arXiv subjects

Martin Gerlach

Publications and source records attributed to Martin Gerlach.

25 records · Page 2Linked to original sources

arXiv2015

Statistical laws in linguistics

Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern availability of large databases of written text allows for tests with an unprecedent statistical accuracy and also a characterization of the fluctuations around the typical behavior. We find that fluctuations are usually much larger than expected based on simplifying statistical assumptions (e.g., independence and lack of correlations between observations).These simplifications appear also in usual statistical tests so that the large fluctuations can be erroneously interpreted as a falsification of the law. Instead, here we argue that linguistic laws are only meaningful (falsifiable) if accompanied by a model for which the fluctuations can be computed (e.g., a generative model of the text). The large fluctuations we report show that the constraints imposed by linguistic laws on the creativity process of text generation are not as tight as one could expect.

physics.soc-ph↗

arXiv2014

Scaling laws and fluctuations in the statistics of word frequencies

In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with database size (Heaps' law), here we report a new scaling of the fluctuations around this average (fluctuation scaling analysis). We explain both scaling laws by modeling the usage of words by simple stochastic processes in which the overall distribution of word-frequencies is fat tailed (Zipf's law) and the frequency of a single word is subject to fluctuations across documents (as in topic models). In this framework, the mean and the variance of the vocabulary size can be expressed as quenched averages, implying that: i) the inhomogeneous dissemination of words cause a reduction of the average vocabulary size in comparison to the homogeneous case, and ii) correlations in the co-occurrence of words lead to an increase in the variance and the vocabulary size becomes a non-self-averaging quantity. We address the implications of these observations to the measurement of lexical richness. We test our results in three large text databases (Google-ngram, Enlgish Wikipedia, and a collection of scientific articles).

physics.soc-ph↗

arXiv2014

Extracting information from S-curves of language change

It is well accepted that adoption of innovations are described by S-curves (slow start, accelerating period, and slow end). In this paper, we analyze how much information on the dynamics of innovation spreading can be obtained from a quantitative description of S-curves. We focus on the adoption of linguistic innovations for which detailed databases of written texts from the last 200 years allow for an unprecedented statistical precision. Combining data analysis with simulations of simple models (e.g., the Bass dynamics on complex networks) we identify signatures of endogenous and exogenous factors in the S-curves of adoption. We propose a measure to quantify the strength of these factors and three different methods to estimate it from S-curves. We obtain cases in which the exogenous factors are dominant (in the adoption of German orthographic reforms and of one irregular verb) and cases in which endogenous factors are dominant (in the adoption of conventions for romanization of Russian names and in the regularization of most studied verbs). These results show that the shape of S-curve is not universal and contains information on the adoption mechanism. (published at "J. R. Soc. Interface, vol. 11, no. 101, (2014) 1044"; DOI: http://dx.doi.org/10.1098/rsif.2014.1044)

physics.soc-ph↗

arXiv2013

Stochastic model for the vocabulary growth in natural languages

We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of words: (i) a finite number of core-words which have higher frequency and do not affect the probability of a new word to be used; and (ii) the remaining virtually infinite number of noncore-words which have lower frequency and once used reduce the probability of a new word to be used in the future. Our model relies on a careful analysis of the google-ngram database of books published in the last centuries and its main consequence is the generalization of Zipf's and Heaps' law to two scaling regimes. We confirm that these generalizations yield the best simple description of the data among generic descriptive models and that the two free parameters depend only on the language but not on the database. From the point of view of our model the main change on historical time scales is the composition of the specific words included in the finite list of core-words, which we observe to decay exponentially in time with a rate of approximately 30 words per year for English.

physics.soc-ph↗

arXiv2012

Kicking electrons

The concept of dominant interaction hamiltonians is introduced and applied to classical planar electron-atom scattering. Each trajectory is governed in different time intervals by two variants of a separable approximate hamiltonian. Switching between them results in exchange of energy between the two electrons. A second mechanism condenses the electron-electron interaction to instants in time and leads to an exchange of energy and angular momentum among the two electrons in form of kicks. We calculate the approximate and full classical deflection functions and show that the latter can be interpreted in terms of the switching sequences of the approximate one. Finally, we demonstrate that the quantum results agree better with the approximate classical dynamical results than with the full ones.

physics.atom-ph↗

arXiv2008

Ground-based calibration and characterization of the Fermi Gamma-Ray Burst Monitor Detectors

One of the scientific objectives of NASA's Fermi Gamma-ray Space Telescope is the study of Gamma-Ray Bursts (GRBs). The Fermi Gamma-Ray Burst Monitor (GBM) was designed to detect and localize bursts for the Fermi mission. By means of an array of 12 NaI(Tl) (8 keV to 1 MeV) and two BGO (0.2 to 40 MeV) scintillation detectors, GBM extends the energy range (20 MeV to > 300 GeV) of Fermi's main instrument, the Large Area Telescope, into the traditional range of current GRB databases. The physical detector response of the GBM instrument to GRBs is determined with the help of Monte Carlo simulations, which are supported and verified by on-ground individual detector calibration measurements. We present the principal instrument properties, which have been determined as a function of energy and angle, including the channel-energy relation, the energy resolution, the effective area and the spatial homogeneity.

astro-ph↗

arXiv2007

Calibration of the GLAST Burst Monitor detectors

The GLAST Burst Monitor (GBM) will augment the capabilities of GLAST for the detection of cosmic gamma-ray bursts by extending the energy range (20 MeV to > 300 GeV) of the Large Area Telescope (LAT) towards lower energies by 2 BGO-detectors (150 keV to 30 MeV) and 12 NaI(Tl) detectors (10 keV to 1 MeV). The physical detector response of the GBM instrument for GRBs is determined with the help of Monte Carlo simulations, which are supported and verified by on-ground calibration measurements, performed extensively with the individual detectors at the MPE in 2005. All flight and spare detectors were irradiated with calibrated radioactive sources in the laboratory (from 14 keV to 4.43 MeV). The energy/channel-relations, the dependences of energy resolution and effective areas on the energy and the angular responses were measured. Due to the low number of emission lines of radioactive sources below 100 keV, calibration measurements in the energy range from 10 keV to 60 keV were performed with the X-ray radiometry working group of the Physikalisch-Technische Bundesanstalt (PTB) at the BESSY synchrotron radiation facility, Berlin.

astro-ph↗