Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

Urbanization, population transition, and growth

This paper analyzes a dual economy consisting of urban market areas and less developed rural areas with or without local markets. Urban areas have better opportunities for earnings and education than rural areas. Rural families choose whether to move to urban areas at costs that differ from location to location. As per capita output grows relative to the moving cost, urbanization proceeds, leading to lower fertility, more investments in human and physical capital per child relative to output per worker, and faster economic growth. These impacts are stronger if rural areas have no access to markets.

Analysis of the wind field and heat budget in an alpine lake basin during summertime fair weather conditions

Observational data collected in the Lake Tekapo hydro catchment of the Southern Alps in New Zealand are used to analyse the wind and temperature fields in the alpine lake basin during summertime fair weather conditions. Measurements from surface stations, pilot balloon and tethersonde soundings, Doppler sodar and an instrumented light aircraft provide evidence of multi-scale interacting wind systems, ranging from microscale slope winds to mesoscale coast-to-basin flows. Thermal forcing of the winds occurred due to differential heating as a consequence of orography and heterogeneous surface features, which is quantified by heat budget and pressure field analysis. The daytime vertical temperature structure was characterised by distinct layering. Features of particular interest are the formation of thermal internal boundary layers due to the lake-land discontinuity and the development of elevated mixed layers. The latter were generated by advective heating from the basin and valley sidewalls by slope winds and by a superimposed valley wind blowing from the basin over Lake Tekapo and up the tributary Godley Valley. Daytime heating in the basin and its tributary valleys caused the development of a strong horizontal temperature gradient between the basin atmosphere and that over the surrounding landscape, and hence the development of a mesoscale heat low over the basin. After noon, air from outside the basin started flowing over mountain saddles into the basin causing cooling in the lowest layers, whereas at ridge top height the horizontal air temperature gradient between inside and outside the basin continued to increase. In the early evening, a more massive intrusion of cold air caused rapid cooling and a transition to a rather uniform slightly stable stratification up to about 2000 m agl. The onset time of this rapid cooling varied about 1-2 h between observation sites and was probably triggered by the decay of up-slope winds inside the basin, which previously countered the intrusion of air over the surrounding ridges. The intrusion of air from outside the basin continued until about mid-night, when a northerly mountain wind from the Godley Valley became dominant. The results illustrate the extreme complexity that can be caused by the operation of thermal forcing processes at a wide range of spatial scales.

Changes in physical symptoms during the menopause transition

This article analyzes physical symptoms experienced by mid-age Australian women in different stages of the menopause transition. A total of 8,623 women, aged 45 to 50 years in 1996, who participated the mid-age cohort of the Australian Longitudinal Study on Women's Health, completed Survey I in 1996 and Survey 2 in 1998. Women were assigned to I of 6 menopause groups according to their menopausal status at Surveys 1 and 2, and compared on symptoms experienced at Surveys I and 2, adjusted for lifestyle, behavioral and demographic factors. At Survey 1, the most commonly reported symptoms were headaches, back pain, stiff joints, tiredness, and difficulty sleeping. Perimenopausal women were more likely than premenopausal or postmenopausal women to report these symptoms. Hot flushes and night sweats were more common among postmenopausal women. Compared with those who remained premenopausal, women who were in the early stages of menopause or perimenopausal were more likely to report tiredness, stiff joints, difficulty sleeping, and hot flushes at Survey 2. Women who remained perimenopausal were also more likely to report back pain and leaking urine. Compared with premenopausal women, odds ratios for night sweats increased for women in consecutive stages of the menopause transition and remained high in the postmenopausal women.

Columnar to equiaxed transition of eutectic in hypoeutectic aluminium-silicon alloys

Directional solidification of unmodified and strontium modified binary, high-purity aluminium-7 wt% silicon and commercial A356 alloys has been carried out to investigate the mechanism of eutectic solidification. The microstructure of the eutectic growth inter-face was investigated with optical microscopy and Electron Backscattering Diffraction (EBSD). In the commercial alloys, the eutectic solidification inter-face extends in the growth direction and creates a eutectic mushy zone. A planar eutectic growth front is observed in the high-purity alloys. The eutectic aluminium has mainly the same crystallographic orientation as the dendrites in the unmodified alloys and the strontium modified high-purity alloy. A more complex eutectic grain structure is found in the strontium modified commercial alloy. A mechanism involving constitutional undercooling and a columnar to equiaxed transition explains the differences between pure and commercial alloys. It is probably caused by the segregation of iron and magnesium and the activation of nucleants in the commercial alloy. (C) 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Lamproites from Gaussberg, Antarctica: Possible transition zone melts of Archaean subducted sediments

