Related papers: What has NMR taught us about stripes and inhomogen…
We show that the lightly doped La_{2-x}Sr_{x}CuO_{4} can be described in terms of a stripe magnetic structure or soliton picture. The internal relationship between the recent neutron observation of the diagonal (x=0.05) to vertical (x >=…
Dynamics reduces the orthorhombicity of magnetic stripes in La_2CuO_4+y. The measured stripe incommensuration can be used to determine the oxygen content of the sample.
An analytic expression for the incommensurability of static stripes in La_{2-x}Sr_xNiO_{4+y} is given, depending on the hole density n_h = x + 2y. Apart from geometry factors the formula is the same as for stripes in the related cuprates…
We argue that the superconducting state found in high-$T_c$ cuprates is inhomogeneous with a corresponding inhomogeneous superfluid density. We introduce two classes of microscopic models which capture the magnetic and superconducting…
We report $^{139}$La nuclear magnetic resonance (NMR) measurements on La$_{2-x}$Sr$_x$CuO$_4$ ($0.07\leq x \leq 0.15$) and La$_{2-x}$Ba$_x$CuO$_4$ ($x=1/8$) single crystals, focusing on the spin freezing observed in 1/8-doped lanthanum…
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…
Neutron diffraction has been a very prominent tool to investigate high-temperature superconductors, in particular through the discovery of an incommensurate magnetic signal known as stripes. We here report the findings of a neutron…
MR imaging techniques are of great benefit to disease diagnosis. However, due to the limitation of MR devices, significant intensity inhomogeneity often exists in imaging results, which impedes both qualitative and quantitative medical…
We present multispectral rendering techniques for visualizing layered materials found in biological specimens. We are the first to use acquired data from the near-infrared and ultraviolet spectra for non-photorealistic rendering (NPR).…
Recent years have witnessed a widespread increase of interest in network representation learning (NRL). By far most research efforts have focused on NRL for homogeneous networks like social networks where vertices are of the same type, or…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
The real-world data usually exhibits heterogeneous properties such as modalities, views, or resources, which brings some unique challenges wherein the key is Heterogeneous Representation Learning (HRL) termed in this paper. This brief…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
We argue that elastic interactions between ions in different valence states can play an essential role in stabilization of stripes(or 2D "sheets")in doped oxides. These interactions are in general long-range and anisotropic (attractive in…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
In this work, we present a comprehensive study combining mathematical and computational analysis to explain why a two-layer neural network struggles to handle high frequencies in both approximation and learning, especially when machine…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
Nuclear magnetic resonance (NMR) of planar oxygen, with its family independent phenomenology, is ideally suited to probe the nature of the quantum matter of superconducting cuprates. Here, with new experiments on La$_{2-x}$Sr$_x$CuO$_4$, in…
The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…