Complete Description Of Structure Research Articles

Arithmetic of certain $\ell$-extensions ramified at three places. IV

Let $\ell$ be an odd regular prime, $k$ be the $\ell$th cyclotomic field, and $K=k(\sqrt[\ell]{a})$, where $a$ is a natural number that has exactly three distinct prime divisors. Assuming that there are exactly three places ramified in $K_\infty/k_\infty$, we study the $\ell$-component of the class group of the field $K$. For $\ell>3$, we prove that there always exists an unramified extension $\mathcal{N}/K$ such that $G(\mathcal{N}/K)\cong (\mathbb Z/\ell\mathbb Z)^3$, and all places over $\ell$ split completely in $\mathcal{N}/K$. If $\ell=3$ and $a$ is of the form $a=p^rq^s$, we give a complete description of the possible structure of the $\ell$-component of the class group of $K$. Some other results are also obtained.

Multilevel atomic structural model for interstratified opal materials

The structure of opal has long fascinated scientists. It occurs in a number of structural states, ranging from amorphous to exhibiting features of stacking disorder. Opal-CT, where C and T signify cristobalite- and tridymite-like interstratification, represents an important link in the length scales between amorphous and crystalline states. However, details about local atomic (dis)order and arrangements extending to long-range stacking faults in opal polymorphs remain incompletely understood. Here, a multilevel modeling approach is reported that considers stacking states in correlation with the abundance of C and T segments as a high-level structural parameter (i.e. not each atom). Optimization accounting for inter-tetrahedral bond lengths and angles and the regularity of the silicate tetrahedra is included as lower levels of structural parameters. Together, a set of parameters with both coarse-grained and atomistic features for different levels of structural details is refined. Structural disorder at the ∼10–100 Å distance scale is evaluated using experimental pair distribution function and diffraction datasets, comparing peak intensities, widths and asymmetry. This work presents a complete multilevel structural description of natural opal-CT and explains many of the unusual features observed in X-ray powder diffraction patterns. This modeling approach can be adopted generally for analyzing layered materials and their assembly into 3D structures.

Co-crystallisation and humanisation of an anti-HER2 single-domain antibody as a theranostic tool.

Human epidermal growth factor receptor-2 (HER2) is a well-recognised biomarker associated with 25% of breast cancers. In most cases, early detection and/or treatment correlates with an increased chance of survival. This study, has identified and characterised a highly specific anti-HER2 single-domain antibody (sdAb), NM-02, as a potential theranostic tool. Complete structural description by X-ray crystallography has revealed a non-overlapping epitope with current anti-HER2 antibodies. To reduce the immunogenicity risk, NM-02 underwent a humanisation process and retained wild type-like binding properties. To further de-risk the progression towards chemistry, manufacturing and control (CMC) we performed full developability profiling revealing favourable thermal and physical biochemical 'drug-like' properties. Finally, the application of the lead humanised NM-02 candidate (variant K) for HER2-specific imaging purposes was demonstrated using breast cancer HER2+/BT474 xenograft mice.

Comparison between Rock-Eval® and temperature-programmed pyrolysis/mass spectrometry for the analysis of environmental and geological samples

Natural organic matter (OM) has a complex structure whose complete structural and chemical description remains a challenge. Rock-Eval® device constitutes a rapid and affordable method for obtaining key quantitative and qualitative parameters on OM. Previous studies on soil samples proposed to deconvolute or to split into temperature slices Rock-Eval® S2 pyrograms in order to distinguish and quantify chemical fractions of increasing thermal lability. In order to provide support for such an assumption, this work proposes a methodological approach based on coupling a temperature-programmed pyrolyser to a standard mass spectrometer (Py-MS). In this manuscript, we compare results acquired by Rock-Eval® pyrolysis with those from Total Ion Current (TIC) traces obtained by Py-MS on a set of reference soil samples, completed by dissolved OM, source rock and coal samples, in order to test the extent to which this approach can be generalized. Our results show good quantitative and qualitative agreements between the two methods. This comparison is a prerequisite before going further and addressing the molecular significance of S2 pyrograms deconvolution through the examination of m/z fragments abundance curves.

Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits

We study a class of measure-theoretic objects that we call cubic couplings, on which there is a common generalization of the Gowers norms and the Host–Kra seminorms. Our main result yields a complete structural description of cubic couplings, using nilspaces. We give three applications. Firstly, we describe the characteristic factors of Host–Kra type seminorms for measure-preserving actions of countable nilpotent groups. This yields an extension of the structure theorem of Host and Kra. Secondly, we characterize sequences of random variables with a property that we call cubic exchangeability. These are sequences indexed by the infinite discrete cube, such that for every integer k ≥ 0 k\geq 0 the joint distribution’s marginals on affine subcubes of dimension k k are all equal. In particular, our result gives a description, in terms of compact nilspaces, of a related exchangeability property considered by Austin, inspired by a problem of Aldous. Finally, using nilspaces we obtain limit objects for sequences of functions on compact abelian groups (more generally on compact nilspaces) such that the densities of certain patterns in these functions converge. The paper thus proposes a measure-theoretic framework on which the area of higher-order Fourier analysis can be based, and which yields new applications of this area in a unified way in ergodic theory and arithmetic combinatorics.

Metal-Mediated DNA Nanotechnology in 3D: Structural Library by Templated Diffraction.

DNA double helices containing metal-mediated DNA (mmDNA) base pairs are constructed from Ag+ and Hg2+ ions between pyrimidine:pyrimidine pairs with the promise of nanoelectronics. Rational design of mmDNA nanomaterials is impractical without a complete lexical and structural description. Here, the programmability of structural DNA nanotechnology toward its founding mission of self-assembling a diffraction platform for biomolecular structure determination is explored. The tensegrity triangle is employed to build a comprehensive structural library of mmDNA pairs via X-ray diffraction and generalized design rules for mmDNA construction are elucidated. Two binding modes are uncovered: N3-dominant, centrosymmetric pairs and major groove binders driven by 5-position ring modifications. Energy gap calculations show additional levels in the lowest unoccupied molecular orbitals (LUMO) of mmDNA structures, rendering them attractive molecular electronic candidates.

Metal-Mediated DNA Nanotechnology in 3D: Structural Library by Templated Diffraction.

DNA double helices containing metal-mediated DNA (mmDNA) base pairs have been constructed from Ag+ and Hg2+ ions between pyrimidine:pyrimidine pairs with the promise of nanoelectronics. Rational design of mmDNA nanomaterials has been impractical without a complete lexical and structural description. Here, we explore the programmability of structural DNA nanotechnology toward its founding mission of self-assembling a diffraction platform for biomolecular structure determination. We employed the tensegrity triangle to build a comprehensive structural library of mmDNA pairs via X-ray diffraction and elucidated generalized design rules for mmDNA construction. We uncovered two binding modes: N3-dominant, centrosymmetric pairs and major groove binders driven by 5-position ring modifications. Energy gap calculations showed additional levels in the lowest unoccupied molecular orbitals (LUMO) of mmDNA structures, rendering them attractive molecular electronic candidates. This article is protected by copyright. All rights reserved.

Humans as intuitive classifiers.

Mainstream decision research rests on two implicit working assumptions, inspired by subjective expected utility theory. The first assumes that the underlying processes can be separated into judgment and decision-making stages without affecting their outcomes. The second assumes that in properly run experiments, the presentation of a complete description of the incentive structure replaces the judgment stage (and eliminates the impact of past experiences that can only affect judgment). While these working assumptions seem reasonable and harmless, the current paper suggests that they impair the derivation of useful predictions. The negative effect of the separation assumption is clarified by the predicted impact of rare events. Studies that separate judgment from decision making document oversensitivity to rare events, but without the separation people exhibit the opposite bias. The negative effects of the assumed impact of description include masking the large and predictable effect of past experiences on the way people use descriptions. We propose that the cognitive processes that underlie decision making are more similar to machine learning classification algorithms than to a two-stage probability judgment and utility weighting process. Our analysis suggests that clear insights can be obtained even when the number of feasible classes is very large, and the effort to list the rules that best describe behavior in each class is of limited value.

