2,001 research outputs found
Maximum Smoothed Likelihood Component Density Estimation in Mixture Models with Known Mixing Proportions
In this paper, we propose a maximum smoothed likelihood method to estimate
the component density functions of mixture models, in which the mixing
proportions are known and may differ among observations. The proposed estimates
maximize a smoothed log likelihood function and inherit all the important
properties of probability density functions. A majorization-minimization
algorithm is suggested to compute the proposed estimates numerically. In
theory, we show that starting from any initial value, this algorithm increases
the smoothed likelihood function and further leads to estimates that maximize
the smoothed likelihood function. This indicates the convergence of the
algorithm. Furthermore, we theoretically establish the asymptotic convergence
rate of our proposed estimators. An adaptive procedure is suggested to choose
the bandwidths in our estimation procedure. Simulation studies show that the
proposed method is more efficient than the existing method in terms of
integrated squared errors. A real data example is further analyzed
Effective theory and universal relations for Fermi gases near a -wave interaction resonance
In this work, we present an effective field theory to describe a
two-component Fermi gas near a -wave interaction resonance. The effective
field theory is renormalizable by matching with the low energy -wave
scattering phase shift. Based on the effective field theory, we derive
universal properties of the Fermi gas by the operator product expansion method.
We find that beyond the contacts defined by adiabatic theorems, the asymptotic
expressions of the momentum distribution and the Raman spectroscopy involve two
extra contacts which provide additional information of correlations of the
system. Our formalism sets the stage for further explorations of many-body
effects in a -wave resonant Fermi gas. Finally we generalise our effective
field theory for interaction resonances of arbitrary higher partial waves.Comment: revised versio
Landau meets Newton: time translation symmetry breaking in classical mechanics
Every classical Newtonian mechanical system can be equipped with a
nonstandard Hamiltonian structure, in which the Hamiltonian is the square of
the canonical Hamiltonian up to a constant shift, and the Poisson bracket is
nonlinear. In such a formalism, time translation symmetry can be spontaneously
broken, provided the potential function becomes negative. A nice analogy
between time translation symmetry breaking and the Landau theory of second
order phase transitions is established, together with several example cases
illustrating time translation breaking ground states. In particular, the
CDM model of FRW cosmology is reformulated as the time translation
symmetry breaking ground states.Comment: 10 pages, 1 figure. V2: minor correction
Tracking of enriched dialog states for flexible conversational information access
Dialog state tracking (DST) is a crucial component in a task-oriented dialog
system for conversational information access. A common practice in current
dialog systems is to define the dialog state by a set of slot-value pairs. Such
representation of dialog states and the slot-filling based DST have been widely
employed, but suffer from three drawbacks. (1) The dialog state can contain
only a single value for a slot, and (2) can contain only users' affirmative
preference over the values for a slot. (3) Current task-based dialog systems
mainly focus on the searching task, while the enquiring task is also very
common in practice. The above observations motivate us to enrich current
representation of dialog states and collect a brand new dialog dataset about
movies, based upon which we build a new DST, called enriched DST (EDST), for
flexible accessing movie information. The EDST supports the searching task, the
enquiring task and their mixed task. We show that the new EDST method not only
achieves good results on Iqiyi dataset, but also outperforms other
state-of-the-art DST methods on the traditional dialog datasets, WOZ2.0 and
DSTC2.Comment: 5 pages, 2 figures, accepted by ICASSP201
Dynamical Transition of Operator Size Growth in Open Quantum Systems
We study the operator size growth in open quantum systems with all-to-all
interactions, in which the operator size is defined by counting the number of
non-trivial system operators. We provide a general argument for the existence
of a transition of the operator size dynamics when the system-bath coupling
is tuned to its critical value . We further demonstrate the
transition through the analytical calculation of the operator size distribution
in a solvable Brownian SYK model. Our results show that: (i) For
, the system is in a dissipative phase where the system
operator size decays with a rate , which indicates the
initial information of the system all dives into the bath eventually. (ii) For
, the system sustains a scrambling phase, where the average
operator size grows exponentially up to the scrambling time and saturates to a value in the long-time
limit. (iii) At the critical point , which separates the two
phases, the operator size distribution at finite size shows a power-law decay
over time.Comment: 6 pages + supplementary materia
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