4,159 research outputs found
About the ergodic regime in the analogical Hopfield neural networks. Moments of the partition function
In this paper we introduce and exploit the real replica approach for a
minimal generalization of the Hopfield model, by assuming the learned patterns
to be distributed accordingly to a standard unit Gaussian. We consider the high
storage case, when the number of patterns is linearly diverging with the number
of neurons. We study the infinite volume behavior of the normalized momenta of
the partition function. We find a region in the parameter space where the free
energy density in the infinite volume limit is self-averaging around its
annealed approximation, as well as the entropy and the internal energy density.
Moreover, we evaluate the corrections to their extensive counterparts with
respect to their annealed expressions. The fluctuations of properly introduced
overlaps, which act as order parameters, are also discussed.Comment: 15 page
The Relativistic Hopfield network: rigorous results
The relativistic Hopfield model constitutes a generalization of the standard
Hopfield model that is derived by the formal analogy between the
statistical-mechanic framework embedding neural networks and the Lagrangian
mechanics describing a fictitious single-particle motion in the space of the
tuneable parameters of the network itself. In this analogy the cost-function of
the Hopfield model plays as the standard kinetic-energy term and its related
Mattis overlap (naturally bounded by one) plays as the velocity. The
Hamiltonian of the relativisitc model, once Taylor-expanded, results in a
P-spin series with alternate signs: the attractive contributions enhance the
information-storage capabilities of the network, while the repulsive
contributions allow for an easier unlearning of spurious states, conferring
overall more robustness to the system as a whole. Here we do not deepen the
information processing skills of this generalized Hopfield network, rather we
focus on its statistical mechanical foundation. In particular, relying on
Guerra's interpolation techniques, we prove the existence of the infinite
volume limit for the model free-energy and we give its explicit expression in
terms of the Mattis overlaps. By extremizing the free energy over the latter we
get the generalized self-consistent equations for these overlaps, as well as a
picture of criticality that is further corroborated by a fluctuation analysis.
These findings are in full agreement with the available previous results.Comment: 11 pages, 1 figur
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
First insights on the differential expression of adaptive candidate genes among contrasting pathotypes of Hemileia vastatrix
info:eu-repo/semantics/publishedVersio
Small-RNA characterization of Coffee Leaf Rust races having different virulence profiles
info:eu-repo/semantics/publishedVersio
Seismicity and Focal Mechanisms at the Calabro-Lucanian boundary along the Apennine chain (southern Italy)
The Calabro-Lucanian boundary is a complex geological zone marking the transition between the highly seismogenic tectonic
domains of Southern Apennines and the Calabrian Arc.
Historical catalogues include earthquakes with macroseismic effects up to VII-VIII MCS (CPTI WORKING GROUP, 2004) and paleoseismological investigations suggested that earthquakes of
magnitude between 6.5 and 7 may have occurred in this area,
between the 6th and the 15th century (MICHETTI et alii, 2000).
More recently, on 9 September 1998, an earthquake of moment
magnitude M5.6 occurred at the north-western margin of the
Pollino massif (GUERRA et alii, 2005; ARRIGO et alii, 2006) and
since the second half of 2010 the same region was interested by a noteworthy seismic activity characterized by several swarms with thousands of events with a maximum magnitude of 3.6
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.
Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule
Within the unified model of Bohr and Mottelson we derive the following linear
energy weighted sum rule for low energy orbital 1 excitations in even-even
deformed nuclei S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon
(B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2^2) \mu^2_N with B(E2) the E2
strength for the transition from the ground state to the first excited state in
the ground state rotational band, the charge r.m.s. radius squared and
the binding energy per nucleon in the nuclear ground state. It is
shown that this energy weighted sum rule is in good agreement with available
experimental data. The sum rule is derived using a simple ansatz for the
intrinsic ground state wave function that predicts also high energy 1
strength at 2 carrying 50\% of the total moment of the
orbital M1 operator.Comment: REVTEX (3.0), 9 pages, RU924
On Integrable Doebner-Goldin Equations
We suggest a method for integrating sub-families of a family of nonlinear
{\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc
G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie}
symmetries. Since the method of integration involves non-local transformations
of dependent and independent variables, general solutions obtained include
implicitly determined functions. By properly specifying one of the arbitrary
functions contained in these solutions, we obtain broad classes of explicit
square integrable solutions. The physical significance and some analytical
properties of the solutions obtained are briefly discussed.Comment: 23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.st
Criticality in diluted ferromagnet
We perform a detailed study of the critical behavior of the mean field
diluted Ising ferromagnet by analytical and numerical tools. We obtain
self-averaging for the magnetization and write down an expansion for the free
energy close to the critical line. The scaling of the magnetization is also
rigorously obtained and compared with extensive Monte Carlo simulations. We
explain the transition from an ergodic region to a non trivial phase by
commutativity breaking of the infinite volume limit and a suitable vanishing
field. We find full agreement among theory, simulations and previous results.Comment: 23 pages, 3 figure
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