Topological Influence and Locality in Swap Schelling Games

Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling’s famous agent-based model for residential segregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors. Very recently, Schelling’s model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics

Diversity-seeking Jump Games in Networks

Recently, many researchers have studied strategic games inspired by Schelling's influential model of residential segregation. In this model, agents belonging to $k$ different types are placed at the nodes of a network. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. In the so-called Schelling games inspired by this model, strategic agents are assumed to be similarity-seeking: their utility is defined as the fraction of its neighbors of the same type as itself. In this paper, we introduce a new type of strategic jump game in which agents are instead diversity-seeking: the utility of an agent is defined as the fraction of its neighbors that is of a different type than itself. We show that it is NP-hard to determine the existence of an equilibrium in such games, if some agents are stubborn. However, in trees, our diversity-seeking jump game always admits a pure Nash equilibrium, if all agents are strategic. In regular graphs and spider graphs with a single empty node, as well as in all paths, we prove a stronger result: the game is a potential game, that is, improving response dynamics will always converge to a Nash equilibrium from any initial placement of agents

Interaction Topologies and Information Flow

Networks are ubiquitous, underlying systems as diverse as the Internet, food webs, societal interactions, the cell, and the brain. Of crucial importance is the coupling of network structure with system dynamics, and much recent attention has focused on how information, such as pathogens, mutations, or ideas, ow through networks. In this dissertation, we advance the understanding of how network structure a ects information ow in two important classes of models. The rst is an independent interaction model, which is used to investigate the propagation of advantageous alleles in evolutionary algorithms. The second is a threshold model, which is used to study the dissemination of ideas, fads, and innovations throughout populations. This journal-format dissertation comprises three interrelated studies, in which we investigate the in uence of network structure on the dynamical properties of information ow. In the rst study, we develop an analytical technique to approximate system dynamics in arbitrarily structured regular interaction topologies. In the second study, we investigate the ow of advantageous alleles in degree-correlated scale-free population structures, and provide a simple topological metric for assessing the selective pressures induced by these networks. In the third study, we characterize the conditions in which global information cascades occur in threshold models of binary decisions with externalities, structured on degree-correlated Poisson-distributed random networks

