<div>Representation learning (RL) for social networks facilitates real-world tasks such as visualization, link prediction and friend recommendation. Many methods have been proposed in this area to learn continuous low-dimensional embedding of nodes, edges or relations in social and information networks. However, most previous network RL methods neglect social signals, such as textual communication between users (nodes). Unlike more typical binary features on edges, such as post likes and retweet actions, social signals are more varied and contain ambiguous information. This makes it more challenging to incorporate them into RL methods, but the ability to quantify social signals should allow RL methods to better capture the implicit relationships among real people in social networks. Second, most previous work in network RL has focused on learning from homogeneous networks (i.e., single type of node, edge, role, and direction) and thus, most existing RL methods cannot capture the heterogeneous nature of relationships in social networks. Based on these identified gaps, this thesis aims to study the feasibility of incorporating heterogeneous information, e.g., texts, attributes, multiple relations and edge types (directions), to learn more accurate, fine-grained network representations. </div><div> </div><div>In this dissertation, we discuss a preliminary study and outline three major works that aim to incorporate textual interactions to improve relational representation learning. The preliminary study learns a joint representation that captures the textual similarity in content between interacting nodes. The promising results motivate us to pursue broader research on using social signals for representation learning. The first major component aims to learn explicit node and relation embeddings in social networks. Traditional knowledge graph (KG) completion models learn latent representations of entities and relations by interpreting them as translations operating on the embedding of the entities. However, existing approaches do not consider textual communications between users, which contain valuable information to provide meaning and context for social relationships. We propose a novel approach that incorporates textual interactions between each pair of users to improve representation learning of both users and relationships. The second major component focuses on analyzing how users interact with each other via natural language content. Although the data is interconnected and dependent, previous research has primarily focused on modeling the social network behavior separately from the textual content. In this work, we model the data in a holistic way, taking into account the connections between the social behavior of users and the content generated when they interact, by learning a joint embedding over user characteristics and user language. In the third major component, we consider the task of learning edge representations in social networks. Edge representations are especially beneficial as we need to describe or explain the relationships, activities, and interactions among users. However, previous work in this area lack well-defined edge representations and ignore the relational signals over multiple views of social networks, which typically contain multi-view contexts (due to multiple edge types) that need to be considered when learning the representation. We propose a new methodology that captures asymmetry in multiple views by learning well-defined edge representations and incorporates textual communications to identify multiple sources of social signals that moderate the impact of different views between users.</div>

The availability and use of knowledge graphs have become commonplace as a compact storage of information and for lookup of facts. However, the discrete representation makes the knowledge graph unavailable for tasks that need a continuous representation, such as predicting relationships between entities, where the most probable relationship needs to be found. The need for a continuous representation has spurred the development of knowledge graph embeddings. The idea is to position the entities of the graph relative to each other in a continuous low-dimensional vector space, so that their relationships are preserved, and ideally leading to clusters of entities with similar characteristics. Several methods to produce knowledge graph embeddings have been created, from simple models that minimize the distance between related entities to complex neural models. Almost all of these embedding methods attempt to create an accurate static representation of each entity and relation. However, as with words in natural language, both entities and relations in a knowledge graph hold different meanings in different local contexts.  With the recent development of Transformer models, and their success in creating contextual representations of natural language, work has been done to apply them to graphs. Initial results show great promise, but there are significant differences in archi- tecture design across papers. There is no clear direction on how Transformer models can be best applied to create contextual knowledge graph embeddings. Two of the main differences in previous work is how the attention mask is applied in the model and what input graph structures the model is trained on.  This report explores how different attention masking methods and graph inputs affect a Transformer model (in this report, BERT) on a link prediction task for triples. Models are trained with five different attention masking methods, which to varying degrees restrict attention, and on three different input graph structures (triples, paths, and interconnected triples).  The results indicate that a Transformer model trained with a masked language model objective has the strongest performance on the link prediction task when there are no restrictions on how attention is directed, and when it is trained on graph structures that are sequential. This is similar to how models like BERT learn sentence structure after being exposed to a large number of training samples. For more complex graph structures it is beneficial to encode information of the graph structure through how the attention mask is applied. There also seems to be some indications that the input graph structure affects the models’ capabilities to learn underlying characteristics in the knowledge graph that is trained upon.

