A Simplified Design for Strict Lyapunov Functions Under Matrosov Conditions

We construct strict Lyapunov functions for broad classes of nonlinear systems satisfying Matrosov type conditions. Our new constructions are simpler than the designs available in the literature. We illustrate the practical interest of our designs using a globally asymptotically stable biological model.     

A new representation of systems with frictional unilateral constraints and its Baumgarte-like relaxation

This paper proposes a new representation of multibody mechanical systems involving three-dimensional frictional unilateral constraints. The new representation is of the form of a differential algebraic inclusion (DAI) employing a normal cone with a non-Euclidean, singular norm metric. It can be seen as a generalization of a differential algebraic equation (DAE) using Lagrange multipliers, which has been used to represent mechanical systems with equality constraints. The paper also presents an approach to approximate the aforementioned DAI by another form of DAI, which can be equivalently converted into an ordinary differential equation (ODE). The approach can be seen as a generalization of the Baumgarte stabilization, which was originally developed for DAEs. The new DAI representation and its ODE approximation are illustrated with some simple examples.     

Interval observers for linear time-invariant systems with disturbances

It is shown that, for any time-invariant exponentially stable linear system with additive disturbances, time-varying exponentially stable interval observers can be constructed. The technique of construction relies on the Jordan canonical form that any real matrix admits and on time-varying changes of coordinates for elementary Jordan blocks which lead to cooperative linear systems. The approach is applied to detectable linear systems.     

On the ERA ranking representability of pairwise bipartite ranking functions

In domains like decision theory and social choice theory it is known for a long time that stochastic transitivity properties yield necessary and sufficient conditions for the ranking or utility representability of reciprocal preference relations. In this article we extend these results for reciprocal preference relations originating from the pairwise comparison of random vectors in a machine learning context. More specifically, the expected ranking accuracy (ERA) is such a reciprocal relation that occurs in multi-class classification problems, when ranking or utility functions are fitted to the data in a pairwise manner. We establish necessary and sufficient conditions for which these pairwise bipartite ranking functions can be simplified to a single ranking function such that the pairwise expected ranking accuracies of both models coincide. Similarly as for more common reciprocal preference relations, cycle transitivity plays a crucial role in this new setting. We first consider the finite sample case, for which expected ranking accuracy can be estimated by means of the area under the ROC curve (AUC), and subsequently, we further generalize these results to the underlying distributions. It turns out that the ranking representability of pairwisely compared random vectors can be expressed elegantly in a distribution-independent way by means of a specific type of cycle transitivity, defined by a conjunctor that is closely related to the algebraic product.     

An intercomparison of bio-optical techniques for detecting dominant phytoplankton size class from satellite remote sensing

Satellite remote sensing of ocean colour is the only method currently available for synoptically measuring wide-area properties of ocean ecosystems, such as phytoplankton chlorophyll biomass. Recently, a variety of bio-optical and ecological methods have been established that use satellite data to identify and differentiate between either phytoplankton functional types (PFTs) or phytoplankton size classes (PSCs). In this study, several of these techniques were evaluated against in situ observations to determine their ability to detect dominant phytoplankton size classes (micro-, nano- and picoplankton). The techniques are applied to a 10-year ocean-colour data series from the SeaWiFS satellite sensor and compared with in situ data (6504 samples) from a variety of locations in the global ocean. Results show that spectral-response, ecological and abundance-based approaches can all perform with similar accuracy. Detection of microplankton and picoplankton were generally better than detection of nanoplankton. Abundance-based approaches were shown to provide better spatial retrieval of PSCs. Individual model performance varied according to PSC, input satellite data sources and in situ validation data types. Uncertainty in the comparison procedure and data sources was considered. Improved availability of in situ observations would aid ongoing research in this field.     

