scholarly journals Combinatorics of one-dimensional simple Toeplitz subshifts

2018 ◽  
Vol 40 (6) ◽  
pp. 1673-1714
Author(s):  
DANIEL SELL
Keyword(s):  
Systematic Study ◽  
Henri Poincaré ◽  
Explicit Formulas ◽  
De Bruijn Graphs ◽  
One Dimensional ◽  
Combinatorial Properties ◽  
Complexity Function ◽  
Schreier Graphs ◽  
The Family ◽  
De Bruijn

This paper provides a systematic study of fundamental combinatorial properties of one-dimensional, two-sided infinite simple Toeplitz subshifts. Explicit formulas for the complexity function, the palindrome complexity function and the repetitivity function are proved. Moreover, a complete description of the de Bruijn graphs of the subshifts is given. Finally, the Boshernitzan condition is characterized in terms of combinatorial quantities, based on a recent result of Liu and Qu [Uniform convergence of Schrödinger cocycles over simple Toeplitz subshift. Ann. Henri Poincaré12(1) (2011), 153–172]. Particular simple characterizations are provided for simple Toeplitz subshifts that correspond to the orbital Schreier graphs of the family of Grigorchuk’s groups, a class of subshifts that serves as the main example throughout the paper.

scholarly journals Further steps on the reconstruction of convex polyominoes from orthogonal projections

2021 ◽  
Author(s):  
Paolo Dulio ◽  
Andrea Frosini ◽  
Simone Rinaldi ◽  
Lama Tarsissi ◽  
Laurent Vuillon
Keyword(s):  
Discrete Geometry ◽  
Convex Subset ◽  
Convex Sets ◽  
A Priori ◽  
Orthogonal Projections ◽  
Reconstruction Process ◽  
Combinatorial Properties ◽  
The Family ◽  
Discrete Counterpart ◽  
Interior Part

AbstractA remarkable family of discrete sets which has recently attracted the attention of the discrete geometry community is the family of convex polyominoes, that are the discrete counterpart of Euclidean convex sets, and combine the constraints of convexity and connectedness. In this paper we study the problem of their reconstruction from orthogonal projections, relying on the approach defined by Barcucci et al. (Theor Comput Sci 155(2):321–347, 1996). In particular, during the reconstruction process it may be necessary to expand a convex subset of the interior part of the polyomino, say the polyomino kernel, by adding points at specific positions of its contour, without losing its convexity. To reach this goal we consider convexity in terms of certain combinatorial properties of the boundary word encoding the polyomino. So, we first show some conditions that allow us to extend the kernel maintaining the convexity. Then, we provide examples where the addition of one or two points causes a loss of convexity, which can be restored by adding other points, whose number and positions cannot be determined a priori.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

scholarly journals Buffering Updates Enables Efficient Dynamic de Bruijn Graphs

2021 ◽  
Author(s):  
Jarno Alanko ◽  
Bahar Alipanahi ◽  
Jonathen Settle ◽  
Christina Boucher ◽  
Travis Gagie
Keyword(s):  
De Bruijn Graphs ◽  
De Bruijn

scholarly journals Cartesian products of graphs as subgraphs of de Bruijn graphs of dimension at least three

1997 ◽  
Vol 79 (1-3) ◽  
pp. 3-34 ◽  
Author(s):  
Thomas Andreae ◽  
Martin Hintz ◽  
Michael Nölle ◽  
Gerald Schreiber ◽  
Gerald W. Schuster ◽  
...  
Keyword(s):  
Cartesian Products ◽  
De Bruijn Graphs ◽  
De Bruijn ◽  
Cartesian Products Of Graphs

Isoflavones from Camphorosma lessingii Inhibit the Organic Anion Transporters OAT1 and OAT3

Planta Medica ◽  
2018 ◽  
Vol 85 (03) ◽  
pp. 225-230 ◽  
Author(s):  
Xinhui Wang ◽  
Dujuan Wang ◽  
Xue Wang ◽  
Manana Khutsishvili ◽  
Kamilla Tamanyan ◽  
...  
Keyword(s):  
Organic Anion ◽  
Inhibitory Effect ◽  
Spectroscopic Methods ◽  
Organic Anion Transporters ◽  
One Dimensional ◽  
Anion Transporters ◽  
Significant Inhibitory Effect ◽  
Phytochemical Investigation ◽  
The Family ◽  
First Time

AbstractPhytochemical investigation of Camphorosma lessingii has resulted in the isolation of four previously unreported isoflavones (1–4) and eight known compounds (5–12). Nine of these compounds (1–6, 8–10) are reported for the first time from members of the family Amaranthaceae. The structures of all isolated compounds were determined by spectroscopic methods, primarily one-dimensional and two-dimensional nuclear magnetic resonance and mass spectrometry. The absolute configuration of 6 was confirmed by circular dichroism. Inhibition of the organic anion transporters, OAT1 and OAT3, by the isolated compounds was evaluated. Among them, 7, 2′-dihydroxy- 6,8-dimethoxyisoflavone (1), 2′-hydroxy-6,7,8-trimethoxyisoflavone (2), 6,2′-dihydroxy-7,8-dimethoxyisoflavone (3), and 7-methoxyflavone (5) showed a significant inhibitory effect on 6-carboxyfluorescein uptake mediated by OAT1 and OAT3.

scholarly journals Integrating long-range connectivity information into de Bruijn graphs

2018 ◽  
Vol 34 (15) ◽  
pp. 2556-2565 ◽  
Author(s):  
Isaac Turner ◽  
Kiran V Garimella ◽  
Zamin Iqbal ◽  
Gil McVean
Keyword(s):  
Long Range ◽  
De Bruijn Graphs ◽  
Connectivity Information ◽  
De Bruijn
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