Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

Transition modes and institutional outcomes in El Salvador and Guatemala

Institutions affect key dimensions of the political process –policy, stability, and conflict. The choice of institutions is thus consequential. I argue that transition modes affect the choice of institutions in predictable and systematic ways. The more balanced power is between the two main bargaining forces –regime elite and opposition– the likelier that the resulting institutions will be pluralistic. Contrarily, the more unbalanced power is in favour of regime elites vis a vis the opposition, the likelier that institutions will be majoritarian. The argument is tested for El Salvador and Guatemala.

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

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On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Metric properties of the braided Thompson's groups

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Probiotic microorganisms: 100 years of innovation and efficacy. Modes of action

AbstractArticle StructureFigures and TablesReferences Benefits from probiotic micro-organisms have been recognised for over 100 years, and as being useful in poultry for 50 years. Fuller (1989) redefined probiotics as ‘a live microbial feed supplement which beneficially affects the host animal by improving its intestinal microbial balance’. Benefits derived from this improved intestinal microbial balance could be reflected in performance or prevention of pathogen colonisation. Probiotic micro-organisms use in poultry production has been widely accepted and new opportunities arose from the 2006 EU ban on antimicrobial growth promoters. The majority of microbial products for compound feeds are made up from a relatively small number of micro-organisms that are normally present in the GI tract. They include non-sporulated bacteria, sporulated bacteria, fungi or yeasts; and presented from single to multi-strain products. A review on the proposed modes of action is presented including recent approaches to quorum sensing interference

Embodied Autonomy in Digital Ecosystems: From Bio-Inspired Agents to Cognitive Systems

This paper proposes to promote autonomy in digital ecosystems so that it provides agents with information to improve the behavior of the digital ecosystem in terms of stability. This work proposes that, in digital ecosystems, autonomous agents can provide fundamental services and information. The final goal is to run the ecosystem, generate novel conditions and let agents exploit them. A set of evaluation measures must be defined as well. We want to provide an outline of some global indicators, such as heterogeneity and diversity, and establish relationships between agent behavior and these global indicators to fully understand interactions between agents, and to understand the dependence and autonomy relations that emerge between the interacting agents. Individual variations, interaction dependencies, and environmental factors are determinants of autonomy that would be considered. The paper concludes with a discussion of situations when autonomy is a milestone

Nanomotors: new strategies of (bio)sensing based on motion

Nanomotors are nanoscale devices capable of converting energy into movement and forces. Among them, self-propelled nanomotors offer considerable promise for developing new and novel bioanalytical and biosensing strategies based on the direct isolation of target biomolecules or changes in their movement in the presence of target analytes. The mainachievements of this project consists on the development of receptor-functionalized nanomotors that offer direct and rapid target detection, isolation and transport from raw biological samples without preparatory and washing steps. For example, microtube engines functionalized with aptamer, antibody, lectin and enzymes receptors were used for the direct isolation of analytes of biomedical interest, including proteins and whole cells, among others. A target protein was also isolated from a complex sample by using an antigen-functionalized microengine navigating into the reservoirs of a lab-on-a-chip device. The new nanomotorbased target biomarkers detection strategy not only offers highly sensitive, rapid, simple and low cost alternative for the isolation and transport of target molecules, but also represents a new dimension of analytical information based on motion. The recognition events can be easily visualized by optical microscope (without any sophisticated analytical instrument) to reveal the target presence and concentration. The use of artificial nanomachines has shown not only to be useful for (bio)recognition and (bio)transport but also for detection of environmental contamination and remediation. In this context, micromotors modified with superhydrophobic layer demonstrated that effectively interacted, captured, transported and removed oil droplets from oil contaminated samples. Finally, a unique micromotor-based strategy for water-quality testing, that mimics live-fish water-quality testing, based on changes in the propulsion behavior of artificial biocatalytic microswimmers in the presence of aquatic pollutants was also developed. The attractive features of the new micromachine-based target isolation and signal transduction protocols developed in this project offer numerous potential applications in biomedical diagnostics, environmental monitoring, and forensic analysis.

Algorithmic aspects of bio-inspired string operations

We present building blocks for algorithms for the efficient reduction of square factor, i.e. direct repetitions in strings. So the basic problem is this: given a string, compute all strings that can be obtained by reducing factors of the form zz to z. Two types of algorithms are treated: an offline algorithm is one that can compute a data structure on the given string in advance before the actual search for the square begins; in contrast, online algorithms receive all input only at the time when a request is made. For offline algorithms we treat the following problem: Let u and w be two strings such that w is obtained from u by reducing a square factor zz to only z. If we further are given the suffix table of u, how can we derive the suffix table for w without computing it from scratch? As the suffix table plays a key role in online algorithms for the detection of squares in a string, this derivation can make the iterated reduction of squares more efficient. On the other hand, we also show how a suffix array, used for the offline detection of squares, can be adapted to the new string resulting from the deletion of a square. Because the deletion is a very local change, this adaption is more eficient than the computation of the new suffix array from scratch.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Multipole surface-plasmon modes on simple metals

The average multipole surface-plasmon energy for simple metals, as well as that of ordinary surface and bulk plasmons, is obtained using energy-weighted moments of the electronic response to sufficiently general external perturbations. A local approximation of exchange and correlation effects is used within a jellium model. Band-structure effects are incorporated through an effective electronic mass. Taking advantage of the transparency of the method, we analyze under what circumstances such modes might be observable. It is shown that due to an interplay between Coulomb and kinetic energies, the multipole modes become unobservable for increasing values of the transferred momentum (q) parallel to the surface. The value of q at which the multipole mode becomes unobservable is much smaller than the cutoff value for Landau damping. The effect of the electronic surface diffuseness is also analyzed. We compare our results with previous density-functional calculations and with recent experimental data for Na, K, and Cs.