Related papers: Dynamical systems theory for music dynamics
This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…
In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
Musical expressivity and coherence are indispensable in music composition and performance, while often neglected in modern AI generative models. In this work, we introduce a listening-based data-processing technique that captures the…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of…
The dynamic range is an important parameter which measures the spread of sound power, and for music signals it is a measure of recording quality. There are various descriptive measures of sound power, none of which has strong statistical…
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…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
We propose the use of specific dynamical processes and more in general of ideas from Physics to model the evolution in time of musical structures. We apply this approach to two \'Etudes by F. Chopin, namely op.10 n.3 and op.25 n.1,…
This Thesis discusses the development of technologies for the automatic resynthesis of music recordings using digital synthesizers. First, the main issue is identified in the understanding of how Music Information Processing (MIP) methods…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
Music listening preferences at a given time depend on a wide range of contextual factors, such as user emotional state, location and activity at listening time, the day of the week, the time of the day, etc. It is therefore of great…
Music is a structured and perceptually rich sequence of sounds in time, whose perception is shaped by the interplay of expectation and uncertainty about what comes next. Yet the uncertainty we infer from music depends on how the musical…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…