Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

Testing Spatial Autocorrelation in Weighted Networks : the Modes Permutation Test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardised exchange matrix appearing in spectral clustering, and generalise to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an acessibility matrix into a exchange matrix with with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.

Plant availability of trace elements in sewage sludge-treated soils: methodology¹

Synthetic root exudates were formulated based on the organic acid composition of root exudates derived from the rhizosphere of aseptically grown corn plants, pH of the rhizosphere, and the background chemical matrices of the soil solutions. The synthetic root exudates, which mimic the chemical conditions of the rhizosphere environment where soil-borne metals are dissolved and absorbed by plants, were used to extract metals from sewage-sludge treated soils 16 successive times. The concentrations of Zn, Cd, Ni, Cr, and Cu of the sludge-treated soil were 71.74, 0.21, 15.90, 58.12, and 37.44 mg kg-1, respectively. The composition of synthetic root exudates consisted of acetic, butyric, glutaric, lactic, maleic, propionic, pyruvic, succinic, tartaric, and valeric acids. The organic acid mixtures had concentrations of 0.05 and 0.1 mol L-1 -COOH. The trace elements removed by successive extractions may be considered representative for the availability of these metals to plants in these soils. The chemical speciation of the metals in the liquid phase was calculated; results showed that metals in sludge-treated soils were dissolved and formed soluble complexes with the different organic acid-based root exudates. The most reactive organic acid ligands were lactate, maleate, tartarate, and acetate. The inorganic ligands of chloride and sulfate played insignificant roles in metal dissolution. Except for Cd, free ions did not represent an important chemical species of the metals in the soil rhizosphere. As different metals formed soluble complexes with different ligands in the rhizosphere, no extractor, based on a single reagent would be able to recover all of the potentially plant-available metals from soils; the root exudate-derived organic acid mixtures tested in this study may be better suited to recover potentially plant-available metals from soils than the conventional extractors.

Comparison between detailed digital and conventional soil maps of an area with complex geology

Since different pedologists will draw different soil maps of a same area, it is important to compare the differences between mapping by specialists and mapping techniques, as for example currently intensively discussed Digital Soil Mapping. Four detailed soil maps (scale 1:10.000) of a 182-ha sugarcane farm in the county of Rafard, São Paulo State, Brazil, were compared. The area has a large variation of soil formation factors. The maps were drawn independently by four soil scientists and compared with a fifth map obtained by a digital soil mapping technique. All pedologists were given the same set of information. As many field expeditions and soil pits as required by each surveyor were provided to define the mapping units (MUs). For the Digital Soil Map (DSM), spectral data were extracted from Landsat 5 Thematic Mapper (TM) imagery as well as six terrain attributes from the topographic map of the area. These data were summarized by principal component analysis to generate the map designs of groups through Fuzzy K-means clustering. Field observations were made to identify the soils in the MUs and classify them according to the Brazilian Soil Classification System (BSCS). To compare the conventional and digital (DSM) soil maps, they were crossed pairwise to generate confusion matrices that were mapped. The categorical analysis at each classification level of the BSCS showed that the agreement between the maps decreased towards the lower levels of classification and the great influence of the surveyor on both the mapping and definition of MUs in the soil map. The average correspondence between the conventional and DSM maps was similar. Therefore, the method used to obtain the DSM yielded similar results to those obtained by the conventional technique, while providing additional information about the landscape of each soil, useful for applications in future surveys of similar areas.

