The Stretch-Engine: A Method for Creating Exaggeration in Animation Through Squash and Stretch

Animators exaggerate character motion to emphasize personality and actions. Exaggeration is expressed by pushing a character’s pose, changing the action’s timing, or by changing a character’s form. This last method, referred to as squash and stretch, creates the most noticeable change in exaggeration. However, without practice, squash and stretch can adversely affect the animation. This work introduces a method to create exaggeration in motion by focusing solely on squash and stretch to control changes in a character’s form. It does this by displaying a limbs' path of motion and altering the shape of that path to create a change in the limb’s form. This paper provides information on tools that exist to create animation and exaggeration, then discusses the functionality and effectiveness of these tools and how they influenced the design of the Stretch-Engine. The Stretch-Engine is a prototype tool developed to demonstrate this approach and is designed to be integrated into an existing animation software, Maya. The Stretch-Engine contains a bipedal-humanoid rig with controls necessary for animation and the ability to squash and stretch. It can be accessed through a user interface that allows the animator to control squash and stretch by changing the shape of generated paths of motion. This method is then evaluated by comparing animations of realistic motion to versions created with the Stretch-Engine. These stretched versions displayed exaggerated results for their realistic counterparts, creating similar effects to Looney Tunes animation. This method fits within the animator’s workflow and helps new artists visualize and control squash and stretch to create exaggeration

Essays on the economics of networks

Networks (collections of nodes or vertices and graphs capturing their linkages) are a common object of study across a range of fields includ- ing economics, statistics and computer science. Network analysis is often based around capturing the overall structure of the network by some reduced set of parameters. Canonically, this has focused on the notion of centrality. There are many measures of centrality, mostly based around statistical analysis of the linkages between nodes on the network. However, another common approach has been through the use of eigenfunction analysis of the centrality matrix. My the- sis focuses on eigencentrality as a property, paying particular focus to equilibrium behaviour when the network structure is fixed. This occurs when nodes are either passive, such as for web-searches or queueing models or when they represent active optimizing agents in network games. The major contribution of my thesis is in the applica- tion of relatively recent innovations in matrix derivatives to centrality measurements and equilibria within games that are function of those measurements. I present a series of new results on the stability of eigencentrality measures and provide some examples of applications to a number of real world examples

Visualized Algorithm Engineering on Two Graph Partitioning Problems

Concepts of graph theory are frequently used by computer scientists as abstractions when modeling a problem. Partitioning a graph (or a network) into smaller parts is one of the fundamental algorithmic operations that plays a key role in classifying and clustering. Since the early 1970s, graph partitioning rapidly expanded for applications in wide areas. It applies in both engineering applications, as well as research. Current technology generates massive data (“Big Data”) from business interactions and social exchanges, so high-performance algorithms of partitioning graphs are a critical need. This dissertation presents engineering models for two graph partitioning problems arising from completely different applications, computer networks and arithmetic. The design, analysis, implementation, optimization, and experimental evaluation of these models employ visualization in all aspects. Visualization indicates the performance of the implementation of each Algorithm Engineering work, and also helps to analyze and explore new algorithms to solve the problems. We term this research method as “Visualized Algorithm Engineering (VAE)” to emphasize the contribution of the visualizations in these works. The techniques discussed here apply to a broad area of problems: computer networks, social networks, arithmetic, computer graphics and software engineering. Common terminologies accepted across these disciplines have been used in this dissertation to guarantee practitioners from all fields can understand the concepts we introduce

Generalization Error Analysis of Neural networks with Gradient Based Regularization

We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve some partial differential equations, mostly in high dimensions in practical applications. In this work, we introduce a general framework to analyze the generalization error of regularized networks. The error estimate relies on two assumptions on the approximation error and the quadrature error. Moreover, we conduct some experiments on the image classification tasks to show that gradient-based methods can significantly improve the generalization ability and adversarial robustness of neural networks. A graphical extension of the gradient-based methods are also considered in the experiments

