Collective Intelligence for Control of Distributed Dynamical Systems

We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, ``The American Economic Review'', 84(2): 406--411 (1994), D. Challet and Y.C. Zhang, ``Physica A'', 256:514 (1998)). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not ``work at cross purposes'', in that their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local free energy functions. We show that a system designed with that theory performs nearly optimally for the bar problem.Comment: 8 page

Testing a Spectral Model of Tonal Affinity with Microtonal Melodies and Inharmonic Spectra

Tonal affinity is the perceived goodness of fit of successive tones. It is important because a preference for certain intervals over others would likely influence preferences for, and prevalences of, “higher-order” musical structures such as scales and chord progressions. We hypothesize that two psychoacoustic (spectral) factors—harmonicity and spectral pitch similarity—have an impact on affinity. The harmonicity of a single tone is the extent to which its partials (frequency components) correspond to those of a harmonic complex tone (whose partials are a multiple of a single fundamental frequency). The spectral pitch similarity of two tones is the extent to which they have partials with corresponding, or close, frequencies. To ascertain the unique effect sizes of harmonicity and spectral pitch similarity, we constructed a computational model to numerically quantify them. The model was tested against data obtained from 44 participants who ranked the overall affinity of tones in melodies played in a variety of tunings (some microtonal) with a variety of spectra (some inharmonic). The data indicate the two factors have similar, but independent, effect sizes: in combination, they explain a sizeable portion of the variance in the data (the model-data squared correlation is r2 = .64). Neither harmonicity nor spectral pitch similarity require prior knowledge of musical structure, so they provide a potentially universal bottom-up explanation for tonal affinity. We show how the model—as optimized to these data—can explain scale structures commonly found in music, both historical and contemporary, and we discuss its implications for experimental microtonal and spectral music

Microtiming patterns and interactions with musical properties in Samba music

In this study, we focus on the interaction between microtiming patterns and several musical properties: intensity, meter and spectral characteristics. The data-set of 106 musical audio excerpts is processed by means of an auditory model and then divided into several spectral regions and metric levels. The resulting segments are described in terms of their musical properties, over which patterns of peak positions and their intensities are sought. A clustering algorithm is used to systematize the process of pattern detection. The results confirm previously reported anticipations of the third and fourth semiquavers in a beat. We also argue that these patterns of microtiming deviations interact with different profiles of intensities that change according to the metrical structure and spectral characteristics. In particular, we suggest two new findings: (i) a small delay of microtiming positions at the lower end of the spectrum on the first semiquaver of each beat and (ii) systematic forms of accelerando and ritardando at a microtiming level covering two-beat and four-beat phrases. The results demonstrate the importance of multidimensional interactions with timing aspects of music. However, more research is needed in order to find proper representations for rhythm and microtiming aspects in such contexts

Perception of isolated chords: Examining frequency of occurrence, instrumental timbre, acoustic descriptors and musical training

This study investigated the perception of isolated chords using a combination of experimental manipulation and exploratory analysis. Twelve types of chord (five triads and seven tetrads) were presented in two instrumental timbres (piano and organ) to listeners who rated the chords for consonance, pleasantness, stability and relaxation. Listener ratings varied by chord, by timbre, and according to musical expertise, and revealed that musicians distinguished consonance from the other variables in a way that other listeners did not. To further explain the data, a principal component analysis and linear regression examined three potential predictors of the listener ratings. First, each chord’s frequency of occurrence was obtained by counting its appearances in selected works of music. Second, listeners rated their familiarity with the instrumental timbre in which the chord was played. Third, chords were described using a set of acoustic features derived using the Timbre Toolbox and MIR Toolbox. Results of the study indicated that listeners’ ratings of both consonance and stability were influenced by the degree of musical training and knowledge of tonal hierarchy. Listeners’ ratings of pleasantness and relaxation, on the other hand, depended more on the instrumental timbre and other acoustic descriptions of the chord

Recursive Blind Image Deconvolution Via Dispersion Minimization

This paper presents an adaptive autoregressive (AR) approach to the blind image deconvolution problem which has several advantages over standard adaptive FIR filters. There is no need to figure out the optimum filter support when using an AR deconvolution filter because it is the same as the support of the blur. Thus there is no distortion introduced by the finite support of the FIR filter. While an FIR filter provides an approximate inverse to the blur at convergence, the AR filter converges to an approximation of the blur itself. Hence, the method can be used for blur identification. Simulations suggest that convergence of the adaptive AR filter coe#cients occur rapidly and the improvement in signal-to-noise ratios are higher than in the FIR case for a given blur (and with the same step-size for the adaptive algorithms). When the adaptive AR method is derived naively to minimize the dispersion, it requires a recursion within a recursion which is computationally complex. We propose a simplification that removes the inner recursion, and prove conditions under which this simplification is valid when dealing with binary images. Simulations are used to show that the method may also be applied to certain multi-valued images as well. Copyright # 2005 John Wiley & Sons, Lt

Sethares, “Convergence analysis of blind image deconvolution via dispersion minimization

A new non-linear adaptive filter called blind image deconvolution via dispersion minimization has recently been proposed for restoring noisy blurred images blindly. This is essentially a two-dimensional version of the constant modulus algorithm that is well known in the field of blind equalization. The two-dimensional extension has been shown capable of reconstructing noisy blurred images using partial a priori information about the true image and the point spread function in a variety of situations by means of simulations. This paper analyses the behaviour of the algorithm by investigating the static properties of the cost function and the dynamic convergence of the parameter estimates. The theoretical results are supported with computer simulations. Copyright # 2006 John Wiley & Sons, Ltd. KEY WORDS: blind image deconvolution; non-linear adaptive filtering; constant modulus algorithm; convergence analysis 1

Periodicity transforms

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Meter and Periodicity in Musical Performance

This paper presents a psychoacoustically based method of data reduction motivated by the desire to analyze the rhythm of musical performances. The resulting information is then analyzed by the “Periodicity Transform ” (which is based on a projection onto “periodic subspaces”) to locate periodicities in the resulting data. These periodicities represent the rhythm at several levels, including the “pulse”, the “measure”, and larger structures such as musical “phrases.” The implications (and limitations) of such automated grouping of rhythmic features is discussed. The method is applied to a number of musical examples, its output is compared to that of the Fourier Transform, and both are compared to a more traditional “musical ” analysis of the rhythm. Unlike many methods of rhythm analysis, the techniques can be applied directly to the digitized performance (i.e., a soundfile) and do not require a musical score or a MIDI transcription. Several examples are presented that highlight both the strengths and weaknesses of the approach.

Exploiting sparsity in adaptive filters

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