The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

A unified view on lifetime distributions arising from selection mechanisms

In this paper, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri and DeGroot (1992) and Arellano-Valle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many models that have been proposed recently in the literature. In constructing this model, we assume that the number of competing causes of the event of interest has a general discrete distribution characterized by its probability generating function. This function has an important role in the selection procedure as well as in computing the conditional personal cure rate. Finally, we illustrate how various models can be deduced as special cases of the proposed model. (C) 2011 Elsevier B.V. All rights reserved.

Chaotic phase synchronization and desynchronization in an oscillator network for object selection

Object selection refers to the mechanism of extracting objects of interest while ignoring other objects and background in a given visual scene. It is a fundamental issue for many computer vision and image analysis techniques and it is still a challenging task to artificial Visual systems. Chaotic phase synchronization takes place in cases involving almost identical dynamical systems and it means that the phase difference between the systems is kept bounded over the time, while their amplitudes remain chaotic and may be uncorrelated. Instead of complete synchronization, phase synchronization is believed to be a mechanism for neural integration in brain. In this paper, an object selection model is proposed. Oscillators in the network representing the salient object in a given scene are phase synchronized, while no phase synchronization occurs for background objects. In this way, the salient object can be extracted. In this model, a shift mechanism is also introduced to change attention from one object to another. Computer simulations show that the model produces some results similar to those observed in natural vision systems.

A network of integrate and fire neurons for visual selection

Biological systems have facility to capture salient object(s) in a given scene, but it is still a difficult task to be accomplished by artificial vision systems. In this paper a visual selection mechanism based on the integrate and fire neural network is proposed. The model not only can discriminate objects in a given visual scene, but also can deliver focus of attention to the salient object. Moreover, it processes a combination of relevant features of an input scene, such as intensity, color, orientation, and the contrast of them. In comparison to other visual selection approaches, this model presents several interesting features. It is able to capture attention of objects in complex forms, including those linearly nonseparable. Moreover, computer simulations show that the model produces results similar to those observed in natural vision systems.

Electronic properties of liquid hydrogen fluoride: A sequential quantum mechanical/Born-Oppenheimer molecular dynamics approach

The electronic properties of liquid hydrogen fluoride (HF) were investigated by carrying out sequential quantum mechanics/Born-Oppenheimer molecular dynamics. The structure of the liquid is in good agreement with recent experimental information. Emphasis was placed on the analysis of polarisation effects, dynamic polarisability and electronic excitations in liquid HF. Our results indicate an increase in liquid phase of the dipole moment (similar to 0.5 D) and isotropic polarisability (5%) relative to their gas-phase values. Our best estimate for the first vertical excitation energy in liquid HF indicates a blue-shift of 0.4 +/- 0.2 eV relative to that of the gas-phase monomer (10.4 eV). (C) 2010 Elsevier B.V. All rights reserved.

NMR Chemical Shielding and Spin-Spin Coupling Constants of Liquid NH(3): A Systematic Investigation using the Sequential QM/MM Method

The NMR spin coupling parameters, (1)J(N,H) and (2)J(H,H), and the chemical shielding, sigma((15)N), of liquid ammonia are studied from a combined and sequential QM/MM methodology. Monte Carlo simulations are performed to generate statistically uncorrelated configurations that are submitted to density functional theory calculations. Two different Lennard-Jones potentials are used in the liquid simulations. Electronic polarization is included in these two potentials via an iterative procedure with and without geometry relaxation, and the influence on the calculated properties are analyzed. B3LYP/aug-cc-pVTZ-J calculations were used to compute the V(N,H) constants in the interval of -67.8 to -63.9 Hz, depending on the theoretical model used. These can be compared with the experimental results of -61.6 Hz. For the (2)J(H,H) coupling the theoretical results vary between -10.6 to -13.01 Hz. The indirect experimental result derived from partially deuterated liquid is -11.1 Hz. Inclusion of explicit hydrogen bonded molecules gives a small but important contribution. The vapor-to-liquid shifts are also considered. This shift is calculated to be negligible for (1)J(N,H) in agreement with experiment. This is rationalized as a cancellation of the geometry relaxation and pure solvent effects. For the chemical shielding, U(15 N) Calculations at the B3LYP/aug-pcS-3 show that the vapor-to-liquid chemical shift requires the explicit use of solvent molecules. Considering only one ammonia molecule in an electrostatic embedding gives a wrong sign for the chemical shift that is corrected only with the use of explicit additional molecules. The best result calculated for the vapor to liquid chemical shift Delta sigma((15)N) is -25.2 ppm, in good agreement with the experimental value of -22.6 ppm.

