Related papers: Complexity, time and music
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional…
We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
If a concept is not well defined, there are grounds for its abuse. This is particularly true of complexity, an inherently interdisciplinary concept that has penetrated very different fields of intellectual activity from physics to…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering…
We revisit the long-standing question of the relation between image appreciation and its statistical properties. We generate two different sets of random images well distributed along three measures of entropic complexity. We run a…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
Computers have been used to analyze and create music since they were first introduced in the 1950s and 1960s. Beginning in the late 1990s, the rise of the Internet and large scale platforms for music recommendation and retrieval have made…
We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…
We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs~\cite{Gacs} and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real…
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and…
In this article, a framework for defining and analysing a family of graphs or networks from symbolic music information is discussed. Such graphs concern different types of elements, such as pitches, chords and rhythms, and the relations…