Recommending on graphs: a comprehensive review from a data perspective

Recent advances in graph-based learning approaches have demonstrated their effectiveness in modelling users' preferences and items' characteristics for Recommender Systems (RSS). Most of the data in RSS can be organized into graphs where various objects (e.g., users, items, and attributes) are explicitly or implicitly connected and influence each other via various relations. Such a graph-based organization brings benefits to exploiting potential properties in graph learning (e.g., random walk and network embedding) techniques to enrich the representations of the user and item nodes, which is an essential factor for successful recommendations. In this paper, we provide a comprehensive survey of Graph Learning-based Recommender Systems (GLRSs). Specifically, we start from a data-driven perspective to systematically categorize various graphs in GLRSs and analyze their characteristics. Then, we discuss the state-of-the-art frameworks with a focus on the graph learning module and how they address practical recommendation challenges such as scalability, fairness, diversity, explainability and so on. Finally, we share some potential research directions in this rapidly growing area.Comment: Accepted by UMUA

Network design and defence

Infrastructure networks are a key feature of an economy. Their functionality depends on the connectivity and sizes of different components and they face a variety of threats, from natural disasters to intelligent attacks. How should networks be defended and designed to ensure the best functionality? We develop a model to study this question. There are two players, the Designer and the Adversary. The Designer forms costly links among n given nodes and chooses to protect some of them at a cost. The Adversary then allocates resources to attack nodes. Successful attack on a node leads to its elimination. We study sub-game perfect equilibria of this game. Our main finding is that if defence is affordable and reliable, then the network is sparse and heterogeneous, and either centrally or fully protected. On the other hand, if defence is relatively costly compared to linking, then dense and homogeneous networks arise in equilibrium.This work was supported by European Research Area Complexity-Net (http://www.complexitynet.eu) through grant, Resilience and interaction of networks in ecology and economics (RESINEE).This is the accepted version of the original publication in Games and Economic Behavior, available online at http://www.sciencedirect.com/science/article/pii/S0899825613000031. Copyright © 2013 Elsevier Inc. All rights reserved

Optimizing Non-pharmaceutical Interventions Using Multi-coaffiliation Networks

Computational modeling is of fundamental significance in mapping possible disease spread, and designing strategies for its mitigation. Conventional contact networks implement the simulation of interactions as random occurrences, presenting public health bodies with a difficult trade off between a realistic model granularity and robust design of intervention strategies. Recently, researchers have been investigating the use of agent-based models (ABMs) to embrace the complexity of real world interactions. At the same time, theoretical approaches provide epidemiologists with general optimization models in which demographics are intrinsically simplified. The emerging study of affiliation networks and co-affiliation networks provide an alternative to such trade off. Co-affiliation networks maintain the realism innate to ABMs while reducing the complexity of contact networks into distinctively smaller k-partite graphs, were each partition represent a dimension of the social model. This dissertation studies the optimization of intervention strategies for infectious diseases, mainly distributed in school systems. First, concepts of synthetic populations and affiliation networks are extended to propose a modified algorithm for the synthetic reconstruction of populations. Second, the definition of multi-coaffiliation networks is presented as the main social model in which risk is quantified and evaluated, thereby obtaining vulnerability indications for each school in the system. Finally, maximization of the mitigation coverage and minimization of the overall cost of intervention strategies are proposed and compared, based on centrality measures

Topics in social network analysis and network science

This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recently, the majority involve only the most basic methods and thus scratch the surface of what might be accomplished. Cutting-edge methods using relevant examples and illustrations in health services research are provided

