State estimation schemes for independent component coupled hidden Markov models

Conventional Hidden Markov models generally consist of a Markov chain observed through a linear map corrupted by additive noise. This general class of model has enjoyed a huge and diverse range of applications, for example, speech processing, biomedical signal processing and more recently quantitative finance. However, a lesser known extension of this general class of model is the so-called Factorial Hidden Markov Model (FHMM). FHMMs also have diverse applications, notably in machine learning, artificial intelligence and speech recognition [13, 17]. FHMMs extend the usual class of HMMs, by supposing the partially observed state process is a finite collection of distinct Markov chains, either statistically independent or dependent. There is also considerable current activity in applying collections of partially observed Markov chains to complex action recognition problems, see, for example, [6]. In this article we consider the Maximum Likelihood (ML) parameter estimation problem for FHMMs. Much of the extant literature concerning this problem presents parameter estimation schemes based on full data log-likelihood EM algorithms. This approach can be slow to converge and often imposes heavy demands on computer memory. The latter point is particularly relevant for the class of FHMMs where state space dimensions are relatively large. The contribution in this article is to develop new recursive formulae for a filter-based EM algorithm that can be implemented online. Our new formulae are equivalent ML estimators, however, these formulae are purely recursive and so, significantly reduce numerical complexity and memory requirements. A computer simulation is included to demonstrate the performance of our results. © Taylor & Francis Group, LLC.

Generalized power method for sparse principal component analysis

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, and are therefore computationally intractable, we rewrite them into the form of an optimization program involving maximization of a convex function on a compact set. The dimension of the search space is decreased enormously if the data matrix has many more columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It appears that our algorithm has best convergence properties in the case when either the objective function or the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced in the block case. Finally, we demonstrate numerically on a set of random and gene expression test problems that our approach outperforms existing algorithms both in quality of the obtained solution and in computational speed. © 2010 Michel Journée, Yurii Nesterov, Peter Richtárik and Rodolphe Sepulchre.

Optimization on the orthogonal group for independent component analysis

This paper derives a new algorithm that performs independent component analysis (ICA) by optimizing the contrast function of the RADICAL algorithm. The core idea of the proposed optimization method is to combine the global search of a good initial condition with a gradient-descent algorithm. This new ICA algorithm performs faster than the RADICAL algorithm (based on Jacobi rotations) while still preserving, and even enhancing, the strong robustness properties that result from its contrast. © Springer-Verlag Berlin Heidelberg 2007.

Geometric optimization methods for independent component analysis applied on gene expression data

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent Component Analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality- because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm. © 2007 IEEE.

Component level strategies for exploiting the lifespan of steel in products

Approximately 40% of annual demand for steel worldwide is used to replace products that have failed. With this percentage set to rise, extending the lifespan of steel in products presents a significant opportunity to reduce demand and thus decrease carbon dioxide emissions from steel production. This article presents a new, simplified framework with which to analyse product failure. When applied to the products that dominate steel use, this framework reveals that they are often replaced because a component/sub-assembly becomes degraded, inferior, unsuitable or worthless. In light of this, four products, which are representative of high steel content products in general, are analysed at the component level, determining steel mass and cost profiles over the lifespan of each product. The results show that the majority of the steel components are underexploited - still functioning when the product is discarded; in particular, the potential lifespan of the steel-rich structure is typically much greater than its actual lifespan. Twelve case studies, in which product or component life has been increased, are then presented. The resulting evidence is used to tailor life-extension strategies to each reason for product failure and to identify the economic motivations for implementing these strategies. The results suggest that a product template in which the long-lived structure accounts for a relatively high share of costs while short-lived components can be easily replaced (offering profit to the producer and enhanced utility to owners) encourages product life extension. © 2013 The Author.

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.

Molecular cloning, promoter analysis and induced expression of the complement component C9 gene in the grass carp Ctenopharyngodon idella

Complement-mediated killing of pathogens through lytic pathway is an important effector mechanism of innate immune response. C9 is the ninth member of complement components, creating the membrane attack complex (MAC). In the present study, a putative cDNA sequence encoding the 650 amino acids of C9 and its genomic organization were identified in grass carp Ctenopharyngodon idella. The deduced amino acid sequence of grass carp C9 (gcC9) showed 48% and 38.5% identity to Japanese flounder and human C9, respectively. Domain search revealed that gcC9 contains a LDL receptor domain, an EGF precursor domain, a MACPF domain and two TSP domain located in the N-terminal and C-terminal, respectively. Phylogenetic analysis demonstrated that gcC9 is clustered in a same clade with Japanese flounder, pufferfish and rainbow trout C9. The gcC9 gene consists of 11 exons with 10 introns, spacing over approximately 7 kb of genomic sequence. Analysis of gcC9 promoter region revealed the presence of a TATA box and some putative transcription factor such as C/EBP, HSF, NF-AT, CHOP-C, HNF-3B, GATA-2, IK-2, EVI- 1, AP-1, CP2 and OCT-1 binding sites. The first intron region contains C/EBPb, HFH-1 and Oct-1 binding sites. RT-PCR and Western blotting analysis demonstrated that the mRNA and protein of gcC9 gene have similar expression patterns, being constitutively expressed in all organs examined of healthy fish, with the highest level in hepatopancreas. By real-time quantitative RT-PCR analysis, gcC9 transcripts were significantly up-regulated in head kidney, spleen, hepatopancreas and down-regulated in intestine from inactivated fish bacterial pathogen Flavobacterium columnare-stimulated fish, demonstrating the role of C9 in immune response. (c) 2007 Elsevier B.V. All rights reserved.

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.

alr0117, a two-component histidine kinase gene, is involved in heterocyst development in Anabaena sp PCC 7120

Anabaena sp. PCC; 7120 was mutagenized by transposon Tn5-1087b, generating a mutant whose heterocysts lack the envelope polysaccharide layer. The transposon was located between nucleotides 342 and 343 of alr0117, a 918 bp gene encoding a histidine kinase for a two-component regulatory system. Complementation of the mutant with a DNA fragment containing alr0117 and targeted inactivation of the gene confirmed that alr0117 is involved in heterocyst development. RT-PCR showed that alr0117 was constitutively expressed in the presence or absence of a combined-nitrogen source. hepA and patB, the two genes turned on during wild-type heterocyst development, were no longer activated in an alr0117-null mutant. The two-component signal transduction system involving alr0117 may control the formation of the envelope polysaccharide layer and certain late events essential to the function of heterocysts.

Second-harmonic generation of Bogoliubov excitations in a two-component Bose-Einstein condensate

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.

The quantum tunnelling between two-component Bose-Einstein condensates in a double-well configuration

We examine in terms of exact solutions of the time-dependent Schrodinger equation, the quantum tunnelling process in Bose-Einstein condensates of two interacting species trapped in a double well configuration. Based on the two series of time-dependent SU(2) gauge transformations, we diagonalize the Hamilton operator and obtain analytic time-evolution formulas of the population imbalance and the berry phase. the particle population imbalance (a(L)(+)aL - a(R)(+)a(R)) of species A between the two wells is studied analytically.

The quantum tunneling between two-component Bose-Einstein condensates in a double-well configuration

In terms of exact solution of the time-dependent Schrodinger equation. we examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We use the two series of time-dependent SU(2) gauge transformation to diagonalize the Hamilton operator obtain analytic time-evolution formulas of the population imbalance and the berry phase. The particle population imbalance (a(L)(+)a(L) - a(R)(+)a(R)) of species A between the two wells is studied analytically.