scholarly journals Fame, Obscurity and Power Laws in Music History

2020 ◽  
Vol 14 (3-4) ◽  
pp. 186
Author(s):  
Andrew Gustar
Keyword(s):  
Power Law ◽  
Power Laws ◽  
Music History ◽  
Average Value ◽  
Musical Activity ◽  
Power Law Exponent ◽  
Fundamental Process ◽  
The Common ◽  
Individual Importance ◽  
Power Law Distributions

This paper investigates the processes leading to musical fame or obscurity, whether for composers, performers, or works themselves. It starts from the observation that the patterns of success, across many historical music datasets, follow a similar mathematical relationship known as a power law, often with an exponent approximately equal to two. It presents several simple models which can produce power law distributions. An examination of these models' transience characteristics suggests parallels with some historical music examples, giving clues to the ways that success and obscurity might emerge in practice and the extent to which success might be influenced by inherent musical quality. These models can be seen as manifestations of a more fundamental process resulting from the law of maximum entropy, subject to a constraint on the average value of the logarithm of the success measure. This implies that musical success is a multiplicative quality, and suggests that musical markets operate to strike a balance between familiarity (socio-cultural importance) and novelty (individual importance). The common power law exponent of two is seen to emerge as a consequence of the tendency for musical activity to be spread evenly across the log-success bands.

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

scholarly journals POWER-LAW DISTRIBUTIONS IN CIRCULATING MONEY: EFFECT OF PREFERENTIAL BEHAVIOR

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2725-2729 ◽  
Author(s):  
NING DING ◽  
YOUGUI WANG ◽  
JUN XU ◽  
NING XI
Keyword(s):  
Computer Simulation ◽  
Statistical Mechanics ◽  
Power Law ◽  
Power Laws ◽  
Generation Mechanism ◽  
Holding Time ◽  
Simulation Results ◽  
Power Law Distributions ◽  
Money Circulation

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mechanism to ensure the robustness of power-law distributions.

Environmental Stress Models

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Critical Phenomena ◽  
Power Law ◽  
Species Interactions ◽  
Fossil Record ◽  
Biotic Interactions ◽  
Power Laws ◽  
Fixed Number ◽  
Stress Models ◽  
Fossil Data ◽  
Power Law Distributions

In chapters 2 to 4 we discussed several models of extinction which make use of ideas drawn from the study of critical phenomena. The primary impetus for this approach was the observation of apparent power-law distributions in a variety of statistics drawn from the fossil record, as discussed in section 1.2; in other branches of science such power laws are often indicators of critical processes. However, there are also a number of other mechanisms by which power laws can arise, including random multiplicative processes (Montroll and Shlesinger 1982; Sornette and Cont 1997), extremal random processes (Sibani and Littlewood 1993), and random barrier-crossing dynamics (Sneppen 1995). Thus the existence of power-law distributions in the fossil data is not on its own sufficient to demonstrate the presence of critical phenomena in extinction processes. Critical models also assume that extinction is caused primarily by biotic effects such as competition and predation, an assumption which is in disagreement with the fossil record. As discussed in section 1.2.2.1, all the plausible causes for specific prehistoric extinctions are abiotic in nature. Therefore an obvious question to ask is whether it is possible to construct models in which extinction is caused by abiotic environmental factors, rather than by critical fluctuations arising out of biotic interactions, but which still give power-law distributions of the relevant quantities. Such models have been suggested by Newman (1996, 1997) and by Manrubia and Paczuski (1998). Interestingly, both of these models are the result of attempts at simplifying models based on critical phenomena. Newman's model is a simplification of the model of Newman and Roberts (see section 3.6), which included both biotic and abiotic effects; the simplification arises from the realization that the biotic part can be omitted without losing the power-law distributions. Manrubia and Paczuski's model was a simplification of the connection model of Solé and Manrubia (see section 4.1), but in fact all direct species-species interactions were dropped, leaving a model which one can regard as driven only by abiotic effects. We discuss these models in turn. The model proposed by Newman (1996, 1997) has a fixed number N of species which in the simplest case are noninteracting.

scholarly journals SPONTANEOUS SCALING EMERGENCE IN GENERIC STOCHASTIC SYSTEMS

1996 ◽  
Vol 07 (05) ◽  
pp. 745-751 ◽  
Author(s):  
SORIN SOLOMON ◽  
MOSHE LEVY
Keyword(s):  
Degrees Of Freedom ◽  
Stochastic Systems ◽  
Evolution Equations ◽  
Power Laws ◽  
Average Value ◽  
Wide Range ◽  
Generic Class ◽  
Parameter Ranges ◽  
Power Law Distributions ◽  
Macroscopic Fluctuations

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range (α < –2.) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents α > −2 there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.

POWER LAWS, WEAK lp ESTIMATE AND WAVELET DE-NOISING

Fractals ◽  
2000 ◽  
Vol 08 (01) ◽  
pp. 73-83
Author(s):  
TOMOHIRO MATSUOKA ◽  
TOSHIHIDE UENO ◽  
TAKASHI ADACHI ◽  
MASAMI OKADA
Keyword(s):  
Power Law ◽  
Power Laws ◽  
Mild Assumption ◽  
Lp Estimate ◽  
Scaling Argument ◽  
Power Law Distributions

Data with power law distributions are studied by a scaling argument. Then related weak lp sequences are characterized. As an application we can show in a transparent way that the wavelet de-noising theory holds under a mild assumption which is given by means of weak lp (quasi-)norms.

