Principal Component Analysis with Noisy and/or Missing Data

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors are more sensitive to the true underlying signal variations rather than being pulled by heteroskedastic measurement noise. Missing data is simply the limiting case of weight=0. The underlying algorithm is a noise weighted Expectation Maximization (EM) PCA, which has additional benefits of implementation speed and flexibility for smoothing eigenvectors to reduce the noise contribution. We present applications of this method on simulated data and QSO spectra from the Sloan Digital Sky Survey.Comment: Accepted for publication in PASP; v2 with minor updates, mostly to bibliograph

Damage and repair classification in reinforced concrete beams using frequency domain data

This research aims at developing a new vibration-based damage classification technique that can efficiently be applied to a real-time large data. Statistical pattern recognition paradigm is relevant to perform a reliable site-location damage diagnosis system. By adopting such paradigm, the finite element and other inverse models with their intensive computations, corrections and inherent inaccuracies can be avoided. In this research, a two-stage combination between principal component analysis and Karhunen-Loéve transformation (also known as canonical correlation analysis) was proposed as a statistical-based damage classification technique. Vibration measurements from frequency domain were tested as possible damage-sensitive features. The performance of the proposed system was tested and verified on real vibration measurements collected from five laboratory-scale reinforced concrete beams modelled with various ranges of defects. The results of the system helped in distinguishing between normal and damaged patterns in structural vibration data. Most importantly, the system further dissected reasonably each main damage group into subgroups according to their severity of damage. Its efficiency was conclusively proved on data from both frequency response functions and response-only functions. The outcomes of this two-stage system showed a realistic detection and classification and outperform results from the principal component analysis-only. The success of this classification model is substantially tenable because the observed clusters come from well-controlled and known state conditions

Solid-state and solution-phase conformations of pseudoproline-containing dipeptides

The conformations of 14 threonine-derived pseudoproline-containing dipeptides (including four d-allo-Thr derivatives) have been investigated by NMR. In solution, the major conformer observed for all dipeptides is that in which the amide bond between the pseudoproline and the preceding amino acid is cis. For dipeptides in which the N-terminus is protected, the ratio of cis- to trans-conformers does not depend significantly on the side chain of the N-terminal amino acid, or the stereochemistry of the Thr residue. However, for dipeptides bearing a free N-terminus, there are significant differences in the ratios of cis- to trans-conformers depending on the side chain present. Three dipeptides were crystallized and their X-ray structures determined. In two cases, (benzyloxycarbonyl (Cbz)-Val-Thr(ΨMe,Mepro)-OMe and Cbz-Val-Thr(ΨMe,Mepro)-OH), the dipeptides adopt a trans-conformation in the solid state, in contrast to the structures observed in solution. In the third case, (9-fluorenylmethoxycarbonyl (Fmoc)-Val-d-allo-Thr(ΨMe,Mepro)-OH), a cis-amide geometry is observed. These structural differences are attributed to crystal-packing interactions

Mono- and dinucleating Ni(II), Cu(II), Zn(II) and Fe(III) complexes of symmetric and unsymmetric Schiff bases incorporating salicylimine functions - Synthetic and structural studies

The known Schiff base, 3-(2-aminophenylamino)-1-phenylbut-2-en-1-one (1), formed by 1:1 condensation of o-phenylenediamine and benzoylacetylacetone reacts at its free amine site with salicylaldehyde and 5-tert-butylsalicylaldehyde in the presence of Ni(II) and Cu(II) acetates, or with 5-tert-butylsalicylaldehyde in the presence of Zn(II) acetate, to generate 1:1 (M:L) diimine complexes (2) of the corresponding doubly deprotonated, unsymmetric, O2N 2-tetradentate ligands. In contrast, reaction of Zn(II) acetate with 1 and salicylaldehyde led to Schiff base exchange (with loss of benzoylacetylacetone) to yield symmetric [ZnL3] [where L3 is N,N′-o-phenylenebis(salicyliminato)]. Similarly, when Fe(II) chloride was substituted for metal acetate in the reaction of 1 with 5-tert-butyl- salicylaldehyde and the initial product crystallised in the presence of dabco (as base), a related Schiff base exchange reaction occurred along with aerial oxidation of the Fe(II) to produce the neutral dinuclear [Fe III(L4)2(μ-O)] species [where L4 is N,N′-o-phenylenebis(5-tert-butylsalicyliminato)] in which Fe(III) centres are linked by an oxo group to produce two 5-coordinate Fe(III) centres; pairs of these (oxo-bridged) dinuclear complex units are further linked via elongated intermolecular Fe-Ophenolic contacts (Fe-O, 2.44 Å) to form an unusual tetranuclear supramolecular cluster. This complex was also synthesised directly by the in situ reaction of 5-tert-butyl-salicylaldehyde, o-phenylenediamine and Fe(II) chloride (2:1:1 mol ratio) in air. In an extension of these studies, the in situ reaction of the 1,3-aryl linked bis-β-diketone, 1,1-(1,3-phenylene)-bis-butane-1,3-dione), o-phenylenediamine, salicylaldehyde and Ni(II) acetate in a 1:2:2:2 ratio yielded [Ni2L5], the dinuclear analogue of the unsymmetric mononuclear Ni(II) complex 2, in which each nickel centre has a square planar environment. Reaction of the above 1,3-phenylene linked bis-β-diketone precursor with o-phenylenediamine in a 1:2 M ratio yields 1,3-bis(4-methyl-3H- benzo[b][1,4]diazepin-2-yl)benzene as its monohydrate (3·H2O) incorporating two 7-membered diaza heterocyclic rings; thus contrasting with the 'open' Schiff base structure observed for 1. X-ray structures of 1, 3·H2O, [NiL1]·py, [NiL1] ·EtOH, [NiL2], [CuL1]·py, [CuL 1]·0.5CHCl3, [(FeL4)2(μ-O) ]2·1.5THF·0.4EtOH·0.6H2O and [NiL5]·0.25EtOH·0.125py are reported

