A Study of Musical Pitch Distance Using a Self-Organized Hierarchical Linear Dynamical System on Acoustic Signals

2016 ◽  
Vol 40 (3) ◽  
pp. 68-82 ◽  
Author(s):  
Goktug T. Cinar ◽  
James P. Sain ◽  
Jose C. Principe
Keyword(s):  
Dynamical System ◽  
Filter Bank ◽  
Acoustic Signals ◽  
Voice Leading ◽  
Representation Space ◽  
Linear Dynamical System ◽  
Self Organized ◽  
Musical Pitch ◽  
Pitch Distance ◽  
Self Organizing

The hierarchical linear dynamical system (HLDS) is a self-organizing architecture to cluster acoustic time series. The HLDS architecture is equivalent to a Kalman filter whose top-layer state learns to create subspaces that tessellate the acoustic signal in regions that correspond to different musical pitches. The observation layer of the HLDS is built from a biologically plausible gammatone filter bank that provides the representation space for the state assignments. An important characteristic of the methodology is that it is adaptive and self-organizing, i.e., previous exposure to the acoustic input is the only requirement for learning and recognition. In this article we show that the representation space that the algorithm learns from acoustic signals preserves the organization found in monophonic notes, and exhibits (for isolated pitches and triads) properties suggested in the theory of efficient chromatic voice leading and neo-Riemannian theories.

A novel unified approach to invariance conditions for a linear dynamical system

2017 ◽  
Vol 298 ◽  
pp. 351-367 ◽  
Author(s):  
Zoltán Horváth ◽  
Yunfei Song ◽  
Tamás Terlaky
Keyword(s):  
Dynamical System ◽  
Linear Dynamical System ◽  
Unified Approach

scholarly journals Communicating vessels: a non-linear dynamical system

2017 ◽  
Vol 39 (3) ◽  
Author(s):  
Roberto De Luca ◽  
Orazio Faella
Keyword(s):  
Dynamical System ◽  
Fluid Flow ◽  
Ideal Fluid ◽  
Oscillatory Motion ◽  
Linear Dynamical System ◽  
Static Properties ◽  
Bernoulli’S Equation ◽  
Non Linear ◽  
Dynamical Properties

The dynamics of an ideal fluid contained in two communicating vessels is studied. Despite the fact that the static properties of this system have been known since antiquity, the knowledge of the dynamical properties of an ideal fluid flowing in two communicating vessels is not similarly widespread. By means of Bernoulli's equation for non-stationary fluid flow, we study the oscillatory motion of the fluid when dissipation can be neglected.

Criticality: How Changes Preserve Stability in Self-Organizing Systems

2018 ◽  
Vol 40 (11) ◽  
pp. 1613-1629 ◽  
Author(s):  
Philippe Accard
Keyword(s):  
Complex System ◽  
System Theory ◽  
Social Systems ◽  
Theoretical Framework ◽  
Fundamental Issue ◽  
Self Organized ◽  
Self Organized Criticality ◽  
New Treatment ◽  
Over Time ◽  
Self Organizing

Self-organizing systems are social systems which are immanently and constantly recreated by agents. In a self-organizing system, agents make changes while preserving stability. If they do not preserve stability, they push the system toward chaos and cannot recreate it. How changes preserve stability is thus a fundamental issue. In current works, changes preserve stability because agents’ ability to make changes is limited by interaction rules and power. However, how agents diffuse the changes throughout the system while preserving its stability has not been addressed in these works. We have addressed this issue by borrowing from a complex system theory neglected thus far in organization theories: self-organized criticality theory. We suggest that self-organizing systems are in critical states: agents have equivalent ability to make changes, and none are able to foresee or control how their changes diffuse throughout the system. Changes, then, diffuse unpredictably – they may diffuse to small or large parts of the system or not at all, and it is this unpredictable diffusion that preserves stability in the system over time. We call our theoretical framework self-organiz ing criticality theory. It presents a new treatment of change and stability and improves the understanding of self-organizing.

scholarly journals Predictability of spatio-temporal patterns in a lattice of coupled FitzHugh–Nagumo oscillators

2013 ◽  
Vol 10 (81) ◽  
pp. 20121016 ◽  
Author(s):  
Miriam Grace ◽  
Marc-Thorsten Hütt
Keyword(s):  
Dynamical System ◽  
Spiral Wave ◽  
Temporal Patterns ◽  
Spiral Waves ◽  
Generic Model ◽  
Homogeneous State ◽  
Drift Speed ◽  
Statistical Fluctuations ◽  
Self Organized ◽  
Spatio Temporal

In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a ‘developmental path’), together with differences in cell properties (‘desynchronization’ of cells on the developmental path) can establish self-organized spatio-temporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHugh–Nagumo oscillators, into a developmental-path framework. In this minimal model of spiral wave generation, we can now study the predictability of spatio-temporal patterns from cell properties as a function of desynchronization (or ‘spread’) of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatio-temporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.

Self-Organized Formation of Various Invariant-Feature Filters in the Adaptive-Subspace SOM

1997 ◽  
Vol 9 (6) ◽  
pp. 1321-1344 ◽  
Author(s):  
Teuvo Kohonen ◽  
Samuel Kaski ◽  
Harri Lappalainen
Keyword(s):  
Network Architecture ◽  
Self Organizing Map ◽  
Restricted Class ◽  
Neural Network Architecture ◽  
Self Organized ◽  
Invariant Feature ◽  
Input Signals ◽  
Orderly Fashion ◽  
Feature Filters ◽  
Self Organizing

The adaptive-subspace self-organizing map (ASSOM) is a modular neural network architecture, the modules of which learn to identify input patterns subject to some simple transformations. The learning process is unsupervised, competitive, and related to that of the traditional SOM (self-organizing map). Each neural module becomes adaptively specific to some restricted class of transformations, and modules close to each other in the network become tuned to similar features in an orderly fashion. If different transformations exist in the input signals, different subsets of ASSOM units become tuned to these transformation classes.

Sign in / Sign up

Export Citation Format

Share Document