Randomized nonlinear component analysis

Copyright © (2014) by the International Machine Learning Society (IMLS) All rights reserved. Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear re-lationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real- world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.

Viscoelastic analysis of single-component and composite PEG and alginate hydrogels

Hydrogels, three-dimensional hydrophilic polymer networks, are appealing candidate materials for studying the cellular microenvironment as their substantial water content helps to better mimic soft tissue. However, hydrogels can lack mechanical stiffness, strength, and toughness. Composite hydrogel systems have been shown to improve upon mechanical properties compared to their singlecomponent counterparts. Poly (ethylene glycol) dimethacrylate (PEGDMA) and alginate are polymers that have been used to form hydrogels for biological applications. Singlecomponent and composite PEGDMA and alginate systems were fabricated with a range of total polymer concentrations. Bulk gels were mechanically characterized using spherical indentation testing and a viscoelastic analysis framework. An increase in shear modulus with increasing polymer concentration was demonstrated for all systems. Alginate hydrogels were shown to have a smaller viscoelastic ratio than the PEGDMA gels, indicating more extensive relaxation over time. Composite alginate and PEGDMA hydrogels exhibited a combination of the mechanical properties of the constituents, as well as a qualitative increase in toughness. Additionally, multiple hydrogel systems were produced that had similar shear moduli, but different viscoelastic behaviors. Accurate measurement of the mechanical properties of hydrogels is necessary in order to determine what parameters are key in modeling the cellular microenvironment. © 2014 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.

A novel method of extraction of blend component structure from SANS measurements of homopolymer bimodal blends

A new method is presented for the extraction of single-chain form factors and interchain interference functions from a range of small-angle neutron scattering (SANS) experiments on bimodal homopolymer blends. The method requires a minimum of three blends, made up of hydrogenated and deuterated components with matched degree of polymerization at two different chain lengths, but with carefully varying deuteration levels. The method is validated through an experimental study on polystyrene homopolymer bimodal blends with M A≈1/2MB. By fitting Debye functions to the structure factors, it is shown that there is good agreement between the molar mass of the components obtained from SANS and from chromatography. The extraction method also enables, for the first time, interchain scattering functions to be produced for scattering between chains of different lengths. © 2014 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.