Related papers: On the Area of Hypercube Layouts
For almost 70 years, researchers have typically selected the width of neural networks' layers either manually or through automated hyperparameter tuning methods such as grid search and, more recently, neural architecture search. This paper…
We optimized designs of permanent magnet systems to study the effect of magnetic nanoparticles on cell cultures in microslide channels. This produced two designs, one of which is based on a large cylindrical magnet that applies a uniform…
As an example of thin composite layers we consider single and double grids of periodically arranged interacting wires loaded with a certain distributed reactive impedance. Currents induced to the wires by a normally incident plane wave are…
The success of neural networks has driven a shift in focus from feature engineering to architecture engineering. However, successful networks today are constructed using a small and manually defined set of building blocks. Even in methods…
The spatial variations of the order parameter, and the local density of states (LDOS) on the corner of s-wave or $d_{x^2-y^2}$-wave superconductors, as well as in superconductor-insulator-normal metal interfaces, are calculated self…
Recent advances in modeling density distributions, so-called neural density fields, can accurately describe the density distribution of celestial bodies without, e.g., requiring a shape model - properties of great advantage when designing…
A method is proposed for estimating the length scale of currents circulating in superconductors. The estimated circulation radius is used to determine the critical current density on the basis of magnetic measurements. The obtained formulas…
The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
A convex body $R$ in the hyperbolic plane is reduced if any convex body $K\subset R$ has a smaller minimal width than $R$. We examine the area of a family of hyperbolic reduced $n$-gons, and prove that, within this family, regular $n$-gons…
A remarkably quantitative understanding of the electrical and mechanical properties of metal wires with a thickness on the scale of a nanometer has been obtained within the free-electron model using semiclassical techniques. Convergent…
Based on first-principles calculations we predict that periodically repeated junctions of armchair graphene nanoribbons of different widths form superlattice structures. In these superlattice heterostructures the width and the energy gap…
The graphene-graphite relationship in structural geometry is a basic principle to predict novel two-dimensional (2D) materials. Here, we demonstrate that this is not the case in binary metallic systems. We use the Bayesian optimization…
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
Computer simulations suggest that ultrathin metal wires should develop exotic, non-crystalline stable atomic structures, once their diameter decreases below a critical size of the order of a few atomic spacings. The new structures, whose…
Random networks of carbon nanotubes and metallic nanowires have shown to be very useful in the production of transparent, conducting films. The electronic transport on the film depends considerably on the network properties, and on the…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We mimic nanorod-based transparent electrodes as random resistor networks (RRN) produced by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. We suppose that the number density…
Bi2Sr2CaCu2O8+x (Bi-2212) superconducting long-length wires are mainly limited in obtaining high critical currents densities (JC) by the internal gas pressure generated during the heat treatment, which expands the wire diameter and…
Recent advances in quantum information processing with superconducting qubits have fueled a growing demand for scaling and miniaturizing circuit layouts. Despite significant progress, predicting the Hamiltonian of complex circuits remains a…