The meta book and size-dependent properties of written language

Evidence is given for a systematic text-length dependence of the power-law index gamma of a single book. The estimated gamma values are consistent with a monotonic decrease from 2 to 1 with increasing length of a text. A direct connection to an extended Heap's law is explored. The infinite book limit is, as a consequence, proposed to be given by gamma = 1 instead of the value gamma=2 expected if the Zipf's law was ubiquitously applicable. In addition we explore the idea that the systematic text-length dependence can be described by a meta book concept, which is an abstract representation reflecting the word-frequency structure of a text. According to this concept the word-frequency distribution of a text, with a certain length written by a single author, has the same characteristics as a text of the same length pulled out from an imaginary complete infinite corpus written by the same author.Comment: 7 pages, 6 figures, 1 tabl

Universality of Zipf's Law

We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows that the behavior of the model is very robust and universal.Comment: 5 eps files included. To be published in J. Phys. Soc. Jp

Bug propagation and debugging in asymmetric software structures

Software dependence networks are shown to be scale-free and asymmetric. We then study how software components are affected by the failure of one of them, and the inverse problem of locating the faulty component. Software at all levels is fragile with respect to the failure of a random single component. Locating a faulty component is easy if the failures only affect their nearest neighbors, while it is hard if the failures propagate further.Comment: 4 pages, 4 figure

Dissociation of CH4 by electron impact: Production of metastable hydrogen and carbon fragments

Metastable fragments produced by electron impact excitation of CH4 have been investigated for incident electron energies from threshold to 300 eV. Only metastable hydrogen and carbon atoms were observed. Onset energies for the production of metastable hydrogen atoms were observed at electron impact energies of 22.0 + or - .5 eV, 25.5 + or - .6 eV, 36.7 + or - .6 eV and 66 + or - 3 eV, and at 26.6 + or - .6 eV for the production of metastable carbon atoms. Most of the fragments appear to have been formed in high-lying Rydberg states. The total metastable hydrogen cross section reaches a maximum value of approximately 1 X 10 to the minus 18th power sq cm at 100 eV. At the same energy, the metastable carbon cross section is 2 x 10 to the minus 19th power sq cm

Emergence of Zipf's Law in the Evolution of Communication

Zipf's law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and hearer in a communication system, we introduce evolution by means of a variational approach to the problem based on Kullback's Minimum Discrimination of Information Principle. Therefore, using a formalism fully embedded in the framework of information theory, we demonstrate that Zipf's law is the only expected outcome of an evolving, communicative system under a rigorous definition of the communicative tension described by Zipf.Comment: 7 pages, 2 figure

Testing the robustness of laws of polysemy and brevity versus frequency

The pioneering research of G.K. Zipf on the relationship between word frequency and other word features led to the formulation of various linguistic laws. Here we focus on a couple of them: the meaning-frequency law, i.e. the tendency of more frequent words to be more polysemous, and the law of abbreviation, i.e. the tendency of more frequent words to be shorter. Here we evaluate the robustness of these laws in contexts where they have not been explored yet to our knowledge. The recovery of the laws again in new conditions provides support for the hypothesis that they originate from abstract mechanisms.Peer ReviewedPostprint (author's final draft

Computer simulation of a pilot in V/STOL aircraft control loops

The objective was to develop a computerized adaptive pilot model for the computer model of the research aircraft, the Harrier II AV-8B V/STOL with special emphasis on propulsion control. In fact, two versions of the adaptive pilot are given. The first, simply called the Adaptive Control Model (ACM) of a pilot includes a parameter estimation algorithm for the parameters of the aircraft and an adaption scheme based on the root locus of the poles of the pilot controlled aircraft. The second, called the Optimal Control Model of the pilot (OCM), includes an adaption algorithm and an optimal control algorithm. These computer simulations were developed as a part of the ongoing research program in pilot model simulation supported by NASA Lewis from April 1, 1985 to August 30, 1986 under NASA Grant NAG 3-606 and from September 1, 1986 through November 30, 1988 under NASA Grant NAG 3-729. Once installed, these pilot models permitted the computer simulation of the pilot model to close all of the control loops normally closed by a pilot actually manipulating the control variables. The current version of this has permitted a baseline comparison of various qualitative and quantitative performance indices for propulsion control, the control loops and the work load on the pilot. Actual data for an aircraft flown by a human pilot furnished by NASA was compared to the outputs furnished by the computerized pilot and found to be favorable

Network properties of written human language

We investigate the nature of written human language within the framework of complex network theory. In particular, we analyse the topology of Orwell's \textit{1984} focusing on the local properties of the network, such as the properties of the nearest neighbors and the clustering coefficient. We find a composite power law behavior for both the average nearest neighbor's degree and average clustering coefficient as a function of the vertex degree. This implies the existence of different functional classes of vertices. Furthermore we find that the second order vertex correlations are an essential component of the network architecture. To model our empirical results we extend a previously introduced model for language due to Dorogovtsev and Mendes. We propose an accelerated growing network model that contains three growth mechanisms: linear preferential attachment, local preferential attachment and the random growth of a pre-determined small finite subset of initial vertices. We find that with these elementary stochastic rules we are able to produce a network showing syntactic-like structures