Related papers: Pairwise Well-Formed Modes and Transformations
The standard theory of musical scales since antiquity has been based on harmony, rather than melody. While recent analyses provide mixed support for a role of melody as well as harmony, we lack a comparative analysis based on cross-cultural…
Domain wall structure which may form in theories with spontaneously broken parity is generically in conflict with standard cosmology. It has been argued that Planck scale suppressed effects can be sufficient for removing such domain walls.…
Large-scale pretrained language models are the major driving force behind recent improvements in performance on the Winograd Schema Challenge, a widely employed test of common sense reasoning ability. We show, however, with a new diagnostic…
We initiate the study of several distinguished bases for the positive half of a quantum supergroup $U_q$ associated to a general super Cartan datum $(\mathrm{I}, (\cdot,\cdot))$ of basic type inside a quantum shuffle superalgebra. The…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both…
Classical {\W}$_3$ transformations are discussed as restricted diffeomorphism transformations (\W-Diff) in two-dimensional space. We formulate them by using Riemannian geometry as a basic ingredient. The extended {\W}$_3$ generators are…
We consider words coding exchange of three intervals with permutation (3,2,1), here called 3iet words. Recently, a characterization of substitution invariant 3iet words was provided. We study the opposite question: what are the morphisms…
We study the thermal phase transitions of a generic real scalar field, without a $Z_2$-symmetry, referred to variously as an inert, sterile or singlet scalar, or $\phi^3+\phi^4$ theory. Such a scalar field arises in a wide range of models,…
A new hierarchy of operads over the linear spans of $\delta$-cliffs, which are some words of integers, is introduced. These operads are intended to be analogues of the operad of permutations, also known as the associative symmetric operad.…
We introduce a structure-aware approach for symbolic piano accompaniment that decouples high-level planning from note-level realization. A lightweight transformer predicts an interpretable, per-measure style plan conditioned on…
Music and language are structurally similar. Such structural similarity is often explained by generative processes. This paper describes the recent development of probabilistic generative models (PGMs) for language learning and symbol…
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples,…
The Wess-Zumino model on N=1/2 nonanticommutative superspace, which contains the dimension-6 term F^3, is shown to be renormalizable to all orders in perturbation theory, upon adding F and F^2 terms to the original Lagrangian. The…
We introduce two classes of morphisms over the alphabet $A=\{0,1\}$ whose fixed points contain infinitely many antipalindromic factors. An antipalindrome is a finite word invariant under the action of the antimorphism…
Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective…
This paper investigates the connections between combinatorial design theory and the creation of new forms of poetry through a specific combinatorial structure called Steiner triple systems. We introduce five original poems constructed using…
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method for Lie group symmetric or nearby values for the argument of the wave function, and show that there emerge Lie-group symmetric…
In most classical models of belief change, epistemic states are represented by theories (AGM) or formulas (Katsuno-Mendelzon) and the new pieces of information by formulas. The Representation Theorem for revision operators says that…