On-Line Learning with Restricted Training Sets: An Exactly Solvable Case

We solve the dynamics of on-line Hebbian learning in large perceptrons exactly, for the regime where the size of the training set scales linearly with the number of inputs. We consider both noiseless and noisy teachers. Our calculation cannot be extended to non-Hebbian rules, but the solution provides a convenient and welcome benchmark with which to test more general and advanced theories for solving the dynamics of learning with restricted training sets.Comment: 19 pages, eps figures included, uses epsfig macr

Role of the Secondary Phase η During High-Temperature Compression of ATI 718Plus®

Abstract High-temperature compression tests were performed on a Ni-base superalloy with a multi-phase microstructure. Particular attention was given on the influence of the η phase on recrystallization of ATI 718Plus®. The compression tests were performed at two temperatures over a variety of strains and strain rates. Meta-dynamic recrystallization was studied by exposing the samples to a set dwell time at the test temperature after deformation. Electron backscatter diffraction (EBSD) was used to investigate the microstructures after the tests. Secondary electron imaging (SEI) and scanning transmission electron microscopy (STEM) were utilized in order to investigate the deformation behavior of η and obtaining a detailed understanding of the recrystallization mechanism. The secondary η phase was found to increase the recrystallized fraction compared to η free tests. However, clusters of thin lamellar η inhibited recrystallization. The flow curve softening was distinctly stronger in the microstructure containing precipitates. It could be shown by SE images that this was due to the breakage and realignment of η. In addition, η was also found to accommodate the stresses by a remarkable deformation without breaking up. This was considered to be due to the composite nature of the precipitate as well as the ongoing recrystallization in the surrounding matrix.</jats:p

Dynamics of Learning with Restricted Training Sets I: General Theory

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions and the learning dynamics is of a spin-glass nature, with the composition of the training set playing the role of quenched disorder. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the two relevant performance measures (training error and generalization error), incorporating the old formalism developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves in this paper to single-layer networks and realizable tasks.Comment: 39 pages, LaTe

Dynamics of on-line Hebbian learning with structurally unrealizable restricted training sets

We present an exact solution for the dynamics of on-line Hebbian learning in neural networks, with restricted and unrealizable training sets. In contrast to other studies on learning with restricted training sets, unrealizability is here caused by structural mismatch, rather than data noise: the teacher machine is a perceptron with a reversed wedge-type transfer function, while the student machine is a perceptron with a sigmoidal transfer function. We calculate the glassy dynamics of the macroscopic performance measures, training error and generalization error, and the (non-Gaussian) student field distribution. Our results, which find excellent confirmation in numerical simulations, provide a new benchmark test for general formalisms with which to study unrealizable learning processes with restricted training sets.Comment: 7 pages including 3 figures, using IOP latex2e preprint class fil

Plasma-Induced Frequency Chirp of Intense Femtosecond Lasers and Its Role in Shaping High-Order Harmonic Spectral Lines

We investigate the self-phase modulation of intense femtosecond laser pulses propagating in an ionizing gas and its effects on collective properties of high-order harmonics generated in the medium. Plasmas produced in the medium are shown to induce a positive frequency chirp on the leading edge of the propagating laser pulse, which subsequently drives high harmonics to become positively chirped. In certain parameter regimes, the plasma-induced positive chirp can help to generate sharply peaked high harmonics, by compensating for the dynamically-induced negative chirp that is caused by the steep intensity profile of intense short laser pulses.Comment: 5 pages, 5 figure

Health Care Delivery Practices in Huntington's Disease Specialty Clinics : An International Survey

The CHDI Foundation, Inc. funds Enroll-HD and the activities of the Enroll-HD Care Improvement Committee, including the present survey. We would like to acknowledge the Enroll-HD and REGISTRY administrative staff that assisted in the recruitment of sites and sites that completed the survey.Peer reviewedPublisher PD

Partially and Fully Frustrated Coupled Oscillators With Random Pinning Fields

We have studied two specific models of frustrated and disordered coupled Kuramoto oscillators, all driven with the same natural frequency, in the presence of random external pinning fields. Our models are structurally similar, but differ in their degree of bond frustration and in their finite size ground state properties (one has random ferro- and anti-ferromagnetic interactions; the other has random chiral interactions). We have calculated the equilibrium properties of both models in the thermodynamic limit using the replica method, with emphasis on the role played by symmetries of the pinning field distribution, leading to explicit predictions for observables, transitions, and phase diagrams. For absent pinning fields our two models are found to behave identically, but pinning fields (provided with appropriate statistical properties) break this symmetry. Simulation data lend satisfactory support to our theoretical predictions.Comment: 37 pages, 7 postscript figure

What effect do substorms have on the content of the radiation belts?

Substorms are fundamental and dynamic processes in the magnetosphere, converting captured solar wind magnetic energy into plasma energy. These substorms have been suggested to be a key driver of energetic electron enhancements in the outer radiation belts. Substorms inject a keV “seed” population into the inner magnetosphere which is subsequently energized through wave-particle interactions up to relativistic energies; however, the extent to which substorms enhance the radiation belts, either directly or indirectly, has never before been quantified. In this study, we examine increases and decreases in the total radiation belt electron content (TRBEC) following substorms and geomagnetically quiet intervals. Our results show that the radiation belts are inherently lossy, shown by a negative median change in TRBEC at all intervals following substorms and quiet intervals. However, there are up to 3 times as many increases in TRBEC following substorm intervals. There is a lag of 1–3 days between the substorm or quiet intervals and their greatest effect on radiation belt content, shown in the difference between the occurrence of increases and losses in TRBEC following substorms and quiet intervals, the mean change in TRBEC following substorms or quiet intervals, and the cross correlation between SuperMAG AL (SML) and TRBEC. However, there is a statistically significant effect on the occurrence of increases and decreases in TRBEC up to a lag of 6 days. Increases in radiation belt content show a significant correlation with SML and SYM-H, but decreases in the radiation belt show no apparent link with magnetospheric activity levels

The Cyborg Astrobiologist: Testing a Novelty-Detection Algorithm on Two Mobile Exploration Systems at Rivas Vaciamadrid in Spain and at the Mars Desert Research Station in Utah

(ABRIDGED) In previous work, two platforms have been developed for testing computer-vision algorithms for robotic planetary exploration (McGuire et al. 2004b,2005; Bartolo et al. 2007). The wearable-computer platform has been tested at geological and astrobiological field sites in Spain (Rivas Vaciamadrid and Riba de Santiuste), and the phone-camera has been tested at a geological field site in Malta. In this work, we (i) apply a Hopfield neural-network algorithm for novelty detection based upon color, (ii) integrate a field-capable digital microscope on the wearable computer platform, (iii) test this novelty detection with the digital microscope at Rivas Vaciamadrid, (iv) develop a Bluetooth communication mode for the phone-camera platform, in order to allow access to a mobile processing computer at the field sites, and (v) test the novelty detection on the Bluetooth-enabled phone-camera connected to a netbook computer at the Mars Desert Research Station in Utah. This systems engineering and field testing have together allowed us to develop a real-time computer-vision system that is capable, for example, of identifying lichens as novel within a series of images acquired in semi-arid desert environments. We acquired sequences of images of geologic outcrops in Utah and Spain consisting of various rock types and colors to test this algorithm. The algorithm robustly recognized previously-observed units by their color, while requiring only a single image or a few images to learn colors as familiar, demonstrating its fast learning capability.Comment: 28 pages, 12 figures, accepted for publication in the International Journal of Astrobiolog