1,689 research outputs found
Information measures and cognitive limits in multilayer navigation
Cities and their transportation systems become increasingly complex and
multimodal as they grow, and it is natural to wonder if it is possible to
quantitatively characterize our difficulty to navigate in them and whether such
navigation exceeds our cognitive limits. A transition between different
searching strategies for navigating in metropolitan maps has been observed for
large, complex metropolitan networks. This evidence suggests the existence of
another limit associated to the cognitive overload and caused by large amounts
of information to process. In this light, we analyzed the world's 15 largest
metropolitan networks and estimated the information limit for determining a
trip in a transportation system to be on the order of 8 bits. Similar to the
"Dunbar number," which represents a limit to the size of an individual's
friendship circle, our cognitive limit suggests that maps should not consist of
more than about connections points to be easily readable. We also show
that including connections with other transportation modes dramatically
increases the information needed to navigate in multilayer transportation
networks: in large cities such as New York, Paris, and Tokyo, more than
of trips are above the 8-bit limit. Multimodal transportation systems in large
cities have thus already exceeded human cognitive limits and consequently the
traditional view of navigation in cities has to be revised substantially.Comment: 16 pages+9 pages of supplementary materia
Generation asset planning under uncertainty.
With the introduction of competition in the electric power industry, generation asset planning must change. In this changed environment, energy companies must be able to capture the extrinsic value of their asset operations and long-term managerial flexibility for sound planning decisions. This dissertation presents a new formulation for the generation asset planning problem under market uncertainty, in which short-term operational and long-term coupling constraints associated with investment decisions are simultaneously reflected in the planning process
Exact results and scaling properties of small-world networks
We study the distribution function for minimal paths in small-world networks.
Using properties of this distribution function, we derive analytic results
which greatly simplify the numerical calculation of the average minimal
distance, , and its variance, . We also discuss the
scaling properties of the distribution function. Finally, we study the limit of
large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3
We have analyzed the morphology of ferroelectric domains in very thin films
of multiferroic BiFeO3. Unlike the more common stripe domains observed in
thicker films BiFeO3 or in other ferroics, the domains tend not to be straight,
but irregular in shape, with significant domain wall roughening leading to a
fractal dimensionality. Also contrary to what is usually observed in other
ferroics, the domain size appears not to scale as the square root of the film
thickness. A model is proposed in which the observed domain size as a function
of film thickness can be directly linked to the fractal dimension of the
domains.Comment: 4 pages, 3 figure
Erratum: Small-world networks: Evidence for a crossover picture
We correct the value of the exponent \tau.Comment: 2 pages, 1 figur
Video Pandemics: Worldwide Viral Spreading of Psy's Gangnam Style Video
Viral videos can reach global penetration traveling through international
channels of communication similarly to real diseases starting from a
well-localized source. In past centuries, disease fronts propagated in a
concentric spatial fashion from the the source of the outbreak via the short
range human contact network. The emergence of long-distance air-travel changed
these ancient patterns. However, recently, Brockmann and Helbing have shown
that concentric propagation waves can be reinstated if propagation time and
distance is measured in the flight-time and travel volume weighted underlying
air-travel network. Here, we adopt this method for the analysis of viral meme
propagation in Twitter messages, and define a similar weighted network distance
in the communication network connecting countries and states of the World. We
recover a wave-like behavior on average and assess the randomizing effect of
non-locality of spreading. We show that similar result can be recovered from
Google Trends data as well.Comment: 10 page
Classes of behavior of small-world networks
Small-world networks are the focus of recent interest because they appear to
circumvent many of the limitations of either random networks or regular
lattices as frameworks for the study of interaction networks of complex
systems. Here, we report an empirical study of the statistical properties of a
variety of diverse real-world networks. We present evidence of the occurrence
of three classes of small-world networks: (a) scale-free networks,
characterized by a vertex connectivity distribution that decays as a power law;
(b) broad-scale networks, characterized by a connectivity distribution that has
a power-law regime followed by a sharp cut-off; (c) single-scale networks,
characterized by a connectivity distribution with a fast decaying tail.
Moreover, we note for the classes of broad-scale and single-scale networks that
there are constraints limiting the addition of new links. Our results suggest
that the nature of such constraints may be the controlling factor for the
emergence of different classes of networks
The architecture of complex weighted networks
Networked structures arise in a wide array of different contexts such as
technological and transportation infrastructures, social phenomena, and
biological systems. These highly interconnected systems have recently been the
focus of a great deal of attention that has uncovered and characterized their
topological complexity. Along with a complex topological structure, real
networks display a large heterogeneity in the capacity and intensity of the
connections. These features, however, have mainly not been considered in past
studies where links are usually represented as binary states, i.e. either
present or absent. Here, we study the scientific collaboration network and the
world-wide air-transportation network, which are representative examples of
social and large infrastructure systems, respectively. In both cases it is
possible to assign to each edge of the graph a weight proportional to the
intensity or capacity of the connections among the various elements of the
network. We define new appropriate metrics combining weighted and topological
observables that enable us to characterize the complex statistical properties
and heterogeneity of the actual strength of edges and vertices. This
information allows us to investigate for the first time the correlations among
weighted quantities and the underlying topological structure of the network.
These results provide a better description of the hierarchies and
organizational principles at the basis of the architecture of weighted
networks
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