Related papers: On the generation of periodic discrete structures …
Existing image generator networks rely heavily on spatial convolutions and, optionally, self-attention blocks in order to gradually synthesize images in a coarse-to-fine manner. Here, we present a new architecture for image generators,…
Periodic signals are critical for representing physical and perceptual phenomena. Scalar, real angular measures, e.g., radians and degrees, result in difficulty processing and distinguishing nearby angles, especially when their absolute…
We consider a segmented structure, possibly connected with a continuous medium, as initially homogeneous, where discontinuities arise as localized strains induced by self-equilibrated localized actions. Under this formulation augmented by…
A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…
In this paper, we present high-level overviews of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals. Fractals have a variety of interesting mathematical…
Heterogeneous graphs are present in various domains, such as social networks, recommendation systems, and biological networks. Unlike homogeneous graphs, heterogeneous graphs consist of multiple types of nodes and edges, each representing…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Periodic configurations of electrodes, in particular of microelectrodes, have been of interest since the advent of microfabrication. In this report, theory which is common to any periodic cell (or any cell that can be extended periodically)…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details.…
We propose and demonstrate a novel method for generating propagation-invariant spatially-stationary fields in a controllable manner. Our method relies on producing incoherent mixtures of plane waves using planar primary sources that are…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
We propose a new causal inference framework to learn causal effects from multiple, decentralized data sources in a federated setting. We introduce an adaptive transfer algorithm that learns the similarities among the data sources by…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
A comparative study is performed to explore the periodic structure formation upon intense femtosecond pulsed irradiation of dielectrics with radially and azimuthally polarised beams. Laser conditions have been selected appropriately to…
The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension.…