Noise spectra of stochastic pulse sequences: application to large scale magnetization flips in the finite size 2D Ising model

We provide a general scheme to predict and derive the contribution to the noise spectrum of a stochastic sequence of pulses from the distribution of pulse parameters. An example is the magnetization noise spectra of a 2D Ising system near its phase transition. At $T\le T_c$, the low frequency spectra is dominated by magnetization flips of nearly the entire system. We find that both the predicted and the analytically derived spectra fit those produced from simulations. Subtracting this contribution leaves the high frequency spectra which follow a power law set by the critical exponents.Comment: 4 pages, 5 figures. We improved text and included a predicted noise curve in Figure 4. 2 examples from Figure 3 are remove

Simple choreographies of the planar Newtonian NN-body Problem

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at least $2^{N-3} + 2^{[(N-3)/2]}$ different main simple choreographies. This confirms a conjecture given by Chenciner and etc. in \cite{CGMS02}.Comment: 31pages, 6 figures. Refinements in notations and proof

Formation of Magnetized Prestellar Cores with Ambipolar Diffusion and Turbulence

We investigate the roles of magnetic fields and ambipolar diffusion during prestellar core formation in turbulent giant molecular clouds (GMCs), using three-dimensional numerical simulations. Our simulations focus on the shocked layer produced by a converging flow within a GMC, and survey varying ionization and angle between the upstream flow and magnetic field. We also include ideal magnetohydrodynamic (MHD) and hydrodynamic models. From our simulations, we identify hundreds of self-gravitating cores that form within 1 Myr, with masses M ~ 0.04 - 2.5 solar-mass and sizes L ~ 0.015 - 0.07 pc, consistent with observations of the peak of the core mass function (CMF). Median values are M = 0.47 solar-mass and L = 0.03 pc. Core masses and sizes do not depend on either the ionization or upstream magnetic field direction. In contrast, the mass-to-magnetic flux ratio does increase with lower ionization, from twice to four times the critical value. The higher mass-to-flux ratio for low ionization is the result of enhanced transient ambipolar diffusion when the shocked layer first forms. However, ambipolar diffusion is not necessary to form low-mass supercritical cores. For ideal MHD, we find similar masses to other cases. These masses are 1 - 2 orders of magnitude lower than the value that defines a magnetically supercritical sphere under post-shock ambient conditions. This discrepancy is the result of anisotropic contraction along field lines, which is clearly evident in both ideal MHD and diffusive simulations. We interpret our numerical findings using a simple scaling argument which suggests that gravitationally critical core masses will depend on the sound speed and mean turbulent pressure in a cloud, regardless of magnetic effects.Comment: 41 pages, 14 figures, 3 tables, accepted for publication in Astrophysical Journa

Unsupervised Network Pretraining via Encoding Human Design

Over the years, computer vision researchers have spent an immense amount of effort on designing image features for the visual object recognition task. We propose to incorporate this valuable experience to guide the task of training deep neural networks. Our idea is to pretrain the network through the task of replicating the process of hand-designed feature extraction. By learning to replicate the process, the neural network integrates previous research knowledge and learns to model visual objects in a way similar to the hand-designed features. In the succeeding finetuning step, it further learns object-specific representations from labeled data and this boosts its classification power. We pretrain two convolutional neural networks where one replicates the process of histogram of oriented gradients feature extraction, and the other replicates the process of region covariance feature extraction. After finetuning, we achieve substantially better performance than the baseline methods.Comment: 9 pages, 11 figures, WACV 2016: IEEE Conference on Applications of Computer Visio

A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are focused on the information fusion estimation problem under bounded noises. In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.Comment: 9 pages, 3 figure