530 research outputs found
Phase Transition in the Density of States of Quantum Spin Glasses
We prove that the empirical density of states of quantum spin glasses on
arbitrary graphs converges to a normal distribution as long as the maximal
degree is negligible compared with the total number of edges. This extends the
recent results of [6] that were proved for graphs with bounded chromatic number
and with symmetric coupling distribution. Furthermore, we generalise the result
to arbitrary hypergraphs. We test the optimality of our condition on the
maximal degree for -uniform hypergraphs that correspond to -spin glass
Hamiltonians acting on distinguishable spin- particles. At the
critical threshold we find a sharp classical-quantum phase
transition between the normal distribution and the Wigner semicircle law. The
former is characteristic to classical systems with commuting variables, while
the latter is a signature of noncommutative random matrix theory.Comment: 21 pages, 2 figure
Visualizing and Interacting with Concept Hierarchies
Concept Hierarchies and Formal Concept Analysis are theoretically well
grounded and largely experimented methods. They rely on line diagrams called
Galois lattices for visualizing and analysing object-attribute sets. Galois
lattices are visually seducing and conceptually rich for experts. However they
present important drawbacks due to their concept oriented overall structure:
analysing what they show is difficult for non experts, navigation is
cumbersome, interaction is poor, and scalability is a deep bottleneck for
visual interpretation even for experts. In this paper we introduce semantic
probes as a means to overcome many of these problems and extend usability and
application possibilities of traditional FCA visualization methods. Semantic
probes are visual user centred objects which extract and organize reduced
Galois sub-hierarchies. They are simpler, clearer, and they provide a better
navigation support through a rich set of interaction possibilities. Since probe
driven sub-hierarchies are limited to users focus, scalability is under control
and interpretation is facilitated. After some successful experiments, several
applications are being developed with the remaining problem of finding a
compromise between simplicity and conceptual expressivity
Recommender Systems
The ongoing rapid expansion of the Internet greatly increases the necessity
of effective recommender systems for filtering the abundant information.
Extensive research for recommender systems is conducted by a broad range of
communities including social and computer scientists, physicists, and
interdisciplinary researchers. Despite substantial theoretical and practical
achievements, unification and comparison of different approaches are lacking,
which impedes further advances. In this article, we review recent developments
in recommender systems and discuss the major challenges. We compare and
evaluate available algorithms and examine their roles in the future
developments. In addition to algorithms, physical aspects are described to
illustrate macroscopic behavior of recommender systems. Potential impacts and
future directions are discussed. We emphasize that recommendation has a great
scientific depth and combines diverse research fields which makes it of
interests for physicists as well as interdisciplinary researchers.Comment: 97 pages, 20 figures (To appear in Physics Reports
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