<p>Partition density functional theory (P-DFT) is a density-based embedding method used to calculate the electronic properties of molecules through self-consistent calculations on fragments. P-DFT features a unique set of fragment densities that can be used to define formal charges and local dipoles. This dissertation is concerned mainly with establishing how the optimal fragment densities and energies of P-DFT depend on the specific methods employed during the self-consistent fragment calculations. First, we develop a procedure to perform P-DFT calculations on three-dimensional heteronuclear diatomic molecules, and we compare and contrast two different approaches to deal with non-integer electron numbers: Fractionally occupied orbitals (FOO) and ensemble averages (ENS). We find that, although both ENS and FOO methods lead to the same total energy and density, the ENS fragment densities are less distorted than those of FOO when compared to their isolated counterparts. Second, we formulate partition spin density functional theory (P-SDFT) and perform numerical calculations on closed- and open-shell diatomic molecules. We find that, for closed-shell molecules, while P-SDFT and P-DFT are equivalent for FOO, they partition the same total density of a molecule differently for ENS. For open-shell molecules, P-SDFT and P-DFT yield different sets of fragment densities for both FOO and ENS. Finally, by considering a one-electron system, we investigate the self-interaction error (SIE) produced by approximate exchange-correlation functionals and find that the molecular SIE can be attributed mainly to the non-additive Hartree-exchange-correlation energy.</p>

The robust pricing and hedging approach in Mathematical Finance, pioneered by Hobson (1998), makes statements about non-traded derivative contracts by imposing very little assumptions about the underlying financial model but directly using information contained in traded options, typically call or put option prices. These prices are informative about marginal distributions of the asset. Mathematically, the theory of Skorokhod embeddings provides one possibility to approach robust problems. In this thesis we consider mostly robust pricing and hedging problems of Lookback options (options written on the terminal maximum of an asset) and Convex Vanilla Options (options written on the terminal value of an asset) and extend the analysis which is predominately found in the literature on robust problems by two features: Firstly, options with multiple maturities are available for trading (mathematically this corresponds to multiple marginal constraints) and secondly, restrictions on the total realized variance of asset trajectories are imposed. Probabilistically, in both cases, we develop new optimal solutions to the Skorokhod embedding problem. More precisely, in Part I we start by constructing an iterated Azema-Yor type embedding (a solution to the n-marginal Skorokhod embedding problem, see Chapter 2). Subsequently, its implications are presented in Chapter 3. From a Mathematical Finance perspective we obtain explicitly the optimal superhedging strategy for Barrier/Lookback options. From a probability theory perspective, we find the maximum maximum of a martingale which is constrained by finitely many intermediate marginal laws. Further, as a by-product, we discover a new class of martingale inequalities for the terminal maximum of a cadlag submartingale, see Chapter 4. These inequalities enable us to re-derive the sharp versions of Doob's inequalities. In Chapter 5 a different problem is solved. Motivated by the fact that in some markets both Vanilla and Barrier options with multiple maturities are traded, we characterize the set of market models in this case. In Part II we incorporate the restriction that the total realized variance of every asset trajectory is bounded by a constant. This has been previously suggested by Mykland (2000). We further assume that finitely many put options with one fixed maturity are traded. After introducing the general framework in Chapter 6, we analyse the associated robust pricing and hedging problem for convex Vanilla and Lookback options in Chapters 7 and 8. Robust pricing is achieved through construction of appropriate Root solutions to the Skorokhod embedding problem. Robust hedging and pathwise duality are obtained by a careful development of dynamic pathwise superhedging strategies. Further, we characterize existence of market models with a suitable notion of arbitrage.

Consider a graph G with vertex set V in which each of the n vertices is assigned a number from the set {1, ..., k} for some positive integer k. This assignment phi is a labeling if all k numbers are used. If phi does not assign adjacent vertices the same label, then phi partitions V into k levels. In a level drawing, the y-coordinate of each vertex matches its label and the edges are drawn strictly y-monotone. This leads to level drawings in the xy-plane where all vertices with label j lie along the line lj = {(x, j) : x in Reals} and where each edge crosses any of the k horizontal lines lj for j in [1..k] at most once. A graph with such a labeling forms a level graph and is level planar if it has a level drawing without crossings.We first consider the class of level trees that are level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). We describe which trees are ULP and provide linear-time level planar drawing algorithms for any labeling. We characterize ULP trees in terms of two forbidden subdivisions so that any other tree must contain a subtree homeomorphic to one of these. We also provide linear-time recognition algorithms for ULP trees. We then extend this characterization to all ULP graphs with five additional forbidden subdivisions, and provide linear-time recogntion and drawing algorithms for any given labeling.

