A Generalized Jarque-Bera Test of Conditional Normality

We consider testing normality in a general class of models that admits nonlinear conditional mean and conditional variance functions. We derive the asymptotic distribution of the skewness and kurtosis coefficients of the model’s standardized residuals and propose an asymptotic x2 test of normality. This test simplifies to the Jarque-Bera test only when: (i) the conditional mean function contains an intercept term but does not depend on past errors, and (ii) the errors are conditionally homoskedastic. Beyond this context, it is shown that the Jarque-Bera test has size distortion but the proposed test does not.conditional heteroskedsaticity, conditional normality, Jarque-Bera test

Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor

We investigate the superconducting phase diagram and boundary modes for a quasi-1D system formed by three Fe-Chains on an s-wave superconductor, motivated by the recent Princeton experiment. The $\vec l\cdot\vec s$ onsite spin-orbit term, inter-chain diagonal hopping couplings, and magnetic disorders in the Fe-chains are shown to be crucial for the superconducting phases, which can be topologically trivial or nontrivial in different parameter regimes. For the topological regime a single Majorana and multiple Andreew bound modes are obtained in the ends of the chain, while for the trivial phase only low-energy Andreev bound states survive. Nontrivial symmetry reduction mechanism induced by the $\vec l\cdot\vec s$ term, diagonal hopping couplings, and magnetic disorder is uncovered to interpret the present results. Our study also implies that the zero-bias peak observed in the recent experiment may or may not reflect the Majorana zero modes in the end of the Fe-chains.Comment: 5 pages, 4 figures; some minor errors are correcte

Unifying and Merging Well-trained Deep Neural Networks for Inference Stage

We propose a novel method to merge convolutional neural-nets for the inference stage. Given two well-trained networks that may have different architectures that handle different tasks, our method aligns the layers of the original networks and merges them into a unified model by sharing the representative codes of weights. The shared weights are further re-trained to fine-tune the performance of the merged model. The proposed method effectively produces a compact model that may run original tasks simultaneously on resource-limited devices. As it preserves the general architectures and leverages the co-used weights of well-trained networks, a substantial training overhead can be reduced to shorten the system development time. Experimental results demonstrate a satisfactory performance and validate the effectiveness of the method.Comment: To appear in the 27th International Joint Conference on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence, 2018. (IJCAI-ECAI 2018

Probing triple-Higgs productions via 4b2γ4b2\gamma decay channel at a 100 TeV hadron collider

The quartic self-coupling of the Standard Model Higgs boson can only be measured by observing the triple-Higgs production process, but it is challenging for the Large Hadron Collider (LHC) Run 2 or International Linear Collider (ILC) at a few TeV because of its extremely small production rate. In this paper, we present a detailed Monte Carlo simulation study of the triple-Higgs production through gluon fusion at a 100 TeV hadron collider and explore the feasibility of observing this production mode. We focus on the decay channel $HHH\rightarrow b\bar{b}b\bar{b}\gamma\gamma$, investigating detector effects and optimizing the kinematic cuts to discriminate the signal from the backgrounds. Our study shows that, in order to observe the Standard Model triple-Higgs signal, the integrated luminosity of a 100 TeV hadron collider should be greater than $1.8\times 10^4$ ab$^{-1}$. We also explore the dependence of the cross section upon the trilinear ($\lambda_3$) and quartic ($\lambda_4$) self-couplings of the Higgs. We find that, through a search in the triple-Higgs production, the parameters $\lambda_3$ and $\lambda_4$ can be restricted to the ranges $[-1, 5]$ and $[-20, 30]$, respectively. We also examine how new physics can change the production rate of triple-Higgs events. For example, in the singlet extension of the Standard Model, we find that the triple-Higgs production rate can be increased by a factor of $\mathcal{O}(10)$.Comment: 33 pages, 11 figures, added references, corrected typos, improved text, affiliation is changed. This is the publication versio