Random Walks: A Review of Algorithms and Applications

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science. Furthermore, in quantum mechanics, quantum walks can be regarded as quantum analogues of classical random walks. Classical random walks and quantum walks can be used to calculate the proximity between nodes and extract the topology in the network. Various random walk related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding. In this paper, we aim to provide a comprehensive review of classical random walks and quantum walks. We first review the knowledge of classical random walks and quantum walks, including basic concepts and some typical algorithms. We also compare the algorithms based on quantum walks and classical random walks from the perspective of time complexity. Then we introduce their applications in the field of computer science. Finally we discuss the open issues from the perspectives of efficiency, main-memory volume, and computing time of existing algorithms. This study aims to contribute to this growing area of research by exploring random walks and quantum walks together.Comment: 13 pages, 4 figure

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

The Venice Variations

From the myth of Arcadia through to the twenty-first century, ideas about sustainability – how we imagine better urban environments – remain persistently relevant, and raise recurring questions. How do cities evolve as complex spaces nurturing both urban creativity and the fortuitous art of discovery, and by which mechanisms do they foster imagination and innovation? While past utopias were conceived in terms of an ideal geometry, contemporary exemplary models of urban design seek technological solutions of optimal organisation. The Venice Variations explores Venice as a prototypical city that may hold unique answers to the ancient narrative of utopia. Venice was not the result of a preconceived ideal but the pragmatic outcome of social and economic networks of communication. Its urban creativity, though, came to represent the quintessential combination of place and institutions of its time. Through a discussion of Venice and two other works owing their inspiration to this city – Italo Calvino’s Invisible Cities and Le Corbusier’s Venice Hospital – Sophia Psarra describes Venice as a system that starts to resemble a highly probabilistic ‘algorithm’, that is, a structure with a small number of rules capable of producing a large number of variations. The rapidly escalating processes of urban development around our big cities share many of the motivations for survival, shelter and trade that brought Venice into existence. Rather than seeing these places as problems to be solved, we need to understand how urban complexity can evolve, as happened from its unprepossessing origins in the marshes of the Venetian lagoon to the ‘model city’ that endured a thousand years. This book frees Venice from stereotypical representations, revealing its generative capacity to inform potential other ‘Venices’ for the future

Space is the machine: a configurational theory of architecture

Since The social logic of space was published in 1984, Bill Hillier and his colleagues at University College London have been conducting research on how space features in the form and functioning of buildings and cities. A key outcome is the concept of ‘spatial configuration’ — meaning relations which take account of other relations in a complex. New techniques have been developed and applied to a wide range of architectural and urban problems. The aim of this book is to assemble some of this work and show how it leads the way to a new type of theory of architecture: an ‘analytic’ theory in which understanding and design advance together. The success of configurational ideas in bringing to light the spatial logic of buildings and cities suggests that it might be possible to extend these ideas to other areas of the human sciences where problems of configuration and pattern are critical