Related papers: Quadratic Term Correction on Heaps' Law
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Numerical test of isotropic turbulence compressibility reduction with helicity in a cyclic box is performed. The ratios of compressibility-relevant-mode spectra over those of kinetic energy present power laws at large wavenumbers in the…
We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the…
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Human language, as a typical complex system, its organization and evolution is an attractive topic for both physical and cultural researchers. In this paper, we present the first exhaustive analysis of the text organization of human speech.…
Understanding texts requires memory: the reader has to keep in mind enough words to create meaning. This calls for a relation between the memory of the reader and the structure of the text. To investigate this interaction, we first identify…
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In the dynamical triangulation model of 4D euclidean quantum gravity we measure two-point functions of the scalar curvature as a function of the geodesic distance. To get the correlations it turns out that we need to subtract a squared…
A many-body quantum system whose topological defects are conserved, abundant and mobile is a correlated quantum liquid. Since topological defects can be classified by homotopy groups, each homotopy identifies a class of quantum liquids.…
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We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range…
Scaling laws for neural networks, in which the loss decays as a power-law in the number of parameters, data, and compute, depend fundamentally on the spectral structure of the data covariance, with power-law eigenvalue decay appearing…
The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
We introduce a data-centric hypothesis-testing framework to quantify the influence of sequentially correlated literary properties--such as thematic continuity--on textual classification tasks. Our method models label sequences as stochastic…
We prove that a finite correlation length, i.e. exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the…
We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As…
Distortion is a fundamental well-studied topic in dimension reduction papers, and intimately related with the underlying intrinsic dimension of a mapping of a high dimensional data set onto a lower dimension. In this paper, we study…