PMC

Braiding of the real and imaginary field components around linear and ring lattices endowed with chiral symmetry. (a,b) Braiding the real and imaginary field components along linear lattices is insensitive to the lattice parity–whether (a) even-sited or (b) odd-sited–due to the free lattice boundaries. (c) Braiding is complete around an even-sited ring lattice. (d) Braiding cannot be completed around an odd-sited ring lattice. Incommensurability breaks the chiral symmetry.

Parity plots of different algorithms for lattice constant a predictions for cubic materials. (a) DNN + complete descriptor set, (b) RF + complete descriptor set, and (c) SVR + complete descriptor set.

(a) Complete 3D lattice cell. For the cell (at lattice coordinates cc ∈ CEL) qubits marked black are S_cc, and gray qubits are F_cc; (b) A primal cell (marked gray) and eight dual cells (physical qubits and entanglement are not represented).

(a) Schematic drawing of the conversion of the S-layer lattice symmetry of SbpA, from square to oblique, and complete loss of crystallinity; (b) TEM image of the rSbpA_31–1268 lattice showing square, and (c) of the rSbpA_31-918 lattice exhibiting oblique lattice symmetry.

SRLM analysis of NEMO immunofluorescence in fibroblasts from (a) IP_GR- and (b) IP_SS-derived samples show an almost complete inability to form higher-order NEMO lattice. (c) Quantitative analysis of NEMO lattice size in fibroblasts as measured by the number of NEMO structures over 400 nm in diameter per μm² of cell area. n is the number of whole cells analysed per condition. Error bars are s.e.m. *P-value of <0.05 after a two-tailed t-test.

Representative micrographs of the (A) body lattice and (B) surface lattice cage designs exhibiting complete fusion across the disc space and lack of peri‐implant fibrotic growth. Matching histomorphometry segmentation images of the (C) body lattice and (D) surface lattice designs are shown with red representing bone area, blue as implant area, and green as fibrous tissue area. Scale bars are 1 mm.

Samples can also be prepared in an intermediate lattice configuration between these extremes that is also metastable. Synthetic conditions have been identified that allow for preservation of the overall NC morphology during anion-exchange reactions, resulting in quantum-confined CsPbBr₃ NRs (right). The thermodynamic orthorhombic phase or metastable intermediate lattice configurations are preserved during the complete, stoichiometric anion exchange.

The random filling of n-length lattice by ℓ-length segments. First segment (shown in light blue) has an equal probability to occupy one of the n − ℓ + 1 position shown in figure. The expected number of occupied sites after the complete filling of the lattice for each configuration will be equal to ℓ plus the expected number of occupied sites for lattice on the right and on the left from the first segment.

An AFM analysis of the CA lattice. (a) Scheme of the experimental setup. A mica disc (gray) on the AFM stage (green) is fully covered by a drop of a buffered solution containing soluble CA protein (yellow triangles). The CA assembles into a planar hexagonal lattice (yellow hexagons represent CA hexamers in the lattice). The AFM images are taken and the lattice is indented at specified points using the AFM tip to analyze its mechanical properties. (b) High-resolution AFM image of a part of the CA planar hexagonal lattice self-assembled on a mica surface. The black scale bar represents 20 nm. (c, d) Force versus z-displacement curve (Fz curve) (c) or Force versus tip-sample separation curve (F-TSS curve) (d) generated during a representative deep indentation of a single point in the CA lattice. A TSS of 0 occurs only when the tip contacts the mica surface underneath the CA lattice. As the experiment progresses, the variation in cantilever deflection may be read rightward in (c), and the variation in force may be read leftward in (d). The initial, horizontal segment of each curve corresponds to the contact-free interval during the AFM tip-lattice surface approach. The linear, sloping segment of the curves (double arrow in (d)) that follows the horizontal segment corresponds to the regime in which the CA lattice is being elastically deformed. When indentation of the lattice is deep enough (higher z/lower TSS) nonlinear variations of cantilever deflection and force may occur that reveal non-elastic events, including disruption of the lattice at the indented point (revealed by drops in force marked by single arrows in (d)). The upper arrow marks the complete local disruption of the lattice as the tip penetrates all the way to the mica surface underneath the lattice. The final segment of each curve (sloping segment at higher z in (c), vertical segment in (d)) is generated once the AFM tip is in contact with the rigid mica surface (TSS = 0) and only the cantilever is being deformed. To see this figure in color, go online.

