New Results on Nyldon Words and Nyldon-like Sets

Grinberg defined Nyldon words as those words which cannot be factorized into a sequence of lexicographically nondecreasing smaller Nyldon words. He was inspired by Lyndon words, defined the same way except with "nondecreasing" replaced by "nonincreasing." Charlier, Philibert, and Stipulanti proved that, like Lyndon words, any word has a unique nondecreasing factorization into Nyldon words. They also show that the Nyldon words form a right Lazard set, and equivalently, a right Hall set. In this paper, we provide a new proof of unique factorization into Nyldon words related to Hall set theory and resolve several questions of Charlier et al. In particular, we prove that Nyldon words of a fixed length form a circular code, we prove a result on factorizing powers of words into Nyldon words, and we investigate the Lazard procedure for generating Nyldon words. We show that these results generalize to a new class of Hall sets, of which Nyldon words are an example, that we name "Nyldon-like sets."Comment: 22 pages; generalized many results to Nyldon-like set

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

“Keep Calm, it's just Vapour”: A Mixed Methods Investigation of Online E-Cigarette Discourse and User Perspectives in Western Australia

The aim of this research was to understand how electronic cigarettes (e-cigarettes) are promoted, accessed, and used within a tightly regulated environment, by exploring the Australian online e-cigarette discourse, and the perspectives of e-cigarette users residing within the Greater Capital City Statistical Area of Perth, Western Australia. To achieve this aim three substudies were undertaken: a) scoping review, b) Twitter inquiry and c) qualitative inquiry

A mixed method study of a gratitude diary intervention on tinnitus-related distress in adults

Background: Tinnitus is a persistent condition which constitutes a challenging and life-changing experience for which there is no medical cure. There is wide-spread consensus that individuals’ interpretation of tinnitus affects how distressing they find it. Research suggests individuals with greater levels of dispositional gratitude are less distressed by tinnitus. However, there is no published research examining whether an experimental manipulation of gratitude reduces tinnitus-related distress. Method: A mixed method design was adopted to evaluate the application and experience of a 3-week gratitude diary intervention in adults with distressing tinnitus. Measures were collected pre- and post-intervention. Primary outcome measures were tinnitus-related distress (Tinnitus Questionnaire) and psychological wellbeing (Warwick-Edinburgh Mental Wellbeing Scale). Outcomes were evaluated using paired t-tests and correlational analysis. In addition, semi-structured interviews were conducted to explore participants’ experience of the intervention and analysed using reflexive thematic analysis. Finally, quantitative and qualitative results were integrated to develop mixed methods inferences. Results: Fifteen participants completed the intervention and analysis showed a statistically significant reduction in tinnitus-related distress but no change in psychological wellbeing. Correlational analysis found a strong negative relationship between tinnitus duration and tinnitus-related distress, suggesting those who had tinnitus for longer received less benefit. In addition, thematic analysis identified three themes capturing participants (N = 6) broadening awareness, feeling empowered, and changing relationship with tinnitus. Conclusion: Findings suggest that a gratitude diary intervention is an acceptable intervention to reduce tinnitus-related distress in adults. Participants reported a changing relationship with tinnitus as greater awareness of the blessings in their lives seemed to have reduced their preoccupation with tinnitus. However, further research is required to compare the intervention against an active control condition and examine its utility in clinical samples

Hall sets, Lazard sets and comma-free codes

International audienceWe investigate the relationship between two constructions of maximal comma-free codes described, respectively, by Eastman and by Scholtz and the notions of Hall sets and Lazard sets introduced in connection with factorizations of free monoids and bases of free Lie algebras

Human-Centered Technologies for Inclusive Collection and Analysis of Public-Generated Data

