scholarly journals Can Menzerath’s law be a criterion of complexity in communication?

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256133
Author(s):  
Iván G. Torre ◽  
Łukasz Dębowski ◽  
Antoni Hernández-Fernández
Keyword(s):  
Power Law ◽  
Null Model ◽  
Exact Form ◽  
Expected Length ◽  
Complex Patterns ◽  
Exponential Formula

Menzerath’s law is a quantitative linguistic law which states that, on average, the longer is a linguistic construct, the shorter are its constituents. In contrast, Menzerath-Altmann’s law (MAL) is a precise mathematical power-law-exponential formula which expresses the expected length of the linguistic construct conditioned on the number of its constituents. In this paper, we investigate the anatomy of MAL for constructs being word tokens and constituents being syllables, measuring its length in graphemes. First, we derive the exact form of MAL for texts generated by the memoryless source with three emitted symbols, which can be interpreted as a monkey typing model or a null model. We show that this null model complies with Menzerath’s law, revealing that Menzerath’s law itself can hardly be a criterion of complexity in communication. This observation does not apply to the more precise Menzerath-Altmann’s law, which predicts an inverted regime for sufficiently range constructs, i.e., the longer is a word, the longer are its syllables. To support this claim, we analyze MAL on data from 21 languages, consisting of texts from the Standardized Project Gutenberg. We show the presence of the inverted regime, not exhibited by the null model, and we demonstrate robustness of our results. We also report the complicated distribution of syllable sizes with respect to their position in the word, which might be related with the emerging MAL. Altogether, our results indicate that Menzerath’s law—in terms of correlations—is a spurious observation, while complex patterns and efficiency dynamics should be rather attributed to specific forms of Menzerath-Altmann’s law.

NON SCALE-INVARIANT ISOCURVATURE PERTURBATIONS PRODUCED IN THE POWER-LAW INFLATION

1991 ◽  
Vol 06 (32) ◽  
pp. 2935-2945 ◽  
Author(s):  
MISAO SASAKI ◽  
BORIS L. SPOKOINY
Keyword(s):  
Scalar Field ◽  
Power Law ◽  
Quantum Fluctuation ◽  
Careful Analysis ◽  
Baryon Density ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Exact Form ◽  
Point Function ◽  
Scale Invariant

We present a careful analysis of non scale-invariant insocurvature perturbation produced in the power-law inflation. We first derive the exact form of the two-point function for a massless scalar field φ in a power-law background, a (t) ∝ t1+n (n≫1). For generality, we allow the scalar field to have a small nonminimal coupling to gravity, ~ ξφ2 R (|ξ|≪1). We then regard φ as an axion-like field whose quantum fluctuation gives rise to an isocurvature perturbation with its amplitude proportional to a trigonometric function of φ. As a concrete example, we consider the case when φ is a Majoron and the baryon density fluctuation is produced in proportion to sin (φ/f) where f is the symmetry breaking scale. We find the resulting spectrum of the (baryon) isocurvature perturbation depends very much on the sign of n*, where 1/n* = 1/n + ξ. For n* > 0, corresponding to an infrared unstable scalar field, the spectrum is white noise on large scales and almost scale-invariant on small scales. On the other hand, for n* < 0, corresponding to an infrared stable scalar field, the spectrum is almost scale-invariant on all the scales.

scholarly journals Analytical models for β-diversity and the power-law scaling of β-deviation

2020 ◽  
Author(s):  
Dingliang Xing ◽  
Fangliang He
Keyword(s):  
Power Law ◽  
Community Assembly ◽  
Species Abundance ◽  
Null Model ◽  
Analytical Models ◽  
List Type ◽  
Species Abundance Distribution ◽  
Abundance Distribution ◽  
Simple Method ◽  
Occurrence Data

ABSTRACTβ-diversity is a primary biodiversity pattern for inferring community assembly. A randomized null model that generates a standardized β-deviation has been widely used for this purpose. However, the null model has been much debated and its application is limited to abundance data.Here we derive analytical models for β-diversity to address the debate, clarify the interpretation, and extend the application to occurrence data.The analytical analyses show unambiguously that the standardized β-deviation is a quantification of the effect size of non-random spatial distribution of species on β-diversity for a given species abundance distribution. It robustly scales with sampling effort following a power law with exponent of 0.5. This scaling relationship offers a simple method for comparing β-diversity of communities of different sizes.Assuming logseries distribution for the metacommunity species abundance distribution, our model allows for calculation of the standardized β-deviation using occurrence data plus a datum on the total abundance.Our theoretical model justifies and generalizes the use of the β null model for inferring community assembly rules.

scholarly journals Power-law Null Model for Bystander Mutations in Cancer

2014 ◽  
Author(s):  
Loes Olde Loohuis ◽  
Andreas Witzel ◽  
Bud Mishra
Keyword(s):  
Power Law ◽  
Copy Number ◽  
Preferential Attachment ◽  
Null Model ◽  
Generative Model ◽  
Power Law Distribution ◽  
Driver Genes ◽  
Underlying Process ◽  
Cancer Driver ◽  
Number Variation

In this paper we study Copy Number Variation (CNV) data. The underlying process generating CNV segments is generally assumed to be memory-less, giving rise to an exponential distribution of segment lengths. In this paper, we provide evidence from cancer patient data, which suggests that this generative model is too simplistic, and that segment lengths follow a power-law distribution instead. We conjecture a simple preferential attachment generative model that provides the basis for the observed power-law distribution. We then show how an existing statistical method for detecting cancer driver genes can be improved by incorporating the power-law distribution in the null model.

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

1968 ◽  
Vol 11 (1) ◽  
pp. 169-178 ◽  
Author(s):  
Alan Gill ◽  
Charles I. Berlin
Keyword(s):  
Power Law ◽  
Response Magnitude ◽  
Single Units ◽  
Spectral Content ◽  
Hearing Sensitivity ◽  
Subjective Magnitude ◽  
Orderly Fashion ◽  
Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

How Useful is the Power Law of Practice for Recognizing Practice in Concentration Tests?

2007 ◽  
Vol 23 (3) ◽  
pp. 157-165 ◽  
Author(s):  
Carmen Hagemeister
Keyword(s):  
Logistic Regression ◽  
Reaction Time ◽  
Power Law ◽  
Error Rate ◽  
Reaction Times ◽  
Practice Effect ◽  
Practice Effects ◽  
Rate Decrease ◽  
Small Practice

Abstract. When concentration tests are completed repeatedly, reaction time and error rate decrease considerably, but the underlying ability does not improve. In order to overcome this validity problem this study aimed to test if the practice effect between tests and within tests can be useful in determining whether persons have already completed this test. The power law of practice postulates that practice effects are greater in unpracticed than in practiced persons. Two experiments were carried out in which the participants completed the same tests at the beginning and at the end of two test sessions set about 3 days apart. In both experiments, the logistic regression could indeed classify persons according to previous practice through the practice effect between the tests at the beginning and at the end of the session, and, less well but still significantly, through the practice effect within the first test of the session. Further analyses showed that the practice effects correlated more highly with the initial performance than was to be expected for mathematical reasons; typically persons with long reaction times have larger practice effects. Thus, small practice effects alone do not allow one to conclude that a person has worked on the test before.

A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽  
2005 ◽  
Vol 1 (2) ◽  
pp. 81-85 ◽  
Author(s):  
Stefan C. Schmukle ◽  
Jochen Hardt
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Null Model ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Fit Indices ◽  
Cautionary Note ◽  
Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

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