Hypertext Semiotics in the Commercialized Internet

Die Hypertext Theorie verwendet die selbe Terminologie, welche seit Jahrzehnten in der semiotischen Forschung untersucht wird, wie z.B. Zeichen, Text, Kommunikation, Code, Metapher, Paradigma, Syntax, usw. Aufbauend auf jenen Ergebnissen, welche in der Anwendung semiotischer Prinzipien und Methoden auf die Informatik erfolgreich waren, wie etwa Computer Semiotics, Computational Semiotics und Semiotic Interface Engineering, legt diese Dissertation einen systematischen Ansatz für all jene Forscher dar, die bereit sind, Hypertext aus einer semiotischen Perspektive zu betrachten. Durch die Verknüpfung existierender Hypertext-Modelle mit den Resultaten aus der Semiotik auf allen Sinnesebenen der textuellen, auditiven, visuellen, taktilen und geruchlichen Wahrnehmung skizziert der Autor Prolegomena einer Hypertext-Semiotik-Theorie, anstatt ein völlig neues Hypertext-Modell zu präsentieren. Eine Einführung in die Geschichte der Hypertexte, von ihrer Vorgeschichte bis zum heutigen Entwicklungsstand und den gegenwärtigen Entwicklungen im kommerzialisierten World Wide Web bilden den Rahmen für diesen Ansatz, welcher als Fundierung des Brückenschlages zwischen Mediensemiotik und Computer-Semiotik angesehen werden darf. Während Computer-Semiotiker wissen, dass der Computer eine semiotische Maschine ist und Experten der künstlichen Intelligenz-Forschung die Rolle der Semiotik in der Entwicklung der nächsten Hypertext-Generation betonen, bedient sich diese Arbeit einer breiteren methodologischen Basis. Dementsprechend reichen die Teilgebiete von Hypertextanwendungen, -paradigmen, und -strukturen, über Navigation, Web Design und Web Augmentation zu einem interdisziplinären Spektrum detaillierter Analysen, z.B. des Zeigeinstrumentes der Web Browser, des Klammeraffen-Zeichens und der sogenannten Emoticons. Die Bezeichnung ''Icon'' wird als unpassender Name für jene Bildchen, welche von der graphischen Benutzeroberfläche her bekannt sind und in Hypertexten eingesetzt werden, zurückgewiesen und diese Bildchen durch eine neue Generation mächtiger Graphic Link Markers ersetzt. Diese Ergebnisse werden im Kontext der Kommerzialisierung des Internet betrachtet. Neben der Identifizierung der Hauptprobleme des eCommerce aus der Perspektive der Hypertext Semiotik, widmet sich der Autor den Informationsgütern und den derzeitigen Hindernissen für die New Economy, wie etwa der restriktiven Gesetzeslage in Sachen Copyright und Intellectual Property. Diese anachronistischen Beschränkungen basieren auf der problematischen Annahme, dass auch der Informationswert durch die Knappheit bestimmt wird. Eine semiotische Analyse der iMarketing Techniken, wie z.B. Banner Werbung, Keywords und Link Injektion, sowie Exkurse über den Browser Krieg und den Toywar runden die Dissertation ab

