1,589 research outputs found
A Quantitative Clustering Approach to Ultrametricity in Spin Glasses
We discuss the problem of ultrametricity in mean field spin glasses by means
of a hierarchical clustering algorithm. We complement the clustering approach
with quantitative testing: we discuss both in some detail. We show that the
elimination of the (in this context accidental) spin flip symmetry plays a
crucial role in the analysis, since the symmetry hides the real nature of the
data. We are able to use in the analysis disorder averaged quantities. We are
able to exhibit a number of features of the low phase of the mean field
theory, and to claim that the full hierarchical structure can be observed
without ambiguities only on very large lattice volumes, not currently
accessible by numerical simulations.Comment: 15 pages with color figure
Quantum discord and information deficit in spin chains
We examine the behavior of quantum correlations of spin pairs in a finite
anisotropic spin chain immersed in a transverse magnetic field, through
the analysis of the quantum discord and the conventional and quadratic one
way-information deficits. We first provide a brief review of these measures,
showing that the last ones can be obtained as particular cases of a generalized
information deficit based on general entropic forms. All these measures
coincide with an entanglement entropy in the case of pure states, but can be
non-zero in separable mixed states, vanishing just for classically correlated
states. It is then shown that their behavior in the exact ground state of the
chain exhibits similar features, deviating significantly from that of the pair
entanglement below the critical field. In contrast with entanglement, they
reach full range in this region, becoming independent of the pair separation
and coupling range in the immediate vicinity of the factorizing field. It is
also shown, however, that significant differences between the quantum discord
and the information deficits arise in the local minimizing measurement that
defines them. Both analytical and numerical results are provided.Comment: 14 pages, 5 figure
Message passing algorithms for non-linear nodes and data compression
The use of parity-check gates in information theory has proved to be very
efficient. In particular, error correcting codes based on parity checks over
low-density graphs show excellent performances. Another basic issue of
information theory, namely data compression, can be addressed in a similar way
by a kind of dual approach. The theoretical performance of such a Parity Source
Coder can attain the optimal limit predicted by the general rate-distortion
theory. However, in order to turn this approach into an efficient compression
code (with fast encoding/decoding algorithms) one must depart from parity
checks and use some general random gates. By taking advantage of analytical
approaches from the statistical physics of disordered systems and SP-like
message passing algorithms, we construct a compressor based on low-density
non-linear gates with a very good theoretical and practical performance.Comment: 13 pages, European Conference on Complex Systems, Paris (Nov 2005
Local Rigidity in Sandpile Models
We address the problem of the role of the concept of local rigidity in the
family of sandpile systems. We define rigidity as the ratio between the
critical energy and the amplitude of the external perturbation and we show, in
the framework of the Dynamically Driven Renormalization Group (DDRG), that any
finite value of the rigidity in a generalized sandpile model renormalizes to an
infinite value at the fixed point, i.e. on a large scale. The fixed point value
of the rigidity allows then for a non ambiguous distinction between
sandpile-like systems and diffusive systems. Numerical simulations support our
analytical results.Comment: to be published in Phys. Rev.
Genetic Intervention: Rights and Ethical Values
Faced on one hand with the sensational innovations brought about by the new biological technologies and on the other with the need to safeguard human rights adequately and also, in increasingly global terms, the rights of the environment and of the ecosystem, the issue that must be tackled is not only the definition of clear rules but also whether the law can effectively intervene in and interact with the on-going progress of science and technology.
The complexity of the problem as well as the recognition of personal and joint responsibility of all the parties involved (society, institutions and healthcare personnel) lead us to reflect on how to best safeguard fundamental community values, in order not to leave social control to regulations alone, but to resort instead to structured, differentiated and circular social approaches and control systems
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