Modelling the laminar connectome of the human brain.

The human connectome is the complete structural description of the network of connections and elements that form the 'wiring diagram' of the brain. Due to the current scarcity of information regarding laminar end points of white matter tracts inside cortical grey matter, tractography remains focused on cortical partitioning into regions, while ignoring radial partitioning into laminar components. To overcome this biased representation of the cortex as a single homogenous unit, we use a recent data-derived model of cortical laminar connectivity, which has been further explored and corroborated in the macaque brain by comparison to published studies. The model integrates multimodal MRI imaging datasets of both white matter connectivity and grey matter laminar composition into a laminar-level connectome. In this study, we model the laminar connectome of healthy human brains (N = 30) and explore them via a set of complex network measures. Our analysis demonstrates a subdivision of network hubs that appear in the standard connectome into each individual component of the laminar connectome, giving a fresh look into the role of laminar components in cortical connectivity and offering new prospects in the fields of both structural and functional connectivity.

One-loop QCD helicity amplitudes for pp → toverline{t}j to O(ε2)

We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals. We provide corrections up to O(ε2) in the dimensional regulator for the first time which are relevant at NNLO. Four independent pentagon integral topologies appear in the complete description of the colour structure for which we provide numerical solutions using canonical form differential equations and the method of generalised power series expansions. Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.

ИХНОФОССИЛИИ И ПАЛЕОПОЧВЫ ПАЛЕОЦЕНА РАЗРЕЗОВ «ПРИВОЛЬСК» И «ШИХАНЫ» САРАТОВСКОГО ПОВОЛЖЬЯ

The article discusses the results of preliminary studies of the Paleocene sections “Privolsk” and “Shikhany” from the Saratov Volga region. A complete description of the geological structure of the sections is given for the first time. Ichnoassemblages, ichnofacies and paleosols are identified. There is an alternation of sands and sandstones of glauconite-quartz, and quartz of various degrees of density (up to quartzite), mainly light dirty gray, micaceous, fine-grained, sometimes obliquely layered. Some of the layers are strongly bioturbated, others are less bioturbated, occasionally there are thin (up to 1 cm) extended interlayers of clays in the studied sections. Fragments of the wood trunks in a sandstone crust, sometimes with elements of the root system, as well as leaf imprints and plant debris, frequent remains of invertebrates are found in many layers. There are at least one well-defined paleosol profile and several undeveloped FPS profiles (fossil paleosols). In total, there are 12 layers or beds from 1 to 5 m each in the summary section, with a total thickness of 25-28.5 m. The entire section is permeated with a variety of ichnofossils that stand out on the weathered surface. According to their morphology, the ichnofossils are divided into several groups that characterize the certain ichnofacies and reflect specific sedimentation environments

Structure of dye-decolorizing peroxidase from Bacillus subtilis in complex with veratryl alcohol

Dye-decolorizing peroxidases (DyPs) are heme-containing peroxidases, which have promising application in biodegradation of phenolic lignin compounds and in detoxification of dyes. In this study, the crystal structure of BsDyP- veratryl alcohol (VA) complex delves deep into the binding of small substrate molecules within the DyP heme cavity. The biochemical analysis shows that BsDyP oxidizes the VA with a turnover number of 0.065 s−1, followed by the oxidation of 2,6-dimethoxyphenol (DMP) and guaiacol with a comparable turnover number (kcat) of 0.07 s−1 and 0.07 s−1, respectively. Moreover, biophysical and computational studies reveal the comparable binding affinity of substrates to BsDyP and produce lower-energy stable BsDyP-ligand(s) complexes. All together with our previous findings, we are providing a complete structural description of substrate-binding sites in DyP. The structural insight of BsDyP helps to modulate its engineering to enhance the activity towards the oxidation of a wide range of substrates.