고차 상호작용하는 복잡계의 떠오름 현상

학위논문(박사) -- 서울대학교대학원 : 자연과학대학 물리·천문학부(물리학전공), 2022.2. 백용주.구성 요소들의 미시적 동역학만으로는 설명할 수 없는 복잡계의 많은 현상들은 구성 요소들의 복잡한 상호작용에 그 근원을 두고 있다. 총괄적 관점에서 복잡계의 성질을 해석하고 이해하는 방법으로 주목을 받았던 네트워크 과학을 통해 설명해 왔던 물리적 현상들 중에는 짝 상호작용으로 환원되지 않는 성질의 상호작용들이 존재한다. 둘 이상의 많은 요소들의 동시다발적 상호작용을 적절하게 표현하기 위해 사용되는 몇 가지 수학적 도구가 도입되었다. 이 학위논문에서는 고차 상호작용을 포함한 구조로 하이퍼그래프와 단체 복합체를 사용하여 이 위에서 기존 짝 상호작용 구조에서 나타나는 보편성과 동역학들이 어떻게 달라지는지를 해석적, 수치적 방법을 통해 탐구한다. 먼저 고차 상호작용으로의 표현이 필요한 사회 현상인 공저자 네트워크 데이터를 분석한다. 우리는 공저자 네트워크 데이터를 단체 복합체로 표현하여 그 위상적 특성의 시간 진화를 확인하였다. 이것의 성장 과정에서 위상적인 불변량인 베티 수가 차원에 따라 순차적으로 창발이 나타난다는 것을 확인하였다. 이러한 위상적 양상과 구조적 특성을 성장 과정에서 모방할 수 있는 단체 복합체 모형을 구성하여 그 특성들을 통계적으로 확인한 결과, 베티 수의 창발이 무한차수 상전이의 특징을 보인다는 것을 발견하였다. 이를 설명할 수 있는 시간 의존 비율방정식의 정상상태를 생성함수 방법으로 접근하여 무한차수 상전이를 이론적으로 규명하였다. 하이퍼그래프는 사회 연결망에서 여러 사람이 함께 하는 팀 사이의 상호작용을 표현하는데에도 사용할 수 있다. 매개 중심성을 하이퍼그래프에서 측정할 전산 알고리즘을 제안하고, 사회 연결망을 묘사할 척도없는 하이퍼그래프 모형을 구성하였다. 이로부터 팀의 매개중심성 분포는 개개인의 매개중심성 분포와는 상이하게 거듭제곱 분포가 왜곡되어 지수함수적 감소를 보임을 확인하고, 이 감소의 정도가 팀의 크기와 관련됨을 보았다. 하지만 실제 데이터에 반영되는 추가 정보를 팀의 가중치로써 도입하면 매개중심성 분포의 거듭제곱 법칙이 재구성됨을 확인하였다. 하지만 팀이 가지는 가중치가 아니라 하이퍼그래프 구조에서 존재하는 위치가 팀의 성과에 더욱 중요한 요소라는 반직관적인 결과를 얻었다. 마지막으로 복잡계에서 보이는 동역학 과정에 미치는 고차 상호작용의 영향을 동기화 현상의 예를 통해 살펴보았다. 동기화 과정은 자연 및 인공 시스템의 광범위한 기능에 중요한 역할을 하기 때문에 그 집단 행동의 형성에 미치는 미시적 상호작용 구조에 대한 이해는 필수불가결하다고 할 수 있다. 우리는 척도없는 하이퍼그래프 위에서의 구라모토 모형을 연속 방정식의 오트-안톤센 가설 풀이법과 평균장 이론을 이용하여 조사하였다. 그 결과로 연결 구조의 불균일함에 따라 연속 상전이에서 불연속 상전이로의 변화가 나타남을 확인하였다. 특히 불연속 상전이는 그 전이점에서 임계 현상을 보이는 하이브리드 상전이임을 확인하였고, 이 임계 지수를 해석적, 수치적으로 결정하였다.Rooted in the complex interactions of components, diverse aspects in complex systems cannot be explained by the microscopic dynamics of components. Among the physical phenomena that have been described through network science, which have received attention as a way of interpreting and understanding the properties of complex systems from a holistic point of view, are intrinsic interactions that cannot be reduced to pairwise interactions. In this dissertation, we analytically and numerically explore the emergent phenomena that appear in these higher-order interactions. As structures include these simultaneous interactions of two or more elements, we use hypergraphs and simplicial complexes. First, the coauthorship data, which is a social relationship that requires the expression of higher-order interactions, is analyzed. We confirmed the time evolution of the topological features by expressing the coauthorship data as a simplicial complex. In the process of its growth, we find that the Betti numbers, topological invariants, sequentially appeared according to the dimension. As a result of statistical confirming the properties by constructing a random simplicial complex model that can imitate these topological aspects and structural characteristics in the growing process, we reveal that the development of the Betti number showed the infinite-order phase transition. By generating function, the steady-state analysis of the time-dependent rate equation that mimics the model algorithms suggests the theoretical explanations of the infinite-order transitions. Hypergraphs also are widely used to express interactions between teams with multiple people in a social network. Here we propose a computational algorithm to measure betweenness centralities in a hypergraph. Furthermore, a scale-free hypergraph model is constructed to describe the features of social networks. From this, we confirm that the distribution of the team's betweenness centrality, showing exponential decaying, is different from the power-law distribution of individual betweenness centrality. Interestingly, the decaying rate is related to the size of the team. However, if additional information reflected in the actual data is introduced as the