Abelian subgroups of Garside groups

In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.Comment: This article replaces our earlier preprint "Stable super summit sets in Garside groups", arXiv:math.GT/060258

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.Comment: 10 pages, 6 figures, published in Eur. Phys. J.

Parton Distributions for Event Generators

In this paper, conventional Global QCD analysis is generalized to produce parton distributions optimized for use with event generators at the LHC. This optimization is accomplished by combining the constraints due to existing hard-scattering experimental data with those from anticipated cross sections for key representative SM processes at LHC (by the best available theory) as joint input to the global analyses. The PDFs obtained in these new type of global analyses using matrix elements calculated in any given order will be best suited to work with event generators of that order, for predictions at the LHC. This is most useful for LO event generators at present. Results obtained from a few candidate PDF sets (labeled as CT09MCS, CT09MC1 and CT09MC2) for LO event generators produced in this way are compared with those from other approaches.Comment: 35 pages, 19 figures, and 4 table

Powerful sets: a generalisation of binary matroids

A set $S\subseteq\{0,1\}^E$ of binary vectors, with positions indexed by $E$, is said to be a \textit{powerful code} if, for all $X\subseteq E$, the number of vectors in $S$ that are zero in the positions indexed by $X$ is a power of 2. By treating binary vectors as characteristic vectors of subsets of $E$, we say that a set $S\subseteq2^E$ of subsets of $E$ is a \textit{powerful set} if the set of characteristic vectors of sets in $S$ is a powerful code. Powerful sets (codes) include cocircuit spaces of binary matroids (equivalently, linear codes over $\mathbb{F}_2$), but much more besides. Our motivation is that, to each powerful set, there is an associated nonnegative-integer-valued rank function (by a construction of Farr), although it does not in general satisfy all the matroid rank axioms. In this paper we investigate the combinatorial properties of powerful sets. We prove fundamental results on special elements (loops, coloops, frames, near-frames, and stars), their associated types of single-element extensions, various ways of combining powerful sets to get new ones, and constructions of nonlinear powerful sets. We show that every powerful set is determined by its clutter of minimal nonzero members. Finally, we show that the number of powerful sets is doubly exponential, and hence that almost all powerful sets are nonlinear.Comment: 19 pages. This work was presented at the 40th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (40ACCMCC), University of Newcastle, Australia, Dec. 201

Differential recruitment of the sensorimotor putamen and frontoparietal cortex during motor chunking in humans

Motor chunking facilitates movement production by combining motor elements into integrated units of behavior. Previous research suggests that chunking involves two processes: concatenation, aimed at the formation of motor-motor associations between elements or sets of elements, and segmentation, aimed at the parsing of multiple contiguous elements into shorter action sets. We used fMRI to measure the trial-wise recruitment of brain regions associated with these chunking processes as healthy subjects performed a cued-sequence production task. A dynamic network analysis identified chunking structure for a set of motor sequences acquired during fMRI and collected over 3 days of training. Activity in the bilateral sensorimotor putamen positively correlated with chunk concatenation, whereas a left-hemisphere frontoparietal network was correlated with chunk segmentation. Across subjects, there was an aggregate increase in chunk strength (concatenation) with training, suggesting that subcortical circuits play a direct role in the creation of fluid transitions across chunks

Reliable Eigenspectra for New Generation Surveys

We present a novel technique to overcome the limitations of the applicability of Principal Component Analysis to typical real-life data sets, especially astronomical spectra. Our new approach addresses the issues of outliers, missing information, large number of dimensions and the vast amount of data by combining elements of robust statistics and recursive algorithms that provide improved eigensystem estimates step-by-step. We develop a generic mechanism for deriving reliable eigenspectra without manual data censoring, while utilising all the information contained in the observations. We demonstrate the power of the methodology on the attractive collection of the VIMOS VLT Deep Survey spectra that manifest most of the challenges today, and highlight the improvements over previous workarounds, as well as the scalability of our approach to collections with sizes of the Sloan Digital Sky Survey and beyond.Comment: 7 pages, 3 figures, accepted to MNRA

The use of Rough Set and Spatial Statistic in evaluating the Periurban Fringe

The distinction among urban, peri-urban and rural areas inside a territory represents a classical example of uncertainty in land classification. The transition among the three classes is not much clear and can be described with Sorites Paradox, considering the residential buildings and the settlements. Peri-urban fringe can be considered as a transition zone between urban and rural areas, as an area with its own intrinsic organic rules, as a built area without formal organisation or as an abandoned rural area contiguous to urban centres. In any case, concepts as density of buildings, services and infrastructures or the degree of rural, residential and industrial activities, will lead to uncertainty in defining classes, due to the uncertainty in combining some properties. One of the methods which can be utilized is the rough sets theory, which represents a different mathematical approach to uncertainty capturing the indiscernibility. The definition of a set is connected to information knowledge and perception about phenomena. Some phenomena can be classified only in the context of the information available about them. Two different phenomena can be indiscernible in some contexts and classified in the same way (Pawlak 83). The rough sets approach to data analysis hinges on two basic concepts, the lower approximation which considers all the elements that doubtlessly belong to the class, and the upper approximation which includes all the elements that possibly belong to the class. The rough sets theory furthermore takes into account only properties which are independent. This approach has been tested in the case of study of Potenza Province. This area, located in Southern Italy, is particularly suitable to the application of this theory, because it includes 100 municipalities with different number of inhabitants, quantity of services and distance from the main road infrastructures.

Lunar tidal acceleration obtained from satellite-derived ocean tide parameters

One hundred sets of mean elements of GEOS-3 computed at 2-day intervals yielded observation equations for the M sub 2 ocean tide from the long periodic variations of the inclination and node of the orbit. The 2nd degree Love number was given the value k sub 2 = 0.30 and the solid tide phase angle was taken to be zero. Combining obtained equations with results for the satellite 1967-92A gives the M sub 2 ocean tide parameter values. Under the same assumption of zero solid tide phase lag, the lunar tidal acceleration was found mostly due to the C sub 22 term in the expansion of the M sub 2 tide with additional small contributions from the 0 sub 1 and N sub 2 tides. Using Lambeck's (1975) estimates for the latter, the obtained acceleration in lunar longitudal in excellent agreement with the most recent determinations from ancient and modern astronomical data