Analysis on Metric Space Q

In this paper, we show that the metric space Q is a positively-curved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of Q. Then we give a stratification of this metric space according to the signature of points in Q. Some properties of this stratification are shown. The second part of this paper is devoted to some basic analysis on the space Q, like the tensor sum and L-p space, which can be of independent interest. In the end, we give another definition of derivative for multiple-valued functions, which is equivalent to the one used by Almgren. An interesting theorem about regular selection of multiple-valued functions which preserves the differentiability concludes this paper.Comment: 24 page

Evidence of Different Formation Mechanisms for Hot versus Warm Super-Earths

Using the Kepler planet sample from Buchhave et al. and the statistical method clarified by Schlaufman, I show that the shorter-period super-Earths have a different dependence on the host star metallicity from the longer-period super-Earths, with the transition period being in the period range from 70 to 100 days. The hosts of shorter-period super-Earths are on average more metal-rich than those of longer-period super-Earths. The existence of such a transition period cannot be explained by any single theory of super-Earth formation, suggesting that super-Earths have formed via at least two mechanisms.Comment: 11 pages, 5 figures; submitted to ApJ Letter

Are valence quarks rotating?

We suggest to compare the deep inelastic scattering structure functions measured in the unpolarized charged-lepton scattering off a transversely polarized proton and off a longitudinally polarized proton at larger Bjorken variable $x$, one may get a direct evidence concerning the valence quark orbital angular momentum in the proton. This possible rotating effect is estimated by using a proton-ensemble model.Comment: 9 pages and 2 figure

A Theorem on Frequency Function for Multiple-Valued Dirichlet Minimizing Functions

This paper discusses the frequency function of multiple-valued Dirichlet minimizing functions in the special case when the domain and range are both two dimensional. It shows that the frequency function must be of value k/2 for some nonnegative integer k. Futhermore, by looking at the blowing-up functions, we characterize the local behavior of the original Dirichlet minimizing function.Comment: 21 page

An Energy Reducing Flow for Multiple-Valued Functions

By the method of discrete Morse flows, we construct an energy reducing multiple-valued function flow. The flow we get is Holder continuous with respect to the L-2 norm. We also give another way of constructing flows in some special cases, where the flow we get behaves like ordinary heat flow.Comment: 29 page

A regularity theory for multiple-valued Dirichlet minimizing maps

This paper discusses the regularity of multiple-valued Dirichlet minimizing maps into the sphere. It shows that even at branched point, as long as the normalized energy is small enough, we have the energy decay estimate. Combined with the previous work by Chun-Chi Lin, we get our first estimate that m-2 dimensional Hausdorff measure of singular set is zero. Furthermore, by looking at the tangent map and using dimension reduction argument, we show that the singular set is at least of codimension 3.Comment: 27 page

Learning Gating ConvNet for Two-Stream based Methods in Action Recognition

For the two-stream style methods in action recognition, fusing the two streams' predictions is always by the weighted averaging scheme. This fusion method with fixed weights lacks of pertinence to different action videos and always needs trial and error on the validation set. In order to enhance the adaptability of two-stream ConvNets and improve its performance, an end-to-end trainable gated fusion method, namely gating ConvNet, for the two-stream ConvNets is proposed in this paper based on the MoE (Mixture of Experts) theory. The gating ConvNet takes the combination of feature maps from the same layer of the spatial and the temporal nets as input and adopts ReLU (Rectified Linear Unit) as the gating output activation function. To reduce the over-fitting of gating ConvNet caused by the redundancy of parameters, a new multi-task learning method is designed, which jointly learns the gating fusion weights for the two streams and learns the gating ConvNet for action classification. With our gated fusion method and multi-task learning approach, a high accuracy of 94.5% is achieved on the dataset UCF101.Comment: 8 pages, 4 figure

End-to-end Video-level Representation Learning for Action Recognition

From the frame/clip-level feature learning to the video-level representation building, deep learning methods in action recognition have developed rapidly in recent years. However, current methods suffer from the confusion caused by partial observation training, or without end-to-end learning, or restricted to single temporal scale modeling and so on. In this paper, we build upon two-stream ConvNets and propose Deep networks with Temporal Pyramid Pooling (DTPP), an end-to-end video-level representation learning approach, to address these problems. Specifically, at first, RGB images and optical flow stacks are sparsely sampled across the whole video. Then a temporal pyramid pooling layer is used to aggregate the frame-level features which consist of spatial and temporal cues. Lastly, the trained model has compact video-level representation with multiple temporal scales, which is both global and sequence-aware. Experimental results show that DTPP achieves the state-of-the-art performance on two challenging video action datasets: UCF101 and HMDB51, either by ImageNet pre-training or Kinetics pre-training.Comment: 10 pages, 6 figures, 6 tables. The explanation for the batch size is added. Accepted by ICPR 201

Thermoelectric effect in a parallel double quantum dot structure

We discuss the thermoelectric properties assisted by the Fano effect of a parallel double quantum dot (QD) structure. By adjusting the couplings between the QDs and leads, we facilitate the nonresonant and resonant channels for the Fano interference. It is found that at low temperature, Fano lineshapes appear in the electronic and thermal conductance spectra, which can also be reversed by an applied local magnetic flux with its phase factor $\phi=\pi$. And, the Fano effect contributes decisively to the enhancement of thermoelectric efficiency. However, at the same temperature, the thermoelectric effect in the case of $\phi=\pi$ is much more apparent, compared with the case of zero magnetic flux. By the concept of Feynman path, we analyze the difference between the quantum interferences in the cases of $\phi=0$ and $\phi=\pi$. It is seen that in the absence of magnetic flux the Fano interference originates from the quantum interference among infinite-order Feynman paths, but it occurs only between two lowest-order Feynman paths when $\phi=\pi$. The increase of temperature inevitably destroys the electron coherent transmission in each paths. So, in the case of zero magnetic field, the thermoelectric effect contributed by the Fano interference is easy to weaken by a little increase of temperature.Comment: 8 pages, 4 figure

D Wave Heavy Mesons

We first extract the binding energy $\bar \Lambda$ and decay constants of the D wave heavy meson doublets $(1^{-},2^{-})$ and $(2^{-},3^{-})$ with QCD sum rule in the leading order of heavy quark effective theory. Then we study their pionic $(\pi, K, \eta)$ couplings using the light cone sum rule, from which the parameter $\bar \Lambda$ can also be extracted. We then calculate the pionic decay widths of the strange/non-strange D wave heavy $D/B$ mesons and discuss the possible candidates for the D wave charm-strange mesons. Further experimental information, such as the ratio between $D_s\eta$ and $DK$ modes, will be very useful to distinguish various assignments for $D_{sJ}(2860, 2715)$.Comment: 10 pages, 3 figuers, 3 tables. Some descriptions changed, typos corrected. Published version in PR