Structures in 3D-cubic lattice. An optimal structure X₀ for sequence S₀ and the unique optimal structure X₁ of S₁ from Table 2 in the 3D-cubic lattice. The coloring shows H-monomers in green and P-monomers in grey.

Bulk band of a square-hexagon lattice GPC. There existed a complete bandgap ranging from 17.45 to 17.95 GHz (yellow region) and the Chern number of each band below the second bandgap is marked (red). The Chern number of the first, second, third and fourth bands was zero, while the total Chen number of the intersecting fifth and sixth bands was −1. The lower left inset is the first Brillouin zone of a square-hexagonal lattice. The lower right inset is the unit cell of square-hexagon lattice.

Average cross-correlation matrices for different structural connectivity: (A) Ring lattice network. (B) Ring lattice network after adding ten edges regularly. (C) Ring lattice network after adding 40 random edges. (D) Complete network.

Nucleated microtubules contact the lattice. Images of nucleated microtubules (red) and pericentrin (yellow) have been merged to show that the number of nucleated microtubules converging at the centrosome (many bundled in G2) and the size of the pericentrin lattice increase from S to G2 (also see Fig. , A and C). The inset in the first panel shows microtubule– lattice contacts in the simple early S phase centrosome. Inset shows the area of interaction (white) demonstrating near complete overlap of microtubule ends with lattice elements. See Materials and Methods. Similar results were obtained with γ-tubulin. Bars, 1 μm.

Structure in FCC lattice model. One optimal structure of sequence S₁ from Table 2 with 50 HH-contacts in the 3D-face centered cubic (FCC) lattice model. The coloring shows H-monomers in green and P-monomers in grey.

Illustration of the four topologies which are taken as structural connectivity architectures and their adjacency matrix (bottom). (A) Ring lattice network. (B) Ring lattice network after adding ten edges regularly. (C) Ring lattice network after adding 40 random edges. (D) Complete network.

Schematic showing possible modes of Gag lattice growth and the expected structures of the lattice edges at positions with one, two, or three missing hexamers. CA_CTD monomers are shown as orange shapes with flat dimerization interfaces. (A) Assembly via addition of hexamers: lattice edges would consist of complete hexamers in this mode of assembly. (B and C) Assembly via addition of dimers: lattice edges would consist of complete dimers in this mode of assembly. In B, the edges consist primarily of dimers in which one component monomer forms part of a complete hexamer giving rise to partial hexamers with one to three contributing monomers. In C, the edges consist primarily of dimers in which both component monomers contribute to partial hexamers, giving rise to partial hexamers with three to five contributing monomers. (C) Mode of assembly consistent with our observations. (D) Binding of a Gag dimer in which only one component monomer is part of a hexamer creates a binding site (outline) where a dimer can bind with both component monomers, as part of two hexamers. If association constant k₁ < k₂, assembly typically proceeds to bind this site before arresting.

Snapshot of the lattice in a simulation with a complete (all three strains) and structured community at epoch 33,000. S is light gray, P is black, and R is dark gray; empty lattice points are white. Strains form clusters that chase one another around the lattice.

Subset lattices with parent set constraints. The top subset lattice is the lattice with parent set restrictions. The bottom lattice, obtained by Causnet, retains only the subsets that are in the complete generational orderings. The red arrows which at base are blue as well, represent the best network

Subset lattices with parent set constraints. The top subset lattice is the lattice with parent set restrictions. The bottom lattice, obtained by Causnet, retains only the subsets that are in the complete generational orderings. The red arrows which at base are blue as well, represent the best network.