A Computer Search for Planar Substitution Tilings with $$n$$ n -Fold Rotational Symmetry

2015 ◽  
Vol 53 (2) ◽  
pp. 445-465 ◽  
Author(s):  
Franz Gähler ◽  
Eugene E. Kwan ◽  
Gregory R. Maloney
Keyword(s):  
Rotational Symmetry ◽  
Computer Search ◽  
Substitution Tilings

scholarly journals On substitution tilings of the plane with n-fold rotational symmetry

2015 ◽  
Vol Vol. 17 no. 1 (Discrete Algorithms) ◽  
Author(s):  
Gregory R. Maloney
Keyword(s):  
Rotational Symmetry ◽  
Substitution Tiling ◽  
Computer Assistance ◽  
Discrete Algorithms ◽  
Special Cases ◽  
International Audience ◽  
Substitution Tilings

Discrete Algorithms International audience A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and includes various special cases that have already been constructed by hand for low values of n. An example constructed by this method for n = 11 is exhibited; this is the first substitution tiling with elevenfold symmetry appearing in the literature.

Primitive substitution tilings with rotational symmetries

2018 ◽  
Vol 74 (4) ◽  
pp. 388-398
Author(s):  
April Lynne D. Say-awen ◽  
Ma. Louise Antonette N. De Las Peñas ◽  
Dirk Frettlöh
Keyword(s):  
Rotational Symmetry ◽  
Primitive Substitution ◽  
Substitution Tilings

This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six- and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented.

scholarly journals Isolation and characterization of the principal ATPase associated with transitional endoplasmic reticulum of rat liver.

1994 ◽  
Vol 127 (6) ◽  
pp. 1871-1883 ◽  
Author(s):  
L Zhang ◽  
C L Ashendel ◽  
G W Becker ◽  
D J Morré
Keyword(s):  
Endoplasmic Reticulum ◽  
Amino Acid ◽  
Golgi Apparatus ◽  
Rat Liver ◽  
Rotational Symmetry ◽  
Amino Acid Sequences ◽  
Computer Search ◽  
Cdna Clones ◽  
Isolation And Characterization ◽  
Transition Vesicles

The transfer of membranes from the endoplasmic reticulum to the Golgi apparatus occurs via 50-70 nm transition vesicles which derive from part-rough, part-smooth transitional elements of the endoplasmic reticulum (TER). Vesicle budding from the TER is an ATP-dependent process both in vivo and in vitro. An ATPase with a monomer molecular weight of 100 kD by SDS-PAGE has been isolated from TER and designated as TER ATPase. The native TER ATPase has been characterized as a hexamer of six 100-kD subunits by gel filtration. The protein catalyzes the hydrolysis of [gamma 32-P]ATP and is phosphorylated in the presence of Mg2+. It is distinct from the classical transport ATPases based on pH optima, ion effects, and inhibitor specificity. Electron microscopy of negatively stained preparations revealed the TER ATPase to be a ring-shaped structure with six-fold rotational symmetry. A 19-amino acid sequence of TER ATPase having 84% identity with valosin-containing protein and 64% identity with a yeast cell-cycle control protein CDC48p was obtained. Anti-synthetic peptide antisera to a 15-amino acid portion of the sequence of TER ATPase recognized a 100-kD protein from TER. These antisera reduced the ATP-dependent cell-free formation of transition vesicles from isolated TER of rat liver. In a reconstituted membrane transfer system, TER ATPase antisera inhibited transfer of radiolabeled material from endoplasmic reticulum to Golgi apparatus, while preimmune sera did not. The results suggest that the TER ATPase is obligatorily involved in the ATP requirements for budding of transition vesicles from the TER. cDNA clones encoding TER ATPase were isolated by immunoscreening a rat liver cDNA library with the affinity-purified TER ATPase antibody. A computer search of deduced amino acid sequences revealed the cloned TER ATPase to be the rat equivalent of porcine valosin-containing protein, a member of a novel family of ATP binding, homo-oligomeric proteins including the N-ethylmaleimide-sensitive fusion protein.

scholarly journals Substitution tilings with dense tile orientations and n-fold rotational symmetry

2017 ◽  
Vol 28 (1) ◽  
pp. 120-131 ◽  
Author(s):  
D. Frettlöh ◽  
A.L.D. Say-awen ◽  
M.L.A.N. De Las Peñas
Keyword(s):  
Rotational Symmetry ◽  
Substitution Tilings

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

Machine Learning of Motor Vehicle Accident Categories from Narrative Data

1996 ◽  
Vol 35 (04/05) ◽  
pp. 309-316 ◽  
Author(s):  
M. R. Lehto ◽  
G. S. Sorock
Keyword(s):  
Machine Learning ◽  
Bayesian Model ◽  
Keyword Search ◽  
Motor Vehicle ◽  
Motor Vehicle Accident ◽  
Computer Search ◽  
Vehicle Accident ◽  
Learning Technique ◽  
Expert Ratings ◽  
Keyword Searches

Abstract:Bayesian inferencing as a machine learning technique was evaluated for identifying pre-crash activity and crash type from accident narratives describing 3,686 motor vehicle crashes. It was hypothesized that a Bayesian model could learn from a computer search for 63 keywords related to accident categories. Learning was described in terms of the ability to accurately classify previously unclassifiable narratives not containing the original keywords. When narratives contained keywords, the results obtained using both the Bayesian model and keyword search corresponded closely to expert ratings (P(detection)≥0.9, and P(false positive)≤0.05). For narratives not containing keywords, when the threshold used by the Bayesian model was varied between p>0.5 and p>0.9, the overall probability of detecting a category assigned by the expert varied between 67% and 12%. False positives correspondingly varied between 32% and 3%. These latter results demonstrated that the Bayesian system learned from the results of the keyword searches.

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