The meteoric rise in the popularity of public engagement platforms such as social media, customer review websites, and public input solicitation efforts strives for establishing an inclusive environment for the public to share their thoughts, ideas, opinions, and experiences. Many decisions made at a personal, local, or national scale are often fueled by data generated by the public. As such, inclusive collection, analysis, sensemaking, and utilization of pubic-generated data are crucial to support the exercise of successful decision-making processes. However, people often struggle to engage, participate, and share their opinions due to inaccessibility, the rigidity of traditional public engagement methods, and the lack of options to provide opinions while avoiding potential confrontations. Concurrently, data analysts and decision-makers grapple with the challenges of analyzing, sensemaking, and making informed decisions based on public-generated data, which includes high dimensionality, ambiguity present in human language, and a lack of tools and techniques catered to their needs. Novel technological interventions are therefore necessary to enable the public to share their input without barriers and allow decision-makers to capture, forage, peruse, and sublimate public-generated data into concrete and actionable insights. The goal of this dissertation is to demonstrate how human-centered approaches involve the stakeholders in the design, development, and evaluation of tools and techniques that can lead to inclusive, effective, and efficient approaches to public-generated data collection and analysis to support informed decision-making. To that end, in this dissertation, I first addressed the challenges of empowering the public to share their opinions by exploring two major opinion-sharing avenues --- social media and public consultation. To learn more about people\u27s social media experiences and challenges, I built two technology probes and conducted a qualitative exploratory study with 16 participants. This study is followed up by exploring the challenges of inclusive participation during public consultations such as town halls. Based on a formative study with 66 participants and 20 organizers, I designed and developed CommunityClick to enable reticent share their opinions silently and anonymously during town halls. Equipped with the knowledge and experiences from these works, I designed, developed, and evaluated technologies and methods to facilitate and accelerate informed data-driven decision-making based on increased public-generated data. Based on interviews with 14 analysts and decision-makers in the civic domain, I built a visual analytics system CommunityClick that can facilitate public input analysis by surfacing hidden insights, people\u27s reflections, and priorities. Leveraging the lessons learned during this work, I created a visual text analytics system that supports serendipitous discovery and balanced analysis of textual data to help make informed decisions. In this work, I contribute an understanding of how people collect and analyze public-generated data to fuel their decisions when they have increased exposure to alternative avenues for opinion-sharing. Through a series of human-centered studies, I highlight the challenges that inhibit inclusivity in opinion sharing and shortcomings of existing methods that prevent decision-makers to account for comprehensive public input that includes marginalized or unpopular opinions. To address these challenges, I designed, developed, and evaluated a collection of interactive systems including CommunityClick, CommunityPulse, and Serendyze. Through a rigorous set of evaluation strategies which include creativity sessions, controlled lab studies, in-the-wild deployment, and field experiments, I involved stakeholders to assess the effectiveness and utility of the built systems. Through the empirical evidence from these studies, I demonstrate how alternative designs for social media could enhance people\u27s social media experiences and enable them to make new connections with others to share opinions. In addition, I show how CommunityClick can be utilized to enable reticent attendees during public consultation to share their opinions while avoiding unwanted confrontation and allowing organizers to capture and account for silent feedback. I highlight how CommunityPulse allowed analysts and decision-makers to examine public input from multiple angles for an accelerated analysis and more informed decision-making. Furthermore, I demonstrate how supporting serendipitous discovery and balanced analysis using Serendyze can lead to more informed data-driven decision-making. I conclude the dissertation with a discussion on future avenues to expand this research including the facilitation of multi-user collaborative analysis, integration of multi-modal signals in the analysis of public-generated data, and potential adoption strategies for decision-support systems designed for inclusive collection and analysis of public-generated data

Zylindrische Dekomposition unter anwendungsorientierten Paradigmen

Quantifier elimination (QE) is a powerful tool for problem solving. Once a problem is expressed as a formula, such a method converts it to a simpler, quantifier-free equivalent, thus solving the problem. Particularly many problems live in the domain of real numbers, which makes real QE very interesting. Among the so far implemented methods, QE by cylindrical algebraic decomposition (CAD) is the most important complete method. The aim of this thesis is to develop CAD-based algorithms, which can solve more problems in practice and/or provide more interesting information as output. An algorithm that satisfies these standards would concentrate on generic cases and postpone special and degenerated ones to be treated separately or to be abandoned completely. It would give a solution, which is locally correct for a region the user is interested in. It would give answers, which can provide much valuable information in particular for decision problems. It would combine these methods with more specialized ones, for subcases that allow for. It would exploit degrees of freedom in the algorithms by deciding to proceed in a way that promises to be efficient. It is the focus of this dissertation to treat these challenges. Algorithms described here are implemented in the computer logic system REDLOG and ship with the computer algebra system REDUCE

Using data mining to repurpose German language corpora. An evaluation of data-driven analysis methods for corpus linguistics

A growing number of studies report interesting insights gained from existing data resources. Among those, there are analyses on textual data, giving reason to consider such methods for linguistics as well. However, the field of corpus linguistics usually works with purposefully collected, representative language samples that aim to answer only a limited set of research questions. This thesis aims to shed some light on the potentials of data-driven analysis based on machine learning and predictive modelling for corpus linguistic studies, investigating the possibility to repurpose existing German language corpora for linguistic inquiry by using methodologies developed for data science and computational linguistics. The study focuses on predictive modelling and machine-learning-based data mining and gives a detailed overview and evaluation of currently popular strategies and methods for analysing corpora with computational methods. After the thesis introduces strategies and methods that have already been used on language data, discusses how they can assist corpus linguistic analysis and refers to available toolkits and software as well as to state-of-the-art research and further references, the introduced methodological toolset is applied in two differently shaped corpus studies that utilize readily available corpora for German. The first study explores linguistic correlates of holistic text quality ratings on student essays, while the second deals with age-related language features in computer-mediated communication and interprets age prediction models to answer a set of research questions that are based on previous research in the field. While both studies give linguistic insights that integrate into the current understanding of the investigated phenomena in German language, they systematically test the methodological toolset introduced beforehand, allowing a detailed discussion of added values and remaining challenges of machine-learning-based data mining methods in corpus at the end of the thesis