team's weight, the power law of the betweenness centrality distribution is reconstructed. Counterintuitively, we observe that the location of a team in the hypergraph structure, such as whether the team is near the hub, not the weight of the team, is a more crucial factor in the team's performance. Finally, the influence of higher-order interactions on the dynamics detected in complex systems is examined through examples of synchronization phenomena. Synchronization appears in a wide range of natural and artificial systems. Thus, an understanding of the microscopic group interaction structure is indispensable. We investigated the Kuramoto model on a scaleless hypergraph using the Ott-Antonsen ansatz of continuity equations and the mean-field theory. As a result, we find that the non-uniformity of the connection structure resulted in a change from continuous phase transition to discontinuous phase transition. In particular, we observe that discontinuous phase transition is indeed a hybrid phase transition, showing a critical phenomenon at its transition point. The critical exponents are determined both analytically and numerically.Abstract i Contents iii List of Figures vii List of Tables ix 1 Introduction 1 1.1 Complex systems in nature 1 1.2 Representations of complex systems 3 1.3 Structure and goal of the dissertation 6 2 Representations of interactions 10 2.1 Interaction 10 2.2 Pairwise represenation: graph theory 11 2.2.1 Definitions and concepts 11 2.2.2 Random graph models 17 2.3 Higher-order representation: concepts of hypergraphs 19 2.3.1 Mathematical definitions 19 2.4 Algebraic topology: special case of higher-order interactions 21 2.4.1 Simplicial complexes 21 2.4.2 Homology groups 22 3 Basics of percolation transitions 25 3.1 What is percolation 25 3.2 Percolation on complex networks 27 4 Homological percolation transitions: numerical approach 29 4.1 Introduction 29 4.2 Results 33 4.2.1 Homological percolation transitions 33 4.2.2 Facet degree distribution 37 4.2.3 Minimal model 39 4.2.4 Kahle localization 42 4.3 Conclusion 44 4.4 Discussion 45 5 Homological percolation transitions: analytical approach 46 5.1 Introduction 46 5.2 Model 49 5.3 Percolation transition 49 5.3.1 Cluster-size distribution, giant cluster, and mean cluster size 49 5.3.2 Graph and facet degree distributions 55 5.4 Homological percolation transition 58 5.4.1 Model generalization and Betti number 58 5.4.2 Rigorous description of the first Betti number 60 5.5 Discussion 63 5.6 Conclusion 64 6 Criticality from shortest path dynamics on hypergraphs: Betweenness centraility distribution 65 6.1 Betweenness centrality in hypergraphs 65 6.2 Random hypergraph model with preferential attachment 68 6.3 Real data analysis 72 6.4 Summary and discussion 76 7 Synchronization of coupled oscillators 81 7.1 Synchronization 81 7.2 Kuramoto model 82 7.2.1 Order parameter 83 7.2.2 Self-consistency equation approaches 84 8 Synchronization transitions in hypergraphs 86 8.1 Introduction 86 8.2 Model 87 8.3 Self-consistency equations 89 8.4 Results 92 8.5 Summary and discussion 92 9 Conclusion 95 Appendices 97 Appendix A Topological data analysis 98 A.1 Persistent homology 98 Appendix B Appendices for chapter 4 100 B.1 Derivation of master equation of joint generating function 100 Appendix C Appendices for chapter 5 103 C.1 BC distributions for the BA-II hypergraphs 103 C.2 Features of our coauthorship data 104 C.3 Parameter analysis 105 C.3.1 Relations among the BCes and parameters 105 C.3.2 Influential parameters for top BCes 107 C.4 Analysis of the small size dataset 108 Appendix D Appendices for chapter 6 118 D.1 Heterogeneous mean-field theory 118 D.2 Critical behavior 120 D.3 Correlation size 121 Bibliography 123 Abstract in Korean 135박

