Related papers: Analyzing the Structure of Mondrian's 1920-1940 Co…
We deal with various splitting methods in algebraic logic. The word `splitting' refers to splitting some of the atoms in a given relation or cylindric algebra each into one or more subatoms obtaining a bigger algebra, where the number of…
Establishing affordable, efficient, accessible, innovative, and multidisciplinary methodologies are key to the creation of modern public policies on cultural heritage. Limited access to large-format paintings is a challenge to restoration…
In these notes we give a brief introduction to decomposition theory and we summarize some classical and well-known results. The main question is that if a partitioning of a topological space (in other words a decomposition) is given, then…
The transition from quasiperiodicity to chaos is studied in a two-dimensional dissipative map with the inverse golden mean rotation number. On the basis of a decimation scheme, it is argued that the (minimal) slope of the critical iterated…
The Thue-Morse sequence is an aperiodically ordered infinite binary sequence. It is used as a one-dimensional way to model the structure of a quasicrystal. For example, taking autocorrelations of these sequences (roughly, measuring how…
Computational models of music, while providing good descriptions of melodic development, still cannot fully grasp the general structure comprised of repetitions, transpositions, and reuse of melodic material. We present a corpus of strongly…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
In part one of the Critique of Judgment, Immanuel Kant wrote that "the judgment of taste...is not a cognitive judgment, and so not logical, but is aesthetic."\cite{Kant} While the condition of aesthetic discernment has long been the subject…
New fundamental physical theories can, so far a posteriori, be seen as emerging from existing ones via some kind of deformation. That is the basis for Flato's ``deformation philosophy", of which the main paradigms are the physics…
In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby…
Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…
Let $S$ be a 2-colored (red and blue) set of $n$ points in the plane. A subset $I$ of $S$ is an island if there exits a convex set $C$ such that $I=C\cap S$. The discrepancy of an island is the absolute value of the number of red minus the…
Intrinsic imaging or intrinsic image decomposition has traditionally been described as the problem of decomposing an image into two layers: a reflectance, the albedo invariant color of the material; and a shading, produced by the…
The fact that a disordered material is not constrained in its properties in the same way as a crystal presents significant and yet largely untapped potential for novel material design. However, unlike their crystalline counterparts,…
A well known generalization of Alon's "splitting nacklace theorem" by Longueville and Zivaljevic states that every k-colored n-dimensional cube can be fairly split using only k cuts in each dimension. Here we prove that for every t there…
A universal partial cycle (or upcycle) for $\mathcal{A}^n$ is a cyclic sequence that covers each word of length $n$ over the alphabet $\mathcal{A}$ exactly once -- like a De Bruijn cycle, except that we also allow a wildcard symbol…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
We study the composition style in deep image matting, a notion that characterizes a data generation flow on how to exploit limited foregrounds and random backgrounds to form a training dataset. Prior art executes this flow in a completely…
Harmony in visual compositions is a concept that cannot be defined or easily expressed mathematically, even by humans. The goal of the research described in this paper was to find a numerical representation of artistic compositions with…