1,357 research outputs found
Operational one-to-one mapping between coherence and entanglement measures
We establish a general operational one-to-one mapping between coherence
measures and entanglement measures: Any entanglement measure of bipartite pure
states is the minimum of a suitable coherence measure over product bases. Any
coherence measure of pure states, with extension to mixed states by convex
roof, is the maximum entanglement generated by incoherent operations acting on
the system and an incoherent ancilla. Remarkably, the generalized CNOT gate is
the universal optimal incoherent operation. In this way, all convex-roof
coherence measures, including the coherence of formation, are endowed with
(additional) operational interpretations. By virtue of this connection, many
results on entanglement can be translated to the coherence setting, and vice
versa. As applications, we provide tight observable lower bounds for
generalized entanglement concurrence and coherence concurrence, which enable
experimentalists to quantify entanglement and coherence of the maximal
dimension in real experiments.Comment: 14 pages, 1 figure, new results added, published in PR
Eminence Grise Coalitions: On the Shaping of Public Opinion
We consider a network of evolving opinions. It includes multiple individuals
with first-order opinion dynamics defined in continuous time and evolving based
on a general exogenously defined time-varying underlying graph. In such a
network, for an arbitrary fixed initial time, a subset of individuals forms an
eminence grise coalition, abbreviated as EGC, if the individuals in that subset
are capable of leading the entire network to agreeing on any desired opinion,
through a cooperative choice of their own initial opinions. In this endeavor,
the coalition members are assumed to have access to full profile of the
underlying graph of the network as well as the initial opinions of all other
individuals. While the complete coalition of individuals always qualifies as an
EGC, we establish the existence of a minimum size EGC for an arbitrary
time-varying network; also, we develop a non-trivial set of upper and lower
bounds on that size. As a result, we show that, even when the underlying graph
does not guarantee convergence to a global or multiple consensus, a generally
restricted coalition of agents can steer public opinion towards a desired
global consensus without affecting any of the predefined graph interactions,
provided they can cooperatively adjust their own initial opinions. Geometric
insights into the structure of EGC's are given. The results are also extended
to the discrete time case where the relation with Decomposition-Separation
Theorem is also made explicit.Comment: 35 page
Welschinger invariants revisited
We establish the enumerativity of (original and modified) Welschinger
invariants for every real divisor on any real algebraic Del Pezzo surface and
give an algebro-geometric proof of the invariance of that count both up to
variation of the point constraints on a given surface and variation of the
complex structure of the surface itself.Comment: 23 pages; several small changes improving the readabilit
Recent progress in exact geometric computation
AbstractComputational geometry has produced an impressive wealth of efficient algorithms. The robust implementation of these algorithms remains a major issue. Among the many proposed approaches for solving numerical non-robustness, Exact Geometric Computation (EGC) has emerged as one of the most successful. This survey describes recent progress in EGC research in three key areas: constructive zero bounds, approximate expression evaluation and numerical filters
Cluster-based cooperative subcarrier sensing using antenna diversity-based weighted data fusion
Cooperative spectrum sensing (CSS) is used in cognitive radio (CR) networks to improve the spectrum sensing performance in shadow fading environments. Moreover, clustering in CR networks is used to reduce reporting time and bandwidth overhead during CSS. Thus, cluster-based cooperative spectrum sensing (CBCSS) has manifested satisfactory spectrum sensing results in harsh environments under processing constraints. On the other hand, the antenna diversity of multiple input multiple output CR systems can be exploited to further improve the spectrum sensing performance. This paper presents the CBCSS performance in a CR network which is comprised of single- as well as multiple-antenna CR systems. We give theoretical analysis of CBCSS for orthogonal frequency division multiplexing signal sensing and propose a novel fusion scheme at the fusion center which takes into account the receiver antenna diversity of the CRs present in the network. We introduce the concept of weighted data fusion in which the sensing results of different CRs are weighted proportional to the number of receiving antennas they are equipped with. Thus, the receiver diversity is used to the advantage of improving spectrum sensing performance in a CR cluster. Simulation results show that the proposed scheme outperforms the conventional CBCSS scheme
Superconductor-Insulator transition and energy localization
We develop an analytical theory for generic disorder-driven quantum phase
transitions. We apply this formalism to the superconductor-insulator transition
and we briefly discuss the applications to the order-disorder transition in
quantum magnets. The effective spin-1/2 models for these transitions are solved
in the cavity approximation which becomes exact on a Bethe lattice with large
branching number K >> 1 and weak dimensionless coupling g << 1. The
characteristic features of the low temperature phase is a large self-formed
inhomogeneity of the order-parameter distribution near the critical point
K_{c}(g) where the critical temperature T_{c} of the ordering transition
vanishes. Near the quantum critical point, the typical value of the order
parameter vanishes exponentially, B_{0}\propto e^{-C/(K-K_{c}(g))}.
In the disordered regime, realized at K<K_{c}(g) we find actually two
distinct phases characterized by different behavior of relaxation rates. The
first phase exists in an intermediate range of K^{*}(g)<K<K_{c}(g). It has two
regimes of energies: at low excitation energies, \omega<\omega_{d}(K,g), the
many-body spectrum of the model is discrete, with zero level widths, while at
\omega>\omega_{d} the level acquire a non-zero width which is self-generated by
the many-body interactions. In this phase the spin model provides by itself an
intrinsic thermal bath. Another phase is obtained at smaller K<K^{*}(g), where
all the eigenstates are discrete, corresponding to full many-body localization.
These results provide an explanation for the activated behavior of the
resistivity in amorphous materials on the insulating side near the SI
transition and a semi-quantitative description of the scanning tunneling data
on its superconductive side.Comment: 59 pages, 11 figure
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