Exploring complex networks by means of adaptive walkers

Finding efficient algorithms to explore large networks with the aim of recovering information about their structure is an open problem. Here, we investigate this challenge by proposing a model in which random walkers with previously assigned home nodes navigate through the network during a fixed amount of time. We consider that the exploration is successful if the walker gets the information gathered back home, otherwise no data are retrieved. Consequently, at each time step, the walkers, with some probability, have the choice to either go backward approaching their home or go farther away. We show that there is an optimal solution to this problem in terms of the average information retrieved and the degree of the home nodes and design an adaptive strategy based on the behavior of the random walker. Finally, we compare different strategies that emerge from the model in the context of network reconstruction. Our results could be useful for the discovery of unknown connections in large-scale networks

Network Discovery by Generalized Random Walks

We investigate network exploration by random walks defined via stationary and adaptive transition probabilities on large graphs. We derive an exact formula valid for arbitrary graphs and arbitrary walks with stationary transition probabilities (STP), for the average number of discovered edges as function of time. We show that for STP walks site and edge exploration obey the same scaling $\sim n^{\lambda}$ as function of time $n$. Therefore, edge exploration on graphs with many loops is always lagging compared to site exploration, the revealed graph being sparse until almost all nodes have been discovered. We then introduce the Edge Explorer Model, which presents a novel class of adaptive walks, that perform faithful network discovery even on dense networks.Comment: 23 pages, 7 figure

Reconstruction, mobility, and synchronization in complex networks

During the last decades, it has become clear that systems formed by many interacting parts show emergent dynamical properties which are inherently related to the topology of the underlying pattern of connections among the constituent parts. Such systems, usually known as complex systems, are in general suitably described through their networks of contacts, that is, in terms of nodes (representing the system's components) and edges (standing for their interactions), which allows to catch their essential features in a simple and general representation. In recent years, increasing interest on this approach, thanks also to a favorable technological progress, led to the accumulation of an increasing amount of data. This situation has allowed the arising of new questions and, therefore, the diversification of the scientific work. Among them, we can point out three general issues that have been receiving a lot of interest: (i) is the available information always reliable and complete? (ii) how does a complex interaction pattern affect the emergence of collective behavior in complex systems? And (iii) which is the role of mobility within the framework of complex networks? This thesis has been developed along these three lines, which are strictly interrelated. We expand on three case-studies, each one of which deals with two the above mentioned macro-issues. We consider the issue of the incompleteness of the available information both in the case of natural (Chapter 2) and artificial (Chapter 3) networks. As a paradigmatic emergent behavior, we focus on the synchronization of coupled phase oscillators (Chapter 2 and Chapter 4), deeply investigating how different patterns of connections can affect the achievement of a globally coherent state. Finally, we include moving agents in two different frameworks, using them as explorers of unknown networks (Chapter 3) and considering them as interacting units able to establish connections with their neighbors (Chapter 4). In Chapter 2, we study the problem of the reconstruction of an unknown interaction network, whose nodes are Kuramoto oscillators. Our aim is to extract topological features of the connectivity pattern from purely dynamical measures, based on the fact that in a heterogeneous network the global dynamics is not only affected by the distribution of the natural frequencies but also by the location of the different values. The gathered topological information ranges from local features, such as the single node connectivity, to the hierarchical structure of functional clusters, and even to the entire adjacency matrix. In Chapter 4, instead, we present a model of integrate and fire oscillators that are moving agents, freely displacing on a plane. The phase of the oscillators evolves linearly in time and when it reaches a threshold value they fire at their neighbors. In this way, the interaction network is a dynamical object by itself since it is re-created at each time step by the motion of the units. Depending on the velocity of the motion, the average number of neighbors, the coupling strength and the size of the agents population, we identify different regimes. Moving agents are employed also in Chapter 3 where they play the role of explorers of unknown artificial networks, having the mission to recover information about their structures. We propose a model in which random walkers with previously assigned home nodes navigate through the network during a fixed amount of time. We consider that the exploration is successful if the walker gets the information gathered back home, otherwise, no data is retrieved. We show that there is an optimal solution to this problem in terms of the average information retrieved and the degree of the home nodes and design an adaptive strategy based on the behavior of the random walker.Durante las últimas décadas, se ha empezado a poner de manifiesto que sistemas formados por muchos elementos en interacción pueden mostrar propiedades dinámicas emergentes relacionadas con la topología del patrón de conexiones entre las partes constituyentes. Estos sistemas, generalmente conocidos como sistemas complejos, en muchos casos pueden ser descritos a través de sus redes de contactos, es decir, en términos de nodos (que representan los componentes del sistema) y de enlaces (sus interacciones). De esta manera es posible capturar sus características esenciales en una representación simple y general. En esta última década, el creciente interés en este enfoque, gracias también a un progreso tecnológico favorable, ha llevado a la acumulación de una cantidad ingente de datos. Eso, a su vez, ha permitido el surgimiento de nuevas preguntas y, por lo tanto, la diversificación de la actividad científica. Entre ellas, podemos destacar tres cuestiones generales que son objeto de mucho interés: (i) ¿la información disponible es siempre fiable y completa? (ii) ¿cómo un patrón de interacción complejo puede afectar el surgimiento de comportamientos colectivos? Y (iii) ¿cual es el papel de la movilidad en el marco de las redes complejas? Esta tesis se ha desarrollado siguiendo estas tres líneas, que están íntimamente relacionadas entre sí. Hemos profundizado en tres casos de estudio, cada uno de los cuales se ocupa de dos de los macro-temas mencionados. Consideramos la cuestión del carácter incompleto de la información disponible tanto en el caso de redes naturales (Capítulo 2) como de redes artificiales (Capítulo 3). Nos centramos en la sincronización de los osciladores de fase acoplados (Capítulos 2 y 4) en cuanto comportamiento emergente paradigmático, investigando en profundidad cómo los diferentes patrones de conexión puedan afectar la consecución de un estado coherente a nivel global. Por último, analizamos el rol de la movilidad incluyendo agentes móviles en dos marcos diferentes. En un caso, los utilizamos como exploradores de redes desconocidas (Capítulo 3), mientras que en otro los consideramos como unidades que interaccionan y son capaces de establecer conexiones con sus vecinos (Capítulo 4)

