Comparing Bayesian Network Classifiers

In this paper, we empirically evaluate algorithms for learning four types of Bayesian network (BN) classifiers - Naive-Bayes, tree augmented Naive-Bayes, BN augmented Naive-Bayes and general BNs, where the latter two are learned using two variants of a conditional-independence (CI) based BN-learning algorithm. Experimental results show the obtained classifiers, learned using the CI based algorithms, are competitive with (or superior to) the best known classifiers, based on both Bayesian networks and other formalisms; and that the computational time for learning and using these classifiers is relatively small. Moreover, these results also suggest a way to learn yet more effective classifiers; we demonstrate empirically that this new algorithm does work as expected. Collectively, these results argue that BN classifiers deserve more attention in machine learning and data mining communities.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Analytic Campanato Spaces and Their Compositions

This paper is devoted to characterizing the analytic Campanato spaces $\mathcal{AL}_{p,\eta}$ (including the analytic Morrey spaces, the analytic John-Nirenberg space, and the analytic Lipschitz/H\"older spaces) on the complex unit disk $\mathbb D$ in terms of the M\"obius mapping and the Littlewood-Paley form, and consequently their compositions with the analytic self-maps of $\mathbb D$.Comment: 23 page

Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay

Motivated by the paper by D. Gerard-Varet and E. Dormy [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equations in Sobolev spaces, this paper aims to extend the result in \cite{GV-D} to the case when the shear flow has general decay. The key observation is to construct an approximate solution that captures the initial layer to the linearized problem motivated by the precise formulation of solutions to the inviscid Prandtl equations

Synthesizing dynamic MRI using long-term recurrent convolutional networks

A method is proposed for converting raw ultrasound signals of respiratory organ motion into high frame rate dynamic MRI using a long-term recurrent convolutional neural network. Ultrasound signals were acquired using a single-element transducer, referred to here as `organ-configuration motion' (OCM) sensor, while sagittal MR images were simultaneously acquired. Both streams of data were used for training a cascade of convolutional layers, to extract relevant features from raw ultrasound, followed by a recurrent neural network, to learn its temporal dynamics. The network was trained with MR images on the output, and was employed to predict MR images at a temporal resolution of 100 frames per second, based on ultrasound input alone, without any further MR scanner input. The method was validated on 7 subjects.Comment: 8 pages, 3 figure

Evolution of Warped Accretion Disks in Active Galactic Nuclei. I. Roles of Feeding at the Outer Boundaries

We investigate the alignment processes of spinning black holes and their surrounding warped accretion disks in a frame of two different types of feeding at the outer boundaries. We consider (1) fixed flows in which gas is continually fed with a preferred angular momentum, and (2) free flows in which there is no gas supply and the disks diffuse freely at their outer edges. As expected, we find that for the cases of fixed flows the black hole disk systems always end up aligning on timescales of several 1e6 yr, irrespective of the initial inclinations. If the initial inclination angles are larger than pi/2, the black hole accretion transits from retrograde to prograde fashion, and the accreted mass onto the black holes during these two phases is comparable. On the other hand, for the cases of free flows, both alignments and anti-alignments can occur, depending on the initial inclinations and the ratios of the angular momentum of the disks to that of the black holes. In such cases, the disks will be consumed within timescales of 1e6 yr by black holes accreting at the Eddington limit. We propose that there is a close connection between the black hole spin and the lifetime for which the feeding persists, which determines the observable episodic lifetimes of active galactic nuclei. We conclude that careful inclusion of the disk feeding at the outer boundaries is crucial for modeling the evolution of the black hole spin.Comment: 12 pages and 9 figures; typos corrected and references added to match the published versio

Alignments Of Black Holes With Their Warped Accretion Disks And Episodic Lifetimes Of Active Galactic Nuclei

Warped accretion disks have attracted intensive attention because of their critical role on shaping the spin of supermassive massive black holes (SMBHs) through the Bardeen-Petterson effect, a general relativistic effect that leads to final alignments or anti-alignments between black holes and warped accretion disks. We study such alignment processes by explicitly taking into account the finite sizes of accretion disks and the episodic lifetimes of AGNs that delineate the duration of gas fueling onto accretion disks. We employ an approximate global model to simulate the evolution of accretion disks, allowing to determine the gravitomagnetic torque that drives the alignments in a quite simple way. We then track down the evolutionary paths for mass and spin of black holes both in a single activity episode and over a series of episodes. Given with randomly and isotropically oriented gas fueling over episodes, we calculate the spin evolution with different episodic lifetimes and find that it is quite sensitive to the lifetimes. We therefore propose that spin distribution of SMBHs can place constraints on the episodic lifetimes of AGNs and vice versa. Applications of our results on the observed spin distributions of SMBHs and the observed episodic lifetimes of AGNs are discussed, although both the measurements at present are yet ambiguous to draw a firm conclusion. Our prescription can be easily incorporated into semi-analytic models for black hole growth and spin evolution.Comment: 11 pages, 8 figures, 1 table, to appear in the Astrophysical Journa

An end-to-end Neural Network Framework for Text Clustering

The unsupervised text clustering is one of the major tasks in natural language processing (NLP) and remains a difficult and complex problem. Conventional \mbox{methods} generally treat this task using separated steps, including text representation learning and clustering the representations. As an improvement, neural methods have also been introduced for continuous representation learning to address the sparsity problem. However, the multi-step process still deviates from the unified optimization target. Especially the second step of cluster is generally performed with conventional methods such as k-Means. We propose a pure neural framework for text clustering in an end-to-end manner. It jointly learns the text representation and the clustering model. Our model works well when the context can be obtained, which is nearly always the case in the field of NLP. We have our method \mbox{evaluated} on two widely used benchmarks: IMDB movie reviews for sentiment classification and $20$-Newsgroup for topic categorization. Despite its simplicity, experiments show the model outperforms previous clustering methods by a large margin. Furthermore, the model is also verified on English wiki dataset as a large corpus

Local-in-time well-posedness for Compressible MHD boundary layer

In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane, with no-slip condition for velocity field, perfect conducting condition for magnetic field and Dirichlet boundary condition for temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer that is described by a Prandtl-type system. By applying a coordinate transformation in terms of stream function as motivated by the recent work \cite{liu2016mhdboundarylayer} on the incompressible MHD system, under the non-degeneracy condition on the tangential magnetic field, we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.Comment: 29p

Justification of Prandtl Ansatz for MHD boundary layer

As a continuation of \cite{LXY}, the paper aims to justify the high Reynolds numbers limit for the MHD system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on velocity field and perfect conducting boundary condition on magnetic field. Under the assumption that the viscosity and resistivity coefficients are of the same order and the initial tangential magnetic field on the boundary is not degenerate, we justify the validity of the Prandtl boundary layer expansion and give a $L^\infty$ estimate on the error by multi-scale analysis.Comment: 34 page

One-step implementation of the Fredkin gate via quantum Zeno dynamics

We study one-step implementation of the Fredkin gate in a bi-modal cavity under both resonant and large detuning conditions based on quantum Zeno dynamics, which reduces the complexity of experiment operations. The influence of cavity decay and atomic spontaneous emission is discussed by numerical calculation. The results demonstrate that the fidelity and the success probability are robust against cavity decay in both models and they are also insensitive to atomic spontaneous emission in the large detuning model. In addition, the interaction time is rather short in the resonant model compared to the large detuning model.Comment: 22 pages, 7 figure