Grafos e matrices. 'Gráficas y matrices'.

Resumen basado en el de la publicación

Grafos e matrices. 'Grafos y matrices'.

Se introduce en el nuevo Bachillerato el tema 'grafos y matrices' cuyo objetivo principal es aportar una nueva justificación de la utilización de las matrices e introducir al alumno en la teoría de los grafos. Se hace una introducción a los elementos básicos de esta teoría definiendo brevemente algunos de ellos.

Introduction of 4-chloro-alpha-cyanocinnamic acid liquid matrices for high sensitivity UV-MALDI MS

Matrix-assisted laser desorption/ionization (MALDI) is a key ionization technique in mass spectrometry (MS) for the analysis of labile macromolecules. An important area of study and improvements in relation to MALDI and its application in high-sensitivity MS is that of matrix design and sample preparation. Recently, 4-chloro-alpha-cyanocinnamic acid (ClCCA) has been introduced as a new rationally designed matrix and reported to provide an improved analytical performance as demonstrated by an increase in sequence coverage of protein digests obtained by peptide mass mapping (PMM) (Jaskolla, T. W.; et al. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12200-12205). This new matrix shows the potential to be a superior alternative to the commonly used and highly successful alpha-cyano-4-hydroxycinnamic acid (CHCA). We have taken this design one step further by developing and optimizing an ionic liquid matrix (ILM) and liquid support matrix (LSM) using ClCCA as the principle chromophore and MALDI matrix compound. These new liquid matrices possess greater sample homogeneity and a simpler morphology. The data obtained from our studies show improved sequence coverage for BSA digests compared to the traditional CHCA crystalline matrix and for the ClCCA-containing ILM a similar performance to the ClCCA crystalline matrix down to 1 fmol of BSA digest prepared in a single MALDI sample droplet with current sensitivity levels in the attomole range. The LSMs show a high tolerance to contamination such as ammonium bicarbonate, a commonly used buffering agent.

Small towns as 'sub-poles' in English rural development: Investigating rural-urban linkages using sub-regional social accounting matrices

This paper uses spatial economic data from four small English towns to measure the strength of economic integration between town and hinterland and to estimate the magnitude of town-hinterland spill-over effects. Following estimation of local integration indicators and inter-locale flows, sub-regional social accounting matrices (SAMs) are developed to estimate the strength of local employment and output multipliers for various economic sectors. The potential value of a town as a 'sub-pole' in local economic development is shown to be dependent on structural differences in the local economy, such as the particular mix of firms within towns. Although the multipliers are generally small, indicating a low level of local linkages, some sectors, particularly financial services and banking, show consistently higher multipliers for both output and employment. (c) 2007 Elsevier Ltd. All rights reserved.

Liquid matrices for analyses by UV-MALDI mass spectrometry

Data are presented for a pH-adjustable liquid UV-matrix-assisted laser desorption ionization (MALDI) matrix for mass spectrometry analysis. The liquid matrix system possesses high analytical sensitivity within the same order of magnitude as that achievable by the commonly used solid UV-MALDI matrices such as 2,5-dihydroxybenzoic acid but with improved spot homogeneity and reproducibility. The pH of the matrix has been adjusted by the addition of up to 0.35% trifluoroacetic acid and up to 200 mM ammonium bicarbonate, achieving an on-target pH range of 3.5-8.6. Alteration of the pH does not seem to affect the overall sample signal intensity or signal-to-noise ratio achievable, nor does it affect the individual peptide ion signals from a mixture of peptides with varying isoelectric points (p1). In addition, the pH adjustment has allowed for the performance of a tryptic digest within the diluted pH-optimized liquid matrix.

Recommendations for the viability assessment of probiotics as concentrated cultures and in food matrices

Due to the fact that probiotic cells need to be alive when they are consumed, culture-based analysis (plate count) is critical in ascertaining the quality (numbers of viable cells) of probiotic products. Since probiotic cells are typically stressed, due to various factors related to their production, processing and formulation, the standard methodology for total plate counts tends to underestimate the cell numbers of these products. Furthermore, products such as microencapsulated cultures require modifications in the release and sampling procedure in order to correctly estimate viable counts. This review examines the enumeration of probiotic bacteria in the following commercial products: powders, microencapsulated cultures, frozen concentrates, capsules, foods and beverages. The parameters which are specifically examined include: sample preparation (rehydration, thawing), dilutions (homogenization, media) and plating (media, incubation) procedures. Recommendations are provided for each of these analytical steps to improve the accuracy of the analysis. Although the recommendations specifically target the analysis of probiotics, many will apply to the analysis of commercial lactic starter cultures used in food fermentations as well.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Sample preparation: a crucial factor for the analytical performance of rationally designed MALDI matrices

Evidence is presented that the performance of the rationally designed MALDI matrix 4-chloro-α-cyanocinnamic acid (ClCCA) in comparison to its well-established predecessor α-cyano-4-hydroxycinnamic acid (CHCA) is significantly dependent on the sample preparation, such as the choice of the target plate. In this context, it becomes clear that any rational designs of MALDI matrices and their successful employment have to consider a larger set of physicochemical parameters, including sample crystallization and morphology/topology, in addition to parameters of basic (solution and/or gas-phase) chemistry.

Ionic liquids and other liquid matrices for sensitive MALDI MS analysis

Although liquid matrix-assisted laser desorption/ionization (MALDI) has been used in mass spectrometry (MS) since the early introduction of MALDI, its substantial lack of sensitivity compared to solid (crystalline) MALDI was for a long time a major hurdle to its analytical competitiveness. In the last decade, this situation has changed with the development of new sensitive liquid matrices, which are often based on a binary matrix acid/base system. Some of these matrices were inspired by the recent progress in ionic liquid research, while others were developed from revisiting previous liquid MALDI work as well as from a combination of these two approaches. As a result, two high-performing liquid matrix classes have been developed, the ionic liquid matrices (ILMs) and the liquid support matrices (LSMs), now allowing MS measurements at a sensitivity level that is very close to the level of solid MALDI and in some cases even surpasses it. This chapter provides some basic information on a selection of highly successful representatives of these new liquid matrices and describes in detail how they are made and applied in MALDI MS analysis.

Rapid selective separation of americium/curium from simulated nuclear forensic matrices using triazine ligands

In analysis of complex nuclear forensic samples containing lanthanides, actinides and matrix elements, rapid selective extraction of Am/Cm for quantification is challenging, in particular due the difficult separation of Am/Cm from lanthanides. Here we present a separation process for Am/Cm(III) which is achieved using a combination of AG1-X8 chromatography followed by Am/Cm extraction with a triazine ligand. The ligands tested in our process were CyMe4-BTPhen, CyMe4- BTBP, CA-BTP and CA-BTPhen. Our process allows for purification and quantification of Am and Cm (recoveries 80%–100%) and other major actinides in < 2d without the use of multiple columns or thiocyanate. The process is unaffected by high level Ca(II)/Fe(III)/Al(III) (10mg mL−1) and thus requires little pre-treatment of samples.

Structural damage identification and location using grammian matrices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)