Basis of Hecke algebras - associated to Coxeter groups - via matrices of inversion for permutations

Applying the matrices of inversion for permutations, we show that every element of S_{n} associates a unique canonical word in the Hecke algebra H_{n-1}(z). That provides an effective and simple algorithm for counting a linear basis of Hecke algebra H_{n}, as binary matrices

Closed braids and knot holders associated to some laser dynamical systems: A pump-modulated Nd-doped Â…ber laser

In this work the arising knots and links for the pump-modulated Nd-doped fiber laser is investigated. For the associated templates, some of their topological invariants, such as braid linking matrix, braid words, crossing number and linking number, are studied. It is recognized that the derived topological invariants are quietly dependent on the control parameters Using the tools of the braid theory, it is shown that pump-modulated Nd-doped fiber laser knots and links are positive fibered knots and links

Matrices of inversions for permutations: Recognition and Applications

This work provides a criterion for a binary strictly upper triangle matrices to be a matrix of inversions for a permutation. It admits an invariant matrices for permutations to being well recognizable. Then it provides a complete algorithmic classi…cation of elements in the symmetric group Sn. Also it gives an algorithm for generating and writing a permutation in a unique canonical form, as a word of transpositions

Solving the recognition problem of Lorenz braids via matrices of inversions for permutations

In this work, we present some needed results about matrices of inversions for permutations. Then we apply it for solving the recognition problem of Lorenz braids. Each Lorenz braid is uniquely determined by a unique simple binary matrix. Then, we got a quick algorithm for counting the trip number (minimal braid index) hence, crossing number and minimal braid representative of the Lorenz knots

Comparison of Fluorescein Isothiocyanate-Conjugated and Texas-Red-Conjugated Nucleotides for Direct Labeling in Comparative Genomic Hybridization

Fil: Larramendy, Marcelo Luis. Cátedra de Citología. Facultad de Ciencias Naturales y Museo. Universidad Nacional de La Plata; ArgentinaFil: Elrifai, Wa`el. Department of Medical Genetics. Haartman Institute. University of Helsinki. Helsinki; FinlandFil: Knuutila, Sakari. Laboratory of Medical Genetics. Helsinki University. Central Hospital. Helsinki; Finlan

Dual Garside structure and reducibility of braids

Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed that if a braid sends a curve to another curve, then the image of this curve after each factor of the left normal form of the braid (with the classical Garside structure) is also standard. We provide a new simple, geometric proof of the result by Benardete-Gutierrez-Nitecki, which can be easily adapted to the case of the dual Garside structure of braid groups, with the appropriate definition of standard curves in the dual setting. This yields a new algorithm for determining the Nielsen-Thurston type of braids

A 14-channel 7 GHz VCO-based EPR-on-a-chip sensor with rapid scan capabilities

This paper presents a VCO-based EPR-on-a-chip (EPRoC) sensor for portable, battery-operated electron paramagnetic resonance (EPR) spectrometers. The proposed chip contains an array of 14 injection-locked VCOs as the sensing element for an improved sensitive volume and phase noise performance. By cointegrating a high-bandwidth PLL, the presented design allows for continuous-wave and rapid-scan EPR experiments with a minimum number of external components. The active loop filter introduces an assisted replica charge pump that mitigates the slewing requirements on the loop-filter amplifier. The measured spin sensitivity of 2×10 9 spins/Hz−−−√ together with the large active volume of 210 nl lead to an 8-fold improvement in concentration sensitivity compared to the state-of-the-art in EPRoC detectors

Translation numbers in a Garside group are rational with uniformly bounded denominators

It is known that Garside groups are strongly translation discrete. In this paper, we show that the translation numbers in a Garside group are rational with uniformly bounded denominators and can be computed in finite time. As an application, we give solutions to some group-theoretic problems.Comment: 12 pages, to appear in J. Pure Appl. Algebr

A Garside-theoretic approach to the reducibility problem in braid groups

Let $D_n$ denote the $n$-punctured disk in the complex plane, where the punctures are on the real axis. An $n$-braid $\alpha$ is said to be \emph{reducible} if there exists an essential curve system \C in $D_n$, called a \emph{reduction system} of $\alpha$, such that \alpha*\C=\C where \alpha*\C denotes the action of the braid $\alpha$ on the curve system \C. A curve system \C in $D_n$ is said to be \emph{standard} if each of its components is isotopic to a round circle centered at the real axis. In this paper, we study the characteristics of the braids sending a curve system to a standard curve system, and then the characteristics of the conjugacy classes of reducible braids. For an essential curve system \C in $D_n$, we define the \emph{standardizer} of \C as \St(\C)=\{P\in B_n^+:P*\C{is standard}\} and show that \St(\C) is a sublattice of $B_n^+$. In particular, there exists a unique minimal element in \St(\C). Exploiting the minimal elements of standardizers together with canonical reduction systems of reducible braids, we define the outermost component of reducible braids, and then show that, for the reducible braids whose outermost component is simpler than the whole braid (including split braids), each element of its ultra summit set has a standard reduction system. This implies that, for such braids, finding a reduction system is as easy as finding a single element of the ultra summit set.Comment: 38 pages, 18 figures, published versio