On the structure and clique‐width of (4K1,C4,C6,C7)‐free graphs

AbstractWe give a complete structural description of ‐free graphs that do not contain a simplicial vertex, and we prove that such graphs have bounded clique‐width. Together with the results of Foley et al., this implies that ‐free graphs that do not contain a simplicial vertex have bounded clique‐width. Consequently, Graph Coloring can be solved in polynomial time for ‐free graphs, that is, for even‐hole‐free graphs of stability number at most three.

Reduction Behavior of Cubic In2O3 Nanoparticles by Combined Multiple In Situ Spectroscopy and DFT.

Indium oxide (In2O3) has emerged as a highly active catalyst for methanol synthesis by CO2 hydrogenation. In this work we elucidate the reduction behavior and oxygen dynamics of cubic In2O3 nanoparticles by in situ Raman and UV-vis spectra in combination with density functional theory (DFT) calculations. We demonstrate that application of UV and visible Raman spectroscopy enables, first, a complete description of the In2O3 vibrational structure fully consistent with theory and, second, the first theoretical identification of the nature of defect-related bands in reduced In2O3. Combining these findings with quasi in situ XPS and in situ UV-vis measurements allows the temperature-dependent structural dynamics of In2O3 to be unraveled. While the surface of a particle is not in equilibrium with its bulk at room temperature, oxygen exchange between the bulk and the surface occurs at elevated temperatures, leading to an oxidation of the surface and an increase in oxygen defects in the bulk. Our results demonstrate the potential of combining different in situ spectroscopic methods with DFT to elucidate the complex redox behavior of In2O3 nanoparticles.

The maximum number of maximum dissociation sets in trees

AbstractA subset of vertices is a maximum independent set if no two of the vertices are adjacent and the subset has maximum cardinality. A subset of vertices is called a maximum dissociation set if it induces a subgraph with vertex degree at most 1, and the subset has maximum cardinality. Zito proved that the maximum number of maximum independent sets of a tree of order is if is odd, and if is even and also characterized all extremal trees with the most maximum independent sets, which solved a question posed by Wilf. Inspired by the results of Zito, in this paper, by establishing four structure theorems and a result of ‐König–Egerváry graph, we show that the maximum number of maximum dissociation sets in a tree of order is and also give complete structural descriptions of all extremal trees on which these maxima are achieved.

13C CPMAS NMR as a Tool for Full Structural Description of 2-Phenyl Substituted Imidazoles That Overcomes the Effects of Fast Tautomerization.

Tautomerization of 2-phenylimidazolecarbaldehydes has not been studied in detail so far, although this process is a well-known phenomenon for imidazole derivatives. That is why we focus our study on a series of 2-phenylimidazolecarbaldehydes and their parent alcohols that were synthesized and studied by detailed 1H and 13C NMR in solution and in the solid state. The apparent problem is that the fast tautomerization impedes the full structural description of the compounds by conventional 13C NMR measurements. Indeed, the 13C NMR spectra in solution exhibit poor resolution, and in most cases, signals from the imidazole ring are not detectable. To avoid this problem, we used 13C CP-MAS NMR as an alternative spectroscopic method for unambiguous spectroscopic characterization of the studied series of 2-phenylimidazoles. The data were analyzed in combination with quantum chemical DFT-GIAO methods by considering the tautomerization process and the intermolecular interactions. The DFT (B3LYP/6-31G(d,p)) calculations allowed to identify and suggest the preferred tautomer in the gas phase and in DMSO solvent, which for alcohols are (2-phenyl-1H-imidazol-4-yl)methanol and its analogs, and for the aldehydes are the 2-phenyl-1H-imidazole-5-carbaldehydes. The gas-phase calculated energy differences between the two possible tautomeric forms are in the range 0.645–1.415 kcal/mol for the alcohols and 2.510–3.059 kcal/mol for the aldehydes. In the DMSO solvent, however, for all compounds, the calculated energy differences go below 1.20 kcal/mol. These data suggest that both tautomeric forms of the studied 2-phenylimidazoles can be present in solution at room temperature. Our data from detailed 2D NMR measurements in the solid state (1H-13C HETCOR and 1H-1H double-quantum coherence MAS NMR) suggested that also in the solid state both tautomers coexist in different crystalline domains. This fact does not obscure the 13C CP-MAS NMR spectra of the studied 2-phenyl substituted imidazoles and suggests this spectroscopic method as a powerful tool for a complete structural description of tautomeric systems with aromatic conjugation.

