An elastomeric grating coupler

We report on a novel nondestructive and reversible method for coupling free space light to planar optical waveguides. In this method, an elastomeric grating is used to produce an effective refractive index modulation on the surface of the optical waveguide. The external elastomeric grating binds to the surface of the waveguide with van der Waals forces and makes conformal contact without any applied pressure. As a demonstration of the feasibility of the approach, we use it to measure the refractive index of a silicon oxynitride film. This technique is nondestructive, reversible, low cost and can easily be applied to the characterization of optical materials for integrated optics

Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines

In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative similarities and differences between them, and their shortcomings. Specifically, using the Boltzmann machine architecture (a fully connected recurrent neural network) with uniformly distributed weights as our model of study, we numerically measure how complexity changes as a function of network dynamics and network parameters. We apply an extension of one such information-theoretic measure of complexity to understand incremental Hebbian learning in Hopfield networks, a fully recurrent architecture model of autoassociative memory. In the course of Hebbian learning, the total information flow reflects a natural upward trend in complexity as the network attempts to learn more and more patterns.Comment: 16 pages, 7 figures; Appears in Entropy, Special Issue "Information Geometry II

Modulation of mitochondrial ion transport by inorganic polyphosphate - essential role in mitochondrial permeability transition pore

Inorganic polyphosphate (polyP) is a biopolymer of phosphoanhydride-linked orthophosphate residues. PolyP is involved in multiple cellular processes including mitochondrial metabolism and cell death. We used artificial membranes and isolated mitochondria to investigate the role of the polyP in mitochondrial ion transport and in activation of PTP. Here, we found that polyP can modify ion permeability of de-energised mitochondrial membranes but not artificial membranes. This permeability was selective for Ba(2+) and Ca(2+) but not for other monovalent and bivalent cations and can be blocked by inhibitors of the permeability transition pore - cyclosporine A or ADP. Lower concentrations of polyP modulate calcium dependent permeability transition pore opening. Increase in polyP concentrations and elongation chain length of the polymer causes calcium independent swelling in energized conditions. Physiologically relevant concentrations of inorganic polyP can regulate calcium dependent as well calcium independent mitochondrial permeability transition pore opening. This raises the possibility that cytoplasmic polyP can be an important contributor towards regulation of the cell death

Compressibility and probabilistic proofs

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.Comment: Invited talk for CiE 2017 (full version

Ultimate behavior of idealized composite floor elements at ambient and elevated temperature

This paper is concerned with the ultimate behavior of composite floor slabs under extreme loading situations resembling those occurring during severe building fires. The study focuses on the failure state associated with rupture of the reinforcement in idealized slab elements, which become lightly reinforced in a fire situation due to the early loss of the steel deck. The paper describes a fundamental approach for assessing the failure limit associated with reinforcement fracture in lightly reinforced beams, representing idealized slab strips. A description of the ambient-temperature tests on isolated restrained elements, carried out to assess the influence of key material parameters on the failure conditions, is firstly presented. The results of a series of material tests, undertaken mainly to examine the effect of elevated temperature on ductility, are also described. A simplified analytical model is employed, in conjunction with the experimental findings, to assess the salient material parameters and their implications on the ultimate response at both ambient and elevated temperature. © 2009 Springer Science+Business Media, LLC

Knockouts, Robustness and Cell Cycles

The response to a knockout of a node is a characteristic feature of a networked dynamical system. Knockout resilience in the dynamics of the remaining nodes is a sign of robustness. Here we study the effect of knockouts for binary state sequences and their implementations in terms of Boolean threshold networks. Beside random sequences with biologically plausible constraints, we analyze the cell cycle sequence of the species Saccharomyces cerevisiae and the Boolean networks implementing it. Comparing with an appropriate null model we do not find evidence that the yeast wildtype network is optimized for high knockout resilience. Our notion of knockout resilience weakly correlates with the size of the basin of attraction, which has also been considered a measure of robustness.Comment: 11 pages, 3 figures, 3 table

The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

PCA and K-Means decipher genome

In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data visualization can help in genomic sequence analysis. Students start with a fragment of genetic text of a bacterial genome and analyze its structure. By means of principal component analysis they ``discover'' that the information in the genome is encoded by non-overlapping triplets. Next, they learn how to find gene positions. This exercise on PCA and K-Means clustering enables active study of the basic bioinformatics notions. Appendix 1 contains program listings that go along with this exercise. Appendix 2 includes 2D PCA plots of triplet usage in moving frame for a series of bacterial genomes from GC-poor to GC-rich ones. Animated 3D PCA plots are attached as separate gif files. Topology (cluster structure) and geometry (mutual positions of clusters) of these plots depends clearly on GC-content.Comment: 18 pages, with program listings for MatLab, PCA analysis of genomes and additional animated 3D PCA plot

Comparative studies on the efficiency of Lemna minor L., Eicchorniacrassipes and Pistiastratiotes in the phytoremediation of refinery waste water

The studies involves a laboratory experiment on the comparative study on the efficiency of Lemna minor L., Eicchorniacrassipes and Pistiastratiotes in the phytoremediation of a stream polluted by waste water from kaduna refinery and Petro-chemical Company. Water samples were collected from Kaduna refinery effluent point, Romi up and Romi down from June to August, 2014. The physico-chemical parameters including some heavy metals were determined before and after the treatment to help in the determination of percentage reduction. The weight of the test plants was also determined before and after treatment for the determination of Net Primary Productivity (NPP). The research shows that Lemnaminoris the best plant to be use in the phytoremediation of water from Kaduna Refining and Petro-chemical Company since it shows the highest percentage reduction ability and the highest net primary productivity.Keywords: Net Primary Productivity, Percentage Reduction, Romi Stream, Heavy Metal