6,073 research outputs found
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
We present several applications of non-linear data modeling, using principal
manifolds and principal graphs constructed using the metaphor of elasticity
(elastic principal graph approach). These approaches are generalizations of the
Kohonen's self-organizing maps, a class of artificial neural networks. On
several examples we show advantages of using non-linear objects for data
approximation in comparison to the linear ones. We propose four numerical
criteria for comparing linear and non-linear mappings of datasets into the
spaces of lower dimension. The examples are taken from comparative political
science, from analysis of high-throughput data in molecular biology, from
analysis of dynamical systems.Comment: 12 pages, 9 figure
Complex networks analysis in socioeconomic models
This chapter aims at reviewing complex networks models and methods that were
either developed for or applied to socioeconomic issues, and pertinent to the
theme of New Economic Geography. After an introduction to the foundations of
the field of complex networks, the present summary adds insights on the
statistical mechanical approach, and on the most relevant computational aspects
for the treatment of these systems. As the most frequently used model for
interacting agent-based systems, a brief description of the statistical
mechanics of the classical Ising model on regular lattices, together with
recent extensions of the same model on small-world Watts-Strogatz and
scale-free Albert-Barabasi complex networks is included. Other sections of the
chapter are devoted to applications of complex networks to economics, finance,
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issues, including results for opinion and citation networks.
Finally, some avenues for future research are introduced before summarizing the
main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared
for Complexity and Geographical Economics - Topics and Tools, P.
Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published
Eigenvector-Based Centrality Measures for Temporal Networks
Numerous centrality measures have been developed to quantify the importances
of nodes in time-independent networks, and many of them can be expressed as the
leading eigenvector of some matrix. With the increasing availability of network
data that changes in time, it is important to extend such eigenvector-based
centrality measures to time-dependent networks. In this paper, we introduce a
principled generalization of network centrality measures that is valid for any
eigenvector-based centrality. We consider a temporal network with N nodes as a
sequence of T layers that describe the network during different time windows,
and we couple centrality matrices for the layers into a supra-centrality matrix
of size NTxNT whose dominant eigenvector gives the centrality of each node i at
each time t. We refer to this eigenvector and its components as a joint
centrality, as it reflects the importances of both the node i and the time
layer t. We also introduce the concepts of marginal and conditional
centralities, which facilitate the study of centrality trajectories over time.
We find that the strength of coupling between layers is important for
determining multiscale properties of centrality, such as localization phenomena
and the time scale of centrality changes. In the strong-coupling regime, we
derive expressions for time-averaged centralities, which are given by the
zeroth-order terms of a singular perturbation expansion. We also study
first-order terms to obtain first-order-mover scores, which concisely describe
the magnitude of nodes' centrality changes over time. As examples, we apply our
method to three empirical temporal networks: the United States Ph.D. exchange
in mathematics, costarring relationships among top-billed actors during the
Golden Age of Hollywood, and citations of decisions from the United States
Supreme Court.Comment: 38 pages, 7 figures, and 5 table
- …