Finite-size effects in on-line learning of multilayer neural networks

We complement recent advances in thermodynamic limit analyses of mean on-line gradient descent learning dynamics in multi-layer networks by calculating fluctuations possessed by finite dimensional systems. Fluctuations from the mean dynamics are largest at the onset of specialisation as student hidden unit weight vectors begin to imitate specific teacher vectors, increasing with the degree of symmetry of the initial conditions. In light of this, we include a term to stimulate asymmetry in the learning process, which typically also leads to a significant decrease in training time.

Finite-size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite-size effects are estimated for comparing the results with the bounds set by Shannon. The critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.

Finite-size effects in low-density parity-check codes applied to cryptography

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A mechanistic description of combined hardening and size effects

Mechanistic models based on geometrically necessary dislocations are re-examined in light of recent experiments exhibiting the indentation size effect. A simple method is developed to combine work hardening, solid solution hardening, radiation hardening and size effects. The model is verified by experiments in ionic salt crystals. © 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Unfolding grain size effects in barium titanate ferroelectric ceramics

Grain size effects on the physical properties of polycrystalline ferroelectrics have been extensively studied for decades; however there are still major controversies regarding the dependence of the piezoelectric and ferroelectric properties on the grain size. Dense BaTiO3 ceramics with different grain sizes were fabricated by either conventional sintering or spark plasma sintering using micro- and nano-sized powders. The results show that the grain size effect on the dielectric permittivity is nearly independent of the sintering method and starting powder used. A peak in the permittivity is observed in all the ceramics with a grain size near 1μm and can be attributed to a maximum domain wall density and mobility. The piezoelectric coefficient d33 and remnant polarization Pr show diverse grain size effects depending on the particle size of the starting powder and sintering temperature. This suggests that besides domain wall density, other factors such as back fields and point defects, which influence the domain wall mobility, could be responsible for the different grain size dependence observed in the dielectric and piezoelectric/ferroelectric properties. In cases where point defects are not the dominant contributor, the piezoelectric constant d33 and the remnant polarization Pr increase with increasing grain size.

An international cohort comparison of size effects on job growth

The contribution of different-sized businesses to job creation continues to attract policymakers’ attention; however, it has recently been recognised that conclusions about size were confounded with the effect of age. We probe the role of size, controlling for age, by comparing the cohorts of firms born in 1998 over their first decade of life, using variation across half a dozen northern European countries Austria, Finland, Germany, Norway, Sweden and the UK to pin down size effects. We find that a very small proportion of the smallest firms play a crucial role in accounting for cross-country differences in job growth. A closer analysis reveals that the initial size distribution and survival rates do not seem to explain job growth differences between countries, rather it is a small number of rapidly growing firms that are driving this result.

Grain size effects on excess Thorium-230 of sediment cores from the Southern Ocean and the South East Atlantic

Excess Thorium-230 (230Thxs) as a constant flux tracer is an essential tool for paleoceanographic studies, but its limitations for flux normalization are still a matter of debate. In regions of rapid sediment accumulation, it has been an open question if 230Thxs-normalized fluxes are biased by particle sorting effects during sediment redistribution. In order to study the sorting effect of sediment transport on 230Thxs, we analyzed the specific activity of 230Thxs in different particle size classes of carbonate-rich sediments from the South East Atlantic, and of opal-rich sediments from the Atlantic sector of the Southern Ocean. At both sites, we compare the 230Thxs distribution in neighboring high vs. low accumulation settings. Two grain-size fractionation methods are explored. We find that the 230Thxs distribution is strongly grain size dependent, and 50-90% of the total 230Thxs inventory is concentrated in fine material smaller than 10 µm, which is preferentially deposited at the high accumulation sites. This leads to an overestimation of the focusing factor Psi, and consequently to an underestimation of the vertical flux rate at such sites. The distribution of authigenic uranium indicates that fine organic-rich material has also been re-deposited from lateral sources. If the particle sorting effect is considered in the flux calculations, it reduces the estimated extent of sediment focusing. In order to assess the maximum effect of particle sorting on Psi, we present an extreme scenario, in which we assume a lateral sediment supply of only fine material (< 10 µm). In this case, the focusing factor of the opal-rich core would be reduced from Psi = 5.9 to Psi = 3.2. In a more likely scenario, allowing silt-sized material to be transported, Psi is reduced from 5.9 to 5.0 if particle sorting is taken into consideration. The bias introduced by particle sorting is most important for strongly focused sediments. Comparing 230Thxs-normalized mass fluxes biased by sorting effects with uncorrected mass fluxes, we suggest that 230Thxs-normalization is still a valid tool to correct for lateral sediment redistribution. However, differences in focusing factors between core locations have to be evaluated carefully, taking the grain size distributions into consideration.

Size effects on self-assembly and melting of silver-alkanethiolate on inert surfaces

