Exponentiated gradient algorithms for large-margin structured classification

We consider the problem of structured classification, where the task is to predict a label y from an input x, and y has meaningful internal structure. Our framework includes supervised training of Markov random fields and weighted context-free grammars as special cases. We describe an algorithm that solves the large-margin optimization problem defined in [12], using an exponential-family (Gibbs distribution) representation of structured objects. The algorithm is efficient—even in cases where the number of labels y is exponential in size—provided that certain expectations under Gibbs distributions can be calculated efficiently. The method for structured labels relies on a more general result, specifically the application of exponentiated gradient updates [7, 8] to quadratic programs.

Adaptive online gradient descent

We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between [square root T] and [log T]. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.

Effective adsorption of sodium dodecylsulfate (SDS) by hydrocalumite (CaAl-LDH-Cl) induced by self-dissolution and re-precipitation mechanism

Hydrocalumite (CaAl-LDH-Cl) were synthesized through a rehydration method involving a freshly prepared tricalcium aluminate (C3A) with CaCl2 solution. To understand the intercalation behaviour of sodium dodecylsulfate (SDS) with CaAl-LDH-Cl, X-ray diffraction (XRD), Fourier transform infrared (FTIR), scanning electron microscopy (SEM), transmission electron microscope (TEM), X-ray photoelectron spectroscopy (XPS), inductively coupled plasma-atomic emission spectrometer (ICP) and elemental analysis have been undertaken. The sorption isotherms with SDS reveal that the maximum sorption amount of SDS by CaAl-LDH-Cl could reach 3.67 mmol•g-1. The results revealed that CaAl-LDH-Cl holds a self-dissolution property, about 20-30% of which is dissolved. And the dissolved Ca2+, Al3+ ions are combined with SDS to form CaAl-SDS or Ca-SDS precipitation. It has been highlighted that the composition of resulting products is strongly dependent upon the SDS concentration. With increasing SDS concentrations, the main resulting product changes from CaAl-SDS to Ca-SDS, and the value of interlayer spacing increased to 3.27 nm.

Thomas Young’s investigations in gradient-index optics

Purpose: James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some fifty years earlier Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young’s contributions. Method: We attempted to derive Young’s equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. Results: We did not confirm Young’s equation for the axial gradient to provide aberration-free optics, but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index towards the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Conclusion: Young’s theoretical work in gradient-index optics received no acknowledgement from either his contemporaries or later authors. While his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young’s work deserves wider recognition.

Anisotropy of articular cartilage reflects the ECM gradient architecture : Hough-Radon Transform Analysis

Tissue-specific extracellular matrix (ECM) is known to be an ideal bioscaffold to inspire the future of regenerative medicine. It holds the secret of how nature has developed such an organization of molecules into a unique functional complexity. This work exploited an innovative image processing algorithm and high resolution microscopy associated with mechanical analysis to establish a correlation between the gradient organization of cartiligous ECM and its anisotropic biomechanical response. This was hypothesized to be a reliable determinant that can elucidate how microarchitecture interrelates with biomechanical properties. Hough-Radon transform of the ECM cross-section images revealed its conformational variation from tangential interface down to subchondral region. As the orientation varied layer by layer, the anisotropic mechanical response deviated relatively. Although, results were in good agreement (Kendall's tau-b > 90%), there were evidences proposing that alignment of the fibrous network, specifically in middle zone, is not as random as it was previously thought.

Discriminating stromatolite formation modes using rare earth element geochemistry: Trapping and binding versus in situ precipitation of stromatolites from the Neoproterozoic Bitter Springs Formation, Northern Territory, Australia

