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

A polynomial training algorithm for calculating perceptrons of optimal stability

Recomi (REpeated COrrelation Matrix Inversion) is a polynomially fast algorithm for searching optimally stable solutions of the perceptron learning problem. For random unbiased and biased patterns it is shown that the algorithm is able to find optimal solutions, if any exist, in at worst O(N^4) floating point operations. Even beyond the critical storage capacity alpha_c the algorithm is able to find locally stable solutions (with negative stability) at the same speed. There are no divergent time scales in the learning process. A full proof of convergence cannot yet be given, only major constituents of a proof are shown.Comment: 11 pages, Latex, 4 EPS figure

A Two-Player Game of Life

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.Comment: 7 pages, 3 figure

Nephelometer and current observations at the STIE site, Panama Basin

The LDGO-Thorndike film recording nephelometer was used in three modes (profiling, short-term tethered and long-term moored) to measure changes in particle concentrations on time scales of minutes to weeks and space scales of meters to 25 km while measurements were being made on production and settling rates of particles. Although the nepheloid layer had no large near-bottom increase suggestive of local resuspension, there was an unusually thick nepheloid layer due to resuspension and advection of sediment from the basin walls. The concentration of particles increased by a factor of 3 between 900 m and the seafloor at 3840 m, while the vertical flux of particles measured in traps increased by only a factor of 1.7 over that distance. The horizontal flux of particles past traps at all depths is estimated to have varied by less than 20% and, therefore, does not appear to influence the flux measured with sediment traps. Changes with time in small-particle concentrations measured by the moored nephelometer were less than 30%, but the concentration of large particles changed by 100%

Parisi Phase in a Neuron

Pattern storage by a single neuron is revisited. Generalizing Parisi's framework for spin glasses we obtain a variational free energy functional for the neuron. The solution is demonstrated at high temperature and large relative number of examples, where several phases are identified by thermodynamical stability analysis, two of them exhibiting spontaneous full replica symmetry breaking. We give analytically the curved segments of the order parameter function and in representative cases compute the free energy, the storage error, and the entropy.Comment: 4 pages in prl twocolumn format + 3 Postscript figures. Submitted to Physical Review Letter

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

CH 3 GHz Observations of the Galactic Center

A 3 $\times$ 3 map of the Galactic Center was made at 9\arcmin resolution and 10\arcmin spacing in the CH $^2\Pi_{1/2}$, J=1/2, F=1-1 transition at 3335 MHz. The CH emission shows a velocity extent that is nearly that of the CO(1-0) line, but the CH line profiles differ markedly from the CO. The 3335 MHz CH transition primarily traces low-density molecular gas and our observations indicate that the mass of this component within $\sim$ 30 pc of the Galactic Center is $\sim$ 9 $\times$ 10$^6$ M$_\odot$. The CO-H$_2$ conversion factor obtained for the low-density gas in the mapped region is greater than that thought to apply to the dense molecular gas at the Galactic Center. In addition to tracing the low-density molecular gas at the Galactic Center, the CH spectra show evidence of emission from molecular clouds along the line of sight both in the foreground and background. The scale height of these clouds ranges from 27 - 109 pc, consistent with previous work based on observations of molecular clouds in the inner Galaxy.Comment: 29 pages, 12 figure

Sinking versus suspended particle size distributions in the North Pacific Subtropical Gyre

The particle size distribution (PSD) is a fundamental property that influences all aspects of phytoplankton ecology. In particular, the size (e.g., diameter d [μm]) and sinking speed w (m/day) of individual particles are inextricable, but much remains unknown about how d and w are related quantitatively for bulk particulate matter. There is significant interest in inferring sinking mass fluxes from PSDs, but doing so requires knowing how both mass and w scale with d . To this end, using both laser diffraction and imaging, we characterized for the first time both sinking and suspended PSDs in the oligotrophic North Pacific subtropical gyre. Comparing these PSDs via a power law parameterization indicates an approximately linear w ‐to‐d scaling, suggesting particles are more fractal‐like than sphere‐like in this respect. This result is robust across multiple instruments, depths, and sediment trap deployments and is made comparatively precise by a high degree of replication