Petrogenetic models for the origin of lamproites are evaluated using new major element, trace element, and Sr, Nd, and Pb isotope data for Holocene lamproites from the Gaussberg volcano in the East Antarctic Shield. Gaussberg lamproites exhibit very unusual Pb isotope compositions (Pb-206/Pb-204 = 17.44-17.55 and Pb-207/Pb-204 = 15.56-15.63), which in common Pb isotope space plot above mantle evolution lines and to the left of the meteorite isochron. Combined with very unradiogenic Nd, such compositions are shown to be inconsistent with an origin by melting of sub-continental lithospheric mantle. Instead, a model is proposed in which late Archaean continent-derived sediment is subducted as K-hollandite and other ultra-high-pressure phases and sequestered in the Transition Zone (or lower mantle) where it is effectively isolated for 2-3 Gyr. The high Pb-207/Pb-204 ratio is thus inherited from ancient continent-derived sediment, and the relatively low Pb-206/Pb-204 ratio is the result of a single stage of U/Pb fractionation by subduction-related U loss during slab dehydration. Sr and Nd isotope ratios, and trace element characteristics (e.g. Nb/Ta ratios) are consistent with sediment subduction and dehydration-related fractionation. Similar models that use variable time of isolation of subducted sediment can be derived for all lamproites. Our interpretation of lamproite sources has important implications for ocean island basalt petrogenesis as well as the preservation of geochemically anomalous reservoirs in the mantle.

Diversity and change in Australia's rangelands: a post-productivist transition with a difference?

Australia's rangelands are experiencing a post-productivist transition at a tempo comparable to Western Europe's, but in contexts that ensure marked divergence in impulses, actors, processes and outcomes. In Australia's most marginal lands, a flimsy mode of pastoral occupance is being displaced by renewed indigenous occupance, conservation and tourism, with significant changes in land ownership, property rights, investment sources and power relations, but also with structural problems arising from fugitive income streams. The sharp delineation between structurally coherent commodity-oriented regions and emerging amenity-oriented regions can provisionally be mapped at a national scale. A comparison of Australia with Western Europe indicates that three distinct but interconnected driving forces are propelling the rural transition, namely: agricultural overcapacity; the emergence of amenity-oriented uses; and changing societal values.

QCD thermal phase transition in the presence of a small chemical potential

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential mu. Derivatives of quark and gluonic observables with respect to mu are computed at mu=0 for two flavors of p4 improved staggered fermions with ma=0.1,0.2 on a 16(3)x4 lattice, and used to calculate the leading order Taylor expansion in mu of the location of the pseudocritical point about mu=0. This expansion should be well behaved for the small values of mu(q)/T(c)similar to0.1 relevant for BNL RHIC phenomenology, and predicts a critical curve T-c(mu) in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of munot equal0 on the equation of state, and comment on the complex phase of the fermion determinant in QCD with munot equal0.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Adsorption in slit-like pores of activated carbons: Improvement of the Horvath and Kawazoe method

Anew thermodynamic approach has been developed in this paper to analyze adsorption in slitlike pores. The equilibrium is described by two thermodynamic conditions: the Helmholtz free energy must be minimal, and the grand potential functional at that minimum must be negative. This approach has led to local isotherms that describe adsorption in the form of a single layer or two layers near the pore walls. In narrow pores local isotherms have one step that could be either very sharp but continuous or discontinuous benchlike for a definite range of pore width. The latter reflects a so-called 0 --> 1 monolayer transition. In relatively wide pores, local isotherms have two steps, of which the first step corresponds to the appearance of two layers near the pore walls, while the second step corresponds to the filling of the space between these layers. All features of local isotherms are in agreement with the results obtained from the density functional theory and Monte Carlo simulations. The approach is used for determining pore size distributions of carbon materials. We illustrate this with the benzene adsorption data on activated carbon at 20, 50, and 80 degreesC, argon adsorption on activated carbon Norit ROX at 87.3 K, and nitrogen adsorption on activated carbon Norit R1 at 77.3 K.

A quantitative state and transition model for the Mitchell grasslands of central western Queensland

Concerns of reduced productivity and land degradation in the Mitchell grasslands of central western Queensland were addressed through a range monitoring program to interpret condition and trend. Botanical and eclaphic parameters were recorded along piosphere and grazing gradients, and across fenceline impact areas, to maximise changes resulting from grazing. The Degradation Gradient Method was used in conjunction with State and Transition Models to develop models of rangeland dynamics and condition. States were found to be ordered along a degradation gradient, indicator species developed according to rainfall trends and transitions determined from field data and available literature. Astrebla spp. abundance declined with declining range condition and increasing grazing pressure, while annual grasses and forbs increased in dominance under poor range condition. Soil erosion increased and litter decreased with decreasing range condition. An approach to quantitatively define states within a variable rainfall environment based upon a time-series ordination analysis is described. The derived model could provide the interpretive framework necessary to integrate on-ground monitoring, remote sensing and geographic information systems to trace states and transitions at the paddock scale. However, further work is needed to determine the full catalogue of states and transitions and to refine the model for application at the paddock scale.