scholarly journals Topological interpretation of color exchange invariants: hexagonal lattice on a torus

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Olivier CEPAS ◽  
Peter M. Akhmetiev
Keyword(s):  
Hexagonal Lattice ◽  
Coloring Problem ◽  
Topological Interpretation ◽  
Linking Numbers ◽  
Special Surface ◽  
Color Exchange ◽  
Additional Constraints

We explain a correspondence between some invariants in the dynamics of color exchange in the coloring problem of a 2d regular hexagonal lattice, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified.

Symmetries of Quotient Networks for Doubly Periodic Patterns on the Hexagonal Lattice

2020 ◽  
Vol 30 (02) ◽  
pp. 2030004
Author(s):  
Ian Stewart ◽  
Dinis Gökaydin
Keyword(s):  
Pattern Formation ◽  
Network Structure ◽  
Nearest Neighbor ◽  
Automorphism Groups ◽  
Hexagonal Lattice ◽  
Lattice Models ◽  
Square Lattice ◽  
Periodic Patterns ◽  
Formation Dynamics ◽  
Additional Constraints

Pattern formation, dynamics and bifurcations for lattice models are strongly influenced by the symmetry of the lattice. However, network structure introduces additional constraints, which sometimes affect the resulting behavior. We compute the automorphism groups of all doubly periodic quotient networks of the hexagonal lattice with nearest-neighbor coupling, with emphasis on “exotic” cases where this quotient network has extra automorphisms not induced by automorphisms of the square lattice. These cases comprise three isolated networks and two infinite families with wreath product structure. We briefly discuss the implications for pattern formation, dynamics and bifurcations. This paper is a sequel to a similar analysis of the square lattice and uses similar methods.

Structural analysis of the photosynthetic membrane from Ectothiorhodospira halochloris

1983 ◽  
Vol 41 ◽  
pp. 740-741
Author(s):  
H. Engelhardt ◽  
R. Guckenberger ◽  
W. Baumeister
Keyword(s):  
Lattice Structure ◽  
Bacterial Species ◽  
Hexagonal Lattice ◽  
Reaction Centre ◽  
Photosynthetic Membrane ◽  
Rhodopseudomonas Viridis ◽  
Photosynthetic Membranes ◽  
Ectothiorhodospira Halochloris ◽  
Main Components

Bacterial photosynthetic membranes contain, apart from lipids and electron transport components, reaction centre (RC) and light harvesting (LH) polypeptides as the main components. The RC-LH complexes in Rhodopseudomonas viridis membranes are known since quite seme time to form a hexagonal lattice structure in vivo; hence this membrane attracted the particular attention of electron microscopists. Contrary to previous claims in the literature we found, however, that 2-D periodically organized photosynthetic membranes are not a unique feature of Rhodopseudomonas viridis. At least five bacterial species, all bacteriophyll b - containing, possess membranes with the RC-LH complexes regularly arrayed. All these membranes appear to have a similar lattice structure and fine-morphology. The lattice spacings of the Ectothiorhodospira haloohloris, Ectothiorhodospira abdelmalekii and Rhodopseudomonas viridis membranes are close to 13 nm, those of Thiocapsa pfennigii and Rhodopseudomonas sulfoviridis are slightly smaller (∼12.5 nm).

Electron Microscope study of commensurate-incommensurate phase transition in BaZnGeO4

1990 ◽  
Vol 48 (4) ◽  
pp. 172-173
Author(s):  
Naoki Yamamoto ◽  
Makoto Kikuchi ◽  
Tooru Atake ◽  
Akihiro Hamano ◽  
Yasutoshi Saito
Keyword(s):  
Phase Transition ◽  
Electron Microscope Study ◽  
Room Temperature ◽  
Hexagonal Lattice ◽  
Ferroelectric Materials ◽  
Temperature Phase ◽  
X Ray Diffraction ◽  
X Ray ◽  
Periodic Arrays ◽  
Modulation Wave Vector

BaZnGeO4 undergoes many phase transitions from I to V phase. The highest temperature phase I has a BaAl2O4 type structure with a hexagonal lattice. Recent X-ray diffraction study showed that the incommensurate (IC) lattice modulation appears along the c axis in the III and IV phases with a period of about 4c, and a commensurate (C) phase with a modulated period of 4c exists between the III and IV phases in the narrow temperature region (—58°C to —47°C on cooling), called the III' phase. The modulations in the IC phases are considered displacive type, but the detailed structures have not been studied. It is also not clear whether the modulation changes into periodic arrays of discommensurations (DC’s) near the III-III' and IV-V phase transition temperature as found in the ferroelectric materials such as Rb2ZnCl4.At room temperature (III phase) satellite reflections were seen around the fundamental reflections in a diffraction pattern (Fig.1) and they aligned along a certain direction deviated from the c* direction, which indicates that the modulation wave vector q tilts from the c* axis. The tilt angle is about 2 degree at room temperature and depends on temperature.