Experimental evidence and model explanation for cell population characteristics modification when applying sequential photodynamic therapy

We present experimental evidence of the existence of cell variability in terms of threshold light dose for Hep G2 (liver cancer cells) cultured. Using a theoretical model to describe the effects caused by successive photodynamic therapy (PDT) sessions, and based on the consequences of a partial response we introduce the threshold dose distribution concept within a tumor. The experimental model consists in a stack of flasks, and simulates subsequent layers of a tissue exposed to PDT application. The result indicates that cells from the same culture could respond in different ways to similar PDT induced-damages. Moreover, the consequence is a partial killing of the cells submitted to PDT, and the death fraction decreased at each in vitro PDT session. To demonstrate the occurrence of cell population modification as a response to PDT, we constructed a simple theoretical model and assumed that the threshold dose distribution for a cell population of a tumor is represented by a modified Gaussian distribution.

Generating segmented meshes from textured color images

This paper presents a new framework for generating triangular meshes from textured color images. The proposed framework combines a texture classification technique, called W-operator, with Imesh, a method originally conceived to generate simplicial meshes from gray scale images. An extension of W-operators to handle textured color images is proposed, which employs a combination of RGB and HSV channels and Sequential Floating Forward Search guided by mean conditional entropy criterion to extract features from the training data. The W-operator is built into the local error estimation used by Imesh to choose the mesh vertices. Furthermore, the W-operator also enables to assign a label to the triangles during the mesh construction, thus allowing to obtain a segmented mesh at the end of the process. The presented results show that the combination of W-operators with Imesh gives rise to a texture classification-based triangle mesh generation framework that outperforms pixel based methods. Crown Copyright (C) 2009 Published by Elsevier Inc. All rights reserved.

Cutpoint selection for discretizing a continuous covariate for generalized estimating equations

We consider consider the problem of dichotomizing a continuous covariate when performing a regression analysis based on a generalized estimation approach. The problem involves estimation of the cutpoint for the covariate and testing the hypothesis that the binary covariate constructed from the continuous covariate has a significant impact on the outcome. Due to the multiple testing used to find the optimal cutpoint, we need to make an adjustment to the usual significance test to preserve the type-I error rates. We illustrate the techniques on one data set of patients given unrelated hematopoietic stem cell transplantation. Here the question is whether the CD34 cell dose given to patient affects the outcome of the transplant and what is the smallest cell dose which is needed for good outcomes. (C) 2010 Elsevier BM. All rights reserved.

A non-normal topology generated by a two-point selection

We construct a two-point selection f : [P](2) -> P, where P is the set of the irrational numbers, such that the space (P, tau(f)) is not normal and it is not collectionwise Hausdorff either. Here, tau(f) denotes the topology generated by the two-point selection f. This example answers a question posed by V. Gutev and T. Nogura. We also show that if f :[X](2) -> X is a two-point selection such that the topology tau(f) has countable pseudocharacter, then tau(f) is a Tychonoff topology. (C) 2008 Elsevier B.V. All rights reserved.

Development of a sequential injection-square wave voltammetry method for determination of paraquat in water samples employing the hanging mercury drop electrode

This work describes the development and optimization of a sequential injection method to automate the determination of paraquat by square-wave voltammetry employing a hanging mercury drop electrode. Automation by sequential injection enhanced the sampling throughput, improving the sensitivity and precision of the measurements as a consequence of the highly reproducible and efficient conditions of mass transport of the analyte toward the electrode surface. For instance, 212 analyses can be made per hour if the sample/standard solution is prepared off-line and the sequential injection system is used just to inject the solution towards the flow cell. In-line sample conditioning reduces the sampling frequency to 44 h(-1). Experiments were performed in 0.10 M NaCl, which was the carrier solution, using a frequency of 200 Hz, a pulse height of 25 mV, a potential step of 2 mV, and a flow rate of 100 mu L s(-1). For a concentration range between 0.010 and 0.25 mg L(-1), the current (i(p), mu A) read at the potential corresponding to the peak maximum fitted the following linear equation with the paraquat concentration (mg L(-1)): ip = (-20.5 +/- 0.3) Cparaquat -(0.02 +/- 0.03). The limits of detection and quantification were 2.0 and 7.0 mu g L(-1), respectively. The accuracy of the method was evaluated by recovery studies using spiked water samples that were also analyzed by molecular absorption spectrophotometry after reduction of paraquat with sodium dithionite in an alkaline medium. No evidence of statistically significant differences between the two methods was observed at the 95% confidence level.

