Morphological Functions with Parallel Sets for the Pore Space of X-ray CT Images of Soil Columns

During the last few decades, new imaging techniques like X-ray computed tomography have made available rich and detailed information of the spatial arrangement of soil constituents, usually referred to as soil structure. Mathematical morphology provides a plethora of mathematical techniques to analyze and parameterize the geometry of soil structure. They provide a guide to design the process from image analysis to the generation of synthetic models of soil structure in order to investigate key features of flow and transport phenomena in soil. In this work, we explore the ability of morphological functions built over Minkowski functionals with parallel sets of the pore space to characterize and quantify pore space geometry of columns of intact soil. These morphological functions seem to discriminate the effects on soil pore space geometry of contrasting management practices in a Mediterranean vineyard, and they provide the first step toward identifying the statistical significance of the observed differences.

Multi-component assessment of chronic obstructive pulmonary disease : an evaluation of the ADO and DOSE indices and the global obstructive lung disease categories in international primary care data sets

Funding The International Primary Care Respiratory Group (IPCRG) provided funding for this research project as an UNLOCK group study for which the funding was obtained through an unrestricted grant by Novartis AG, Basel, Switzerland. The latter funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. Database access for the OPCRD was provided by the Respiratory Effectiveness Group (REG) and Research in Real Life; the OPCRD statistical analysis was funded by REG. The Bocholtz Study was funded by PICASSO for COPD, an initiative of Boehringer Ingelheim, Pfizer and the Caphri Research Institute, Maastricht University, The Netherlands.

Isotropic isotopy and symplectic null sets

Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity. After examples of open null sets and codimension-2 non-null sets, geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow; it follows that sets of dimension 0 and 1 are null. For isotropic sets of higher dimensions, obstructions to the perturbation are found in homotopy groups of the orthogonal groups.

Plastid-localized acetyl-CoA carboxylase of bread wheat is encoded by a single gene on each of the three ancestral chromosome sets

5′-End fragments of two genes encoding plastid-localized acetyl-CoA carboxylase (ACCase; EC 6.4.1.2) of wheat (Triticum aestivum) were cloned and sequenced. The sequences of the two genes, Acc-1,1 and Acc-1,2, are 89% identical. Their exon sequences are 98% identical. The amino acid sequence of the biotin carboxylase domain encoded by Acc-1,1 and Acc-1,2 is 93% identical with the maize plastid ACCase but only 80–84% identical with the cytosolic ACCases from other plants and from wheat. Four overlapping fragments of cDNA covering the entire coding region were cloned by PCR and sequenced. The wheat plastid ACCase ORF contains 2,311 amino acids with a predicted molecular mass of 255 kDa. A putative transit peptide is present at the N terminus. Comparison of the genomic and cDNA sequences revealed introns at conserved sites found in the genes of other plant multifunctional ACCases, including two introns absent from the wheat cytosolic ACCase genes. Transcription start sites of the plastid ACCase genes were estimated from the longest cDNA clones obtained by 5′-RACE (rapid amplification of cDNA ends). The untranslated leader sequence encoded by the Acc-1 genes is at least 130–170 nucleotides long and is interrupted by an intron. Southern analysis indicates the presence of only one copy of the gene in each ancestral chromosome set. The gene maps near the telomere on the short arm of chromosomes 2A, 2B, and 2D. Identification of three different cDNAs, two corresponding to genes Acc-1,1 and Acc-1,2, indicates that all three genes are transcriptionally active.

Statistical modeling of large microarray data sets to identify stimulus-response profiles

A statistical modeling approach is proposed for use in searching large microarray data sets for genes that have a transcriptional response to a stimulus. The approach is unrestricted with respect to the timing, magnitude or duration of the response, or the overall abundance of the transcript. The statistical model makes an accommodation for systematic heterogeneity in expression levels. Corresponding data analyses provide gene-specific information, and the approach provides a means for evaluating the statistical significance of such information. To illustrate this strategy we have derived a model to depict the profile expected for a periodically transcribed gene and used it to look for budding yeast transcripts that adhere to this profile. Using objective criteria, this method identifies 81% of the known periodic transcripts and 1,088 genes, which show significant periodicity in at least one of the three data sets analyzed. However, only one-quarter of these genes show significant oscillations in at least two data sets and can be classified as periodic with high confidence. The method provides estimates of the mean activation and deactivation times, induced and basal expression levels, and statistical measures of the precision of these estimates for each periodic transcript.

Sets of EcoRI fragments containing ribosomal RNA sequences are conserved among different strains of Listeria monocytogenes.