Influence of digestion methods on the recovery of Iron, Zinc, Nickel, Chromium, Cadmium and Lead contents in 11 organic residues

There are currently many devices and techniques to quantify trace elements (TEs) in various matrices, but their efficacy is dependent on the digestion methods (DMs) employed in the opening of such matrices which, although "organic", present inorganic components which are difficult to solubilize. This study was carried out to evaluate the recovery of Fe, Zn, Cr, Ni, Cd and Pb contents in samples of composts and cattle, horse, chicken, quail, and swine manures, as well as in sewage sludges and peat. The DMs employed were acid digestion in microwaves with HNO3 (EPA 3051A); nitric-perchloric digestion with HNO3 + HClO4 in a digestion block (NP); dry ashing in a muffle furnace and solubilization of residual ash in nitric acid (MDA); digestion by using aqua regia solution (HCl:HNO3) in the digestion block (AR); and acid digestion with HCl and HNO3 + H2O2 (EPA 3050). The dry ashing method led to the greatest recovery of Cd in organic residues, but the EPA 3050 protocol can be an alternative method for the same purpose. The dry ashing should not be employed to determine the concentration of Cr, Fe, Ni, Pb and Zn in the residues. Higher Cr and Fe contents are recovered when NP and EPA 3050 are employed in the opening of organic matrices. For most of the residues analyzed, AR is the most effective method for recovering Ni. Microwave-assisted digestion methods (EPA3051 and 3050) led to the highest recovery of Pb. The choice of the DM that provides maximum recovery of Zn depends on the organic residue and trace element analyzed.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Observables de partículas relativistas

We study the most general unitary transformation that transform the Hamiltonians of particles of spins 0, 1/2 or 1, into Hamiltonians containing even or odd matrices only. We present also the expressions for the position operators for each transformation that are valid for the three kinds of particles mentioned above.

The long-term culture of porcine urothelial cells and induction of urothelial stratification.

OBJECTIVE: To assess porcine urothelial cell cultures and the in vitro induction of urothelial stratification in long-term cultures, to study their morphological, functional and genetic behaviour, and thus provide potential autologous urothelium for tissue-engineered substitutes for demucosalized gastric or colonic tissue. MATERIALS AND METHODS: Primary cultures of porcine urothelium were established and the cells passaged thereafter. Cell specificity was confirmed by cytokeratin analysis, cell membrane stability assessed using lactate dehydrogenase leakage, cell de-differentiation by gamma-glutamyl transferase activity and genomic stability by karyotype investigations. Histology and scanning electron microscopy were performed to study the cultured cells and the stratified constructs. Furthermore, collagen matrices were tested as cell scaffolds. RESULTS: The cells were cultured for 180 days; 10 subcultures were established during this period. Stratification was induced in a culture flask and on a collagen matrix. Cytokeratins 7, 8, 17 and 18 were expressed in all cultures, and cell membranes were stable, with no evident de-differentiation. The cultures were stable in their genotype and no chromosomal aberrations were found. The histology and immunohistochemistry of the stratified porcine constructs, and cell membrane stability and cell de-differentiation, were compared with those in the human system. CONCLUSION: Pig and human urothelial cells can be cultured over a long period with no signs of senescence. Urothelial stratification can be induced in vitro. The collagen matrix seems to be an excellent scaffold, allowing cell adherence and growth.

Discriminant ECOC: a heuristic method for application dependent design of error correcting output codes

We present a heuristic method for learning error correcting output codes matrices based on a hierarchical partition of the class space that maximizes a discriminative criterion. To achieve this goal, the optimal codeword separation is sacrificed in favor of a maximum class discrimination in the partitions. The creation of the hierarchical partition set is performed using a binary tree. As a result, a compact matrix with high discrimination power is obtained. Our method is validated using the UCI database and applied to a real problem, the classification of traffic sign images.

Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

Integrated methodologies to study human transcriptional regulation from functional genomics data