Cryo-Electron Microscopy and Correlation Averaging of Frozen-Hydrated, Polymorphic 2D Crystals of the Mitochondrial Outer Membrane Channel

1990 ◽  
Vol 48 (1) ◽  
pp. 100-101
Author(s):  
Xiao-Wei Guo
Keyword(s):  
Outer Membrane ◽  
Hexagonal Lattice ◽  
Mitochondrial Outer Membrane ◽  
Rectangular Lattice ◽  
Electron Microscopic ◽  
Cryo Electron Microscopy ◽  
Voltage Dependent ◽  
Outer Membrane Channel ◽  
2D Crystals ◽  
Vdac Channel

Voltage-dependent, anion-selective channels (VDAC) are formed in the mitochondrial outer membrane (mitOM) by a 30-kDa polypeptide. These channels form ordered 2D arrays when mitOMs from Neurospora crassa are treated with soluble phospholipase A2. We obtain low-dose electron microscopic images of unstained specimens of VDAC crystals preserved in vitreous ice, using a Philips EM420 equipped with a Gatan cryo-transfer stage. We then use correlation analysis to compute average projections of the channel crystals. The procedure involves Fourier-filtration of a region within a crystal field to obtain a preliminary average that is subsequently cross-correlated with the entire crystal. Subregions are windowed from the crystal image at coordinates of peaks in the cross-correlation function (CCF, see Figures 1 and 2) and summed to form averages (Figure 3).The VDAC channel forms several different types of crystalline arrays in mitOMs. The polymorph first observed during phospholipase treatment is a parallelogram array (a=13 run, b=11.5 run, θ==109°) containing 6 water-filled pores per unit cell. Figure 1 shows the CCF of a sub-field of such an “oblique” array used to compute the correlation average of Figure 3A. With increased phospholipase treatment, other polymorphs are observed, often co-existing within the same crystal. For example, two distinct (but closely related) types of lattices occur in the field corresponding to the CCF of Figure 2: a “contracted” version of the parallelogram lattice (a=13 run, b=10 run, θ=99°), and a near-rectangular lattice (a=8.5 run, b=5 nm). The pattern of maxima in this CCF suggests that a third, near-hexagonal lattice (a=4.5 nm) may also be present. The correlation averages of Figures 3B-D were computed from polycrystalline fields, using peak coordinates in regions of CCFs corresponding to each of the three lattice types.

Microdiffraction analysis of precipitate crystallography and morphology in Al alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 954-955
Author(s):  
B.C. Muddle ◽  
G.R. Hugo
Keyword(s):  
Point Group ◽  
Hexagonal Lattice ◽  
Intersection Point ◽  
Saed Pattern ◽  
Point Symmetry ◽  
Hexagonal Symmetry ◽  
Precipitate Crystal ◽  
The Matrix ◽  
The Subject ◽  
Electron Microdiffraction

Electron microdiffraction has been used to determine the crystallography of precipitation in Al-Cu-Mg-Ag and Al-Ge alloys for individual precipitates with dimensions down to 10 nm. The crystallography has been related to the morphology of the precipitates using an analysis based on the intersection point symmetry. This analysis requires that the precipitate form be consistent with the intersection point group, defined as those point symmetry elements common to precipitate and matrix crystals when the precipitate crystal is in its observed orientation relationship with the matrix.In Al-Cu-Mg-Ag alloys with high Cu:Mg ratios and containing trace amounts of silver, a phase designated Ω readily precipitates as thin, hexagonal-shaped plates on matrix {111}α planes. Examples of these precipitates are shown in Fig. 1. The structure of this phase has been the subject of some controversy. An SAED pattern, Fig. 2, recorded from matrix and precipitates parallel to a <11l>α axis is suggestive of hexagonal symmetry and a hexagonal lattice has been proposed on the basis of such patterns.

Reconstruction of Chitin-Protein Complexes Using Correlation Averaging Methods: Ovipositor of the Ichneumon Fly Megarhyssa

1980 ◽  
Vol 38 ◽  
pp. 38-39
Author(s):  
L. T. Germinario ◽  
J. Blackwell ◽  
J. Frank
Keyword(s):  
Protein Complexes ◽  
Hexagonal Lattice ◽  
Uranyl Acetate ◽  
Optical Diffraction ◽  
Insect Cuticle ◽  
High Dose ◽  
Wide Angle ◽  
X Ray ◽  
Averaging Methods ◽  
Digital Correlation

This report describes the use of digital correlation and averaging methods 1,2 for the reconstruction of high dose electron micrographs of the chitin-protein complex from Megarhyssa ovipositor. Electron microscopy of uranyl acetate stained insect cuticle has demonstrated a hexagonal array of unstained chitin monofibrils, 2.4−3.0 nm in diameter, in a stained protein matrix3,4. Optical diffraction Indicated a hexagonal lattice with a = 5.1-8.3 nm3 A particularly well ordered complex is found in the ovipositor of the ichneumon fly Megarhyssa: the small angle x-ray data gives a = 7.25 nm, and the wide angle pattern shows that the protein consists of subunits arranged in a 61 helix, with an axial repeat of 3.06 nm5.

scholarly journals Linking numbers and nucleosomes.