Multi-photon entanglement and applications in quantum information

Since the awareness of entanglement was raised by Einstein, Podolski, Rosen and Schrödinger in the beginning of the last century, it took almost 55 years until entanglement entered the laboratories as a new resource. Meanwhile, entangled states of various quantum systems have been investigated. Sofar, their biggest variety was observed in photonic qubit systems. Thereby, the setups of today's experiments on multi-photon entanglement can all be structured in the following way: They consist of a photon source, a linear optics network by which the photons are processed and the conditional detection of the photons at the output of the network. In this thesis, two new linear optics networks are introduced and their application for several quantum information tasks is presented. The workhorse of multi-photon quantum information, spontaneous parametric down conversion, is used in different configurations to provide the input states for the networks. The first network is a new design of a controlled phase gate which is particularly interesting for applications in multi-photon experiments as it constitutes an improvement of former realizations with respect to stability and reliability. This is explicitly demonstrated by employing the gate in four-photon experiments. In this context, a teleportation and entanglement swapping protocol is performed in which all four Bell states are distinguished by means of the phase gate. A similar type of measurement applied to the subsystem parts of two copies of a quantum state, allows further the direct estimation of the state's entanglement in terms of its concurrence. Finally, starting from two Bell states, the controlled phase gate is applied for the observation of a four photon cluster state. The analysis of the results focuses on measurement based quantum computation, the main usage of cluster states. The second network, fed with the second order emission of non-collinear type II spontaneous parametric down conversion, constitutes a tunable source of a whole family of states. Up to now the observation of one particular state required one individually tailored setup. With the network introduced here many different states can be obtained within the same arrangement by tuning a single, easily accessible experimental parameter. These states exhibit many useful properties and play a central role in several applications of quantum information. Here, they are used for the solution of a four-player quantum Minority game. It is shown that, by employing four-qubit entanglement, the quantum version of the game clearly outperforms its classical counterpart. Experimental data obtained with both networks are utilized to demonstrate a new method for the experimental discrimination of different multi-partite entangled states. Although theoretical classifications of four-qubit entangled states exist, sofar there was no experimental tool to easily assign an observed state to the one or the other class. The new tool presented here is based on operators which are formed by the correlations between local measurement settings that are typical for the respective quantum state.Fast 55 Jahre vergingen bis die Entdeckung des Phänomens der Verschränkung durch Einstein, Podolski, Rosen und Schrödinger Ende des zwanzigsten Jahrhunderts Einzug in die Labore hielt. Mittlerweile wurde eine Vielfalt von verschränkten Zuständen untersucht; die größte davon in Systemen photonischer Qubits. Alle modernen Experimente zu viel-Photonen Verschränkung lassen sich in drei wesentliche Bestandteile untergliedern: Eine Photonenquelle, ein Netzwerk aus linearen optischen Komponenten welches die Photonen verarbeitet, und eine bedingte Detektion der Photonen am Ausgang des Netzwerks. Die vorliegende Arbeit führt zwei neue Netzwerke ein und präsentiert deren Anwendungen in verschiedenen Problemstellungen der Quanteninformation. Als Photonenquelle dient hierbei der Prozeß der spontanen parametrischen Fluoreszenz in unterschiedlichen Konfigurationen. Das erste Netzwerk ist ein neuartiges Kontroll-Phasengatter das sich gegenüber früheren Realisierungen vor allem durch seine hohe Stabilität auszeichnet. Wie anhand mehrerer Beispiele gezeigt wird, eignet es sich besonders für den Einsatz in mehr-Photonen Experimenten. Mit Hilfe des Gatters werden alle vier Bell Zustände in einem Teleportations- und "entanglement swapping" Experiment unterschieden. Ein ähnlicher experimenteller Aufbau erlaubt ferner die direkte Messung der Verschränkung zweier Kopien eines Zustands in Form der "Concurrence". Ausgehend von zwei Bell Zuständen wird das Gatter darüberhinaus zur Beobachtung eines Vier-Photonen "Cluster Zustands" verwendet. Die Analyse der Ergebnisse konzentriert sich dabei auf die Hauptanwendung von Cluster Zuständen, das meßbasierte Quantenrechnen. Das zweite Netzwerk bildet, zusammen mit der Emission zweiter Ordnung der parametrischen Fluoreszenz als Input, eine einstellbare Quelle verschiedenster Zustände. Während die Beobachtung eines Zustands bisher einen individuell maßgeschneiderten Versuchsaufbau benötigte, können mit dem neuen Netzwerk viele verschiedene Zustände innerhalb desselben Aufbaus beobachtet werden. Dies erfordert lediglich die Veränderung eines einzelnen, leicht zugänglichen experimentellen Parameters. Die so erzeugten Zustände besitzen eine Reihe nützlicher Eigenschaften und spielen eine zentrale Rolle in vielen Anwendungen. Hier werden sie zur Lösung eines vier-Parteien Quanten "Minority" Spiels verwendet. Es wird gezeigt, dass die Quanten Version des Spiels durch den Einsatz von vier-Qubit Verschränkung sein klassisches Pendant an Möglichkeiten deutlich übertrifft. Mit Hilfe experimenteller Daten beider Netzwerke wird eine neue Methode der Unterscheidung vier-Qubit verschränkter Zustände vorgestellt. Obwohl theoretische Klassifizierungen verschränkter Zustände existieren, gab es bisher keine einfache experimentelle Methode einen beobachteten Zustand der einen oder anderen Klasse zuzuordnen. Das hier vorgestellte Konzept ermöglicht eine experimentelle Klassifizierung basierend auf Operatoren die aus zustandsabhängigen Korrelationsmessungen bestimmt werden

Introduction to the Modeling and Analysis of Complex Systems

Keep up to date on Introduction to Modeling and Analysis of Complex Systems at http://bingweb.binghamton.edu/~sayama/textbook/! Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example. This textbook is available for purchase in both grayscale and color via Amazon.com and CreateSpace.com.https://knightscholar.geneseo.edu/oer-ost/1013/thumbnail.jp

Human mobility and social ties in context: from places to personality

Recent years saw an increasing proliferation of the use of digitally generated traces of data for understanding human behaviour. The quantitative understanding of social networks as well as patterns of human mobility benefited tremendously from these new sources of data. The main dynamics of both social networks and human mobility such as a propensity of humans for heterogeneous behaviour, how humans choose to explore new places, or the fact that both spheres are intrinsically linked are now fairly well understood. However, how various other factors mediate the observed dynamics is still relatively unknown, not least due to the difficulty in obtaining adequate data. Thus, for my thesis I focus on how a variety of factors---places, longer-term dynamics, the personality of individuals, or neighbourhoods---might be a driver of various aspects of social and mobility behaviour. I used data from the Copenhagen network study that tracked 847 students with smartphones and measured their social encounters as well as the locations they visited for a whole academic year. I further utilised a variety of methods for analysing the data ranging from applied machine learning over inferential statistics to social network analysis. Using this dataset, I found that the qualities of places were very informative for understanding future encounters between students, that the longer-term dynamics shaped both social and mobility behaviour, and that while personality had a significant effect on the observed regularity of behaviour, its effect was rather small