Nano-mineralogy Studies by Advanced Electron Microscopy

Extended abstract of a paper presented at Microscopy and Microanalysis 2007 in Ft. Lauderdale, Florida, USA, August 5 – August 9, 2007

Davisite, CaScAlSiO_6, a new pyroxene from the Allende meteorite

Davisite, ideally CaScAlSiO_6, is a new member of the Ca clinopyroxene group, where Sc^(3+) is dominant in the M1 site. It occurs as micro-sized crystals along with perovskite and spinel in an ultra-refractory inclusion from the Allende meteorite. The mean chemical composition determined by electron microprobe analysis is (wt%) SiO_2 26.24, CaO 23.55, Al_2O_3 21.05, Sc_2O_3 14.70, TiO_2 (total) 8.66, MgO 2.82, ZrO_2 2.00, Y_2O_3 0.56, V_2O_3 0.55, FeO 0.30, Dy_2O_3 0.27, Gd_2O_3 0.13, Er_2O_3 0.08, sum 100.91. Its empirical formula calculated on the basis of 6 O atoms is Ca_(0.99)(Sc_(0.50)Ti^(3+)0.16^(Mg)0.16Ti^(4+)0.10 Zr_(0.04)V^(3+)_(0.02)Fe^(2+)_(0.01)Y_(0.01))_(∑1.00)(Si_(1.03)Al_(0.97))_(∑2).00O_6. Davisite is monoclinic, C2/c; a = 9.884 Å, b = 8.988 Å, c = 5.446 Å, β =105.86°, V = 465.39 Å^3, and Z = 4. Its electron back-scattered diffraction pattern is an excellent match to that of synthetic CaScAlSiO6 with the C2/c structure. The strongest calculated X-ray powder diffraction lines are [d spacing in Å (I) (hkl)]: 3.039 (100) (221), 2.989 (31) (310), 2.943 (18) (311), 2.619 (40) (002), 2.600 (26) (131), 2.564 (47) (221), 2.159 (18) (331), 2.137 (15) (421), 1.676 (20) (223), and 1.444 (18) (531). The name is for Andrew M. Davis, a cosmochemist at the University of Chicago, Illinois

Transforming Bell's Inequalities into State Classifiers with Machine Learning

Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to determine if a given quantum state is entangled or not. However, the process of a complete characterization of quantum states, known as quantum state tomography, is a resource-consuming operation in general. An attractive proposal would be the use of Bell's inequalities as an entanglement witness, where only partial information of the quantum state is needed. The problem is that entanglement is necessary but not sufficient for violating Bell's inequalities, making it an unreliable state classifier. Here we aim at solving this problem by the methods of machine learning. More precisely, given a family of quantum states, we randomly picked a subset of it to construct a quantum-state classifier, accepting only partial information of each quantum state. Our results indicated that these transformed Bell-type inequalities can perform significantly better than the original Bell's inequalities in classifying entangled states. We further extended our analysis to three-qubit and four-qubit systems, performing classification of quantum states into multiple species. These results demonstrate how the tools in machine learning can be applied to solving problems in quantum information science

Numerical study of fluid flow, mass transfer and cell growth in a three-dimensional bioreactor for bone marrow culture

Imperial Users onl

Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often require proper regularization (e.g. trimming, regularized cost, projection) in order to guarantee fast convergence. For vanilla procedures such as gradient descent, however, prior theory either recommends highly conservative learning rates to avoid overshooting, or completely lacks performance guarantees. This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models. In fact, gradient descent follows a trajectory staying within a basin that enjoys nice geometry, consisting of points incoherent with the sampling mechanism. This "implicit regularization" feature allows gradient descent to proceed in a far more aggressive fashion without overshooting, which in turn results in substantial computational savings. Focusing on three fundamental statistical estimation problems, i.e. phase retrieval, low-rank matrix completion, and blind deconvolution, we establish that gradient descent achieves near-optimal statistical and computational guarantees without explicit regularization. In particular, by marrying statistical modeling with generic optimization theory, we develop a general recipe for analyzing the trajectories of iterative algorithms via a leave-one-out perturbation argument. As a byproduct, for noisy matrix completion, we demonstrate that gradient descent achieves near-optimal error control --- measured entrywise and by the spectral norm --- which might be of independent interest.Comment: accepted to Foundations of Computational Mathematics (FOCM

Discovery of meteoritic baghdadite, Ca_3(Zr,Ti)Si_2O_9, in Allende: The first solar silicate with structurally essential zirconium?

During an ongoing nanomineralogy investigation of the Allende CV3 carbonaceous chondrite, baghdadite, Ca_3(Zr,Ti)Si_2O_9, has been identified in a V-rich, fluffy Type A Ca-Al-rich refractory inclusion (CAI), AWP1, in USNM 7617. Reported here is the first meteoritic occurrence of baghdadite, as an ultra-refractory silicate mineral in a CAI from a primitive meteorite, among the first solid materials formed in the solar system. Field-emission scanning electron microscope (SEM), energy-dispersive X-ray spectroscopy (EDS), electron back-scatter diffraction (EBSD) and electron probe microanalyzer (EPMA) were used to characterize baghdadite and associated phases. Three new minerals burnettite (IMA 2013-054; CaV^(3+)AlSiO_6), paqueite (IMA 2013-053; Ca_3TiSi_2(Al_2Ti)O_(14)) and beckettite (IMA 2015-001; Ca2V^(3+)_6Al_6O_(20)), were also discovered in A-WP1 [1-4]

Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy

We analyze the correlation properties of the Erdos-Renyi random graph (RG) and the Barabasi-Albert scale-free network (SF) under the attack and repair strategy with detrended fluctuation analysis (DFA). The maximum degree k_max, representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability p_re. The average degree , revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of p_re.Comment: 5 pages, 4 figure