Stromatolites consist primarily of trapped and bound ambient sediment and/or authigenic mineral precipitates, but discrimination of the two constituents is difficult where stromatolites have a fine texture. We used laser ablation-inductively coupled plasma-mass spectrometry to measure trace element (rare earth element – REE, Y and Th) concentrations in both stromatolites (domical and branched) and closely associated particulate carbonate sediment in interspaces (spaces between columns or branches) from bioherms within the Neoproterozoic Bitter Springs Formation, central Australia. Our high resolution sampling allows discrimination of shale-normalised REE patterns between carbonate in stromatolites and immediately adjacent, fine-grained ambient particulate carbonate sediment from interspaces. Whereas all samples show similar negative La and Ce anomalies, positive Gd anomalies and chondritic Y/Ho ratios, the stromatolites and non-stromatolite sediment are distinguishable on the basis of consistently elevated light REEs (LREEs) in the stromatolitic laminae and relatively depleted LREEs in the particulate sediment samples. Additionally, concentrations of the lithophile element Th are higher in ambient sediment samples than in stromatolites, consistent with accumulation of some fine siliciclastic detrital material in the ambient sediment but a near absence in the stromatolites. These findings are consistent with the stromatolites consisting dominantly of in situ carbonate precipitates rather than trapped and bound ambient sediment. Hence, high resolution trace element (REE + Y, Th) geochemistry can discriminate fine-grained carbonates in these stromatolites from coeval non-stromatolitic carbonate sediment and demonstrates that the sampled stromatolites formed primarily from in situ precipitation, presumably within microbial mats/biofilms, rather than by trapping and binding of ambient sediment. Identification of the source of fine carbonate in stromatolites is significant, because if it is not too heavily contaminated by trapped ambient sediment, it may contain geochemical biosignatures and/or direct evidence of the local water chemistry in which the precipitates formed.

A note on a reaction-diffusion model describing the bone morphogen protein gradient in Drosophila embryonic patterning

In this article, we consider the Eldar model [3] from embryology in which a bone morphogenic protein, a short gastrulation protein, and their compound react and diffuse. We carry out a perturbation analysis in the limit of small diffusivity of the bone morphogenic protein. This analysis establishes conditions under which some elementary results of [3] are valid.

A spectroscopic comparison of YBCO superconductors synthesised by solid-state and co-precipitation methods

Raman spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM) have been used to compare samples of YBa2Cu3O7 (YBCO) synthesised by the solid-state method and a novel co-precipitation technique. XRD results indicate that YBCO prepared by these two methods are phase pure, however the Raman and SEM results show marked differences between these samples.

Manufacture of specific BSCCO powder compositions by co-precipitation

A co-precipitation process for large-scale manufacture of bismuth-based HTSC powders has been demonstrated. Powders manufactured by this process have a high phase purity and precisely reproducible stoichiometry. Controlled time and temperature variations are used to convert precursors to HTSC compounds and to obtain specific particle-size distributions. The process has been demonstrated for a variety of compositions in the BSCCO system. Electron microscopy X-ray diffraction, inductively coupled plasma spectroscopy and magnetic-susceptibility measurements are used to characterize the powders.

Calcite precipitation induced by clay-bleach cation exchange in andesitic reservoir rocks

Experiments were carried out on the sodium hypochlorite bleach sensitivity of a deep subsurface andesitic reservoir in order to predict possible deleterious mineral transformations during a downhole clean-up job. Experiments involved examination of core samples from the reservoir using an Environmental Scanning Electron Microscope (ESEM) with an attached Energy Dispersive Spectrometer (EDS) before and after the samples were immersed in bleach. Bleach immersion of whole-rock samples resulted in rapid (less than 1 min) precipitation of abundant 3.0-10.0-μm-wide calcite rhombs within clay-associated micropores and on clay and feldspar grain surfaces. Abundant microporefilling calcite rhombs also formed in pure separates of constituent chlorite/corrensite, whereas no calcite formed in a pure separate of constituent zeolite. These experiments indicate that corrensite is the likely calcium source in this experimental fluid-rock system. Formation of calcite occurs via a cation exchange reaction in which calcium in the smectitic interlayers of corrensite exchanges for sodium in the bleach. Serious formation damage due to calcite precipitation would have occurred in the andesite reservoir had it been exposed to bleach. This finding gives credence to earlier suggestions that cation exchange reactions have the potential to cause calcite precipitation in some sandstone reservoirs when exposed to drilling, completion or stimulation fluids. © 1993.