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (> 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

Multi-agent simulation: new approaches to exploring space-time dynamics in GIS

As part of the long term quest to develop more disaggregate, temporally dynamic models of spatial behaviour, micro-simulation has evolved to the point where the actions of many individuals can be computed. These multi-agent systems/simulation(MAS) models are a consequence of much better micro data, more powerful and user-friendly computer environments often based on parallel processing, and the generally recognised need in spatial science for modelling temporal process. In this paper, we develop a series of multi-agent models which operate in cellular space.These demonstrate the well-known principle that local action can give rise to global pattern but also how such pattern emerges as the consequence of positive feedback and learned behaviour. We first summarise the way cellular representation is important in adding new process functionality to GIS, and the way this is effected through ideas from cellular automata (CA) modelling. We then outline the key ideas of multi-agent simulation and this sets the scene for three applications to problems involving the use of agents to explore geographic space. We first illustrate how agents can be programmed to search route networks, finding shortest routes in adhoc as well as structured ways equivalent to the operation of the Bellman-Dijkstra algorithm. We then demonstrate how the agent-based approach can be used to simulate the dynamics of water flow, implying that such models can be used to effectively model the evolution of river systems. Finally we show how agents can detect the geometric properties of space, generating powerful results that are notpossible using conventional geometry, and we illustrate these ideas by computing the visual fields or isovists associated with different viewpoints within the Tate Gallery.Our forays into MAS are all based on developing reactive agent models with minimal interaction and we conclude with suggestions for how these models might incorporate cognition, planning, and stronger positive feedbacks between agents

Formation of new property rights on government land through informal co-management: Case studies on countryside guerilla gardening

Extant research on guerilla gardening, defined as the unauthorized cultivation of land belonging to another, has hitherto focused on public space in urban areas, neglecting those that occur in rural settings. This rural land policy study examines a form of guerilla gardening in the countryside in Hong Kong, carried out by specific walker communities who routinely do early morning walks. Most of the gardens they have cultivated have become part of country park protected areas. This study identifies five phases of land use status evolution undergone by these morning walkers’ gardens (MWG), from the time the phenomenon of guerilla gardening in the countryside began in the 1960s to recent times, illustrating the role of land use change in enabling squatters with a degree of property rights by way of informal land resource co-management. Through the three case studies presented in this article, it is argued that MWGs can represent the emergence of incipient forms of natural resource co-management in Hong Kong. This study emphasizes the important role of resource user leadership in enhancing the land use value of land in itself and for the wider community. Some recommendations are provided to enhance resource user participation in land resource management