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.

Analysis of the spectral response of fractal antennas related with its geometry and current paths

Fractal antennas have been proposed to improve the bandwidth of resonant structures and optical antennas. Their multiband characteristics are of interest in radiofrequency and microwave technologies. In this contribution we link the geometry of the current paths built-in the fractal antenna with the spectral response. We have seen that the actual currents owing through the structure are not limited to the portion of the fractal that should be geometrically linked with the signal. This fact strongly depends on the design of the fractal and how the different scales are arranged within the antenna. Some ideas involving materials that could actively respond to the incoming radiation could be of help to spectrally select the response of the multiband design.

Can fractal-like spectra be experimentally observed in aperiodic superlattices?

We numerically investigate the effects of inhomogeneities in the energy spectrum of aperiodic semiconductor superlattices, focusing our attention on Thue-Morse and Fibonacci sequences. In the absence of disorder, the corresponding electronic spectra are self-similar. The presence of a certain degree of randomness, due to imperfections occurring during the growth processes, gives rise to a progressive loss of quantum coherence, smearing out the finer details of the energy spectra predicted for perfect aperiodic superlattices and spurring the onset of electron localization. However, depending on the degree of disorder introduced, a critical size for the system exists, below which peculiar transport properties, related to the pre-fractal nature of the energy spectrum, may be measured.

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.

On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

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.

¿Podemos considerar la docencia como un fractal?

Este trabajo surge de una reflexión de las tantas que se plantea el profesor cada curso académico. Estas reflexiones nos han llevado a analizar los distintos puntos de vista del estudiante y del profesor frente a la realidad que se desarrolla en el aula, tratando aspectos como la motivación y el trabajo del estudiante, la masificación de las aulas y el diseño de las actividades formativas. Resultado de este estudio, se propone un modelo docente basado en los principios de la geometría fractal, en el sentido de que se plantean diferentes niveles de abstracción para las diversas actividades formativas y éstas son auto similares, es decir, se descomponen una y otra vez. En cada nivel una actividad se descompone en tareas de un nivel inferior junto con su evaluación correspondiente. Con este modelo se fomenta la retroalimentación y la motivación del estudiante. El modelo presentado se contextualiza en una asignatura de introducción a la programación pero es totalmente generalizable a otra materia.

On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials

In this paper we give a new characterization of the closure of the set of the real parts of the zeros of a particular class of Dirichlet polynomials that is associated with the set of dimensions of fractality of certain fractal strings. We show, for some representative cases of nonlattice Dirichlet polynomials, that the real parts of their zeros are dense in their associated critical intervals, confirming the conjecture and the numerical experiments made by M. Lapidus and M. van Frankenhuysen in several papers.

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.

Teaching as a fractal: from experience to model

The aim of this work is to improve students’ learning by designing a teaching model that seeks to increase student motivation to acquire new knowledge. To design the model, the methodology is based on the study of the students’ opinion on several aspects we think importantly affect the quality of teaching (such as the overcrowded classrooms, time intended for the subject or type of classroom where classes are taught), and on our experience when performing several experimental activities in the classroom (for instance, peer reviews and oral presentations). Besides the feedback from the students, it is essential to rely on the experience and reflections of lecturers who have been teaching the subject several years. This way we could detect several key aspects that, in our opinion, must be considered when designing a teaching proposal: motivation, assessment, progressiveness and autonomy. As a result we have obtained a teaching model based on instructional design as well as on the principles of fractal geometry, in the sense that different levels of abstraction for the various training activities are presented and the activities are self-similar, that is, they are decomposed again and again. At each level, an activity decomposes into a lower level tasks and their corresponding evaluation. With this model the immediate feedback and the student motivation are encouraged. We are convinced that a greater motivation will suppose an increase in the student’s working time and in their performance. Although the study has been done on a subject, the results are fully generalizable to other subjects.