SIMPLE MODELS OF WAITING LISTS

2003 ◽  
Vol 06 (02) ◽  
pp. 215-222 ◽  
Author(s):  
G. J. RODGERS ◽  
Y. J. YAP ◽  
T. P. YOUNG
Keyword(s):  
Power Law ◽  
Empirical Studies ◽  
Length Distribution ◽  
Power Laws ◽  
Waiting Lists ◽  
Waiting List ◽  
Power Law Distributions ◽  
Simple Models

Motivated by recent empirical studies of the length distribution of hospital waiting lists, we introduce and solve a set of models that imitate the formation of waiting lists. Patients arriving in the system must choose a waiting list to join, based on its length. At the same time patients leave the lists as they get served. The model illustrates how the power-law distributions found in the empirical studies might arise, but indicates that the mechanism causing the power-laws is unlikely to be the preferential behavior of patients or their physicians.

scholarly journals Half Way There: Theoretical Considerations for Power Laws and Sticks in Diffusion MRI for Tissue Microstructure

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1871
Author(s):  
Matt G. Hall ◽  
Carson Ingo
Keyword(s):  
Power Law ◽  
Power Laws ◽  
Tissue Microstructure ◽  
Confluent Hypergeometric Functions ◽  
A Value ◽  
Power Law Exponent ◽  
Weighted Magnetic Resonance Imaging ◽  
Diffusion Weighting ◽  
Theoretical Considerations ◽  
Insight Into

In this article, we consider how differing approaches that characterize biological microstructure with diffusion weighted magnetic resonance imaging intersect. Without geometrical boundary assumptions, there are techniques that make use of power law behavior which can be derived from a generalized diffusion equation or intuited heuristically as a time dependent diffusion process. Alternatively, by treating biological microstructure (e.g., myelinated axons) as an amalgam of stick-like geometrical entities, there are approaches that can be derived utilizing convolution-based methods, such as the spherical means technique. Since data acquisition requires that multiple diffusion weighting sensitization conditions or b-values are sampled, this suggests that implicit mutual information may be contained within each technique. The information intersection becomes most apparent when the power law exponent approaches a value of 12, whereby the functional form of the power law converges with the explicit stick-like geometric structure by way of confluent hypergeometric functions. While a value of 12 is useful for the case of solely impermeable fibers, values that diverge from 12 may also reveal deep connections between approaches, and potentially provide insight into the presence of compartmentation, exchange, and permeability within heterogeneous biological microstructures. All together, these disparate approaches provide a unique opportunity to more completely characterize the biological origins of observed changes to the diffusion attenuated signal.

Classes of preferential attachment and triangle preferential attachment models with power-law spectra

2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Nicole Eikmeier ◽  
David F Gleich
Keyword(s):  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Power Laws ◽  
Network Data ◽  
Degree Sequences ◽  
Graph Models ◽  
Attachment Model ◽  
Power Law Distributions ◽  
Real Network Data

Abstract Preferential attachment (PA) models are a common class of graph models which have been used to explain why power-law distributions appear in the degree sequences of real network data. Among other properties of real-world networks, they commonly have non-trivial clustering coefficients due to an abundance of triangles as well as power laws in the eigenvalue spectra. Although there are triangle PA models and eigenvalue power laws in specific PA constructions, there are no results that existing constructions have both. In this article, we present a specific Triangle Generalized Preferential Attachment Model that, by construction, has non-trivial clustering. We further prove that this model has a power law in both the degree distribution and eigenvalue spectra.

Power Laws and Skew Distributions

2012 ◽  
Vol 12 (3) ◽  
pp. 721-731
Author(s):  
Reinhard Mahnke ◽  
Jevgenijs Kaupužs ◽  
Mārtiņš Brics
Keyword(s):  
Exact Solutions ◽  
Numerical Simulations ◽  
Power Law ◽  
Power Laws ◽  
Skew Distributions ◽  
Evolving Systems ◽  
Power Law Distributions

AbstractPower-law distributions and other skew distributions, observed in various models and real systems, are considered. A model, describing evolving systems with increasing number of elements, is considered to study the distribution over element sizes. Stationary power-law distributions are found. Certain non-stationary skew distributions are obtained and analyzed, based on exact solutions and numerical simulations.

scholarly journals Power law statistics of force and acoustic emission from a slowly penetrated granular bed

2014 ◽  
Vol 21 (1) ◽  
pp. 1-8 ◽  
Author(s):  
K. Matsuyama ◽  
H. Katsuragi
Keyword(s):  
Acoustic Emission ◽  
Power Law ◽  
Glass Bead ◽  
Power Laws ◽  
Solid Sphere ◽  
Granular Bed ◽  
Power Law Distribution ◽  
Energy Scaling ◽  
Power Law Exponent ◽  
Ae Signal

Abstract. Penetration-resistant force and acoustic emission (AE) from a plunged granular bed are experimentally investigated through their power law distribution forms. An AE sensor is buried in a glass bead bed. Then, the bed is slowly penetrated by a solid sphere. During the penetration, the resistant force exerted on the sphere and the AE signal are measured. The resistant force shows power law relation to the penetration depth. The power law exponent is independent of the penetration speed, while it seems to depend on the container's size. For the AE signal, we find that the size distribution of AE events obeys power laws. The power law exponent depends on grain size. Using the energy scaling, the experimentally observed power law exponents are discussed and compared to the Gutenberg–Richter (GR) law.

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