Correlations between hidden units in multilayer neural networks and replica symmetry breaking

We consider feed-forward neural networks with one hidden layer, tree architecture and a fixed hidden-to-output Boolean function. Focusing on the saturation limit of the storage problem the influence of replica symmetry breaking on the distribution of local fields at the hidden units is investigated. These field distributions determine the probability for finding a specific activation pattern of the hidden units as well as the corresponding correlation coefficients and therefore quantify the division of labor among the hidden units. We find that although modifying the storage capacity and the distribution of local fields markedly replica symmetry breaking has only a minor effect on the correlation coefficients. Detailed numerical results are provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and nonoverlapping receptive fields.Comment: 9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev.

Correlated patterns in non-monotonic graded-response perceptrons

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.Comment: 4 pages, 4 figure

Influence of various fabrication methods on the compressive strength of titanium skin- stringer panels

Influence of fabrication methods on compressive strength of titanium alloy skin stringer panel

Attempted Bethe ansatz solution for one-dimensional directed polymers in random media

We study the statistical properties of one-dimensional directed polymers in a short-range random potential by mapping the replicated problem to a many body quantum boson system with attractive interactions. We find the full set of eigenvalues and eigenfunctions of the many-body system and perform the summation over the entire spectrum of excited states. The analytic continuation of the obtained exact expression for the replica partition function from integer to non-integer replica parameter N turns out to be ambiguous. Performing the analytic continuation simply by assuming that the parameter N can take arbitrary complex values, and going to the thermodynamic limit of the original directed polymer problem, we obtain the explicit universal expression for the probability distribution function of free energy fluctuations.Comment: 32 pages, 1 figur

Optimally adapted multi-state neural networks trained with noise

The principle of adaptation in a noisy retrieval environment is extended here to a diluted attractor neural network of Q-state neurons trained with noisy data. The network is adapted to an appropriate noisy training overlap and training activity which are determined self-consistently by the optimized retrieval attractor overlap and activity. The optimized storage capacity and the corresponding retriever overlap are considerably enhanced by an adequate threshold in the states. Explicit results for improved optimal performance and new retriever phase diagrams are obtained for Q=3 and Q=4, with coexisting phases over a wide range of thresholds. Most of the interesting results are stable to replica-symmetry-breaking fluctuations.Comment: 22 pages, 5 figures, accepted for publication in PR

Correlation of internal representations in feed-forward neural networks

Feed-forward multilayer neural networks implementing random input-output mappings develop characteristic correlations between the activity of their hidden nodes which are important for the understanding of the storage and generalization performance of the network. It is shown how these correlations can be calculated from the joint probability distribution of the aligning fields at the hidden units for arbitrary decoder function between hidden layer and output. Explicit results are given for the parity-, and-, and committee-machines with arbitrary number of hidden nodes near saturation.Comment: 6 pages, latex, 1 figur

CP Asymmetries in B to f_0 K_S Decays

We consider the branching ratio and the CP asymmetries in B to f_0(980)K_S decay to the end of determining the deviation of the time-dependent CP asymmetry from sin(2 beta) arising from Standard Model physics. We obtain Delta S_{f_0 K_S} within the context of the QCD factorization framework for the B to f_0(980)K_S decay amplitudes assuming the f_0(980) is a q\bar{q} state and employing a random scan over the theoretical parameter space to assess the possible range in Delta S_{f_0 K_S}. Imposing the value of the experimental branching ratio within 1 sigma and 3 sigma, respectively, of its central value as a constraint, we find the range of Delta S_{f_0 K_S} to be [0.018, 0.033] for a scan in which the parameters are allowed to vary within 1 sigma of their central values and the range [-0.019, 0.064] for a scan in which the parameters vary within 3 sigma of their central values.Comment: 27 pages, 10 figures, references adde

A canonical ensemble approach to graded-response perceptrons

Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner-Derrida canonical ensemble approach. Soft non- negative error measures are introduced allowing for extended retrieval properties. In particular, the performance of these systems for a linear and quadratic error measure, corresponding to the perceptron respectively the adaline learning algorithm, is compared with the performance for a rigid error measure, simply counting the number of errors. Replica-symmetry-breaking effects are evaluated.Comment: 26 pages, 10 ps figure

Spin-exchange relaxation free magnetometry with Cs vapor

We describe a Cs atomic magnetometer operating in the spin-exchange relaxation-free (SERF) regime. With a vapor cell temperature of $103^\circ\rm{C}$ we achieve intrinsic magnetic resonance widths $\Delta B=17 {\rm \mu G}$ corresponding to an electron spin-relaxation rate of $300 {\rm s^{-1}}$ when the spin-exchange rate is $\Gamma_{SE}=14000 {\rm s^{-1}}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about $400\thinspace{\rm pG/\sqrt{Hz}}$. Based on photon shot noise, we project a sensitivity of $40 {\rm pG/\sqrt{Hz}}$. A theoretical optimization of the magnetometer indicates sensitivities on the order of $2 {\rm pG/\sqrt{Hz}}$ should be achievable in a $1 {\rm cm^3}$ volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.Comment: 8 pages, 6 figures. submitted to PR