3,560 research outputs found
Hypothesis test for normal mixture models: The EM approach
Normal mixture distributions are arguably the most important mixture models,
and also the most technically challenging. The likelihood function of the
normal mixture model is unbounded based on a set of random samples, unless an
artificial bound is placed on its component variance parameter. Moreover, the
model is not strongly identifiable so it is hard to differentiate between over
dispersion caused by the presence of a mixture and that caused by a large
variance, and it has infinite Fisher information with respect to mixing
proportions. There has been extensive research on finite normal mixture models,
but much of it addresses merely consistency of the point estimation or useful
practical procedures, and many results require undesirable restrictions on the
parameter space. We show that an EM-test for homogeneity is effective at
overcoming many challenges in the context of finite normal mixtures. We find
that the limiting distribution of the EM-test is a simple function of the
and distributions when the mixing
variances are equal but unknown and the when variances are unequal
and unknown. Simulations show that the limiting distributions approximate the
finite sample distribution satisfactorily. Two genetic examples are used to
illustrate the application of the EM-test.Comment: Published in at http://dx.doi.org/10.1214/08-AOS651 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
The Sachdev-Ye-Kitaev model is an N-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-N limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size M ≤ N/2. We also consider generalizations of the SYK model with quadratic random hopping term or U(1) charge conservation
Anti-shadowing Effect on Charmonium Production at a Fixed-target Experiment Using LHC Beams
We investigate charmonium production in Pb+Pb collisions at LHC beam energy
=2.76 A TeV at fixed-target experiment (=72 GeV). In the frame of a transport approach including cold
and hot nuclear matter effects on charmonium evolution, we focus on the
anti-shadowing effect on the nuclear modification factors and
for the yield and transverse momentum. The yield is more suppressed at
less forward rapidity (2) than that at very forward
rapidity (4) due to the shadowing and anti-shadowing in
different rapidity bins.Comment: 7 pages, 3 figures; submitted to Advances in High Energy Physics.
arXiv admin note: text overlap with arXiv:1409.555
Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random
interaction, which displays many interesting properties such as non-Fermi
liquid behavior, quantum chaos, emergent conformal symmetry and holographic
duality. Here we consider a SYK model or a chain of SYK models with
Majorana fermion modes coupled to another SYK model with Majorana fermion
modes, in which the latter has many more degrees of freedom and plays the role
as a thermal bath. For a single SYK model coupled to the thermal bath, we show
that although the Lyapunov exponent is still proportional to temperature, it
monotonically decreases from (, is
temperature) to zero as the coupling strength to the thermal bath increases.
For a chain of SYK models, when they are uniformly coupled to the thermal bath,
we show that the butterfly velocity displays a crossover from a
-dependence at relatively high temperature to a linear -dependence
at low temperature, with the crossover temperature also controlled by the
coupling strength to the thermal bath. If only the end of the SYK chain is
coupled to the thermal bath, the model can introduce a spatial dependence of
both the Lyapunov exponent and the butterfly velocity. Our models provide
canonical examples for the study of thermalization within chaotic models.Comment: 28 pages, 9 figures. References adde
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