Quantum multipartite entangled states, classical and quantum error correction

Studying entanglement is essential for our understanding of such diverse areas as high-energy physics, condensed matter physics, and quantum optics. Moreover, entanglement allows us to surpass classical physics and technologies enabling better information processing, computation, and improved metrology. Recently, entanglement also played a prominent role in characterizing and simulating quantum many-body states and in this way deepened our understanding of quantum matter. While bipartite entanglement is well understood, multipartite entanglement is much richer and leads to stronger contradictions with classical physics. Among all possible entangled states, a special class of states has attracted attention for a wide range of tasks. These states are called k-uniform states and are pure multipartite quantum states of n parties and local dimension q with the property that all of their reductions to k parties are maximally mixed. Operationally, in a k-uniform state any subset of at most k parties is maximally entangled with the rest. The k = bn/2c-uniform states are called absolutely maximally entangled because they are maximally entangled along any splitting of the n parties into two groups. These states find applications in several protocols and, in particular, are the building blocks of quantum error correcting codes with a holographic geometry, which has provided valuable insight into the connections between quantum information theory and conformal field theory. Their properties and the applications are however intriguing, as we know little about them: when they exist, how to construct them, how they relate to other multipartite entangled states, such as graph states, or how they connect under local operations and classical communication. With this motivation in mind, in this thesis we first study the properties of k-uniform states and then present systematic methods to construct closed-form expressions of them. The structure of our methods proves to be particularly fruitful in understanding the structure of these quantum states, their graph-state representation and classification under local operations and classical communication. We also construct several examples of absolutely maximally entangled states whose existence was open so far. Finally, we explore a new family of quantum error correcting codes that generalize and improve the link between classical error correcting codes, multipartite entangled states, and the stabilizer formalism. The results of this thesis can have a role in characterizing and studying the following three topics: multipartite entanglement, classical error correcting codes and quantum error correcting codes. The multipartite entangled states can provide a link to find different resources for quantum information processing tasks and quantify entanglement. Constructing two sets of highly entangled multipartite states, it is important to know if they are equivalent under local operations and classical communication. By understanding which states belong to the same class of quantum resource, one may discuss the role they play in some certain quantum information tasks like quantum key distribution, teleportation and constructing optimum quantum error correcting codes. They can also be used to explore the connection between the Antide Sitter/Conformal Field Theory holographic correspondence and quantum error correction, which will then allow us to construct better quantum error correcting codes. At the same time, their roles in the characterization of quantum networks will be essential to design functional networks, robust against losses and local noise.El estudio del entrelazamiento cuántico es esencial para la comprensión de diversas áreas como la óptica cuántica, la materia condensada e incluso la física de altas energías. Además, el entrelazamiento nos permite superar la física y tecnologías clásicas llevando a una mejora en el procesado de la información, la computación y la metrología. Recientemente se ha descubierto que el entrelazamiento desarrolla un papel central en la caracterización y simulación de sistemas cuánticos de muchos cuerpos, de esta manera facilitando nuestra comprensión de la materia cuántica. Mientras que se tiene un buen conocimiento del entrelazamiento en estados puros bipartitos, nuestra comprensión del caso de muchas partes es mucho más limitada, a pesar de que sea un escenario más rico y que presenta un contraste más fuerte con la física clásica. De entre todos los posibles estados entrelazados, una clase especial ha llamado la atención por su amplia gama de aplicaciones. Estos estados se llaman k-uniformes y son los estados multipartitos de n cuerpos con dimensión local q con la propiedad de que todas las reducciones a k cuerpos son máximamente desordenadas. Operacionalmente, en un estado k-uniforme cualquier subconjunto de hasta k cuerpos está máximamente entrelazado con el resto. Los estados k = n/2 -uniformes se llaman estados absolutamente máximamente entrelazados porque son máximamente entrelazados respecto a cualquier partición de los n cuerpos en dos grupos. Estos estados encuentran aplicaciones en varios protocolos y, en particular, forman los elementos de base para la construcción de los códigos de corrección de errores cuánticos con geometría holográfica, los cuales han aportado intuición importante sobre la conexión entre la teoría de la información cuántica y la teoría conforme de campos. Las propiedades y aplicaciones de estos estados son intrigantes porque conocemos poco sobre las mismas: cuándo existen, cómo construirlos, cómo se relacionan con otros estados con entrelazamiento multipartito, cómo los estados grafo, o como se relacionan mediante operaciones locales y comunicación clásica. Con esta motivación en mente, en esta tesis primero estudiamos las propiedades de los estados k-uniformes y luego presentamos métodos sistemáticos para construir expresiones cerradas de los mismos. La naturaleza de nuestros métodos resulta ser muy útil para entender la estructura de estos estados cuánticos, su representación como estados grafo y su clasificación bajo operaciones locales y comunicación clásica. También construimos varios ejemplos de estados absolutamente máximamente entrelazados, cuya existencia era desconocida. Finalmente, exploramos una nueva familia de códigos de corrección de errores cuánticos que generalizan y mejoran la conexión entre los códigos de corrección de errores clásicos, los estados entrelazados multipartitos y el formalismo de estabilizadores. Los resultados de esta tesis pueden desarrollar un papel importante en la caracterización y el estudio de las tres siguientes áreas: entrelazamiento multipartito, códigos de corrección de errores clásicos y códigos de corrección de errores cuánticos. Los estados de entrelazamiento multipartito pueden aportar una conexión para encontrar diferentes recursos para tareas de procesamiento de la información cuántica y cuantificación del entrelazamiento. Al construir dos conjuntos de estados multipartitos altamente entrelazados, es importante saber si son equivalentes entre operaciones locales y comunicación clásica. Entendiendo qué estados pertenecen a la misma clase de recurso cuántico, se puede discutir qué papel desempeñan en ciertas tareas de información cuántica, como la distribución de claves criptográficas cuánticas, la teleportación y la construcción de códigos de corrección de errores cuánticos óptimos. También se pueden usar para explorar la conexión entre la correspondencia holográfica Anti-de Sitter/Conformal Field Theory y códigos de corrección de errores cuánticos, que nos permitiría construir mejores códigos de corrección de errores. A la vez, su papel en la caracterización de redes cuánticas será esencial en el diseño de redes funcionales, robustas ante pérdidas y ruidos locales