1976 ◽  
Vol 73 (8) ◽  
pp. 2639-2643 ◽  
Author(s):  
F. H. Crick
Keyword(s):  
Linking Numbers

scholarly journals Cluster-Wise Weighted NMF for Hyperspectral Images Unmixing with Imbalanced Data

2021 ◽  
Vol 13 (2) ◽  
pp. 268
Author(s):  
Xiaochen Lv ◽  
Wenhong Wang ◽  
Hongfu Liu
Keyword(s):  
Spatial Information ◽  
Hyperspectral Image ◽  
Imbalanced Data ◽  
Reconstruction Error ◽  
Hyperspectral Data ◽  
Weight Matrix ◽  
Hyperspectral Images ◽  
Mixed Data ◽  
Sparsity Constraints ◽  
Additional Constraints

Hyperspectral unmixing is an important technique for analyzing remote sensing images which aims to obtain a collection of endmembers and their corresponding abundances. In recent years, non-negative matrix factorization (NMF) has received extensive attention due to its good adaptability for mixed data with different degrees. The majority of existing NMF-based unmixing methods are developed by incorporating additional constraints into the standard NMF based on the spectral and spatial information of hyperspectral images. However, they neglect to exploit the nature of imbalanced pixels included in the data, which may cause the pixels mixed with imbalanced endmembers to be ignored, and thus the imbalanced endmembers generally cannot be accurately estimated due to the statistical property of NMF. To exploit the information of imbalanced samples in hyperspectral data during the unmixing procedure, in this paper, a cluster-wise weighted NMF (CW-NMF) method for the unmixing of hyperspectral images with imbalanced data is proposed. Specifically, based on the result of clustering conducted on the hyperspectral image, we construct a weight matrix and introduce it into the model of standard NMF. The proposed weight matrix can provide an appropriate weight value to the reconstruction error between each original pixel and the reconstructed pixel in the unmixing procedure. In this way, the adverse effect of imbalanced samples on the statistical accuracy of NMF is expected to be reduced by assigning larger weight values to the pixels concerning imbalanced endmembers and giving smaller weight values to the pixels mixed by majority endmembers. Besides, we extend the proposed CW-NMF by introducing the sparsity constraints of abundance and graph-based regularization, respectively. The experimental results on both synthetic and real hyperspectral data have been reported, and the effectiveness of our proposed methods has been demonstrated by comparing them with several state-of-the-art methods.

scholarly journals The “Emerging” Reality from “Hidden” Spaces

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 75
Author(s):  
Richard Pincak ◽  
Alexander Pigazzini ◽  
Saeid Jafari ◽  
Cenap Ozel
Keyword(s):  
Dark Matter ◽  
String Theory ◽  
Topological Approach ◽  
New Approach ◽  
Topological Interpretation ◽  
New Interpretation ◽  
M Theory

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of “emergent space” as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole, but mainly we provide a topological interpretation, using this new approach, to M-Theory and String Theory in 10 dimensions. Further, we present some conclusions which this new interpretation suggests, and also some remarks considering a unifying approach between strings and dark matter. The approach shown in the paper considers that reality, as it appears to us, can be the “emerging” part of a more complex hidden structure. Pacs numbers: 11.25.Yb; 11.25.-w; 02.40.Ky; 02.40.-k; 04.50.-h; 95.35.+d.

scholarly journals An Antigenic Thrift-Based Approach to Influenza Vaccine Design

Vaccines ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 657
Author(s):  
Jai S. Bolton ◽  
Hannah Klim ◽  
Judith Wellens ◽  
Matthew Edmans ◽  
Uri Obolski ◽  
...  
Keyword(s):  
Influenza Vaccine ◽  
Influenza Season ◽  
Vaccine Design ◽  
Antigenic Drift ◽  
Influenza Vaccines ◽  
Immune Protection ◽  
Immune Selection ◽  
Drift Theory ◽  
Gradual Accumulation ◽  
Additional Constraints

The antigenic drift theory states that influenza evolves via the gradual accumulation of mutations, decreasing a host’s immune protection against previous strains. Influenza vaccines are designed accordingly, under the premise of antigenic drift. However, a paradox exists at the centre of influenza research. If influenza evolved primarily through mutation in multiple epitopes, multiple influenza strains should co-circulate. Such a multitude of strains would render influenza vaccines quickly inefficacious. Instead, a single or limited number of strains dominate circulation each influenza season. Unless additional constraints are placed on the evolution of influenza, antigenic drift does not adequately explain these observations. Here, we explore the constraints placed on antigenic drift and a competing theory of influenza evolution – antigenic thrift. In contrast to antigenic drift, antigenic thrift states that immune selection targets epitopes of limited variability, which constrain the variability of the virus. We explain the implications of antigenic drift and antigenic thrift and explore their current and potential uses in the context of influenza vaccine design.

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