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 dd-wave interaction resonance

In this work, we present an effective field theory to describe a two-component Fermi gas near a $d$-wave interaction resonance. The effective field theory is renormalizable by matching with the low energy $d$-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 $d$-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 $\Lambda$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 $\gamma$ is tuned to its critical value $\gamma_c$. 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 $\gamma>\gamma_c$, the system is in a dissipative phase where the system operator size decays with a rate $\sim (\gamma-\gamma_c)$, which indicates the initial information of the system all dives into the bath eventually. (ii) For $\gamma<\gamma_c$, the system sustains a scrambling phase, where the average operator size grows exponentially up to the scrambling time $t_s\sim (\gamma_c-\gamma)^{-1}\log N$ and saturates to a $O(N)$ value in the long-time limit. (iii) At the critical point $\gamma=\gamma_c$, which separates the two phases, the operator size distribution at finite size shows a power-law decay over time.Comment: 6 pages + supplementary materia