Developing a fluorimetric sequential injection methodology to study adsorption/desorption of glyphosate on soil and sediment samples

This paper describes the development of a sequential injection method to automate the fluorimetric determination of glyphosate based on a first step of oxidation to glycine by hypochlorite at 48 degrees C, followed by reaction with the fluorogenic reagent o-phthaldialdehyde in presence of 2-mercaptoethanol in borate buffer (pH > 9) to produce a fluorescent 1-(2`-hydroxyethylthio)-2-N-alkylisoindole. The proposed method has a linear response for glyphosate concentrations between 0.25 and 25.0 mu mol L(-1), with limits of detection and quantification of 0.08 and 0.25 mu mol L(-1), respectively. The sampling rate of the method is 18 samples per hour, consuming only a fraction of reagents consumed by the chromatographic method based on the same chemistry. The method was applied to study adsorption/desorption properties in a soil and in a sediment sample. Adsorption and desorption isotherms were properly fitted by Freundlich and Langmuir equations, leading to adsorption capacities of 1384 +/- 26 and 295 +/- 30 mg kg(-1) for the soil and sediment samples, respectively. These values are consistent with the literature, with the larger adsorption capacity of the soil being explained by its larger content of clay minerals, while the sediment was predominantly sandy. (C) 2011 Elsevier B.V. All rights reserved.

Development of a sequential injection chromatography (SIC) method for determination of simazine, atrazine, and propazine

This paper describes the development of a sequential injection chromatography (SIC) procedure for separation and quantification of the herbicides simazine, atrazine, and propazine exploring the low backpressure of a 2.5 cm long monolithic C(18) column. The separation of the three compounds was achieved in less than 90 s with resolution > 1.5 using a mobile phase composed by ACN/1.25 mmol/L acetate buffer (pH 4.5) at the volumetric ratio of 35:65 and flow rate of 40 mu L/s. Detection was made at 223 nm using a flow cell with 40 mm of optical path length. The LOD was 10 mu g/L for the three triazines and the quantification limits were of 30 mu g/L for simazine and propazine and 40 mu g/L for atrazine. The sampling frequency is 27 samples per hour, consuming 1.1 mL of ACN per analysis. The proposed methodology was applied to spiked water samples and no statistically significant differences were observed in comparison to a conventional HPLC-UV method. The major metabolites of atrazine and other herbicides did not interfere in the analysis, being eluted from the column either together with the unretained peak, or at retention times well-resolved from the studied compounds.

Applying sequential injection analysis (SIA) and response surface methodology for optimization of Fenton-based processes

This work presents the use of sequential injection analysis (SIA) and the response surface methodology as a tool for optimization of Fenton-based processes. Alizarin red S dye (C.I. 58005) was used as a model compound for the anthraquinones family. whose pigments have a large use in coatings industry. The following factors were considered: [H(2)O(2)]:[Alizarin] and [H(2)O(2)]:[FeSO(4)] ratios and pH. The SIA system was designed to add reagents to the reactor and to perform on-line sampling of the reaction medium, sending the samples to a flow-through spectrophotometer for monitoring the color reduction of the dye. The proposed system fed the statistical program with degradation data for fast construction of response surface plots. After optimization, 99.7% of the dye was degraded and the TOC content was reduced to 35% of the original value. Low reagents consumption and high sampling throughput were the remarkable features of the SIA system. (C) 2008 Published by Elsevier B.V.

Implementing stepwise solvent elution in sequential injection chromatography for fluorimetric determination of intracellular free amino acids in the microalgae Tetraselmis gracilis

The concept of sequential injection chromatography (SIC) was exploited to automate the fluorimetric determination of amino acids after pre-column derivatization with ophthaldialdehyde (OPA) in presence of 2-mercaptoethanol (2MCE) using a reverse phase monolithic C(18) stationary phase. The method is low-priced and based on five steps of isocratic elutions. The first step employs the mixture methanol: tetrahydrofuran: 10 mmol L(-1) phosphate buffer (pH 7.2) at the volumetric ratio of 8:1:91; the other steps use methanol: 10 mmol L-1 phosphate buffer (pH 7.2) at volumetric ratios of 20:80, 35:65, SO:SO and 65:35. At a flow rate of 10 mu L s(-1) a 25 mm long-column was able to separate aspartic acid (Asp), glutamic acid (Glu), asparagine (Asn), serine (Ser), glutamine (Gln), glycine (Gly), threonine (Thr), citruline (Ctr), arginine (Arg), alanine (Ala), tyrosine (Tyr), phenylalanine (Phe), ornithine (Orn) and lysine (Lys) with resolution >1.2 as well as methionine (Met) and valine (Val) with resolution of 0.6. Under these conditions isoleucine (Ile) and leucine (Leu) co-eluted. The entire cycle of amino acids derivatization, chromatographic separation and column conditioning at the end of separation lasted 25 min. At a flow rate of 40 mu L s(-1) such time was reduced to 10 min at the cost of resolution worsening for the pairs Ctr/Arg and Orn/Lys. The detection limits varied from 0.092 mu mol L(-1) for Tyr to 0.51 mu mol L(-1) for Orn. The method was successfully applied to the determination of intracellular free amino acids in the green alga Tetraselmis gracilis during a period of seven days of cultivation. Samples spiked with known amounts of amino acids resulted in recoveries between 94 and 112%. (C) 2008 Elsevier B.V. All rights reserved.