Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula

Computing homotopy groups of spheres has long been a fundamental objective in algebraic topology. Various theoretical and algorithmic approaches have been developed to tackle this problem. In this paper we take a step towards the goal of comprehending the group-theoretic structure of the generators of these homotopy groups by leveraging the power of machine learning. Specifically, in the simplicial group setting of Wu's formula, we reformulate the problem of generating simplicial cycles as a problem of sampling from the intersection of algorithmic datasets related to Dyck languages. We present and evaluate language modelling approaches that employ multi-label information for input sequences, along with the necessary group-theoretic toolkit and non-neural baselines.Comment: 20 page

Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammar

Two characterisation results of multiple context-free grammars and their application to parsing

In the first part of this thesis, a Chomsky-Schützenberger characterisation and an automaton characterisation of multiple context-free grammars are proved. Furthermore, a framework for approximation of automata with storage is described. The second part develops each of the three theoretical results into a parsing algorithm

A study of the experiences of migrant student mothers in a context of corporate social responsibility in higher education

This case study research focuses on the experience of Migrant Student Mothers (MSM) as a particular stakeholder group in an inner city Higher Education Institution (HEI) within a context of Corporate Social Responsibility (CSR). Widening Participation (WP) and the Employability agenda of the contemporary Higher Education (HE) environment are given a particular focus as relevant aspects of the discussion with regard to MSM and the importance of considering a CSR approach to HE stakeholders. Affect Theory was utilised as the lens through which the data was thematically analysed, given the affective attributes that mothers assign to CSR and the affective overarching embodiment of affects as emerged from this research. This study argues that the central theme attributed to affects in the individual’s experiences is hope. The findings highlight the invisibility of MSM in HE and that the significance of a reciprocal relationship between material experiences and affective understanding, enables this particular subgroup of the students, to act and progress, both as migrant mothers and as students, through their migration and education trajectories, enabling both themselves and their children to occupy a place as future global citizens. The findings support that the material vehicles available to stakeholders groups are paramount in facilitating such hope and therefore the needs for business entities to actively respond to the needs of these stakeholders. The research approach that was undertaken, adopting an interpretivist paradigm, was carried out through case study method, utilising several data collection tools in order to gain a rich and in-depth picture of the chosen case. Semi-structured interviews were undertaken at two key points of the academic year with four different stakeholder groups, including over 230 hours verbatim transcription; biographical personal self-definition forms, research diary; and, an in-depth investigation of the University’s policies, documentation, existing statistics, generic emails, management address and publicly available information such as the university website. The thesis points out that across the many CSR definitions and research there is still an untouched discourse that fails to recognise the heterogeneous complexity of stakeholder groups and within them ‘invisible stakeholders’. Building on a synthesis of Hopkins’ (2016) CSR definition which adopts a stakeholder orientation, the thesis builds on current stakeholder theory by promulgating a three-phase CSR process, encompassing a new CSR model: The Triplex-Invisible Stakeholders, which recognises the heterogeneity of different stakeholder groups through exploring linkages between them, and thus making the invisible stakeholders visible

Arctic Canada and Zambia: A Comparison of Development Processes in the Fourth and Third Worlds

An analysis of the processes behind socio-economic development is necessary to further the understanding of contemporary Inuit conditions in arctic Canada. It is apparent that many of the realities and reasons underlying development in the North are similar to those in the Third World. The term development encompasses strategies and programs to improve living conditions of the target population, processes that either directly or indirectly transform indigenous economies into ones like those of the Western world, and theories that seek to explain these changes and their outcomes. People from government, business, and religion were the agents of development in both Canada and Africa. One of the most overt changes to indigenous societies brought about by these agents was a shift to a modern market-oriented economy. Education is part of a development process and contributed to this change. Education in arctic Canada and a Third Word country, Zambia, is based on teaching local residents to participate in a Euro-North American economic system. In both countries, however, the national or regional economies cannot sustain employment for many of the educated indigenous people. In Lwawu, a remote part of Zambia, this has led to social tensions and polarization between socio-economic classes. In arctic Canada, it has contributed to confusion over one's cultural identity and an inability to participate economically in either the modern or traditional sectors. The Inuit face added difficulties in that to obtain wage employment they must integrate within national cultural, economic, and political systems governed by people who are of different races and cultures and not indigenous to Canada. The end result of these and similar situations is that indigenous people are not necessarily better off than before contact with development agents.

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

Analytic combinatorics : functional equations, rational and algebraic functions

This report is part of a series whose aim is to present in a synthetic way the major methods and models in analytic combinatorics. Here, we detail the case of rational and algebraic functions and discuss systematically closure properties, the location of singularities, and consequences regarding combinatorial enumeration. The theory is applied to regular and context-free languages, finite state models, paths in graphs, locally constrained permutati- ons, lattice paths and walks, trees, and planar maps

Learners' environmental awareness, effects on home and school practices towards littering : an action research case

The presence of pre-packed items contributes toward littering in schools and at home milieu. Most people particularly, and learners’ discard packages of pre-packed wrappers on the ground, thus contribute to littering. This study is intended to help all relevant stakeholders to plan activities that could reduce littering. The study is grounded within the critical theory and living paradigm exploring the effect of household and school practices on learners’ environmental awareness (EA) towards littering. This case study employed action research as a methodology to unpack the problem. Fourteen learners, who are referred to as co-researchers in this study, were selected randomly from seven classes and their parents were inevitably included in the study. Three cycles were conducted with the co-researchers. Five data collection methods are used to collect data. Tables, score total percentages and coding used to analyse data. The results of the study show that environmental activities could be useful within home and school setup and continued practice of environmental activities will in the end conscientise learners towards littering if approached through action research.Science and Technology EducationM. Ed. (Environmental Education