25,621 research outputs found
Doped AB_2 Hubbard Chain: Spiral, Nagaoka and RVB States, Phase Separation and Luttinger Liquid Behavior
We present an extensive numerical study of the Hubbard model on the doped
AB chain, both in the weak coupling and the infinite-U limit. Due to the
special unit cell topology, this system displays a rich variety of phases as
function of hole doping () away from half-filling. Near half-filling,
spiral states develop in the weak coupling regime, while Nagaoka itinerant
ferromagnetism is observed in the infinite-U limit. For higher doping the
system phase-separates before reaching a Mott insulating phase of short-range
RVB states at . Moreover, for we observe a crossover,
which anticipates the Luttinger liquid behavior for .Comment: 11 pages, 13 figure
The role of bipartite structure in R&D collaboration networks
A number of real-world networks are, in fact, one-mode projections of
bipartite networks comprised of two types of nodes. For institutions engaging
in collaboration for technological innovation, the underlying network is
bipartite with institutions (agents) linked to the patents they have filed
(artifacts), while the projection is the co-patenting network. Projected
network topology is highly affected by the underlying bipartite structure,
hence a lack of understanding of the bipartite network has consequences for the
information that might be drawn from the one-mode co-patenting network. Here,
we create an empirical bipartite network using data from 2.7 million patents.
We project this network onto the agents (institutions) and look at properties
of both the bipartite and projected networks that may play a role in knowledge
sharing and collaboration. We compare these empirical properties to those of
synthetic bipartite networks and their projections in order to understand the
processes that might operate in the network formation. A good understanding of
the topology is critical for investigating the potential flow of technological
knowledge. We show how degree distributions and small cycles affect the
topology of the one-mode projected network - specifically degree and clustering
distributions, and assortativity. We propose new network-based metrics to
quantify how collaborative agents are in the co-patenting network. We find that
several large corporations that are the most collaborative agents in the
network, however such organisations tend to have a low diversity of
collaborators. In contrast, the most prolific institutions tend to collaborate
relatively little but with a diverse set of collaborators. This indicates that
they concentrate the knowledge of their core technical research, while seeking
specific complementary knowledge via collaboration with smaller companies.Comment: 23 pages, 12 figures, 2 table
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