The main results of this dissertation show evidence supporting the Successive Surface Scaffolding Conjecture. This is a new conjecture that, if true, guarantees the existence of all the wye-delta-order minimal obstructions of a surface S as subgraphs of the irreducible triangulations of the surface S with a crosscap added. A new data structure, i.e. an augmented rotation system, is presented and used to create an exponential-time algorithm for embedding graphs in any surface with a constant-time check of the change in genus when inserting an edge. A depiction is a new formal definition for representing an embedding graphically, and it is shown that more than one depiction can be given for nonplanar embeddings, and that sometimes two depictions for the same embedding can be drastically different from each other. An algorithm for finding the essential cycles of an embedding is given, and is used to confirm for the projective-plane obstructions, a theorem that shows any embedding of an obstruction must have every edge in an essential cycle. Obstructions of a general surface S that are minor-minimal and not double-wye-delta-minimal are shown to each have an embedding on the surface S with a crosscap added. Finally, open questions for further research are presented. / Graduate

Entrepreneurial opportunities are frequently noted and addressed in the literature of immigrant entrepreneurship; however, little is known about how these entrepreneurial opportunities come into existence and how immigrant entrepreneurs create such opportunities. The purpose of this thesis is to examine why and how immigrant entrepreneurs create entrepreneurial opportunities through embedding processes in the home country and the host country. Sweden was chosen as the country of residence of immigrant entrepreneurs from Lebanon, Syria, Cameroon and Mexico. Four cases were selected in this study. Each case illustrates an opportunity creation process in a different industry, between a different home country and Sweden as the host country and by immigrant entrepreneurs with different backgrounds. By using the mixed embeddedness perspective as the theoretical lens in combination with the literature on entrepreneurial opportunity and immigrant entrepreneurship, this thesis develops a model of entrepreneurial opportunity creation as an integration process. The findings suggest that entrepreneurial opportunity creation can be considered as a process of local integration by immigrant entrepreneurs into the host country and a re-integration of these entrepreneurs into the home country. At the beginning of the opportunity creation process, immigrant entrepreneurs feel socially excluded in the host country. Throughout the opportunity creation process, immigrant entrepreneurs interact with different actors in the host country and gradually move from being socially excluded to socially included, which illustrates a local integration process. In this process, immigrant entrepreneurs become localized through different activities that embed them in the local context. The process of entrepreneurial idea and business concept development and the refinement of the business concept in this thesis illustrates an ongoing and non-linear process of: being locally integrated through creating trust in the local people, acculturating and creating a sense of belonging; and being re-integrated to the home country through maintaining and establishing new links to the home country. The study contributes to the mainstream entrepreneurship and immigrant entrepreneurship in several ways. First, it contributes to studies on immigrant entrepreneurship by investigating why immigrants embark on a journey to be entrepreneurs and how immigrant entrepreneurs create entrepreneurial opportunities through embedding processes in the home and the host country. The study demonstrates how an entrepreneurial opportunity is created as a social integration process. Second, the study contributes to literature on entrepreneurship and immigrant entrepreneurship by incorporating the entrepreneurial opportunity creation process with acculturation strategies. It illustrates how the entrepreneurial opportunity creation process intertwines with the four strategies of acculturation. Third, the study contributes to the mixed embeddedness perspective by adopting the process approach and proposing mixed embedding as a new concept which centers on the interplay between the home and the host country’s influences on immigrants’ business activities; by extending mixed embeddedness from the national level of the home country or the host country to the transnational level between the home country and the host country; and by proposing an alternative way to view an entrepreneurial opportunity as a creation process instead of being discovered. Fourth, the study contributes to the immigrant entrepreneurship literature in Sweden by furthering the understanding of entrepreneurial opportunity creation by immigrant entrepreneurs in Sweden. Furthermore, the study suggests some implications for practice. The study proposes some embedding mechanisms which can be implemented in business support programs for immigrant entrepreneurs and in integration programs for immigrants in general. The design of the business support programs can aim to help immigrant entrepreneurs to: create credibility through contacts and experiences that they establish and gain in the local community; create familiarity to the local community through associating business concepts with well-known values; engage in the local life to understand customers’ mindsets, master the local language to understand local customers’ needs; and establish new/strengthen connections to the home country. The design of integration programs can aim to undertake activities that help immigrants increase the interaction between the local people and themselves. This type of interaction could be increased by organizing meetings and activities in which immigrants are introduced to different local sports clubs and hobby clubs. An approach in which the host country’s language is practiced and mastered anywhere and anytime should be adopted in the integration programs.

