Validation of nonlinear PCA

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an independent test set, fail when applied to nonlinear PCA because of its inherent unsupervised characteristics. This paper presents a new approach for validating the complexity of nonlinear PCA models by using the error in missing data estimation as a criterion for model selection. It is motivated by the idea that only the model of optimal complexity is able to predict missing values with the highest accuracy. While standard test set validation usually favours over-fitted nonlinear PCA models, the proposed model validation approach correctly selects the optimal model complexity.Comment: 12 pages, 5 figure

Photoacid behaviour in a fluorinated green fluorescent protein chromophore:Ultrafast formation of anion and zwitterion states

The photophysics of the chromophore of the green fluorescent protein in Aequorea victoria (avGFP) are dominated by an excited state proton transfer reaction. In contrast the photophysics of the same chromophore in solution are dominated by radiationless decay, and photoacid behaviour is not observed. Here we show that modification of the pKa of the chromophore by fluorination leads to an excited state proton transfer on an extremely fast (50 fs) time scale. Such a fast rate suggests a barrierless proton transfer and the existence of a pre-formed acceptor site in the aqueous solution, which is supported by solvent and deuterium isotope effects. In addition, at lower pH, photochemical formation of the elusive zwitterion of the GFP chromophore is observed by means of an equally fast excited state proton transfer from the cation. The significance of these results for understanding and modifying the properties of fluorescent proteins are discusse

Coffee consumption and prostate cancer risk: further evidence for inverse relationship

<p>Abstract</p> <p>Background</p> <p>Higher consumption of coffee intake has recently been linked with reduced risk of aggressive prostate cancer (PC) incidence, although meta-analysis of other studies that examine the association between coffee consumption and overall PC risk remains inconclusive. Only one recent study investigated the association between coffee intake and grade-specific incidence of PC, further evidence is required to understand the aetiology of aggressive PCs. Therefore, we conducted a prospective study to examine the relationship between coffee intake and overall as well as grade-specific PC risk.</p> <p>Methods</p> <p>We conducted a prospective cohort study of 6017 men who were enrolled in the Collaborative cohort study in the UK between 1970 and 1973 and followed up to 31st December 2007. Cox Proportional Hazards Models were used to evaluate the association between coffee consumption and overall, as well as Gleason grade-specific, PC incidence.</p> <p>Results</p> <p>Higher coffee consumption was inversely associated with risk of high grade but not with overall risk of PC. Men consuming 3 or more cups of coffee per day experienced 55% lower risk of high Gleason grade disease compared with non-coffee drinkers in analysis adjusted for age and social class (HR 0.45, 95% CI 0.23-0.90, p value for trend 0.01). This association changed a little after additional adjustment for Body Mass Index, smoking, cholesterol level, systolic blood pressure, tea intake and alcohol consumption.</p> <p>Conclusion</p> <p>Coffee consumption reduces the risk of aggressive PC but not the overall risk.</p

Expected Shannon entropy and Shannon differentiation between subpopulations for neutral genes under the finite island model

<div><p>Shannon entropy <i>H</i> and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information (“Shannon differentiation”) between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (<i>Sturnus vulgaris</i>) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.</p></div

Dispersion engineered Ge11.5As24Se64.5 nanowire for supercontinuum generation: A parametric study

A promising design of Ge11.5As24Se64.5 nanowires for supercontinuum generation is proposed through numerical simulations. It can be used for generating a supercontinuum with 1300-nm bandwidth. The dispersion parameters upto eighth-order are obtained by calculating the effective mode index with the finite-element method. We have investigated dispersion curves for a number of nanowire geometries. Through dispersion engineering and by varying dimensions of the nanowires we have identified a promising structure that shows possibility of realizing a wideband supercontinuum. We have found significant variations in its bandwidth with the inclusion of higher-order dispersion coefficients and indicated the possibility of obtaining spurious results if the adequate number of dispersion coefficients is not considered. To confirm the accuracy of dispersion coefficients obtained through numerical computations, we have shown that a data-fitting procedure based on the Taylor series expansion provides good agreement with the actual group velocity dispersion curve obtained by using a full-vectorial finite-element mode-solver

Focusing and Compression of Ultrashort Pulses through Scattering Media

Light scattering in inhomogeneous media induces wavefront distortions which pose an inherent limitation in many optical applications. Examples range from microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible by wavefront shaping techniques. However, when ultrashort pulses are employed scattering induces temporal distortions which hinder their use in nonlinear processes such as in multiphoton microscopy and quantum control experiments. Here we show that correction of both spatial and temporal distortions can be attained by manipulating only the spatial degrees of freedom of the incident wavefront. Moreover, by optimizing a nonlinear signal the refocused pulse can be shorter than the input pulse. We demonstrate focusing of 100fs pulses through a 1mm thick brain tissue, and 1000-fold enhancement of a localized two-photon fluorescence signal. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media

Robotic Wireless Sensor Networks

In this chapter, we present a literature survey of an emerging, cutting-edge, and multi-disciplinary field of research at the intersection of Robotics and Wireless Sensor Networks (WSN) which we refer to as Robotic Wireless Sensor Networks (RWSN). We define a RWSN as an autonomous networked multi-robot system that aims to achieve certain sensing goals while meeting and maintaining certain communication performance requirements, through cooperative control, learning and adaptation. While both of the component areas, i.e., Robotics and WSN, are very well-known and well-explored, there exist a whole set of new opportunities and research directions at the intersection of these two fields which are relatively or even completely unexplored. One such example would be the use of a set of robotic routers to set up a temporary communication path between a sender and a receiver that uses the controlled mobility to the advantage of packet routing. We find that there exist only a limited number of articles to be directly categorized as RWSN related works whereas there exist a range of articles in the robotics and the WSN literature that are also relevant to this new field of research. To connect the dots, we first identify the core problems and research trends related to RWSN such as connectivity, localization, routing, and robust flow of information. Next, we classify the existing research on RWSN as well as the relevant state-of-the-arts from robotics and WSN community according to the problems and trends identified in the first step. Lastly, we analyze what is missing in the existing literature, and identify topics that require more research attention in the future