A study of singular spectrum analysis with global optimization techniques

Singular spectrum analysis has recently become an attractive tool in a broad range of applications. Its main mechanism of alternating between rank reduction and Hankel projection to produce an approximation to a particular component of the original time series, however, deserves further mathematical justification. One paramount question to ask is how good an approximation that such a straightforward apparatus can provide when comparing to the absolute optimal solution. This paper reexamines this issue by exploiting a natural parametrization of a general Hankel matrix via its Vandermonde factorization. Such a formulation makes it possible to recast the notion of singular spectrum analysis as a semi-linear least squares problem over a compact feasible set, whence global optimization techniques can be employed to find the absolute best approximation. This framework might not be immediately suitable for practical application because global optimization is expectedly more expensive, but it does provide a theoretical baseline for comparison. As such, our empirical results indicate that the simpler SSA algorithm usually is amazingly sufficient as a handy tool for constructing exploratory model. The more complicated global methods could be used as an alternative of rigorous affirmative procedure for verifying or assessing the quality of approximation.     

In situ Synthesis of Oligonucleotide Arrays on Surfaces Coated with Crosslinked Polymer Multilayers

We report an approach to the in situ synthesis of oligonucleotide arrays on surfaces coated with crosslinked polymer multilayers. Our approach makes use of methods for the 'reactive' layer-by-layer assembly of thin, amine-reactive multilayers using branched polyethyleneimine (PEI) and the azlactone-functionalized polymer poly(2-vinyl-4,4'-dimethylazlactone) (PVDMA). Post-fabrication treatment of film-coated glass substrates with d-glucamine or 4-amino-1-butanol yielded hydroxyl-functionalized films suitable for the Maskless Array Synthesis (MAS) of oligonucleotide arrays. Glucamine-functionalized films yielded arrays of oligonucleotides with fluorescence intensities and signal-to-noise ratios (after hybridization with fluorescently labeled complementary strands) comparable to those of arrays fabricated on conventional silanized glass substrates. These arrays could be exposed to multiple hybridization-dehybridization cycles with only moderate loss of hybridization density. The versatility of the layer-by-layer approach also permitted synthesis directly on thin sheets of film-coated poly(ethylene terephthalate) (PET) to yield flexible oligonucleotide arrays that could be readily manipulated (e.g., bent) and cut into smaller arrays. To our knowledge, this work presents the first use of polymer multilayers as a substrate for the multi-step synthesis of complex molecules. Our results demonstrate that these films are robust and able to withstand the ~450 individual chemical processing steps associated with MAS (as well as manipulations required to hybridize, image, and dehybridize the arrays) without large-scale cracking, peeling, or delamination of the thin films. The combination of layer-by-layer assembly and MAS provides a means of fabricating functional oligonucleotide arrays on a range of different materials and substrates. This approach may also prove useful for the fabrication of supports for the solid-phase synthesis and screening of other macromolecular or small-molecule agents.     

Generating and routing light-bullets using slab waveguide arrays

Light-bullet routing and control is theoretically demonstrated in a slab waveguide architecture using a fully addressable electronic current injection mechanism for gain control. By exploiting gain mediated interactions between bullets, photonic NAND and NOR logic gates are produced on the same chip design. The robustness, simplicity, and control offered by light-bullets in slab waveguide architectures suggest that such devices should be seriously considered as candidates for technological development.

     

Comparison of RAFT‐derived poly(vinylpyrrolidone) verses poly(oligoethyleneglycol methacrylate) for the stabilization of glycosylated gold nanoparticles

Carbohydrates dictate many biological processes including infection by pathogens. Glycosylated polymers and nanomaterials which have increased affinity due to the cluster glycoside effect, are therefore useful tools to probe function, but also as prophylactic therapies or diagnostic tools. Here, the effect of polymer structure on the coating of gold nanoparticles is studied in the context of grafting density, buffer stability, and in a lectin binding assay. RAFT polymerization is used to generate poly(oligoethyleneglycol methacrylates) and poly(N‐vinylpyrrolidones) with a thiol end‐group for subsequent immobilization onto the gold. It is observed that poly(oligoethylene glycol methacrylates), despite being widely used particle coatings, lead to low grafting densities which in turn resulted in lower stability in biological buffers. A depression of the cloud point upon nanoparticle immobilization is also seen, which might compromise performance. In comparison poly(vinylpyrrolidones) resulted in stable particles with higher grafting densities due to the compact size of each monomer unit. The higher grafting density also enabled an increase in the number of carbohydrates which can be installed per nanoparticle at the chain ends, and gave increased binding in a lectin recognition assay. These results will guide the development of new nanoparticle biosensors with enhanced specificity, affinity, and stability. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 55, 1200–1208