4,853 research outputs found
Syndetic proximality and scrambled sets
This paper is a systematic study about the syndetically proximal relation and
the possible existence of syndetically scrambled sets for the dynamics of
continuous self-maps of compact metric spaces. Especially we consider various
classes of transitive subshifts, interval maps, and topologically Anosov maps.
We also present many constructions and examples
Probing Limits of Information Spread with Sequential Seeding
We consider here information spread which propagates with certain probability
from nodes just activated to their not yet activated neighbors. Diffusion
cascades can be triggered by activation of even a small set of nodes. Such
activation is commonly performed in a single stage. A novel approach based on
sequential seeding is analyzed here resulting in three fundamental
contributions. First, we propose a coordinated execution of randomized choices
to enable precise comparison of different algorithms in general. We apply it
here when the newly activated nodes at each stage of spreading attempt to
activate their neighbors. Then, we present a formal proof that sequential
seeding delivers at least as large coverage as the single stage seeding does.
Moreover, we also show that, under modest assumptions, sequential seeding
achieves coverage provably better than the single stage based approach using
the same number of seeds and node ranking. Finally, we present experimental
results showing how single stage and sequential approaches on directed and
undirected graphs compare to the well-known greedy approach to provide the
objective measure of the sequential seeding benefits. Surprisingly, applying
sequential seeding to a simple degree-based selection leads to higher coverage
than achieved by the computationally expensive greedy approach currently
considered to be the best heuristic
Concurrence in arbitrary dimensions
We argue that a complete characterisation of quantum correlations in
bipartite systems of many dimensions may require a quantity which, even for
pure states, does not reduce to a single number. Subsequently, we introduce
multi-dimensional generalizations of concurrence and find evidence that they
may provide useful tools for the analysis of quantum correlations in mixed
bipartite states. We also introudce {\it biconcurrence} that leads to a
necessary and sufficient condition for separability.Comment: RevTeX 7 page
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