12,979 research outputs found
Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model
We derive the effective potentials for composite operators in a
Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in
each case they are equivalent to the corresponding effective potentials based
on an auxiliary scalar field. The both effective potentials could lead to the
same possible spontaneous breaking and restoration of symmetries including
chiral symmetry if the momentum cutoff in the loop integrals is large enough,
and can be transformed to each other when the Schwinger-Dyson (SD) equation of
the dynamical fermion mass from the fermion-antifermion vacuum (or thermal)
condensates is used. The results also generally indicate that two effective
potentials with the same single order parameter but rather different
mathematical expressions can still be considered physically equivalent if the
SD equation corresponding to the extreme value conditions of the two potentials
have the same form.Comment: 7 pages, no figur
Update-Efficient Regenerating Codes with Minimum Per-Node Storage
Regenerating codes provide an efficient way to recover data at failed nodes
in distributed storage systems. It has been shown that regenerating codes can
be designed to minimize the per-node storage (called MSR) or minimize the
communication overhead for regeneration (called MBR). In this work, we propose
a new encoding scheme for [n,d] error- correcting MSR codes that generalizes
our earlier work on error-correcting regenerating codes. We show that by
choosing a suitable diagonal matrix, any generator matrix of the [n,{\alpha}]
Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR
codes with the least update complexity can be found. An efficient decoding
scheme is also proposed that utilizes the [n,{\alpha}] RS code to perform data
reconstruction. The proposed decoding scheme has better error correction
capability and incurs the least number of node accesses when errors are
present.Comment: Submitted to IEEE ISIT 201
Statistical Geometry of Packing Defects of Lattice Chain Polymer from Enumeration and Sequential Monte Carlo Method
Voids exist in proteins as packing defects and are often associated with
protein functions. We study the statistical geometry of voids in
two-dimensional lattice chain polymers. We define voids as topological features
and develop a simple algorithm for their detection. For short chains, void
geometry is examined by enumerating all conformations. For long chains, the
space of void geometry is explored using sequential Monte Carlo importance
sampling and resampling techniques. We characterize the relationship of
geometric properties of voids with chain length, including probability of void
formation, expected number of voids, void size, and wall size of voids. We
formalize the concept of packing density for lattice polymers, and further
study the relationship between packing density and compactness, two parameters
frequently used to describe protein packing. We find that both fully extended
and maximally compact polymers have the highest packing density, but polymers
with intermediate compactness have low packing density. To study the
conformational entropic effects of void formation, we characterize the
conformation reduction factor of void formation and found that there are strong
end-effect. Voids are more likely to form at the chain end. The critical
exponent of end-effect is twice as large as that of self-contacting loop
formation when existence of voids is not required. We also briefly discuss the
sequential Monte Carlo sampling and resampling techniques used in this study.Comment: 29 pages, including 12 figure
Hidden Caldeira-Leggett dissipation in a Bose-Fermi Kondo model
We show that the Bose-Fermi Kondo model (BFKM), which may find applicability
both to certain dissipative mesoscopic qubit devices and to heavy fermion
systems described by the Kondo lattice model, can be mapped exactly onto the
Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an
Ising-type coupling between the latter and the impurity spin. This allows us to
conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum
phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic
numerical renormalization group approach, we thoroughly probe physical
quantities close to the quantum phase transition.Comment: Final version appearing in Physical Review Letter
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Spousal Dictator Game: Household Decisions and Other-Regarding Preferences
Using a laboratory experiment, we collected data on dictator giving among student strangers and married couples in a suburban area in the United States. Confirming common belief and prior empirical evidence, we find that giving among spouses is greater than giving among anonymous students. We further investigated factors associated with spousal giving which may provide insight for the development of future theories, or into explaining other-regarding preferences. Our data shows that giving is positively associated with who manages household money and controls household income. This result is robust after controlling for each spouse’s personal income and using various econometric specifications. The results suggest that spousal giving may be due to household economic roles in addition to other-regarding preferences
Evolving small-world networks with geographical attachment preference
We introduce a minimal extended evolving model for small-world networks which
is controlled by a parameter. In this model the network growth is determined by
the attachment of new nodes to already existing nodes that are geographically
close. We analyze several topological properties for our model both
analytically and by numerical simulations. The resulting network shows some
important characteristics of real-life networks such as the small-world effect
and a high clustering.Comment: 11 pages, 4 figure
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