Parameterization of computational domain in isogeometric analysis: Methods and comparison

Parameterization of computational domain plays an important role in isogeometric analysis as mesh generation in finite element analysis. In this paper, we investigate this problem in the 2D case, i.e., how to parametrize the computational domains by planar B-spline surface from the given CAD objects (four boundary planar B-spline curves). Firstly, two kinds of sufficient conditions for injective B-spline parameterization are derived with respect to the control points. Then we show how to find good parameterization of computational domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of planar B-spline parameterization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of planar B-spline parameterization. By using this method, the resulted parameterization has no self-intersections, and the isoparametric net has good uniformity and orthogonality. After introducing a posteriori error estimation for isogeometric analysis, we propose r-refinement method to optimize the parameterization by repositioning the inner control points such that the estimated error is minimized. Several examples are tested on isogeometric heat conduction problem to show the effectiveness of the proposed methods and the impact of the parameterization on the quality of the approximation solution. Comparison examples with known exact solutions are also presented.     

MetaMol: high-quality visualization of molecular skin surface

Modeling and visualizing molecular surfaces is an important and challenging task in bioinformatics. Such surfaces play an essential role in better understanding the chemical and physical properties of molecules. However, constructing and displaying molecular surfaces requires complex algorithms. In this article we introduce MetaMol, a new program that generates high-quality images in interactive time. In contrast with existing software that discretizes the surface with triangles or grids, our program is based on a GPU accelerated ray-casting algorithm that directly uses the piecewise-defined algebraic equation of the molecular skin surface. As a result, both better performances and higher quality are obtained.     

Top-down proteomic analysis by MALDI-TOF profiling: Concentration-independent biomarkers

Although numerous protein biomarkers have been correlated with advanced disease states, no new clinical assays have been developed. Goals often anticipate disease-specific protein changes that exceed values among healthy individuals, a property common to acute phase reactants. This review considers somewhat different approaches. It focuses on intact protein isoform ratios that present a biomarker without change in the total concentration of the protein. These will seldom be detected by peptide level analysis or by most antibody-based assays. For example, application of an inexpensive method to large sample groups resulted in observation of several polymorphisms, including the first structural polymorphism of apolipoprotein C1. Isoform distribution of this protein was altered and was eventually linked to increased obesity. Numerous other protein isoforms included C- and N-terminal proteolysis, changes of glycoisoform ratios and certain types of sulfhydryl oxidation. While many of these gave excellent statistical correlation with advanced disease, clinical utility was not apparent. More important may be that protein isoform ratios were very stable in each individual. Diagnosis by longitudinal analysis of the same individual might increase sensitivity of protein biomarkers by 20-fold or more. Protein changes that exceed the range of values found among healthy individuals may be uncommon.     

Comparative Efficiency Of Three Systems (O3, O3/H2O2, and O3/TiO2) For The Oxidation Of Natural Organic Matter In Water

CATAZONE is a new process of heterogeneous catalytic ozonation in which water is ozonated in the presence of a solid catalyst composed of titanium dioxide. The efficiency of this O₃/TiO₂ system has been compared to the two well-known oxidant systems: ozone alone and ozone combined with hydrogen peroxide.

This comparison was undertaken on three models of natural organic compounds : an aquatic fulvic acid, a protein and a disaccharide. The first results showed the following order of relative efficiency: O₃/TiO₂ > O₃/H₂O₂ > O₃ as far as Total Organic Carbon (TOC) removal was concerned.     

Roll manufacturing of flexible microfluidic devices in thin PMMA and COC foils by embossing and lamination

Microfluidics on foil is gaining momentum due to a number of advantages of employing thin films combined with the capability of cost-effective high-volume manufacturing of devices. In this work, ultra-thin, flexible Y-microreactors with microchannels of 100 μm width and 30 μm depth were fabricated in thermoplastic polymer foils. The fluidic pattern was hot roll embossed in 125 μm thick poly-methyl-methacrylate (PMMA) and 130 μm thick cyclic-olefin-copolymer (COC) films using a dry-etched microstructured silicon wafer as a flat embossing tool in a laminator. The sealing of the channels was performed with two different techniques, one based on lamination of SU8 dry film resist (DFR) and the other one based on spin-coated poly-dimethylsiloxane (PDMS). Testing of the interconnected microreactor was carried out using two dye colorant solutions to demonstrate mixing.