Month: November 2021

Towards a Measure for Characterizing the Informational Content of Audio Signals and the Relation between Complexity and Auditory Encoding

Daniel Guerrero, Pedro Rivera, Gerardo Febres, and Carlos Gershenson

Entropy 2021, 23(12), 1613

The accurate description of a complex process should take into account not only the interacting elements involved but also the scale of the description. Therefore, there can not be a single measure for describing the associated complexity of a process nor a single metric applicable in all scenarios. This article introduces a framework based on multiscale entropy to characterize the complexity associated with the most identifiable characteristic of songs: the melody. We are particularly interested in measuring the complexity of popular songs and identifying levels of complexity that statistically explain the listeners’ preferences. We analyze the relationship between complexity and popularity using a database of popular songs and their relative position in a preferences ranking. There is a tendency toward a positive association between complexity and acceptance (success) of a song that is, however, not significant after adjusting for multiple testing.

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Natural selection of mutants that modify population structure

Josef Tkadlec, Kamran Kaveh, Krishnendu Chatterjee, Martin A. Nowak
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we study how natural selection acts on mutants that have the same reproductive rate, but experience different population structures. In our framework, mutation alters population structure, which is given by a graph that specifies the dispersal of offspring. Reproduction can be either genetic or cultural. Competing mutants disperse their offspring on different graphs. A more connected graph implies higher motility. We show that enhanced motility tends to increase an invader’s fixation probability, but there are interesting exceptions. For island models, we show that the magnitude of the effect depends crucially on the exact layout of the additional links. Finally, we show that for low-dimensional lattices, the effect of altered motility is comparable to that of altered fitness: in the limit of large population size, the invader’s fixation probability is either constant or exponentially small, depending on whether it is more or less motile than the resident.

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Hidden transition in multiplex networks

R. A. da Costa, G. J. Baxter, S. N. Dorogovtsev, J. F. F. Mendes
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, P(0)=0. Above a critical value of a control parameter, the removal of a tiny fraction Δ of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, Π=P(1). We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point Πc, respectively. In the limit Δ→0 the total collapse for Π>Πc takes a time T∝1/(Π−Πc), while there is an exponential relaxation below Πc with a relaxation time τ∝1/[Πc−Π].

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