Les schémas de routage locaux basés sur des coordonnées prises dans le plan hyperbolique ont attiré un intérêt croissant depuis quelques années. Cependant, les solutions proposées sont toutes appliquées à des réseaux au topologie aléatoire et au nombre de nœuds limités. Dans le même temps, plusieurs travaux se sont concentrés sur la création de modèle topologique basé sur les lois de la géométrie hyperbolique. Dans ce cas, Il est montré que les graphes ont des topologies semblables à Internet et qu'un routage local hyperbolique atteint une efficacité proche de la perfection. Cependant, ces graphes ne garantissent pas le taux de réussite du routage même si aucune panne ne se produit. Dans cette thèse, l'objectif est de construire un système passant à l'échelle pour la création de réseau recouvrant capable de fournir à ses membres un service d'adressage et de routage résilient dans un environnement dynamique. Ensuite, nous étudions de quelle manière les réseaux P2PTV pourraient supporter un nombre d'utilisateur croissant. Dans cette thèse, nous essayons de répondre à cette question en étudiant les facteurs d'efficacité et de passage à l'échelle dans un système de diffusion vidéo P2P typique. Au travers des données fournies par Zattoo, producteur de réseau P2PTV, nous réalisons des simulations dont les résultats montrent qu'il y a encore des obstacles à surmonter avant que les réseaux P2P de diffusion vidéo puissent dépendre uniquement de leurs utilisateurs. / Local routing schemes based on virtual coordinates taken from the hyperbolic plane have attracted considerable interest in recent years.However, solutions have been applied to ad-hoc and sensor networks having a random topology and a limited number of nodes. In other hand, some research has focused on the creation of network topology models based on hyperbolic geometric laws. In this case, it has been shown that these graphs have an Internet-like topology and that local hyperbolic routing achieves a near perfect efficiency. However, with these graphs, routing success is not guaranteed even if no failures happen. In this thesis, we aim at building a scalable system for creating overlay networks on top of the Internet that would provide reliable addressing and routing service to its members in a dynamic environment.Next, we investigate how well P2PTV networks would support a growing number of users. In this thesis, we try to address this question by studying scalability and efficiency factors in a typical P2P based live streaming network. Through the use of the data provided by Zattoo a production P2PTV network, we carry out simulations whose results show that there are still hurdles to overcome before P2P based live streaming could depend uniquely of their users.

This thesis centers around dimensionality reduction and its usage on landmark-type data which are often used in anthropology and morphometrics. In particular we focus on non-linear dimensionality reduction methods - locally linear embedding and multidimensional scaling. We introduce a new approach to dimensionality reduction called multipass dimensionality reduction and show that improves the quality of classification as well as requiring less dimensions for successful classification than the traditional singlepass methods.

Master of Science / Department of Computing and Information Sciences / William H. Hsu / Automatic rigging is a targeting approach that takes a 3-D character mesh and an adapted skeleton and automatically embeds it into the mesh. Automating the embedding step provides a savings over traditional character rigging approaches, which require manual guidance, at the cost of occasional errors in recognizing parts of the mesh and aligning bones of the skeleton with it. In this thesis, I examine the problem of reducing such errors in an auto-rigging system and apply a density-based clustering algorithm to correct errors in a particular system, Pinocchio (Baran & Popovic, 2007). I show how the density-based clustering algorithm DBSCAN (Ester et al., 1996) is able to filter out some impossible vertices to correct errors at character extremities (hair, hands, and feet) and those resulting from clothing that hides extremities such as legs.