5,864 research outputs found
Statistical mechanics of error exponents for error-correcting codes
Error exponents characterize the exponential decay, when increasing message
length, of the probability of error of many error-correcting codes. To tackle
the long standing problem of computing them exactly, we introduce a general,
thermodynamic, formalism that we illustrate with maximum-likelihood decoding of
low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and
the binary symmetric channel (BSC). In this formalism, we apply the cavity
method for large deviations to derive expressions for both the average and
typical error exponents, which differ by the procedure used to select the codes
from specified ensembles. When decreasing the noise intensity, we find that two
phase transitions take place, at two different levels: a glass to ferromagnetic
transition in the space of codewords, and a paramagnetic to glass transition in
the space of codes.Comment: 32 pages, 13 figure
A hard-sphere model on generalized Bethe lattices: Statics
We analyze the phase diagram of a model of hard spheres of chemical radius
one, which is defined over a generalized Bethe lattice containing short loops.
We find a liquid, two different crystalline, a glassy and an unusual
crystalline glassy phase. Special attention is also paid to the close-packing
limit in the glassy phase. All analytical results are cross-checked by
numerical Monte-Carlo simulations.Comment: 24 pages, revised versio
Complex systems approach to natural language
The review summarizes the main methodological concepts used in studying
natural language from the perspective of complexity science and documents their
applicability in identifying both universal and system-specific features of
language in its written representation. Three main complexity-related research
trends in quantitative linguistics are covered. The first part addresses the
issue of word frequencies in texts and demonstrates that taking punctuation
into consideration restores scaling whose violation in the Zipf's law is often
observed for the most frequent words. The second part introduces methods
inspired by time series analysis, used in studying various kinds of
correlations in written texts. The related time series are generated on the
basis of text partition into sentences or into phrases between consecutive
punctuation marks. It turns out that these series develop features often found
in signals generated by complex systems, like long-range correlations or
(multi)fractal structures. Moreover, it appears that the distances between
punctuation marks comply with the discrete variant of the Weibull distribution.
In the third part, the application of the network formalism to natural language
is reviewed, particularly in the context of the so-called word-adjacency
networks. Parameters characterizing topology of such networks can be used for
classification of texts, for example, from a stylometric perspective. Network
approach can also be applied to represent the organization of word
associations. Structure of word-association networks turns out to be
significantly different from that observed in random networks, revealing
genuine properties of language. Finally, punctuation seems to have a
significant impact not only on the language's information-carrying ability but
also on its key statistical properties, hence it is recommended to consider
punctuation marks on a par with words.Comment: 113 pages, 49 figure
Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca
The entropic brain hypothesis holds that the key facts concerning
psychedelics are partially explained in terms of increased entropy of the
brain's functional connectivity. Ayahuasca is a psychedelic beverage of
Amazonian indigenous origin with legal status in Brazil in religious and
scientific settings. In this context, we use tools and concepts from the theory
of complex networks to analyze resting state fMRI data of the brains of human
subjects under two distinct conditions: (i) under ordinary waking state and
(ii) in an altered state of consciousness induced by ingestion of Ayahuasca. We
report an increase in the Shannon entropy of the degree distribution of the
networks subsequent to Ayahuasca ingestion. We also find increased local and
decreased global network integration. Our results are broadly consistent with
the entropic brain hypothesis. Finally, we discuss our findings in the context
of descriptions of "mind-expansion" frequently seen in self-reports of users of
psychedelic drugs.Comment: 27 pages, 6 figure
Drawing Elena Ferrante's Profile. Workshop Proceedings, Padova, 7 September 2017
Elena Ferrante is an internationally acclaimed Italian novelist whose real identity has been kept secret by E/O publishing house for more than 25 years. Owing to her popularity, major Italian and foreign newspapers have long tried to discover her real identity. However, only a few attempts have been made to foster a scientific debate on her work.
In 2016, Arjuna Tuzzi and Michele Cortelazzo led an Italian research team that conducted a preliminary study and collected a well-founded, large corpus of Italian novels comprising 150 works published in the last 30 years by 40 different authors. Moreover, they shared their data with a select group of international experts on authorship attribution, profiling, and analysis of textual data: Maciej Eder and Jan Rybicki (Poland), Patrick Juola (United States), Vittorio Loreto and his research team, Margherita Lalli and Francesca Tria (Italy), George Mikros (Greece), Pierre Ratinaud (France), and Jacques Savoy (Switzerland).
The chapters of this volume report the results of this endeavour that were first presented during the international workshop Drawing Elena Ferrante's Profile in Padua on 7 September 2017 as part of the 3rd IQLA-GIAT Summer School in Quantitative Analysis of Textual Data. The fascinating research findings suggest that Elena Ferrante\u2019s work definitely deserves \u201cmany hands\u201d as well as an extensive effort to understand her distinct writing style and the reasons for her worldwide success
Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron
In this article the framework for Parisi's spontaneous replica symmetry
breaking is reviewed, and subsequently applied to the example of the
statistical mechanical description of the storage properties of a
McCulloch-Pitts neuron. The technical details are reviewed extensively, with
regard to the wide range of systems where the method may be applied. Parisi's
partial differential equation and related differential equations are discussed,
and a Green function technique introduced for the calculation of replica
averages, the key to determining the averages of physical quantities. The
ensuing graph rules involve only tree graphs, as appropriate for a
mean-field-like model. The lowest order Ward-Takahashi identity is recovered
analytically and is shown to lead to the Goldstone modes in continuous replica
symmetry breaking phases. The need for a replica symmetry breaking theory in
the storage problem of the neuron has arisen due to the thermodynamical
instability of formerly given solutions. Variational forms for the neuron's
free energy are derived in terms of the order parameter function x(q), for
different prior distribution of synapses. Analytically in the high temperature
limit and numerically in generic cases various phases are identified, among
them one similar to the Parisi phase in the Sherrington-Kirkpatrick model.
Extensive quantities like the error per pattern change slightly with respect to
the known unstable solutions, but there is a significant difference in the
distribution of non-extensive quantities like the synaptic overlaps and the
pattern storage stability parameter. A simulation result is also reviewed and
compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi,
eepic), accepted for Physics Report
Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron
In this article the framework for Parisi's spontaneous replica symmetry
breaking is reviewed, and subsequently applied to the example of the
statistical mechanical description of the storage properties of a
McCulloch-Pitts neuron. The technical details are reviewed extensively, with
regard to the wide range of systems where the method may be applied. Parisi's
partial differential equation and related differential equations are discussed,
and a Green function technique introduced for the calculation of replica
averages, the key to determining the averages of physical quantities. The
ensuing graph rules involve only tree graphs, as appropriate for a
mean-field-like model. The lowest order Ward-Takahashi identity is recovered
analytically and is shown to lead to the Goldstone modes in continuous replica
symmetry breaking phases. The need for a replica symmetry breaking theory in
the storage problem of the neuron has arisen due to the thermodynamical
instability of formerly given solutions. Variational forms for the neuron's
free energy are derived in terms of the order parameter function x(q), for
different prior distribution of synapses. Analytically in the high temperature
limit and numerically in generic cases various phases are identified, among
them one similar to the Parisi phase in the Sherrington-Kirkpatrick model.
Extensive quantities like the error per pattern change slightly with respect to
the known unstable solutions, but there is a significant difference in the
distribution of non-extensive quantities like the synaptic overlaps and the
pattern storage stability parameter. A simulation result is also reviewed and
compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi,
eepic), accepted for Physics Report
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