A Hebbian approach to complex network generation

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic connection between the kind of interactions among components and the emergent topology describing the system itself; also, it allows to effectively address the statistical mechanics on the resulting networks. Indeed, a wide class of analytically treatable, weighted random graphs with a tunable level of correlation can be recovered and controlled. We especially focus on the case of imitative couplings among components endowed with similar patterns (i.e. attributes), which, as we show, naturally and without any a-priori assumption, gives rise to small-world effects. We also solve the thermodynamics (at a replica symmetric level) by extending the double stochastic stability technique: free energy, self consistency relations and fluctuation analysis for a picture of criticality are obtained

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

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

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

Characterization of the S = 9 excited state in Fe8Br8 by Electron Paramagnetic Resonance

High Frequency electron paramagnetic resonance has been used to observe the magnetic dipole, $\Delta$ M$_s$ = $\pm$ 1, transitions in the $S = 9$ excited state of the single molecule magnet Fe$_8$Br$_8$. A Boltzmann analysis of the measured intensities locates it at 24 $\pm$ 2 K above the $S = 10$ ground state, while the line positions yield its magnetic parameters D = -0.27 K, E = $\pm$0.05 K, and B$_4^0$ = -1.3$\times$ 10$^{-6}$ K. D is thus smaller by 8% and E larger by 7% than for $S = 10$. The anisotropy barrier for $S = 9$ is estimated as 22 K,which is 25% smaller than that for $S = 10$ (29 K). These data also help assign the spin exchange constants(J's) and thus provide a basis for improved electronic structure calculations of Fe$_8$Br$_8$.Comment: 7 pages, Figs included in text, submitted to PR

An alternate model for magnetization plateaus in the molecular magnet V_15

Starting from an antiferromagnetic Heisenberg Hamiltonian for the fifteen spin-1/2 ions in V_15, we construct an effective spin Hamiltonian involving eight low-lying states (spin-1/2 and spin-3/2) coupled to a phonon bath. We numerically solve the time-dependent Schrodinger equation of this system, and obtain the magnetization as a function of temperature in a time-dependent magnetic field. The magnetization exhibits unusual patterns of hysteresis and plateaus as the field sweep rate and temperature are varied. The observed plateaus are not due to quantum tunneling but are a result of thermal averaging. Our results are in good agreement with recent experimental observations.Comment: Revtex, 4 pages, 5 eps figure

Composición y estructura de la vegetación epífita vascular en un bosque primario de Olivillo (Aextoxicon punctatum R. et P.) en el sur de Chile

Vascular epiphytes represent 10% of the total vascular plants of the world. Nevertheless, because it is hard to reach them in the forest upper-canopy where they usually live, there are few studies (especially in Chile) about them. With the objective of identifying the vascular epiphytes growing on tree stems (under 1.5 m height), we sampled three transects in an Olivillo old-growth stand, in the Rucamanque forest, in the central valley of south-central Chile, near the city of Temuco. Several variables were measured for both the vascular epiphytes and their host-trees. We studied the floristic composition of the vascular epiphytes community, and their relationship with their host-trees, as well as their sociability, cover, and frequency. Eight vascular epiphytes species were identified, corresponding to four genus distributed in three families: Hymenophyllum and Hymenoglossum (Hymenophyllaceae), Asplenium (Aspleniaceae) and Sarmienta (Gesneriaceae). We found only a non-statistically significant linear correlation between vascular epiphytes and their host-trees. We determined that Hymenophyllum cuneatum was the most important vascular epiphytes species

Nonadiabatic Landau Zener tunneling in Fe_8 molecular nanomagnets

The Landau Zener method allows to measure very small tunnel splittings \Delta in molecular clusters Fe_8. The observed oscillations of \Delta as a function of the magnetic field applied along the hard anisotropy axis are explained in terms of topological quantum interference of two tunnel paths of opposite windings. Studies of the temperature dependence of the Landau Zener transition rate P gives access to the topological quantum interference between exited spin levels. The influence of nuclear spins is demonstrated by comparing P of the standard Fe_8 sample with two isotopically substituted samples. The need of a generalized Landau Zener transition rate theory is shown.Comment: 5 pages, 6 figure

A statistical mechanics approach to autopoietic immune networks

The aim of this work is to try to bridge over theoretical immunology and disordered statistical mechanics. Our long term hope is to contribute to the development of a quantitative theoretical immunology from which practical applications may stem. In order to make theoretical immunology appealing to the statistical physicist audience we are going to work out a research article which, from one side, may hopefully act as a benchmark for future improvements and developments, from the other side, it is written in a very pedagogical way both from a theoretical physics viewpoint as well as from the theoretical immunology one. Furthermore, we have chosen to test our model describing a wide range of features of the adaptive immune response in only a paper: this has been necessary in order to emphasize the benefit available when using disordered statistical mechanics as a tool for the investigation. However, as a consequence, each section is not at all exhaustive and would deserve deep investigation: for the sake of completeness, we restricted details in the analysis of each feature with the aim of introducing a self-consistent model.Comment: 22 pages, 14 figur