To classify Listeria monocytogenes using taxonomic characters derived from the rRNA operons and their flanking sequences, we studied a sample of 1346 strains within the taxon. DNA from each strain was digested with a restriction endonuclease, EcoRI. The fragments were separated by gel electrophoresis, immobilized on a membrane, and hybridized with a labeled rRNA operon from Escherichia coli. The pattern of bands, positions, and intensities of hybridized fragments were electronically captured. Software was used to normalize the band positions relative to standards, scale the signal intensity, and reduce the background so that each strain was reproducibly represented in a data base as a pattern. With these methods, L. monocytogenes was resolved into 50 pattern types differing in the length of at least one polymorphic fragment. Pattern types representing multiple strains were recorded as the mathematical average of the strain patterns. Pattern types were arranged by size polymorphisms of assigned rRNA regions into subsets, which revealed the branching genetic structure of the species. Subtracting the polymorphic variants of a specific assigned region from the pattern types and averaging the types within each subset resulted in reduced sets of conserved fragments that could be used to recognize strains of the species. Pattern types and reduced sets of conserved fragments were conserved among different strains of L. monocytogenes but were not observed in total among strains of other species.

A historical account of types of fuzzy sets and their relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

On the nullstellensätze for stein spaces and C-analytic sets.

In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ⊂ Rn in terms of the saturation of Łojasiewicz’s radical in O(X): The ideal I(Ƶ(a)) of the zero-set Ƶ(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of Łojasiewicz’s radical (Formula presented). If Ƶ(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(Ƶ(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(Ƶ(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of Ƶ(p).

Motzkin decomposition of closed convex sets via truncation

A nonempty set F is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set C with a closed convex cone D. In that case, the sets C and D are called compact and conic components of F. This paper provides new characterizations of the Motzkin decomposable sets involving truncations of F (i.e., intersections of FF with closed halfspaces), when F contains no lines, and truncations of the intersection F̂ of F with the orthogonal complement of the lineality of F, otherwise. In particular, it is shown that a nonempty closed convex set F is Motzkin decomposable if and only if there exists a hyperplane H parallel to the lineality of F such that one of the truncations of F̂ induced by H is compact whereas the other one is a union of closed halflines emanating from H. Thus, any Motzkin decomposable set F can be expressed as F=C+D, where the compact component C is a truncation of F̂. These Motzkin decompositions are said to be of type T when F contains no lines, i.e., when C is a truncation of F. The minimality of this type of decompositions is also discussed.

On the stability of the Motzkin representation of closed convex sets

A set is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set with a closed convex cone. This paper analyzes the continuity properties of the set-valued mapping associating to each couple (C,D) formed by a compact convex set C and a closed convex cone D its Minkowski sum C + D. The continuity properties of other related mappings are also analyzed.

Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl. 154(2), 2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements—normals and/or subdifferentials.

Pitfalls in the Evaluation of the Thermodynamic Consistency of Experimental VLE Data Sets

The thermodynamic consistency of almost 90 VLE data series, including isothermal and isobaric conditions for systems of both total and partial miscibility in the liquid phase, has been examined by means of the area and point-to-point tests. In addition, the Gibbs energy of mixing function calculated from these experimental data has been inspected, with some rather surprising results: certain data sets exhibiting high dispersion or leading to Gibbs energy of mixing curves inconsistent with the total or partial miscibility of the liquid phase, surprisingly, pass the tests. Several possible inconsistencies in the tests themselves or in their application are discussed. Related to this is a very interesting and ambitious initiative that arose within the NIST organization: the development of an algorithm to assess the quality of experimental VLE data. The present paper questions the applicability of two of the five tests that are combined in the algorithm. It further shows that the deviation of the experimental VLE data from the correlation obtained by a given model, the basis of some point-to-point tests, should not be used to evaluate the quality of these data.

Algorithm for the detection of outliers based on the theory of rough sets

Outliers are objects that show abnormal behavior with respect to their context or that have unexpected values in some of their parameters. In decision-making processes, information quality is of the utmost importance. In specific applications, an outlying data element may represent an important deviation in a production process or a damaged sensor. Therefore, the ability to detect these elements could make the difference between making a correct and an incorrect decision. This task is complicated by the large sizes of typical databases. Due to their importance in search processes in large volumes of data, researchers pay special attention to the development of efficient outlier detection techniques. This article presents a computationally efficient algorithm for the detection of outliers in large volumes of information. This proposal is based on an extension of the mathematical framework upon which the basic theory of detection of outliers, founded on Rough Set Theory, has been constructed. From this starting point, current problems are analyzed; a detection method is proposed, along with a computational algorithm that allows the performance of outlier detection tasks with an almost-linear complexity. To illustrate its viability, the results of the application of the outlier-detection algorithm to the concrete example of a large database are presented.