Generalized north-south dynamics on the space of geodesic currents

We prove uniform north-south dynamics type results for the action of $\varphi\in Out(F_{N})$ on the space of projectivized geodesic currents $\mathbb{P}Curr(S)=\mathbb{P}Curr(F_{N})$, where $\varphi$ is induced by a pseudo-Anosov homeomorphism on a compact surface S with boundary such that $\pi_{1}(S)=F_{N}$. As an application, we show that for a subgroup $H\le Out(F_N)$, containing an iwip, either $H$ contains a hyperbolic iwip or $H$ is contained in the image in $Out(F_N)$ of the mapping class group of a surface with a single boundary component.Comment: 20 pages, 2 figures, v3: Minor correction

Perron-Frobenius theory and frequency convergence for reducible substitutions

We prove a general version of the classical Perron-Frobenius convergence property for reducible matrices. We then apply this result to reducible substitutions and use it to produce limit frequencies for factors and hence invariant measures on the associated subshift. The analogous results are well known for primitive substitutions and have found many applications, but for reducible substitutions the tools provided here were so far missing from the theory.Comment: v.2 Minor revisions for submissio

On the Geometric Measures of Entanglement

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three qubit case is discussed and argued that the distance to the W states is a new monotone.Comment: 7 pages, 1 figures, minor content change, references added, 1 figure adde

Analysis of Discrete Fractional Operators and Discrete Fractional Rheological Models

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental definitions and formulas in discrete fractional calculus. In the third chapter, we introduce two new monotonicity concepts for nonnegative or nonpositive valued functions defined on discrete domains, and then we prove some monotonicity criteria based on the sign of the fractional difference operator of a function. In the fourth chapter, we emphasize the rheological models: We start by giving a brief introduction to rheological models such as Maxwell and Kelvin-Voigt, and then we construct and solve discrete fractional rheological constitutive equations. Finally, we finish this thesis by describing the conclusion and future work

