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Register a new userCorrelated patterns in non-monotonic graded-response perceptrons
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The optimal capacity of graded-response perceptrons storing biased and spatially correlated patterns with non-monotonic input-output relations is studied. It is shown that only the structure of the output patterns is important for the overall performance of the perceptrons.
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We address the general problem of heat conduction in one dimensional harmonic chain, with correlated isotopic disorder, attached at its ends to white noise or oscillator heat baths. When the low wavelength $mu$ behavior of the power spectrum $W$ (of the fluctuations of the random masses around their common mean value) scales as $W(mu)sim mu^beta$, the asymptotic thermal conductivity $kappa$ scales with the system size $N$ as $kappa sim N^{(1+beta)/(2+beta)}$ for free boundary conditions, whereas for fixed boundary conditions $kappa sim N^{(beta-1)/(2+beta)}$; where $beta>-1$, which is the usual power law scaling for one dimensional systems. Nevertheless, if $W$ does not scale as a power law in the low wavelength limit, the thermal conductivity may not scale in its usual form $kappasim N^{alpha}$, where the value of $alpha$ depends on the particular one dimensional model. As an example of the latter statement, if $W(mu)sim exp(-1/mu)/mu^2$, $kappa sim N/(log N)^3$ for fixed boundary conditions and $kappa sim N/log(N)$ for free boundary conditions, which represent non-standard scalings of the thermal conductivity.
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all networks characterized by diverging degree fluctuations, independently of the structure of the connectivity correlation functions characterizing the population network. By means of analytical and numerical results, we show that the outbreak time evolution follows a precise hierarchical dynamics. Once reached the most highly connected hubs, the infection pervades the network in a progressive cascade across smaller degree classes. Finally, we show the influence of the initial conditions and the relevance of statistical results in single case studies concerning heterogeneous networks. The emerging theoretical framework appears of general interest in view of the recently observed abundance of natural networks with complex topological features and might provide useful insights for the development of adaptive strategies aimed at epidemic containment.
We study the problem of determining the capacity of the binary perceptron for two variants of the problem where the corresponding constraint is symmetric. We call these variants the rectangle-binary-perceptron (RPB) and the $u-$function-binary-perceptron (UBP). We show that, unlike for the usual step-function-binary-perceptron, the critical capacity in these symmetric cases is given by the annealed computation in a large region of parameter space (for all rectangular constraints and for narrow enough $u-$function constraints, $K<K^*$). We prove this fact (under two natural assumptions) using the first and second moment methods. We further use the second moment method to conjecture that solutions of the symmetric binary perceptrons are organized in a so-called frozen-1RSB structure, without using the replica method. We then use the replica method to estimate the capacity threshold for the UBP case when the $u-$function is wide $K>K^*$. We conclude that full-step-replica-symmetry breaking would have to be evaluated in order to obtain the exact capacity in this case.
Anticipation is a strategy used by neural fields to compensate for transmission and processing delays during the tracking of dynamical information, and can be achieved by slow, localized, inhibitory feedback mechanisms such as short-term synaptic depression, spike-frequency adaptation, or inhibitory feedback from other layers. Based on the translational symmetry of the mobile network states, we derive generic fluctuation-response relations, providing unified predictions that link their tracking behaviors in the presence of external stimuli to the intrinsic dynamics of the neural fields in their absence.
We report experimental observations of a novel magnetoresistance (MR) behavior of two-dimensional electron systems in perpendicular magnetic field in the ballistic regime, for k_BTtau/hbar>1. The MR grows with field and exhibits a maximum at fields B>1/mu, where mu is the electron mobility. As temperature increases the magnitude of the maximum grows and its position moves to higher fields. This effect is universal: it is observed in various Si- and GaAs- based two-dimensional electron systems. We compared our data with recent theory based on the Kohn anomaly modification in magnetic field, and found qualitative similarities and discrepancies.
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