11 research outputs found

    On formal inverse of the Prouhet-Thue-Morse sequence

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    Let pp be a prime number and consider a pp-automatic sequence u=(un)n∈N{\bf u}=(u_{n})_{n\in\N} and its generating function U(X)=∑n=0∞unXn∈Fp[[X]]U(X)=\sum_{n=0}^{\infty}u_{n}X^{n}\in\mathbb{F}_{p}[[X]]. Moreover, let us suppose that u0=0u_{0}=0 and u1≠0u_{1}\neq 0 and consider the formal power series V∈Fp[[X]]V\in\mathbb{F}_{p}[[X]] which is a compositional inverse of U(X)U(X), i.e., U(V(X))=V(U(X))=XU(V(X))=V(U(X))=X. In this note we initiate the study of arithmetic properties of the sequence of coefficients of the power series V(X)V(X). We are mainly interested in the case when un=tnu_{n}=t_{n}, where tn=s2(n)(mod2)t_{n}=s_{2}(n)\pmod{2} and t=(tn)n∈N{\bf t}=(t_{n})_{n\in\N} is the Prouhet-Thue-Morse sequence defined on the two letter alphabet {0,1}\{0,1\}. More precisely, we study the sequence c=(cn)n∈N{\bf c}=(c_{n})_{n\in\N} which is the sequence of coefficients of the compositional inverse of the generating function of the sequence t{\bf t}. This sequence is clearly 2-automatic. We describe the sequence a{\bf a} characterizing solutions of the equation cn=1c_{n}=1. In particular, we prove that the sequence a{\bf a} is 2-regular. We also prove that an increasing sequence characterizing solutions of the equation cn=0c_{n}=0 is not kk-regular for any kk. Moreover, we present a result concerning some density properties of a sequence related to a{\bf a}.Comment: 16 pages; revised version will appear in Discrete Mathematic

    Crowdsourcing User-Centered Teams

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    Crowdsourcing has become an increasingly important tool for team formation and collaboration. This thesis investigates how User-Centered Design, an iterative process that prioritizes users and their needs, can be applied to improve the efficiency and effectiveness of crowdsourcing systems for teamwork and team formation. To achieve this, we conducted a series of studies to explore the role of various factors in shaping crowd workers' behaviour and preferences in collaborative contexts. The main findings of our research are as follows. In online team formation settings, crowd workers prefer disclosing overt traits (e.g., age, gender, topical interests) and avoid sharing sensitive information (e.g., ethnicity, depression). However, they are willing to share information regarding their personality and values, typically considered deep-level sensitive traits. Well-defined digital nudging interventions, such as a diversity progress bar, can promote diverse team formation. In contrast, subtler forms of nudging may inadvertently trigger biases working against the intended objectives. Ad-hoc crowd teams working under pressure can benefit from systems that account for differences in personality traits, as these can influence collaboration outcomes and perceptions. Designing crowdsourcing systems for emergency response requires modelling communication tools that aid, assist, and monitor the shared load, considering the strictly cooperative roles and task- and user-dependent communication styles between collaborators. When forming teams, crowd workers tend to balance attributes between and within groups, with a preference for Openness to Experience among the Big-5 personality traits. Based on these findings, we recommend applying a User-Centered approach to design collaborative crowdsourcing systems, considering user needs, behaviour, intents, and perceptions of digital environments. Future research should continue to explore and evaluate innovative strategies for promoting effective collaboration and team formation in crowdsourcing contexts

    Critical Thinking Skills Profile of High School Students In Learning Science-Physics

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    This study aims to describe Critical Thinking Skills high school students in the city of Makassar. To achieve this goal, the researchers conducted an analysis of student test results of 200 people scattered in six schools in the city of Makassar. The results of the quantitative descriptive analysis of the data found that the average value of students doing the interpretation, analysis, and inference in a row by 1.53, 1.15, and 1.52. This value is still very low when compared with the maximum value that may be obtained by students, that is equal to 10.00. This shows that the critical thinking skills of high school students are still very low. One fact Competency Standards science subjects-Physics is demonstrating the ability to think logically, critically, and creatively with the guidance of teachers and demonstrate the ability to solve simple problems in daily life. In fact, according to Michael Scriven stated that the main task of education is to train students and or students to think critically because of the demands of work in the global economy, the survival of a democratic and personal decisions and decisions in an increasingly complex society needs people who can think well and make judgments good. Therefore, the need for teachers in the learning device scenario such as: driving question or problem, authentic Investigation: Science Processes

    Teacher roles during amusement park visits – insights from observations, interviews and questionnaires

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    Amusement parks offer rich possibilities for physics learning, through observations and experiments that illustrate important physical principles and often involve the whole body. Amusement parks are also among the most popular school excursions, but very often the learning possibilities are underused. In this work we have studied different teacher roles and discuss how universities, parks or event managers can encourage and support teachers and schools in their efforts to make amusement park visits true learning experiences for their students

    On the automaticity of the Hankel determinants of a family of automatic sequences

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