Homesick L\'evy walk: A mobility model having Ichi-go Ichi-e and scale-free properties of human encounters

In recent years, mobility models have been reconsidered based on findings by analyzing some big datasets collected by GPS sensors, cellphone call records, and Geotagging. To understand the fundamental statistical properties of the frequency of serendipitous human encounters, we conducted experiments to collect long-term data on human contact using short-range wireless communication devices which many people frequently carry in daily life. By analyzing the data we showed that the majority of human encounters occur once-in-an-experimental-period: they are Ichi-go Ichi-e. We also found that the remaining more frequent encounters obey a power-law distribution: they are scale-free. To theoretically find the origin of these properties, we introduced as a minimal human mobility model, Homesick L\'evy walk, where the walker stochastically selects moving long distances as well as L\'evy walk or returning back home. Using numerical simulations and a simple mean-field theory, we offer a theoretical explanation for the properties to validate the mobility model. The proposed model is helpful for evaluating long-term performance of routing protocols in delay tolerant networks and mobile opportunistic networks better since some utility-based protocols select nodes with frequent encounters for message transfer.Comment: 8 pages, 10 figure

Influence of QED Corrections on the Orientation of Chiral Symmetry Breaking in the NJL model

We study QED corrections to chiral symmetry breaking in the Nambu--Jona-Lasinio (NJL) model with two flavors of quarks. In this model, the isospin symmetry is broken by the differences between the current quark masses and the electromagnetic charges of the up and down quarks. To leading order in the 1/N expansion, we calculate the effective potential of the model with one-loop QED corrections at finite temperature. Evaluating the effective potential, we study the influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass plays an essential role in maintaining the orientation of the chiral symmetry breaking. If the average of the up and down quark masses is small enough, we find a phase in which the pion field has non-vanishing expectation value and dynamical CP violation takes place.Comment: 22 pages, 13 figures; added discussion about pion mass differenc

Phase structure of NJL model with finite quark mass and QED correction

We study QED corrections to the chiral symmetry breaking in Nambu-Jona-Lasinio (NJL) model with two flavors of quarks. In the model the isospin symmetry is broken by differences of the current quark masses and the electromagnetic charges between up and down quarks. In the leading order of the 1/N expansion we calculate the effective potential of the model with one-loop QED corrections. Evaluating the effective potential, we study an influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass has an important contribution for the orientation of chiral symmetry breaking.Comment: 7 pages, 8 figures, To appear in the proceedings of the Workshop on Origin of Mass and Strong Coupling Gauge Theories, Nagoya, Japan, 21-24 November 200

Similarity and Probability Distribution Functions in Many-body Stochastic Processes with Multiplicative Interactions

Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability distribution functions of the processes generally have similarity solutions with power-law tails. Growth rates of the system and power-law exponents of the tails are determined via transcendental equations. Good agreement is achieved between analytical calculations and Monte Carlo simulations.Comment: 8 pages, 4 figures, CN-Kyoto proceeding

INSTRUMENTATION-BASED MUSIC SIMILARITY USING SPARSE REPRESENTATIONS

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