Modeling the co-precipitation of silica and calcium oxalate in sugar solutions

Solution chemistry plays a significant role in the rate and type of foulant formed on heated industrial surfaces. This paper describes the effect of sucrose, silica (SiO2), Ca2+ and Mg2+ ions, and trans-aconitic acid on the kinetics and solubility of SiO2 and calcium oxalate monohydrate (COM) in mixed salt solutions containing sucrose and refines models previously proposed. The developed SiO2 models show that sucrose and SiO2 concentrations are the main parameters that determine apparent order (n) and apparent rate of reaction (k) and SiO2 solubility over a 24 h period. The calcium oxalate solubility model shows that while increasing [Mg2+] increases COM solubility, the reverse is so with increasing sucrose concentrations. The role of solution species on COM crystal habit is discussed and the appearance of the uncommon (001) face is explained.

An investigation of goethite-seeded Al(OH)3 precipitation using in situ X-ray diffraction and Rietveld-based quantitative phase analysis

An in situ X-ray diffraction investigation of goethite-seeded Al(OH)3 precipitation from synthetic Bayer liquor at 343 K has been performed. The presence of iron oxides and oxyhydroxides in the Bayer process has implications for alumina reversion, which causes significant process losses through unwanted gibbsite precipitation, and is also relevant for the nucleation and growth of scale on mild steel process equipment. The gibbsite, bayerite and nordstrandite polymorphs of Al(OH)3 precipitated from the liquor; gibbsite appeared to precipitate first, with subsequent formation of bayerite and nordstrandite. A Rietveld-based approach to quantitative phase analysis was implemented for the determination of absolute phase abundances as a function of time, from which kinetic information for the formation of the Al(OH)3 phases was determined.

The roles of adsorption in hydrate precipitation

It has been well established that organic compounds with adjacent hydroxyl groups in Bayer process liquor can inhibit gibbsite precipitation by acting as seed poisons. The degree of inhibition is a function of the number and stereochemistry of the hydroxyl groups. Seed poisons generally adsorb strongly onto hydrate surfaces, implying that surface coverage is the mechanism for yield inhibition. There are examples however of organics that strongly adsorb but do not lead to yield inhibition. There is a possibility that this apparent contradiction may be an artifact of differences in conditions between the adsorption and precipitation experiments. The present work investigates the adsorption and inhibition effects of a range of compounds under strictly similar conditions to clarify the role of adsorption on yield inhibition.

Adaptive online gradient descent

We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between [square root T] and [log T]. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.

Child health and the income gradient : evidence from Australia

The positive relationship between household income and child health is well documented in the child health literature but the precise mechanisms via which income generates better health and whether the income gradient is increasing in child age are not well understood. This paper presents new Australian evidence on the child health–income gradient. We use data from the Longitudinal Study of Australian Children (LSAC), which involved two waves of data collection for children born between March 2003 and February 2004 (B-Cohort: 0–3 years), and between March 1999 and February 2000 (K-Cohort: 4–7 years). This data set allows us to test the robustness of some of the findings of the influential studies of Case et al. [Case, A., Lubotsky, D., Paxson, C., 2002. Economic status and health in childhood: the origins of the gradient. The American Economic Review 92 (5) 1308–1344] and Currie and Stabile [Currie, J., Stabile, M., 2003. Socioeconomic status and child health: why is the relationship stronger for older children. The American Economic Review 93 (5) 1813–1823], and a recent study by Currie et al. [Currie, A., Shields, M.A., Price, S.W., 2007. The child health/family income gradient: evidence from England. Journal of Health Economics 26 (2) 213–232]. The richness of the LSAC data set also allows us to conduct further exploration of the determinants of child health. Our results reveal an increasing income gradient by child age using similar covariates to Case et al. [Case, A., Lubotsky, D., Paxson, C., 2002. Economic status and health in childhood: the origins of the gradient. The American Economic Review 92 (5) 1308–1344]. However, the income gradient disappears if we include a rich set of controls. Our results indicate that parental health and, in particular, the mother's health plays a significant role, reducing the income coefficient to zero; suggesting an underlying mechanism that can explain the observed relationship between child health and family income. Overall, our results for Australian children are similar to those produced by Propper et al. [Propper, C., Rigg, J., Burgess, S., 2007. Child health: evidence on the roles of family income and maternal mental health from a UK birth cohort. Health Economics 16 (11) 1245–1269] on their British child cohort.