Correction to the article The heat kernel on an asymptotically conic manifold

In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the low-energy resolvent, we give a complete description of the asymptotic structure of the heat kernel in all spatial and temporal regimes. We apply this structure to define and investigate a renormalized zeta function and determinant of the Laplacian on M.

Spatial structure of the pair wave function and the density correlation functions throughout the BEC-BCS crossover

By an exact numerical calculation of the BCS pair wavefunction and the density correlation functions both between atoms in the same and in different spin states, we extract the spatial large distance behavior of the respective functions. After different initial transients, those distributions show an algebraic dependence accompanied with their own exponential decay and a well defined periodic oscillatory behavior. While in general, in the BCS side there are long-range correlations and in the BEC region the behavior is dominated by tight pairs formation, each distribution shows its own overall behavior. We derive analytic expressions for the mean pair size and the correlation lengths of the same and different density correlation functions. The whole analysis yields a quite complete description of the spatial structure of the superfluid along the crossover.

Group-Like Uninorms

Uninorms play a prominent role both in the theory and the applications of aggregations and fuzzy logic. In this paper a class of uninorms, called group-like uninorms will be introduced and a complete structural description will be given for a large subclass of them. First, the four versions of a general construction—called partial lex product—will be recalled. Then two particular variants of them will be specified: the first variant constructs, starting from ℝ (the additive group of the reals) and modifying it in some way by ℤ’s (the additive group of the integers) what we will coin basic group-like uninorms, whereas the second variant can enlarge any group-like uninorm by a basic group-like uninorm resulting in another group-like uninorm. All grouplike uninorms obtained this way are “square” and have finitely many idempotent elements. On the other hand, we prove that any square group-like uninorm which has finitely many idempotent elements can be constructed by consecutive applications of the second variant (finitely many times) using only basic group-like uninorms as building blocks. Any basic group-like uninorm can be built by the first variant using only ℝ and ℤ, and any square group-like uninorm which has finitely many idempotent elements can be built using the second variant using only basic group-like uninorms: ultimately, all such uninorms can be built from ℝ and ℤ. In this way a complete characterization for square group-like uninorms which possess finitely many idempotent elements is given. The characterization provides, for potential applications in several fields of fuzzy theory or aggregation theory, the whole spectrum of choice of those square group-like uninorms which possess finitely many idempotent elements.

Substitutive Structure of Jeandel–Rao Aperiodic Tilings

Jeandel and Rao proved that 11 is the size of the smallest set of Wang tiles, i.e., unit squares with colored edges, that admit valid tilings (contiguous edges of adjacent tiles have the same color) of the plane, none of them being invariant under a nontrivial translation. We study herein the Wang shift $\Omega_0$ made of all valid tilings using the set $\mathcal{T}_0$ of 11 aperiodic Wang tiles discovered by Jeandel and Rao. We show that there exists a minimal subshift $X_0$ of $\Omega_0$ such that every tiling in $X_0$ can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of 19 self-similar and aperiodic Wang tiles. We suggest that this provides an almost complete description of the substitutive structure of Jeandel-Rao tilings, as we believe that $\Omega_0\setminus X_0$ is a null set for any shift-invariant probability measure on $\Omega_0$. The proof is based on 12 elementary steps, 10 of which involve the same procedure allowing one to desubstitute Wang tilings from the existence of a subset of marker tiles. The 2 other steps involve the addition of decorations to deal with fault lines and changing the base of the $\mathbb{Z}^2$-action through a shear conjugacy. Algorithms are provided to find markers, recognizable substitutions, and shear conjugacy from a set of Wang tiles.