Geometric data understanding : deriving case specific features

There exists a tradition using precise geometric modeling, where uncertainties in data can be considered noise. Another tradition relies on statistical nature of vast quantity of data, where geometric regularity is intrinsic to data and statistical models usually grasp this level only indirectly. This work focuses on point cloud data of natural resources and the silhouette recognition from video input as two real world examples of problems having geometric content which is intangible at the raw data presentation. This content could be discovered and modeled to some degree by such machine learning (ML) approaches like deep learning, but either a direct coverage of geometry in samples or addition of special geometry invariant layer is necessary. Geometric content is central when there is a need for direct observations of spatial variables, or one needs to gain a mapping to a geometrically consistent data representation, where e.g. outliers or noise can be easily discerned. In this thesis we consider transformation of original input data to a geometric feature space in two example problems. The first example is curvature of surfaces, which has met renewed interest since the introduction of ubiquitous point cloud data and the maturation of the discrete differential geometry. Curvature spectra can characterize a spatial sample rather well, and provide useful features for ML purposes. The second example involves projective methods used to video stereo-signal analysis in swimming analytics. The aim is to find meaningful local geometric representations for feature generation, which also facilitate additional analysis based on geometric understanding of the model. The features are associated directly to some geometric quantity, and this makes it easier to express the geometric constraints in a natural way, as shown in the thesis. Also, the visualization and further feature generation is much easier. Third, the approach provides sound baseline methods to more traditional ML approaches, e.g. neural network methods. Fourth, most of the ML methods can utilize the geometric features presented in this work as additional features.Geometriassa käytetään perinteisesti tarkkoja malleja, jolloin datassa esiintyvät epätarkkuudet edustavat melua. Toisessa perinteessä nojataan suuren datamäärän tilastolliseen luonteeseen, jolloin geometrinen säännönmukaisuus on datan sisäsyntyinen ominaisuus, joka hahmotetaan tilastollisilla malleilla ainoastaan epäsuorasti. Tämä työ keskittyy kahteen esimerkkiin: luonnonvaroja kuvaaviin pistepilviin ja videohahmontunnistukseen. Nämä ovat todellisia ongelmia, joissa geometrinen sisältö on tavoittamattomissa raakadatan tasolla. Tämä sisältö voitaisiin jossain määrin löytää ja mallintaa koneoppimisen keinoin, esim. syväoppimisen avulla, mutta joko geometria pitää kattaa suoraan näytteistämällä tai tarvitaan neuronien lisäkerros geometrisia invariansseja varten. Geometrinen sisältö on keskeinen, kun tarvitaan suoraa avaruudellisten suureiden havainnointia, tai kun tarvitaan kuvaus geometrisesti yhtenäiseen dataesitykseen, jossa poikkeavat näytteet tai melu voidaan helposti erottaa. Tässä työssä tarkastellaan datan muuntamista geometriseen piirreavaruuteen kahden esimerkkiohjelman suhteen. Ensimmäinen esimerkki on pintakaarevuus, joka on uudelleen virinneen kiinnostuksen kohde kaikkialle saatavissa olevan datan ja diskreetin geometrian kypsymisen takia. Kaarevuusspektrit voivat luonnehtia avaruudellista kohdetta melko hyvin ja tarjota koneoppimisessa hyödyllisiä piirteitä. Toinen esimerkki koskee projektiivisia menetelmiä käytettäessä stereovideosignaalia uinnin analytiikkaan. Tavoite on löytää merkityksellisiä paikallisen geometrian esityksiä, jotka samalla mahdollistavat muun geometrian ymmärrykseen perustuvan analyysin. Piirteet liittyvät suoraan johonkin geometriseen suureeseen, ja tämä helpottaa luonnollisella tavalla geometristen rajoitteiden käsittelyä, kuten väitöstyössä osoitetaan. Myös visualisointi ja lisäpiirteiden luonti muuttuu helpommaksi. Kolmanneksi, lähestymistapa suo selkeän vertailumenetelmän perinteisemmille koneoppimisen lähestymistavoille, esim. hermoverkkomenetelmille. Neljänneksi, useimmat koneoppimismenetelmät voivat hyödyntää tässä työssä esitettyjä geometrisia piirteitä lisäämällä ne muiden piirteiden joukkoon