Sparse Exploratory Factor Analysis

Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction. We revisit the most popular procedures for exploratory factor analysis, maximum likelihood and least squares. Sparse factor loadings are obtained for them by, first, adopting a special reparameterization and, second, by introducing additional [Formula: see text]-norm penalties into the standard factor analysis problems. As a result, we propose sparse versions of the major factor analysis procedures. We illustrate the developed algorithms on well-known psychometric problems. Our sparse solutions are critically compared to ones obtained by other existing methods

Sparsest factor analysis for clustering variables: a matrix decomposition approach

We propose a new procedure for sparse factor analysis (FA) such that each variable loads only one common factor. Thus, the loading matrix has a single nonzero element in each row and zeros elsewhere. Such a loading matrix is the sparsest possible for certain number of variables and common factors. For this reason, the proposed method is named sparsest FA (SSFA). It may also be called FA-based variable clustering, since the variables loading the same common factor can be classified into a cluster. In SSFA, all model parts of FA (common factors, their correlations, loadings, unique factors, and unique variances) are treated as fixed unknown parameter matrices and their least squares function is minimized through specific data matrix decomposition. A useful feature of the algorithm is that the matrix of common factor scores is re-parameterized using QR decomposition in order to efficiently estimate factor correlations. A simulation study shows that the proposed procedure can exactly identify the true sparsest models. Real data examples demonstrate the usefulness of the variable clustering performed by SSFA

Data-adaptive harmonic spectra and multilayer Stuart-Landau models

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled---provided the decay of temporal correlations is sufficiently well-resolved---within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.Comment: 26 pages, double columns; 15 figure

Learning a Factor Model via Regularized PCA

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those produced by pre-existing factor analysis approaches. We also establish theoretical results that explain how our algorithm corrects the biases induced by conventional approaches. An important feature of our algorithm is that its computational requirements are similar to those of PCA, which enjoys wide use in large part due to its efficiency

Amino-terminal dimerization of an erythropoietin mimetic peptide results in increased erythropoietic activity

AbstractBackground: Erythropoietin (EPO), the hormone involved in red blood cell production, activates its receptor by binding to the receptor's extracellular domain and presumably dimerizing two receptor monomers to initiate signal transduction. EPO-mimetic peptides, such as EMP1, also bind and activate the receptor by dimerization. These mimetic peptides are not as potent as EPO, however. The crystal structure of the EPO receptor (EBP) bound to EMP1 reveals the formation of a complex consisting of two peptides bound to two receptors, so we sought to improve the biological activity of EPO-mimetic peptides by constructing covalent dimers of EMP1 and other peptide mimetics linked by polyethylene glycol (PEG).Results: The potency of the PEG-dimerized EPO peptide mimetics both in vitro and in vivo was improved up to 1,000-fold compared to the corresponding peptide monomers. The dinners were constructed using peptide monomers which have only one reactive amine per molecule, allowing us to conclude that the increase in potency can be attributed to a structure in which two peptides are linked through their respective amino termini to the difunctional PEG molecule. In addition, an inactive peptide was converted into a weak agonist by PEG-induced dimerization.Conclusions: The potency of previously isolated peptides that are modest agonists of the EPO receptor was dramatically increased by PEG-induced dimerization. The EPO receptor is thought to be dimerized during activation, so our results are consistent with the proposed 2:2 receptor : peptide stoichiometry. The conversion of an inactive peptide into an agonist further supports the idea that dimerization can mediate receptor activation

Thiosquaramides: pH switchable anion transporters

The transport of anions across cellular membranes is an important biological function governed by specialised proteins. In recent years, many small molecules have emerged that mimick the anion transport behaviour of these proteins, but only a few of these synthetic molecules also display the gating/switching behaviour seen in biological systems. A small series of thiosquar-amides was synthesised and their pH-dependent chloride binding and anion transport behaviour was investigated using 1H NMR titrations, single crystal X-ray diffraction and a variety of vesicle-based techniques. Spectrophotometric titrations and DFT calculations revealed that the thiosquaramides are significantly more acidic than their oxosquaramide analogues, with pKa values between 4.0 and 9.0. This led to the observation that at pH 7.2 the anion transport ability of the thiosquaramides is fully switched OFF due to deprotonation of the receptor, but is completely switched ON at lower pH