115,703 research outputs found
Holographic entanglement entropy in two-order insulator/superconductor transitions
We study holographic superconductor model with two scalar fields coupled to
one single Maxwell field in the AdS soliton background away from the probe
limit. We disclose properties of phase transitions mostly from the holographic
topological entanglement entropy approach. With different sets of parameters,
we observe various types of transitions, especially a new first order phase
transition between the condensation of different order parameters in the
insulator/superconductor system. Our results show that the entanglement entropy
is a good probe to critical phase transition points and the order of phase
transitions in the two-order model. We also conclude that the entanglement
entropy is useful to some extent in determining the physically supported
phases. In addition, we investigate properties of the condensation through the
scalar operator and the charge density in the dual theory. As a summary, we
draw the complete phase diagram of the effects of the scalar charge on phase
transitions. At last, we give some qualitative understanding and obtain the
analytical condition for the first order phase transition to occur.Comment: 12 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1512.0895
Between order and disorder: a 'weak law' on recent electoral behavior among urban voters?
A new viewpoint on electoral involvement is proposed from the study of the
statistics of the proportions of abstentionists, blank and null, and votes
according to list of choices, in a large number of national elections in
different countries. Considering 11 countries without compulsory voting
(Austria, Canada, Czech Republic, France, Germany, Italy, Mexico, Poland,
Romania, Spain and Switzerland), a stylized fact emerges for the most populated
cities when one computes the entropy associated to the three ratios, which we
call the entropy of civic involvement of the electorate. The distribution of
this entropy (over all elections and countries) appears to be sharply peaked
near a common value. This almost common value is typically shared since the
1970's by electorates of the most populated municipalities, and this despite
the wide disparities between voting systems and types of elections. Performing
different statistical analyses, we notably show that this stylized fact reveals
particular correlations between the blank/null votes and abstentionists ratios.
We suggest that the existence of this hidden regularity, which we propose to
coin as a `weak law on recent electoral behavior among urban voters', reveals
an emerging collective behavioral norm characteristic of urban citizen voting
behavior in modern democracies. Analyzing exceptions to the rule provide
insights into the conditions under which this normative behavior can be
expected to occur.Comment: Version 1: main text 19 pages, 13 figures, 2 tables; Supporting
Information: 19 pages. Version 2: minor correction
Entropy of English text: Experiments with humans and a machine learning system based on rough sets
The goal of this paper is to show the dependency of the entropy of English text on the subject of the experiment, the type of English text, and the methodology used to estimate the entropy. Claude Shannon first described the technique for estimating the entropy of English text by a human subject guessing the next letter after viewing a string of characters taken from actual text. We show how this result is affected by using different humans in the experiment (Shannon used only his wife) and by using different types of text material (Shannon used only a single book). We also show how the results are affected when we replace the human subjects with a machine learning system based on rough sets. Automating the play of the guessing game with this system, called LERS, gives rise to a lossless data compression scheme. (C) Elsevier Science Inc. 1998
On Hilberg's Law and Its Links with Guiraud's Law
Hilberg (1990) supposed that finite-order excess entropy of a random human
text is proportional to the square root of the text length. Assuming that
Hilberg's hypothesis is true, we derive Guiraud's law, which states that the
number of word types in a text is greater than proportional to the square root
of the text length. Our derivation is based on some mathematical conjecture in
coding theory and on several experiments suggesting that words can be defined
approximately as the nonterminals of the shortest context-free grammar for the
text. Such operational definition of words can be applied even to texts
deprived of spaces, which do not allow for Mandelbrot's ``intermittent
silence'' explanation of Zipf's and Guiraud's laws. In contrast to
Mandelbrot's, our model assumes some probabilistic long-memory effects in human
narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic
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