Related papers: Generalized Carlos Scales
The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
We will give an overview of four families of cardinal characteristics defined on subspaces $\prod_{\alpha\in\kappa}b(\alpha)$ of the generalised Baire space ${}^\kappa\kappa$, where $\kappa$ is strongly inaccessible and…
We consider the problem of finding a color scale which performs well when converted to a grayscale. We assume that each color is converted to a shade of gray with the same intensity as the color. We also assume that the color scales have a…
Musical scales are used throughout the world, but the question of how they evolved remains open. Some suggest that scales based on the harmonic series are inherently pleasant, while others propose that scales are chosen that are easy to…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
Order statistics of periodic, Gaussian noise with 1/f^{\alpha} power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d_k=<x_k-x_{k+1}> between the k-th and…
This paper provides a new mathematical axiom system for classical harmony, which is a prescriptive rule system for composing music, introduced in the second half of the 18th century. The clearest model of classical harmony is given by the…
We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…
We discuss a remarkable new approach initiated by Cachazo, Svrcek and Witten for calculating gauge theory amplitudes. The formalism amounts to an effective scalar perturbation theory which in many cases offers a much simpler alternative to…
The quantum and classical aspects of a deformed $c=1$ matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of Toda lattice hierarchy. The Whittaker functions now play the role of…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
The idea of the principle of nested intervals or the concept of convergent sequences which is equivalent to this idea dates back to the ancient world. Archimedes calculated the unknown in excess and deficiency, approximating with two sets…
The cosmological constant, usually named Lambda, was introduced by Einstein in 1917 and abandoned by him as his biggest "blunder". It currently seems to make a spectacular comeback in the framework of the new cosmological standard model.…
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…
We present a comparative analysis of current observational constraints on three recently discussed alternative models for explaining the low-redshift acceleration of the universe: the so-called steady-state torsion model, the generalized…
This paper deals with two notions: a polarized partition relations $\left( \begin{array}{c} \alpha \beta \end{array} \right) \to \left( \begin{array}{cc} \gamma & \eta \delta & \lambda \end{array} \right)$ and product of generalized strong…
Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe,…
This paper argues that the half-Cauchy distribution should replace the inverse-Gamma distribution as a default prior for a top-level scale parameter in Bayesian hierarchical models, at least for cases where a proper prior is necessary. Our…
This paper investigates end-to-end learnable models for attributing composers to musical scores. We introduce several pooled, convolutional architectures for this task and draw connections between our approach and classical learning…