Emergent statistical-mechanical structure in the dynamics along the period-doubling route to chaos

We consider both the dynamics within and towards the supercycle attractors along the period-doubling route to chaos to analyze the development of a statistical-mechanical structure. In this structure the partition function consists of the sum of the attractor position distances known as supercycle diameters and the associated thermodynamic potential measures the rate of approach of trajectories to the attractor. The configurational weights for finite $2^{N}$, and infinite $N \rightarrow \infty$, periods can be expressed as power laws or deformed exponentials. For finite period the structure is undeveloped in the sense that there is no true configurational degeneracy, but in the limit $N\rightarrow \infty$ this is realized together with the analog property of a Legendre transform linking entropies of two ensembles. We also study the partition functions for all $N$ and the action of the Central Limit Theorem via a binomial approximation.Comment: 11 pages, 3 figures. arXiv admin note: text overlap with arXiv:1312.071

Idealized computational models for auditory receptive fields

This paper presents a theory by which idealized models of auditory receptive fields can be derived in a principled axiomatic manner, from a set of structural properties to enable invariance of receptive field responses under natural sound transformations and ensure internal consistency between spectro-temporal receptive fields at different temporal and spectral scales. For defining a time-frequency transformation of a purely temporal sound signal, it is shown that the framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters, with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal temporal window functions. When applied to the definition of a second-layer of receptive fields from a spectrogram, it is shown that the framework leads to two canonical families of spectro-temporal receptive fields, in terms of spectro-temporal derivatives of either spectro-temporal Gaussian kernels for non-causal time or the combination of a time-causal generalized Gammatone filter over the temporal domain and a Gaussian filter over the logspectral domain. For each filter family, the spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Within each domain of either non-causal or time-causal time, these receptive field families are derived by uniqueness from the assumptions. It is demonstrated how the presented framework allows for computation of basic auditory features for audio processing and that it leads to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields measured in the inferior colliculus (ICC) and primary auditory cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table

Analytic models of ducted turbomachinery tone noise sources. Volume 1: Analysis

The analytic models developed for computing the periodic sound pressure of subsonic fans and compressors in an infinite, hardwall annular duct with uniform flow are described. The basic sound-generating mechanism is the scattering into sound waves of velocity disturbances appearing to the rotor or stator blades as a series of harmonic gusts. The models include component interactions and rotor alone

Exploitation dynamics of fish stocks

I address the question of the fluctuations in fishery landings. Using the fishery statistics time-series collected by the Food and Agriculture Organization of the United Nations since the early 1950s, I here analyze fishing activities and find two scaling features of capture fisheries production: (i) the standard deviation of growth rate of the domestically landed catches decays as a power-law function of country landings with an exponent of value 0.15; (ii) the average number of fishers in a country scales to the 0.7 power of country landings. I show how these socio-ecological patterns may be related, yielding a scaling relation between these exponents. The predicted scaling relation implies that the width of the annual per capita growth-rate distribution scales to the 0.2 power of country landings, i.e. annual fluctuations in per capita landed catches increase with increased per capita catches in highly producing countries. Beside the scaling behavior, I report that fluctuations in the annual domestic landings have increased in the last 30 years, while the mean of the annual growth rate declined significantly after 1972.Comment: 27 pages, 19 figure

Statistical models for natural sounds

It is important to understand the rich structure of natural sounds in order to solve important tasks, like automatic speech recognition, and to understand auditory processing in the brain. This thesis takes a step in this direction by characterising the statistics of simple natural sounds. We focus on the statistics because perception often appears to depend on them, rather than on the raw waveform. For example the perception of auditory textures, like running water, wind, fire and rain, depends on summary-statistics, like the rate of falling rain droplets, rather than on the exact details of the physical source. In order to analyse the statistics of sounds accurately it is necessary to improve a number of traditional signal processing methods, including those for amplitude demodulation, time-frequency analysis, and sub-band demodulation. These estimation tasks are ill-posed and therefore it is natural to treat them as Bayesian inference problems. The new probabilistic versions of these methods have several advantages. For example, they perform more accurately on natural signals and are more robust to noise, they can also fill-in missing sections of data, and provide error-bars. Furthermore, free-parameters can be learned from the signal. Using these new algorithms we demonstrate that the energy, sparsity, modulation depth and modulation time-scale in each sub-band of a signal are critical statistics, together with the dependencies between the sub-band modulators. In order to validate this claim, a model containing co-modulated coloured noise carriers is shown to be capable of generating a range of realistic sounding auditory textures. Finally, we explored the connection between the statistics of natural sounds and perception. We demonstrate that inference in the model for auditory textures qualitatively replicates the primitive grouping rules that listeners use to understand simple acoustic scenes. This suggests that the auditory system is optimised for the statistics of natural sounds