Abstract : The human body is composed of a huge number of cells acting together in a concerted manner. The current understanding is that proteins perform most of the necessary activities in keeping a cell alive. The DNA, on the other hand, stores the information on how to produce the different proteins in the genome. Regulating gene transcription is the first important step that can thus affect the life of a cell, modify its functions and its responses to the environment. Regulation is a complex operation that involves specialized proteins, the transcription factors. Transcription factors (TFs) can bind to DNA and activate the processes leading to the expression of genes into new proteins. Errors in this process may lead to diseases. In particular, some transcription factors have been associated with a lethal pathological state, commonly known as cancer, associated with uncontrolled cellular proliferation, invasiveness of healthy tissues and abnormal responses to stimuli. Understanding cancer-related regulatory programs is a difficult task, often involving several TFs interacting together and influencing each other's activity. This Thesis presents new computational methodologies to study gene regulation. In addition we present applications of our methods to the understanding of cancer-related regulatory programs. The understanding of transcriptional regulation is a major challenge. We address this difficult question combining computational approaches with large collections of heterogeneous experimental data. In detail, we design signal processing tools to recover transcription factors binding sites on the DNA from genome-wide surveys like chromatin immunoprecipitation assays on tiling arrays (ChIP-chip). We then use the localization about the binding of TFs to explain expression levels of regulated genes. In this way we identify a regulatory synergy between two TFs, the oncogene C-MYC and SP1. C-MYC and SP1 bind preferentially at promoters and when SP1 binds next to C-NIYC on the DNA, the nearby gene is strongly expressed. The association between the two TFs at promoters is reflected by the binding sites conservation across mammals, by the permissive underlying chromatin states 'it represents an important control mechanism involved in cellular proliferation, thereby involved in cancer. Secondly, we identify the characteristics of TF estrogen receptor alpha (hERa) target genes and we study the influence of hERa in regulating transcription. hERa, upon hormone estrogen signaling, binds to DNA to regulate transcription of its targets in concert with its co-factors. To overcome the scarce experimental data about the binding sites of other TFs that may interact with hERa, we conduct in silico analysis of the sequences underlying the ChIP sites using the collection of position weight matrices (PWMs) of hERa partners, TFs FOXA1 and SP1. We combine ChIP-chip and ChIP-paired-end-diTags (ChIP-pet) data about hERa binding on DNA with the sequence information to explain gene expression levels in a large collection of cancer tissue samples and also on studies about the response of cells to estrogen. We confirm that hERa binding sites are distributed anywhere on the genome. However, we distinguish between binding sites near promoters and binding sites along the transcripts. The first group shows weak binding of hERa and high occurrence of SP1 motifs, in particular near estrogen responsive genes. The second group shows strong binding of hERa and significant correlation between the number of binding sites along a gene and the strength of gene induction in presence of estrogen. Some binding sites of the second group also show presence of FOXA1, but the role of this TF still needs to be investigated. Different mechanisms have been proposed to explain hERa-mediated induction of gene expression. Our work supports the model of hERa activating gene expression from distal binding sites by interacting with promoter bound TFs, like SP1. hERa has been associated with survival rates of breast cancer patients, though explanatory models are still incomplete: this result is important to better understand how hERa can control gene expression. Thirdly, we address the difficult question of regulatory network inference. We tackle this problem analyzing time-series of biological measurements such as quantification of mRNA levels or protein concentrations. Our approach uses the well-established penalized linear regression models where we impose sparseness on the connectivity of the regulatory network. We extend this method enforcing the coherence of the regulatory dependencies: a TF must coherently behave as an activator, or a repressor on all its targets. This requirement is implemented as constraints on the signs of the regressed coefficients in the penalized linear regression model. Our approach is better at reconstructing meaningful biological networks than previous methods based on penalized regression. The method is tested on the DREAM2 challenge of reconstructing a five-genes/TFs regulatory network obtaining the best performance in the "undirected signed excitatory" category. Thus, these bioinformatics methods, which are reliable, interpretable and fast enough to cover large biological dataset, have enabled us to better understand gene regulation in humans.

CE-ESI-TOF/MS for human growth hormone analysis.

CE is a powerful analytical tool used to separate intact biomolecules such as proteins. The coupling of CE with TOF/MS produces a very promising method that can be used to detect and identify proteins in different matrices. This paper describes an efficient, rapid, and simple CE-ESI-TOF/MS procedure for the analysis of endogenous human growth hormone and recombinant human growth hormone without sample preparation. Operational factors were optimized using an experimental design, and the method was successfully applied to distinguish human growth hormone and recombinant human growth hormone in unknown samples.