Computationally efficient algorithms for the two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2^d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n^2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Omega(n^2.lg(n)), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test

Combinatorial synthesis of oxysulfides in the lanthanum-bismuth-copper system

Establishing synthesis methods for a target material constitutes a grand challenge in materials research, which is compounded with use-inspired specifications on the format of the material. Solar photochemistry using thin film materials is a promising technology for which many complex materials are being proposed, and the present work describes application of combinatorial methods to explore the synthesis of predicted La–Bi–Cu oxysulfide photocathodes, in particular alloys of LaCuOS and BiCuOS. The variation in concentration of three cations and two anions in thin film materials, and crystallization thereof, is achieved by a combination of reactive sputtering and thermal processes including reactive annealing and rapid thermal processing. Composition and structural characterization establish composition-processing-structure relationships that highlight the breadth of processing conditions required for synthesis of LaCuOS and BiCuOS. The relative irreducibility of La oxides and limited diffusion indicate the need for high temperature processing, which conflicts with the temperature limits for mitigating evaporation of Bi and S. Collectively the results indicate that alloys of these phases will require reactive annealing protocols that are uniquely tailored to each composition, motivating advancement of dynamic processing capabilities to further automate discovery of synthesis routes

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Sharp lines in the absorption edge of EuTe and Pb0.1_{0.1}Eu0.9_{0.9}Te in high magnetic fields

The optical absorption spectra in the region of the \fd transition energies of epitaxial layers of of EuTe and \PbEuTe, grown by molecular beam epitaxy, were studied using circularly polarized light, in the Faraday configuration. Under \sigmam polarization a sharp symmetric absorption line (full width at half-maximum 0.041 eV) emerges at the low energy side of the band-edge absorption, for magnetic fields intensities greater than 6 T. The absorption line shows a huge red shift (35 meV/T) with increasing magnetic fields. The peak position of the absorption line as a function of magnetic field is dominated by the {\em d-f} exchange interaction of the excited electron and the \Euion spins in the lattice. The {\em d-f} exchange interaction energy was estimated to be $J_{df}S=0.15\pm 0.01$ eV. In \PbEuTe the same absorption line is detected, but it is broader, due to alloy disorder, indicating that the excitation is localized within a finite radius. From a comparison of the absorption spectra in EuTe and \PbEuTe the characteristic radius of the excitation is estimated to be $\sim 10$\AA.Comment: Journal of Physics: Condensed Matter (2004, at press

The enhancement of ferromagnetism in uniaxially stressed diluted magnetic semiconductors

We predict a new mechanism of enhancement of ferromagnetic phase transition temperature $T_c$ in uniaxially stressed diluted magnetic semiconductors (DMS) of p-type. Our prediction is based on comparative studies of both Heisenberg (inherent to undistorted DMS with cubic lattice) and Ising (which can be applied to strongly enough stressed DMS) models in a random field approximation permitting to take into account the spatial inhomogeneity of spin-spin interaction. Our calculations of phase diagrams show that area of parameters for existence of DMS-ferromagnetism in Ising model is much larger than that in Heisenberg model.Comment: Accepted for publication in Phys. Rev.

Analyzing machine learning models to accelerate generation of fundamental materials insights

Machine learning for materials science envisions the acceleration of basic science research through automated identification of key data relationships to augment human interpretation and gain scientific understanding. A primary role of scientists is extraction of fundamental knowledge from data, and we demonstrate that this extraction can be accelerated using neural networks via analysis of the trained data model itself rather than its application as a prediction tool. Convolutional neural networks excel at modeling complex data relationships in multi-dimensional parameter spaces, such as that mapped by a combinatorial materials science experiment. Measuring a performance metric in a given materials space provides direct information about (locally) optimal materials but not the underlying materials science that gives rise to the variation in performance. By building a model that predicts performance (in this case photoelectrochemical power generation of a solar fuels photoanode) from materials parameters (in this case composition and Raman signal), subsequent analysis of gradients in the trained model reveals key data relationships that are not readily identified by human inspection or traditional statistical analyses. Human interpretation of these key relationships produces the desired fundamental understanding, demonstrating a framework in which machine learning accelerates data interpretation by leveraging the expertize of the human scientist. We also demonstrate the use of neural network gradient analysis to automate prediction of the directions in parameter space, such as the addition of specific alloying elements, that may increase performance by moving beyond the confines of existing data

Bi Alloying into Rare Earth Double Perovskites Enhances Synthesizability and Visible Light Absorption

A high throughput combinatorial synthesis utilizing inkjet printing of precursor inks was used to rapidly evaluate Bi-alloying into double perovskite oxides for enhanced visible light absorption. The fast visual screening of photo image scans of the library plates identifies 4-metal oxide compositions displaying an increase in light absorption, which subsequent UV–vis spectroscopy indicates is due to bandgap reduction. Structural characterization by X-ray diffraction (XRD) and Raman spectroscopy demonstrates that the visually darker composition range contains Bi-alloyed Sm₂MnNiO₆ (double perovskite structure), of the form (Bi,Sm)₂MnNiO₆. Bi alloying not only increases the visible absorption but also facilitates crystallization of this structure at the relatively low annealing temperature of 615 °C. Investigation of additional seven combinations of a rare earth (RE) and a transition metal (TM) with Bi and Mn indicates that Bi-alloying on the RE site occurs with similar effect in the family of rare earth oxide double perovskites

Enhanced Bulk Transport in Copper Vanadate Photoanodes Identified by Combinatorial Alloying

The impact of alloying on the performance of β-Cu₂V₂O₇ photoanodes was investigated using inkjet printing of composition libraries containing 1,809 Cu₂V₂O₇-based photoanodes. Six elements (Zr, Ca, Hf, Gd, La, and Lu) were alloyed and pairwise co-alloyed at concentrations up to 7 at % into Cu-rich, stoichiometric, and Cu-deficient host Cu₂V₂O₇. A 1.7-fold increase in oxygen evolution photocurrent in pH 9.2 electrolyte was obtained by alloying Ca into β-Cu₂V₂O₇. Experiments employing a hole scavenger to better characterize bulk charge separation and transport revealed a 2.2-fold increase in photoactivity via alloying with Hf, Zr, and La, which increased to 2.7-fold upon co-alloying these elements with Ca. Concurrent with increased photoactivity is substantially decreased photon absorption between 1.5 and 2 eV, a range reported to coincide with high exciton absorption in β-Cu₂V₂O₇, motivating further exploration of whether these co-alloy compositions may destabilize the excitonic state that appears to have limited performance to date