Compressing over-the counter markets. ECMI Working Paper No 11 12 Nov 2020.

Over-the-counter markets are at the centre of the global reform of the financial system. The authors of this paper show how the size and structure of these markets can undergo rapid and extensive changes when participants engage in portfolio compression, which is an optimisation technology that exploits multilateral netting opportunities. They find that tightly knit and concentrated trading structures, as featured by many large over-the-counter markets, are especially susceptible to reductions of notional amounts and network reconfiguration resulting from compression activities. Using a unique transaction-level dataset on credit-default-swaps markets, they estimate reduction levels suggesting that the adoption of this technology can account for a large share of the historical development observed in these markets since the Global Financial Crisis. Finally, the authors test the effect of a mandate to centrally clear over the counter markets in terms of size and structure. When participants engage in both central clearing and portfolio compression with the clearinghouse, results show large netting failures if clearinghouses proliferate. Allowing for compression across clearinghouses by-and-large offsets this adverse effect

Network-centric methods for heterogeneous multiagent systems

We present tools for a network topology based characterization of heterogeneity in multiagent systems, thereby providing a framework for the analysis and design of heterogeneous multiagent networks from a network structure view-point. In heterogeneous networks, agents with a diverse set of resources coordinate with each other. Coordination among different agents and the structure of the underlying network topology have significant impacts on the overall behavior and functionality of the system. Using constructs from graph theory, a qualitative as well as a quantitative analysis is performed to examine an inter-relationship between the network topology and the distribution of agents with various capabilities in heterogeneous networks. Our goal is to allow agents maximally exploit heterogeneous resources available within the network through local interactions, thus exploring a promise heterogeneous networks hold to accomplish complicated tasks by leveraging upon the assorted capabilities of agents. For a reliable operations of such systems, the issue of security against intrusions and malicious agents is also addressed. We provide a scheme to secure a network against a sequence of intruder attacks through a set of heterogeneous guards. Moreover, robustness of networked systems against noise corruption and structural changes in the underlying network topology is also examined.Ph.D