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

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

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

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

Weighted estimates for the multilinear maximal function on the upper half-spaces

For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of $\mathfrak{M}.$ We obtain a natural extension to the multilinear setting of Muckenhoupt's weak-type characterization. We also partially obtain characterizations of Muckenhoupt's strong-type inequalities with one weight. Assuming the reverse H\"{o}lder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hyt\"{o}nen-P\'{e}rez type weighted estimates.Comment: 21 pages; accepted by Mathematische Nachrichte

Stochastic Modeling and Analysis of User-Centric Network MIMO Systems

This paper provides an analytical performance characterization of both uplink (UL) and downlink (DL) user-centric network multiple-input multiple-output (MIMO) systems, where a cooperating BS cluster is formed for each user individually and the clusters for different users may overlap. In this model, cooperating BSs (each equipped with multiple antennas) jointly perform zero-forcing beamforming to the set of single-antenna users associated with them. As compared to a baseline network MIMO systems with disjoint BS clusters, the effect of user-centric clustering is that it improves signal strength in both UL and DL, while reducing cluster-edge interference in DL. This paper quantifies these effects by assuming that BSs and users form Poisson point processes and by further approximating both the signal and interference powers using Gamma distributions of appropriate parameters. We show that BS cooperation provides significant gain as compared to single-cell processing for both UL and DL, but the advantage of user-centric clustering over the baseline disjoint clustering system is significant for the DL cluster-edge users only. Although the analytic results are derived with the assumption of perfect channel state information and infinite backhaul between the cooperating BSs, they nevertheless provide architectural insight into the design of future cooperative cellular networks.Comment: 14 pages, 12 figures, to appear in IEEE Transactions on Communication

Hurwitz-Hodge integral identities from the cut-and-join equation

In this paper, we present some Hurwitz-Hodge integral identities which are derived from the Laplace transform of the cut-and-join equation for the orbifold Hurwitz numbers. As an application, we prove a conjecture on Hurwitz-Hodge integral proposed by J. Zhou in 2008

RCR: Robust Compound Regression for Robust Estimation of Errors-in-Variables Model

The errors-in-variables (EIV) regression model, being more realistic by accounting for measurement errors in both the dependent and the independent variables, is widely adopted in applied sciences. The traditional EIV model estimators, however, can be highly biased by outliers and other departures from the underlying assumptions. In this paper, we develop a novel nonparametric regression approach - the robust compound regression (RCR) analysis method for the robust estimation of EIV models. We first introduce a robust and efficient estimator called least sine squares (LSS). Taking full advantage of both the new LSS method and the compound regression analysis method developed in our own group, we subsequently propose the RCR approach as a generalization of those two, which provides a robust counterpart of the entire class of the maximum likelihood estimation (MLE) solutions of the EIV model, in a 1-1 mapping. Technically, our approach gives users the flexibility to select from a class of RCR estimates the optimal one with a predefined regression efficiency criterion satisfied. Simulation studies and real-life examples are provided to illustrate the effectiveness of the RCR approach

A new modified Altarelli-Parisi evolution equation with parton recombination in proton

The coefficients of the nonlinear terms in a modified Altarelli-Parisi evolution equation with parton recombination are determined in the leading logarithmic ($Q^2$) approximation. The results are valid in the whole $x$ region and contain the translation $GG\to q\bar q$, which is inhibited in the double leading logarithmic approximation. The comparisons of the new evolution equation with the Gribov-Levin-Ryskin equation are presented.Comment: 26 pages, 12 figures. The complete derivations of the parton recombination functions are presented in a new Appendi