293 research outputs found
Emergence of Leadership in Communication
We study a neuro-inspired model that mimics a discussion (or information
dissemination) process in a network of agents. During their interaction, agents
redistribute activity and network weights, resulting in emergence of leader(s).
The model is able to reproduce the basic scenarios of leadership known in
nature and society: laissez-faire (irregular activity, weak leadership, sizable
inter-follower interaction, autonomous sub-leaders); participative or
democratic (strong leadership, but with feedback from followers); and
autocratic (no feedback, one-way influence). Several pertinent aspects of these
scenarios are found as well---e.g., hidden leadership (a hidden clique of
agents driving the official autocratic leader), and successive leadership (two
leaders influence followers by turns). We study how these scenarios emerge from
inter-agent dynamics and how they depend on behavior rules of agents---in
particular, on their inertia against state changes.Comment: 17 pages, 11 figure
Community Detection with and without Prior Information
We study the problem of graph partitioning, or clustering, in sparse networks
with prior information about the clusters. Specifically, we assume that for a
fraction of the nodes their true cluster assignments are known in
advance. This can be understood as a semi--supervised version of clustering, in
contrast to unsupervised clustering where the only available information is the
graph structure. In the unsupervised case, it is known that there is a
threshold of the inter--cluster connectivity beyond which clusters cannot be
detected. Here we study the impact of the prior information on the detection
threshold, and show that even minute [but generic] values of shift the
threshold downwards to its lowest possible value. For weighted graphs we show
that a small semi--supervising can be used for a non-trivial definition of
communities.Comment: 6 pages, 2 figure
Phase Transitions in Community Detection: A Solvable Toy Model
Recently, it was shown that there is a phase transition in the community
detection problem. This transition was first computed using the cavity method,
and has been proved rigorously in the case of groups. However, analytic
calculations using the cavity method are challenging since they require us to
understand probability distributions of messages. We study analogous
transitions in so-called "zero-temperature inference" model, where this
distribution is supported only on the most-likely messages. Furthermore,
whenever several messages are equally likely, we break the tie by choosing
among them with equal probability. While the resulting analysis does not give
the correct values of the thresholds, it does reproduce some of the qualitative
features of the system. It predicts a first-order detectability transition
whenever , while the finite-temperature cavity method shows that this is
the case only when . It also has a regime analogous to the "hard but
detectable" phase, where the community structure can be partially recovered,
but only when the initial messages are sufficiently accurate. Finally, we study
a semisupervised setting where we are given the correct labels for a fraction
of the nodes. For , we find a regime where the accuracy jumps
discontinuously at a critical value of .Comment: 6 pages, 6 figure
Magnetic Phase Diagrams of Multiferroic Hexagonal RMnO3 (R=Er, Yb, Tm, and Ho)
The magnetic phase diagrams of RMnO3 (R = Er, Yb, Tm, Ho) are investigated up
to 14 Tesla via magnetic and dielectric measurements. The stability range of
the AFM order below the Neel temperature of the studied RMnO3 extends to far
higher magnetic fields than previously assumed. Magnetic irreversibility
indicating the presence of a spontaneous magnetic moment is found near 50 K for
R=Er, Yb, and Tm. At very low temperatures and low magnetic fields the phase
boundary defined by the ordering of the rare earth moments is resolved. The
sizable dielectric anomalies observed along all phase boundaries are evidence
for strong spin-lattice coupling in the hexagonal RMnO3. In HoMnO3 the strong
magnetoelastic distortions are investigated in more detail via magnetostriction
experiments up to 14 Tesla. The results are discussed based on existing data on
magnetic symmetries and the interactions between the Mn-spins, the rare earth
moments, and the lattice.Comment: 23 pages, 16 figures, to be published in JMR's Aug. focus issue on
multiferroic
Magnetic phase diagrams of the Kagome staircase compound Co3V2O8
At zero magnetic field, a series of five phase transitions occur in Co3V2O8.
The Neel temperature, TN=11.4 K, is followed by four additional phase changes
at T1=8.9 K, T2=7.0 K, T3=6.9 K, and T4=6.2 K. The different phases are
distinguished by the commensurability of the b-component of its spin density
wave vector. We investigate the stability of these various phases under
magnetic fields through dielectric constant and magnetic susceptibility
anomalies. The field-temperature phase diagram of Co3V2O8 is completely
resolved. The complexity of the phase diagram results from the competition of
different magnetic states with almost equal ground state energies due to
competing exchange interactions and frustration.Comment: Proceedings of the 2007 Conference on Strongly Correlated Electron
Systems, 2 pages, 2 figure
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