1,010 research outputs found
The role of initial conditions in the ageing of the long-range spherical model
The kinetics of the long-range spherical model evolving from various initial
states is studied. In particular, the large-time auto-correlation and -response
functions are obtained, for classes of long-range correlated initial states,
and for magnetized initial states. The ageing exponents can depend on certain
qualitative features of initial states. We explicitly find the conditions for
the system to cross over from ageing classes that depend on initial conditions
to those that do not.Comment: 15 pages; corrected some typo
Doi Masatoshiun: "osservatore" giapponese al Vaticano II
La presencia de los «observadores delegados
», provenientes de iglesias diversas de la romana,
en el Concilio Vaticano ii fue importante por la variedad
de sus aportaciones y la relevancia teológica y cultural
de las mismas. Entre ellos, cabe recordar a Doi
Masatoshi de la Nihon Kirisuto Kiyoudan, que participó
en la segunda y tercera sesión de la asamblea conciliar.
Sus aportaciones manifiestan libertad de juicio
y capacidad de captar aspectos peculiares, litúrgicos y
dogmáticos, sobre todo en el tema del diálogo. En este
sector, siguiendo las enseñanzas de Tillich, pero profundizadas
con originalidad propia, insistió en el mutuo
conocimiento no solo entre las denominaciones
cristianas sino también con los patrimonios de otras
religiones. En los años sucesivos al Concilio, siguió profundizando
en estas temáticas
Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
The structure of states of the perturbed p-spin spherical spin-glass is
analyzed. At low enough free energy metastable states have a supersymmetric
structure, while at higher free energies the supersymmetry is broken. The
transition between the supersymmetric and the supersymmetry-breaking phase is
triggered by a change in the stability of states
Inelastic scattering of atoms in a double well
We study a mixture of two light spin-1/2 fermionic atoms and two heavy atoms
%in a Mott state in a double well potential. Inelastic scattering processes
between both atomic species excite the heavy atoms and renormalize the
tunneling rate and the interaction of the light atoms (polaron effect). The
effective interaction of the light atoms changes its sign and becomes
attractive for strong inelastic scattering. This is accompanied by a crossing
of the energy levels from singly occupied sites at weak inelastic scattering to
a doubly occupied and an empty site for stronger inelastic scattering. We are
able to identify the polaron effect and the level crossing in the quantum
dynamics.Comment: 12 pages, 9 figure
Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models
We study dynamic heterogeneities in the out-of-equilibrium coarsening
dynamics of the spherical ferromagnet after a quench from infinite temperature
to its critical point. A standard way of probing such heterogeneities is by
monitoring the fluctuations of correlation and susceptibility, coarse-grained
over mesoscopic regions. We discuss how to define fluctuating coarse-grained
correlations (C) and susceptibilities (Chi) in models where no quenched
disorder is present. Our focus for the spherical model is on coarse-graining
over the whole volume of spins, which requires accounting for N^{-1/2}
non-Gaussian fluctuations of the spin. The latter are treated as a perturbation
about the leading order Gaussian statistics. We obtain exact results for these
quantities, which enable us to characterise the joint distribution of C and Chi
fluctuations. We find that this distribution is qualitatively different, even
for equilibrium above criticality, from the spin-glass scenario where C and Chi
fluctuations are linked in a manner akin to the fluctuation-dissipation
relation between the average C and Chi. Our results show that coarsening at
criticality is clearly heterogeneous for d>4 and suggest that, as in other
glassy systems, there is a well-defined timescale on which fluctuations across
thermal histories are largest. Surprisingly, however, neither this timescale
nor the amplitude of the heterogeneities increase with the age of the system,
as would be expected from the growing correlation length. For d<4, the strength
of the fluctuations varies on a timescale proportional to the age of the
system; the corresponding amplitude also grows with age, but does not scale
with the correlation volume as might have been expected naively.Comment: 39 pages, 9 figures, version for publication in J. Stat. Mech.
Shortened by cutting all technical details in section 6, with minor
corrections elsewher
Retrieving Infinite Numbers of Patterns in a Spin-Glass Model of Immune Networks
The similarity between neural and immune networks has been known for decades,
but so far we did not understand the mechanism that allows the immune system,
unlike associative neural networks, to recall and execute a large number of
memorized defense strategies {\em in parallel}. The explanation turns out to
lie in the network topology. Neurons interact typically with a large number of
other neurons, whereas interactions among lymphocytes in immune networks are
very specific, and described by graphs with finite connectivity. In this paper
we use replica techniques to solve a statistical mechanical immune network
model with `coordinator branches' (T-cells) and `effector branches' (B-cells),
and show how the finite connectivity enables the system to manage an extensive
number of immune clones simultaneously, even above the percolation threshold.
The system exhibits only weak ergodicity breaking, so that both multiple
antigen defense and homeostasis can be accomplished.Comment: Editor's Choice 201
Immune networks: multi-tasking capabilities at medium load
Associative network models featuring multi-tasking properties have been
introduced recently and studied in the low load regime, where the number of
simultaneously retrievable patterns scales with the number of nodes as
. In addition to their relevance in artificial intelligence,
these models are increasingly important in immunology, where stored patterns
represent strategies to fight pathogens and nodes represent lymphocyte clones.
They allow us to understand the crucial ability of the immune system to respond
simultaneously to multiple distinct antigen invasions. Here we develop further
the statistical mechanical analysis of such systems, by studying the medium
load regime, with . We derive three main
results. First, we reveal the nontrivial architecture of these networks: they
exhibit a high degree of modularity and clustering, which is linked to their
retrieval abilities. Second, by solving the model we demonstrate for
the existence of large regions in the phase diagram where the network can
retrieve all stored patterns simultaneously. Finally, in the high load regime
we find that the system behaves as a spin glass, suggesting that
finite-connectivity frameworks are required to achieve effective retrieval.Comment: 26 pages, 10 figure
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