1,901 research outputs found
Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs
We propose a model of nonequilibrium quantum transport of particles and
energy in a system connected to mesoscopic Fermi reservoirs (meso-reservoir).
The meso-reservoirs are in turn thermalized to prescribed temperatures and
chemical potentials by a simple dissipative mechanism described by the Lindblad
equation. As an example, we study transport in monoatomic and diatomic chains
of non-interacting spinless fermions. We show numerically the breakdown of the
Onsager reciprocity relation due to the dissipative terms of the model.Comment: 5pages, 4 figure
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
Analogue neural networks on correlated random graphs
We consider a generalization of the Hopfield model, where the entries of
patterns are Gaussian and diluted. We focus on the high-storage regime and we
investigate analytically the topological properties of the emergent network, as
well as the thermodynamic properties of the model. We find that, by properly
tuning the dilution in the pattern entries, the network can recover different
topological regimes characterized by peculiar scalings of the average
coordination number with respect to the system size. The structure is also
shown to exhibit a large degree of cliquishness, even when very sparse.
Moreover, we obtain explicitly the replica symmetric free energy and the
self-consistency equations for the overlaps (order parameters of the theory),
which turn out to be classical weighted sums of 'sub-overlaps' defined on all
possible sub-graphs. Finally, a study of criticality is performed through a
small-overlap expansion of the self-consistencies and through a whole
fluctuation theory developed for their rescaled correlations: Both approaches
show that the net effect of dilution in pattern entries is to rescale the
critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure
How glassy are neural networks?
In this paper we continue our investigation on the high storage regime of a
neural network with Gaussian patterns. Through an exact mapping between its
partition function and one of a bipartite spin glass (whose parties consist of
Ising and Gaussian spins respectively), we give a complete control of the whole
annealed region. The strategy explored is based on an interpolation between the
bipartite system and two independent spin glasses built respectively by
dichotomic and Gaussian spins: Critical line, behavior of the principal
thermodynamic observables and their fluctuations as well as overlap
fluctuations are obtained and discussed. Then, we move further, extending such
an equivalence beyond the critical line, to explore the broken ergodicity phase
under the assumption of replica symmetry and we show that the quenched free
energy of this (analogical) Hopfield model can be described as a linear
combination of the two quenched spin-glass free energies even in the replica
symmetric framework
STABILIZATION POLICIES AND AGRICULTURAL IMPACTS IN DEVELOPING COUNTRIES: THE CASE OF BOLIVIA
This research examines the success of stabilization policies to control hyperinflation in Bolivia. Money demand functions for the hyperinflation and stabilization periods were econometrically estimated and statistically tested. We conclude that the demand for money in Bolivia changed after stabilization policies were implemented, indicating that the new government's objectives were met. Stabilization policies resulted in real economic growth for Bolivia's economy, including its agricultural sector, where agricultural export shares increased tenfold as stabilization policies corrected overvalued exchange rates.Bolivia, Developing countries, Hyperinflation, Money demand, Stabilization policies, Political Economy,
Equilibrium statistical mechanics on correlated random graphs
Biological and social networks have recently attracted enormous attention
between physicists. Among several, two main aspects may be stressed: A non
trivial topology of the graph describing the mutual interactions between agents
exists and/or, typically, such interactions are essentially (weighted)
imitative. Despite such aspects are widely accepted and empirically confirmed,
the schemes currently exploited in order to generate the expected topology are
based on a-priori assumptions and in most cases still implement constant
intensities for links. Here we propose a simple shift in the definition of
patterns in an Hopfield model to convert frustration into dilution: By varying
the bias of the pattern distribution, the network topology -which is generated
by the reciprocal affinities among agents - crosses various well known regimes
(fully connected, linearly diverging connectivity, extreme dilution scenario,
no network), coupled with small world properties, which, in this context, are
emergent and no longer imposed a-priori. The model is investigated at first
focusing on these topological properties of the emergent network, then its
thermodynamics is analytically solved (at a replica symmetric level) by
extending the double stochastic stability technique, and presented together
with its fluctuation theory for a picture of criticality. At least at
equilibrium, dilution simply decreases the strength of the coupling felt by the
spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main
difference with respect to previous investigations and a naive picture is that
within our approach replicas do not appear: instead of (multi)-overlaps as
order parameters, we introduce a class of magnetizations on all the possible
sub-graphs belonging to the main one investigated: As a consequence, for these
objects a closure for a self-consistent relation is achieved.Comment: 30 pages, 4 figure
Stress field around arbitrarily shaped cracks in two-dimensional elastic materials
The calculation of the stress field around an arbitrarily shaped crack in an
infinite two-dimensional elastic medium is a mathematically daunting problem.
With the exception of few exactly soluble crack shapes the available results
are based on either perturbative approaches or on combinations of analytic and
numerical techniques. We present here a general solution of this problem for
any arbitrary crack. Along the way we develop a method to compute the conformal
map from the exterior of a circle to the exterior of a line of arbitrary shape,
offering it as a superior alternative to the classical Schwartz-Cristoffel
transformation. Our calculation results in an accurate estimate of the full
stress field and in particular of the stress intensity factors K_I and K_{II}
and the T-stress which are essential in the theory of fracture.Comment: 7 pages, 4 figures, submitted for PR
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