고난이도 이러닝 콘텐츠에서 텍스트 또는 내레이션 제시 효과

학위논문 (석사) -- 서울대학교 대학원 : 사범대학 교육학과(교육공학전공), 2021. 2. 임철일.인터넷 및 통신 기술 (ICT)의 발달로 인해 교육의 추세와 방식이 수년에 걸쳐 변화해 왔다. 이러한 컴퓨터 기술, 인터넷 기술의 발전과 이를 사용할 수 있는 사람들의 수가 증가함에 따라 e- 러닝은 가장 인기있는 학습 매체 중 하나가 되었다. 전자 학습-교육 목적으로 휴대폰, 태블릿, 노트북 및 기타 기술 도구와 같은 다양한 유형의 ICT를 사용하는 것으로 생각할 수 있으며 여러 학습 기술과 전략을 통합한다. e- 러닝은 교육에서 학습 경험을 풍부하게 하므로 교육에 긍정적인 영향을 미칠 수 있는 잠재력이 있다. 이러닝은 정보 사회의 발전과 함께 성장하고 있으며 이러한 발전에 따라 이러닝 콘텐츠가 전달되는 방식도 변화하고 있다. 또한 콘텐츠가 멀티미디어로 제공되는 경우 사람들은 순차적 방식이 아닌 텍스트, 그래픽 또는 오디오를 동시에 제공함으로써 효과적인 학습 경험을 가능하게 하므로 학습에 더 많이 참여할 가능성이 높다. 멀티미디어는 교육 분야에서 고유 한 이점을 제공하지만 다른 학습 프로그램과 마찬가지로 멀티미디어 학습 설계는 효과를 위해 중요하다. 그렇기 때문에 멀티미디어 준비 원칙을 고려하는 것이 중요하다. 이러한 디자인 원칙 중 모달리티 원칙은 다른 멀티미디어 디자인 원칙보다 더 광범위하게 연구되었다. 모달리티 원칙은 그림과 구두 텍스트에서 학습하는 것이 그림과 화면 텍스트에서 학습하는 것보다 더 효과적임을 시사한다. 이 원칙의 경험적 지원이 높지만 그 효과는 특정 조건으로 제한된다. 그 중에서도 이 연구는 어려운 정보에 초점을 맞추었다. 즉, 학습자에서 정보가 복잡하다면 내레이션을 사용하는 것보다 화면 텍스트가 더 나은 선택이다는 제안을 고려하여 모달리티 원칙이 검증되지 않았던 상황인 한 멀티미디어 콘텐츠에서 화면상의 텍스트와 내레이션을 사용하는 효과를 검증하였다. 본 연구는 통제 및 실험 집단에서 파일럿 테스트, 사전 지식 설문지 및 회상 검사를 사용하였다. 60 명의 참가자는 사진들과 내레이션만 제시된 멀티메디아 콘텐츠를 학습할 집단(통제집단) 과 또는 내레이션과 화면텍스트 제시된 멀티메디아 콘텐츠를 학습할 집단(실험집단)에 무작위로 배정되었다. 실험집단은 사진들과 함께 내레이션을 봤으나 정보가 어려운 부분에서 사진들과 함께 내레이션 대신 화면 텍스트로 학습하였다. 멀티미디어 콘텐츠인 교육 영상을 본 후 회상검사를 실시했습니다. 데이터 수집 후 그룹의 평균 점수를 비교하기 위해 독립 샘플 t검증을 수행했습니다. 회상검사를 데이터 분석에 따르면, 통계 결과는 정보가 어려울 때 멀티미디어 자료에 내레이션 대신 화면 텍스트를 제공하는 것이 내레이션 만 제공하는 것보다 정보를 기억할 때에 더 효과적임을 보여주었다. 본 연구는 다음과 같은 점에서 의의가 있다. 첫째, 정보가 복잡 할 때 화면상 활용을 모색함으로써 본 연구는 멀티미디어 자료 설계에 대한 연구 기반의 성장에 기여한다. 이 연구에서 얻은 결과는 교육 설계자가 참고 자료로 사용할 수 있으며 긍정적인 학습 결과에 기여할 수 있기 때문이다. 둘째, 모달리티 원리의 다양한 상황을 검증할 필요가 있기 때문에 본 연구는 문헌에 기여한다. 마지막으로, 정보가 복잡 할 때 나레이션 대신 텍스트를 사용하는 것에 대한 조사가 많지 않기 때문에 동기, 학습 인식 등 학습 외에 다른 변수를 검증하는 측면에서 향후 연구의 기초 연구가 될 수 있기 때문에 현재 연구가 중요합니다.The trends and the ways of education have been changing over the years thanks to developments on the Internet and communication technology (ICT). These advancements in computer technology, Internet technology, and an increase in the number of people who can use them have made e-learning one of the most popular mediums of learning and it has been gaining popularity day-by-day. E-learning can be thought of as using different types of ICTs such as mobile phones, tablets, laptops, and other technological tools for educational purposes and it incorporates several learning technologies and strategies. E-learning enriches the learning experience in education, so it has the potential to affect education positively. E-learning is growing with the development of the information society and with these developments, the way how e-learning content is delivered has been changing too. Moreover, people are more likely to be engaged with learning if the content is presented as multimedia because it enables an effective learning experience by providing text, graphics, or audio simultaneously rather than in a sequential manner Multimedia offers unique advantages in the field of education however, as in any learning program, designing multimedia learning is important for effectiveness. That is why it is important to consider principles for preparing multimedia. Among those design principles, the modality principle has been more widely tested than any other principle of multimedia design. The modality principle suggests that learning from pictures and verbal text is more effective than learning from pictures and on-screen text. Although the modality principle has high empirical support, its effect is limited to certain conditions. Among those conditions, this research focused on difficult information. It was suggested that if the context of information is complicated for the learners then the printed text is a better option than using narration. Besides, among the circumstances that the modality principle has not been tested, it was suggested that there is a need to test the effect of using on-screen text and narration in one multimedia learning design. By taking these results into account, this study tested the use of printed-text and verbal text along with visuals when the content is difficult through conducting a recall test. This study used a pilot-test, prior knowledge questionnaire, and recall test on control and treatment groups. 60 participants were randomly assigned to either the narration-only group (NO) which is the control group or the narration-text group (NT) which is the treatment group. An instructional video was prepared for each treatment group. Participants in NO group received a self-paced, computer-based instructional video that includes narration only to explain the Artificial Intelligence and related concepts. The NT group received the same computer-based instructional video; however, the same explanation was presented as the narration. The narration part was removed, and the on-screen text was added when the incoming information is complicated. After they watched the instructional video, the recall test was conducted. After collecting data, independent samples t-test was conducted to compare the mean score of the groups. According to data analysis of recall test, the statistical results showed that providing on-screen text instead of narration in multimedia material when the information is difficult is more effective on recalling the information than providing the narration only. This study has significance due to the following reasons. Firstly, by exploring the use of on-screen when the information is convoluted, the present study contributes to the growing research base on the design of multimedia materials. The results obtained from this study can be used by instructional designers as a reference. and it can contribute to positive learning outcomes. Secondly, since there is a need for testing different circumstances of modality principle, this study makes contributions to literature. Finally, since there is no investigation about using text instead of narration when information is complicated, the present study is important because it can be a base study for future studies in terms of testing other variables besides learning such as motivation, learning perception, and, so on.I. INTRODUCTION 1 1. Background of the Study 1 1.1. Statement of the Problem 8 1.2. Needs of the Research 12 2. Research Questions 16 3. Definition of Terms 17 II. LITERATURE REVIEW 21 1. Theoretical Framework 21 1.1. Cognitive Load Theory 21 1.2. Cognitive Theory of Multimedia Learning 26 2. The Modality Principle 32 2.1. Evidence Studies for Modality Principle 33 III. RESEARCH METHODOLOGY 36 1. Overall Research Design 36 2. Materials and Instruments 38 2.1. Instructional Video 38 2.2. Instruments 43 2.2.1. Pilot Phase Process 44 2.2.2. Prior Knowledge Questionnaire 44 2.2.3. Recall Test 46 3. Participants 53 4. Data Analysis 54 4.1. Use of Prior Knowledge Questionnaire 57 4.2. Recall Test Analyses 58 IV. RESULTS 61 1. Prior Knowledge Questionnaire 61 2. Recall Test Analyses Results 61 3. Independent Samples T-test Results 63 4. Summary 64 V.DISCUSSIONS AND CONCLUSION 67 1. Contributions of the Study 71 2. Implications of the Study 72 3. Limitations and Future Directions 74 4. Conclusions 76 REFERENCES 79 APPENDIX 99 국문초록 111Maste