores how a group of Chinese mothers organise playgroups for their children to socialise with each other in linguistic and non-linguistic plays to enrich their children’s cultural and linguistic environment. Guided by Bourdieu’s signature concepts of habitus and capital, this study attempts to understand grassroots organisations in the Chinese communities through a socialisation lens. It examines how organisers’/mothers’ sociocultural disposition about, practical knowledge of, and cultural attitudes towards socialisation become unintended forms of social and cultural capital for heritage/community language development. Data sources include observations, recorded playing activities, and unstructured interviews. Using discourse analysis and narrative enquiry as analytical framework, the study focuses on the types of activities organised, language functions and forms in socialisation, and the sociocultural dispositions articulated by the parents. The study highlights how heritage languages can be developed despite symbolic structural constraints that are unfavourable for heritage language learning. The study contributes to the field of FLP by illustrating how parents use their social, cultural and economic capital in locating and using accessible resources to help their children build a transnational cultural capital.</p

‘来来, 大家一起玩’ (C’mon, let’s play together):grassroots planning from a Bourdieusian perspective

This paper presents an on-going study of grassroots language-planning engagement in the Chinese transnational communities in the UK. It explores how a group of Chinese mothers organise playgroups for their children to socialise with each other in linguistic and non-linguistic plays to enrich their children’s cultural and linguistic environment. Guided by Bourdieu’s signature concepts of habitus and capital, this study attempts to understand grassroots organisations in the Chinese communities through a socialisation lens. It examines how organisers’/mothers’ sociocultural disposition about, practical knowledge of, and cultural attitudes towards socialisation become unintended forms of social and cultural capital for heritage/community language development. Data sources include observations, recorded playing activities, and unstructured interviews. Using discourse analysis and narrative enquiry as analytical framework, the study focuses on the types of activities organised, language functions and forms in socialisation, and the sociocultural dispositions articulated by the parents. The study highlights how heritage languages can be developed despite symbolic structural constraints that are unfavourable for heritage language learning. The study contributes to the field of FLP by illustrating how parents use their social, cultural and economic capital in locating and using accessible resources to help their children build a transnational cultural capital.</p

Proof of the Feldman-Karlin Conjecture on the Maximum Number of Equilibria in an Evolutionary System

Feldman and Karlin conjectured that the number of isolated fixed points for deterministic models of viability selection and recombination among n possible haplotypes has an upper bound of 2^n - 1. Here a proof is provided. The upper bound of 3^{n-1} obtained by Lyubich et al. (2001) using Bezout's Theorem (1779) is reduced here to 2^n through a change of representation that reduces the third-order polynomials to second order. A further reduction to 2^n - 1 is obtained using the homogeneous representation of the system, which yields always one solution `at infinity'. While the original conjecture was made for systems of viability selection and recombination, the results here generalize to viability selection with any arbitrary system of bi-parental transmission, which includes recombination and mutation as special cases. An example is constructed of a mutation-selection system that has 2^n - 1 fixed points given any n, which shows that 2^n - 1 is the sharpest possible upper bound that can be found for the general space of selection and transmission coefficients.Comment: 9 pages, 1 figure; v.4: final minor revisions, corrections, additions; v.3: expands theorem to cover all cases, obviating v.2 distinction of reducible/irreducible; details added to: discussion of Lyubich (1992), example that attains upper bound, and homotopy continuation method