Implementation of the Walrasian correspondence by market games

In this paper we present a set of axioms guaranteeing that, in exchange economies with or without indivisible goods, the set of Nash, Strong and active Walrasian Equilibria all coincide in the framework of market games.

The generic Hanna Neumann conjecture and post correspondence problem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Agronomic and commercial performance of four Spanish carob cultivars

The carob tree (Ceratonia siliqua) shows interesting prospects for some coastal Mediterranean growing areas and is widely used for industrial, agricultural, and ornamental purposes. It can be an alternative crop adapted to part-time farming and can also be used to regenerate vegetation in areas with a mild climate and erosion problems. Four Spanish carob cultivars were examined (Banya de Cabra, Duraio, Matalafera, and Rojal) to determine the one that performed the best for planting new orchards in northeastern Spain (Catalonia). The trees in this rain-fed trial (average rainfall of 500 mm) were planted in 1986 using seedling rootstocks that were budded in 1987. The trees were trained using the free-vase system and were spaced 8 x 9 m (138 trees/ha including 12% pollinators). The results showed that ‘Rojal’ was the earliest bearing cultivar. However, no significant differences were observed for cumulative pod production 18 years after budding. With respect to cumulative seed yield, ‘Duraio’ had the highest production (95 kg/tree). The lowest tree vigor (trunk cross-section) was observed in ‘Matalafera’. ‘Rojal’ trees produced the largest pods (average fruit weight of 18.9 g) and lowest seed content (11.8%), while ‘Banya de Cabra’ and ‘Duraio’ produced the smallest fruit (weighing 15.3 and 16.2 g, respectively) with the highest seed content (15.2% and 17.3%, respectively). Gum content, expressed as a percentage of the dry weight, was highest in ‘Duraio’ (56.9%) and was lowest in ‘Rojal’ (54.1%). Thus, in terms of kernel and pod production, ‘Duraio’ appeared to be the best-performing female cultivar for planting new carob orchards

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

A short motif in Drosophila SECIS Binding Protein 2 provides differential binding affinity to SECIS RNA hairpins

Selenoproteins contain the amino acid selenocysteine which is encoded by a UGA Sec codon. Recoding UGA Sec requires a complex mechanism, comprising the cis-acting SECIS RNA hairpin in the 3′UTR of selenoprotein mRNAs, and trans-acting factors. Among these, the SECIS Binding Protein 2 (SBP2) is central to the mechanism. SBP2 has been so far functionally characterized only in rats and humans. In this work, we report the characterization of the Drosophila melanogaster SBP2 (dSBP2). Despite its shorter length, it retained the same selenoprotein synthesis-promoting capabilities as the mammalian counterpart. However, a major difference resides in the SECIS recognition pattern: while human SBP2 (hSBP2) binds the distinct form 1 and 2 SECIS RNAs with similar affinities, dSBP2 exhibits high affinity toward form 2 only. In addition, we report the identification of a K (lysine)-rich domain in all SBP2s, essential for SECIS and 60S ribosomal subunit binding, differing from the well-characterized L7Ae RNA-binding domain. Swapping only five amino acids between dSBP2 and hSBP2 in the K-rich domain conferred reversed SECIS-binding properties to the proteins, thus unveiling an important sequence for form 1 binding.

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Canonical correspondence analysis in social science research

The use of simple and multiple correspondence analysis is well-established in socialscience research for understanding relationships between two or more categorical variables.By contrast, canonical correspondence analysis, which is a correspondence analysis with linearrestrictions on the solution, has become one of the most popular multivariate techniques inecological research. Multivariate ecological data typically consist of frequencies of observedspecies across a set of sampling locations, as well as a set of observed environmental variablesat the same locations. In this context the principal dimensions of the biological variables aresought in a space that is constrained to be related to the environmental variables. Thisrestricted form of correspondence analysis has many uses in social science research as well,as is demonstrated in this paper. We first illustrate the result that canonical correspondenceanalysis of an indicator matrix, restricted to be related an external categorical variable, reducesto a simple correspondence analysis of a set of concatenated (or stacked ) tables. Then weshow how canonical correspondence analysis can be used to focus on, or partial out, aparticular set of response categories in sample survey data. For example, the method can beused to partial out the influence of missing responses, which usually dominate the results of amultiple correspondence analysis.

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

The contributions of rare objects in correspondence analysis

Correspondence analysis, when used to visualize relationships in a table of counts(for example, abundance data in ecology), has been frequently criticized as being too sensitiveto objects (for example, species) that occur with very low frequency or in very few samples. Inthis statistical report we show that this criticism is generally unfounded. We demonstrate this inseveral data sets by calculating the actual contributions of rare objects to the results ofcorrespondence analysis and canonical correspondence analysis, both to the determination ofthe principal axes and to the chi-square distance. It is a fact that rare objects are oftenpositioned as outliers in correspondence analysis maps, which gives the impression that theyare highly influential, but their low weight offsets their distant positions and reduces their effecton the results. An alternative scaling of the correspondence analysis solution, the contributionbiplot, is proposed as a way of mapping the results in order to avoid the problem of outlying andlow contributing rare objects.

On commercial media bias

Within the spokes model of Chen and Riordan (2007) that allowsfor non-localized competition among arbitrary numbers of media outlets, we quantify the effect of concentration of ownership on qualityand bias of media content. A main result shows that too few commercial outlets, or better, too few separate owners of commercial outlets can lead to substantial bias in equilibrium. Increasing the number of outlets (commercial and non-commercial) tends to bring down this bias; but the strongest effect occurs when the number of owners is increased. Allowing for free entry provides lower bounds on fixed costs above which substantial commercial bias occurs in equilibrium.

Consistency and the Walrasian allocations correspondence

We characterize the Walrasian allocations correspondence, in classesof exchange economies with smooth and convex preferences, by means of consistency requirements and other axioms. We present three characterizationresults; all of which require consistency, converse consistency and standard axioms. Two characterizations hold also on domains with a finite number ofpotential agents, one of them requires envy freeness (with respect to trades) and the other--core selection; a third characterization, that requires coreselection, applies only to a variable number of agents domain, but is validalso when the domain includes only a small variety of preferences.

Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.

An adaptation of correspondence analysis for square tables

The application of correspondence analysis to square asymmetrictables is often unsuccessful because of the strong role played by thediagonal entries of the matrix, obscuring the data off the diagonal. A simplemodification of the centering of the matrix, coupled with the correspondingchange in row and column masses and row and column metrics, allows the tableto be decomposed into symmetric and skew--symmetric components, which canthen be analyzed separately. The symmetric and skew--symmetric analyses canbe performed using a simple correspondence analysis program if the data areset up in a special block format.