5,328 research outputs found
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
Topological Learning for Brain Networks
This paper proposes a novel topological learning framework that can integrate
networks of different sizes and topology through persistent homology. This is
possible through the introduction of a new topological loss function that
enables such challenging task. The use of the proposed loss function bypasses
the intrinsic computational bottleneck associated with matching networks. We
validate the method in extensive statistical simulations with ground truth to
assess the effectiveness of the topological loss in discriminating networks
with different topology. The method is further applied to a twin brain imaging
study in determining if the brain network is genetically heritable. The
challenge is in overlaying the topologically different functional brain
networks obtained from the resting-state functional MRI (fMRI) onto the
template structural brain network obtained through the diffusion MRI (dMRI)
Parallel processing in immune networks
In this work we adopt a statistical mechanics approach to investigate basic,
systemic features exhibited by adaptive immune systems. The lymphocyte network
made by B-cells and T-cells is modeled by a bipartite spin-glass, where,
following biological prescriptions, links connecting B-cells and T-cells are
sparse. Interestingly, the dilution performed on links is shown to make the
system able to orchestrate parallel strategies to fight several pathogens at
the same time; this multitasking capability constitutes a remarkable, key
property of immune systems as multiple antigens are always present within the
host. We also define the stochastic process ruling the temporal evolution of
lymphocyte activity, and show its relaxation toward an equilibrium measure
allowing statistical mechanics investigations. Analytical results are compared
with Monte Carlo simulations and signal-to-noise outcomes showing overall
excellent agreement. Finally, within our model, a rationale for the
experimentally well-evidenced correlation between lymphocytosis and
autoimmunity is achieved; this sheds further light on the systemic features
exhibited by immune networks.Comment: 21 pages, 9 figures; to appear in Phys. Rev.
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