Self-assembled materials produced in the reaction between alkanethiol and Ag are characterized and compared. It is revealed that the size of the Ag substrate has a significant role in the self-assembly process and determines the reaction products. Alkanethiol adsorbs on the surface of Ag continuous planar thin films and only forms self-assembled monolayers (SAMs), while the reaction between alkanethiol and Ag clusters on inert surfaces is more aggressive and generates a significantly larger amount of alkanethiolate. Two dissimilar products are yielded depending on the size of the clusters. Small Ag clusters are more likely to be converted into multilayer silver-alkanethiolate (AgSR, R = CnH2n+1) crystals, while larger Ag clusters form monolayer-protected clusters (MPCs). The AgSR crystals are initially small and can ripen into large lamellae during thermal annealing. The crystals have facets and flat terraces with extended area, and have a strong preferred orientation in parallel with the substrate surface. The MPCs move laterally upon annealing and reorganize into a single-layer network with their separation distance approximately equal to the length of an extended alkyl chain. AgSR lamellar crystals grown on inert surfaces provide an excellent platform to study the melting characteristics of crystalline lamellae of polymeric materials with the thickness in the nanometer scale. This system is also unique in that each crystal has integer number of layers – magic-number size (thickness). The size of the crystals is controlled by adjusting the amount of Ag and the annealing temperature. X-ray diffraction (XRD) and atomic force microscopy (AFM) are combined to accurately determine the size (number of layers) of the lamellar crystals. The melting characteristics are measured with nanocalorimetry and show discrete melting transitions which are attributed to the magic-number sizes of the lamellar crystals. The discrete melting temperatures are intrinsic properties of the crystals with particular sizes. Smaller lamellar crystals with less number of layers melt at lower temperatures. The melting point depression is inversely proportional to the total thickness of the lamellae – the product of the number of layers and the layer thickness.

Effects of temper level on the dependence of fatigue crack growth threshold and crack closure on the prior austenitic grain size

An attempt has been made to systematically investigate the effects of microstructural parameters, such as the prior austenite grain size (PAGS), in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels in a quenched and tempered high-strength steel. By austenitizing at various temperatures, the PAGS was varied from about 0.7 to 96 μm. The microstructures with these grain sizes were tempered at 200 °C, 400 °C, and 530 °C and tested for fatigue thresholds and crack closure. It has been found that, in general, three different trends in the dependence of both the total threshold stress intensity range, ΔK th , and the intrinsic threshold stress intensity range, ΔK eff, th , on the PAGS are observable. By considering in detail the factors such as cyclic stress-strain behavior, environmental effects on FCG, and embrittlement during tempering, the present observations could be rationalized. The strong dependence of ΔK th and ΔK eff, th on PAGS in microstructures tempered at 530 °C has been primarily attributed to cyclic softening and thereby the strong interaction of the crack tip deformation field with the grain boundary. On the other hand, a less strong dependence of ΔK th and ΔK eff, th on PAGS is suggested to be caused by the cyclic hardening behavior of lightly tempered microstructures occurring in 200 °C temper. In both microstructures, crack closure influenced near-threshold FCG (NTFCG) to a significant extent, and its magnitude was large at large grain sizes. Microstructures tempered at the intermediate temperatures failed to show a systematic variation of ΔKth and ΔKeff, th with PAGS. The mechanisms of intergranular fracture vary between grain sizes in this temper. A transition from “microstructure-sensitive” to “microstructure-insensitive” crack growth has been found to occur when the zone of cyclic deformation at the crack tip becomes more or less equal to PAGS. Detailed observations on fracture morphology and crack paths corroborate the grain size effects on fatigue thresholds and crack closure.

The Size-Dependent Elastic Properties of Nanofilms with Surface Effects

Size-dependent elastic constants are investigated theoretically with reference to a nanoscale single-crystal thin film. A three-dimensional _3D_ model is presented with the relaxation on the surface of the nanofilm taken into consideration. The constitutive relation of the 3D model is derived by using the energy approach, and analytical expressions for the four nonzero elastic constants of the nanofilm are obtained. The size effects of the four elastic constants are then discussed, and the dependence of these elastic constants on the surface relaxation and the ambiguity in the definition of the thickness of the nanofilm are also analyzed. In addition, the elastic moduli of the nanofilm in two kinds of plane problem are obtained and discussed in the case of a special boundary condition.

Size-Dependent Elastic Modulus And Fracture Toughness Of The Nanofilm With Surface Effects

The effective elastic modulus and fracture toughness of the nanofilm were derived with the surface relaxation and the surface energy taken into consideration by means of the interatomic potential of an ideal crystal. The size effects of the effective elastic modulus and fracture toughness were discussed when the thickness of the nanofilm was reduced. And the dependence of the size effects on the surface relaxation and surface energy was also analyzed.

Effects of diet and body size on phosphorus utilization of Liza haematocheila T. & S.

A 21-d laboratory experiment was conducted to study, the phosphorus (P) utilization of two different diets by redlip mullet Liza haematocheila T. & S. Sand-filtered water in salinity 30 and temperature 25 degrees C was used. Twenty-nine fish individuals were divided into three groups: 11 to group 1 (G1) fed on diet 1, 11 to group 2 (G2) fed on diet 2, and 7 to contrast group. Diet 1 was a commercial feed, more valuable in nutrition than diet 2 that similar to natural detritus. The results show the intake phosphorus (IP) of G1 was significantly higher than that of G2, and both increased linearly with body size at a certain amount of diet. The retention phosphorus (RP) in fish of G1 was lower than G2. The relationship between retention phosphorus and body size was positive and stronger in G2. Significant difference in faecal phosphorus (FP) was found between G1 and G2. Body size significantly impacted the excretion phosphorus (EP) in G1 but G2. The loss of intake phosphor-us in G1 was 10.83-20.27 mg per g fish weight gain, higher than that in G2 for 6.63-9.56. Of the phosphor-us, about 10% was allocated into growth, 50% in faeces, and the rest lost in excretion. The main part of phosphorus was lost in faeces but excretion. The phosphorus budget of the fish could be described as 100IP = 7.40RP + 47.39FP + 36.63EP (Diet 1) or 100IP = 11.93RP + 56.64FP + 21.76EP (Diet 2).

Effects of dietary calcium levels and limestone particicle size on the performance, tibia and blood of laying hens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effects of meal size and proximal-distal segmentation on gastric activity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effects of Alloyed and Oxide Phases on Methanol Oxidation of Pt-Ru/C Nanocatalysts of the Same Particle Size

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)