arXiv subjects

Jianjun Xu

Publications and source records attributed to Jianjun Xu.

30 records · Page 2Linked to original sources

arXiv2021

A new RKHS-based global testing for functional linear model

This article studies global testing of the slope function in functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The asymptotic distribution of the testing statistic is established under null hypothesis. It is shown that the null asymptotic distribution is determined jointly by the reproducing kernel and the covariance function. Our theoretical analysis shows that the proposed testing is consistent over a class of smooth local alternatives. Despite the generality of the method of regularization, we show the procedure is easily implementable. Numerical examples are provided to demonstrate the empirical advantages over the competing methods.

math.ST↗

arXiv2019

A new reproducing kernel based nonlinear dimension reduction method for survival data

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed and discussed. An isometrically isomorphism is constructed based on RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements which reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate weight function or conditional survival function to adjust for the censoring bias. The sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen-decomposition problem. Our method is computationally efficient with fast calculation speed and small computational burden. The asymptotic property and the convergence rate of the estimator are also discussed based on the perturbation theory. Finally, we illustrate the performance of RDSIR on simulated and real data to confirm that RDSIR is comparable with linear SDR method. The most important is that RDSIR can also extract nonlinearity in survival data effectively.

math.ST↗

arXiv2019

Pretraining-Based Natural Language Generation for Text Summarization

In this paper, we propose a novel pretraining-based encoder-decoder framework, which can generate the output sequence based on the input sequence in a two-stage manner. For the encoder of our model, we encode the input sequence into context representations using BERT. For the decoder, there are two stages in our model, in the first stage, we use a Transformer-based decoder to generate a draft output sequence. In the second stage, we mask each word of the draft sequence and feed it to BERT, then by combining the input sequence and the draft representation generated by BERT, we use a Transformer-based decoder to predict the refined word for each masked position. To the best of our knowledge, our approach is the first method which applies the BERT into text generation tasks. As the first step in this direction, we evaluate our proposed method on the text summarization task. Experimental results show that our model achieves new state-of-the-art on both CNN/Daily Mail and New York Times datasets.

cs.CL↗

arXiv2015

Nambu--Jona-Lasinio Model Revisited with a Simple Regularization-Renormalization Method

According to the pioneering model proposed by Nambu and Jona-Lasinio (NJL) \cite{2,3}, a massless fermion acquires its mass via a vacuum phase transition (VPT) process. Our discussion is considerably simplified because an effective Hamiltonian for VPT is proposed and a simple regularization-renormalization method (RRM) is adopted. An unambiguous constraint is found as $\frac{π^2}{GΔ^2_1}=\frac{2}{3}$, where $G$ is the coupling constant first introduced in the NJL model while $Δ_1$ the mass of fermion ($f$) created after the VPT. The masses of bosons with spin-parity $J^P=0^+, 0^-,1^+$ and $1^-$ as collective modes composed of fermion-antifermion pairs ($f\bar{f}$s) are also calculated by the method of random phase approximation (RPA).

hep-th↗

arXiv2015

Recognition of Brain Waves of Left and Right Hand Movement Imagery with Portable Electroencephalographs

With the development of the modern society, mind control applied to both the recovery of disabled individuals and auxiliary control of normal people has obtained great attention in numerous researches. In our research, we attempt to recognize the brain waves of left and right hand movement imagery with portable electroencephalographs. Considering the inconvenience of wearing traditional multiple-electrode electroencephalographs, we choose Muse to collect data which is a portable headband launched lately with a number of useful functions and channels and it is much easier for the public to use. Additionally, previous researches generally focused on discrimination of EEG of left and right hand movement imagery by using data from C3 and C4 electrodes which locate on the top of the head. However, we choose the gamma wave channels of F7 and F8 and obtain data when subjects imagine their left or right hand to move with their eyeballs rotated in the corresponding direction. With the help of the Common Space Pattern algorithm to extract features of brain waves between left and right hand movement imagery, we make use of the Support Vector Machine to classify different brain waves. Traditionally, the accuracy rate of classification was approximately 90% using the EEG data from C3 and C4 electrode poles; however, the accuracy rate reaches 95.1% by using the gamma wave data from F7 and F8 in our experiment. Finally, we design a plane program in Python where a plane can be controlled to go left or right when users imagine their left or right hand to move. 8 subjects are tested and all of them can control the plane flexibly which reveals that our model can be applied to control hardware which is useful for disabled individuals and normal people.

cs.HC↗

arXiv2015

Prediction of Brain States of Concentration and Relaxation in Real Time with Portable Electroencephalographs

In our research, we attempt to help people recognize their brain state of concentration or relaxation more conveniently and in real time. Considering the inconvenience of wearing traditional multiple electrode electroencephalographs, we choose Muse to collect data which is a portable headband launched lately with a number of useful functions and channels and it is much easier for the public to use. Besides, traditional online analysis did not focus on the synchronism between users and computers and the time delay problem did exist. To solve the problem, by building the Analytic Hierarchy Model, we choose the two gamma wave channels of F7 and F8 as the data source instead of using both beta and alpha channels traditionally.Using the Common Space Pattern algorithm and the Support Vector Machine model, the channels we choose have a higher recognition accuracy rate and smaller amount of data to be dealt with by the computer than the traditional ones. Furthermore, we make use of the Feedforward Neural Network Model to predict subjects'brain states in half a second. Finally, we design a plane program in Python where a plane can be controlled to go up or down when users concentrate or relax. The SVM model and the Feedforward Neural Network model have both been tested by 12 subjects and they give an evaluation ranging from 1 to 10 points. The former gets 7.58 points while the latter gets 8.83, which proves that the time delay problem is improved once more.

cs.HC↗

arXiv2013

Discrete Symmetry in Relativistic Quantum Mechanics

EPR experiment on $K^0-\bar{K}^0$ system in 1998\cite{1} strongly hints that one should use operators $\hat{E}_c=-i\hbar\frac{\partial}{\partial t}$ and $\hat{\bf p}_c=i\hbar\nabla$ for the wavefunction (WF) of antiparticle. Further analysis on Klein-Gordon (KG) equation reveals that there is a discrete symmetry hiding in relativistic quantum mechanics (RQM) that ${\cal P}{\cal T}={\cal C}$. Here ${\cal P}{\cal T}$ means the (newly defined) combined space-time inversion (with ${\bf x}\to -{\bf x}, t\to-t$), while ${\cal C}$ the transformation of WF $ψ$ between particle and its antiparticle whose definition is just residing in the above symmetry. After combining with Feshbach-Villars (FV) dissociation of KG equation ($ψ=ϕ+χ$)\cite{2}, this discrete symmetry can be rigorously reformulated by the invariance of coupling equation of $ϕ$ and $χ$ under either the combined space-time inversion ${\cal P}{\cal T}$ or the mass inversion ($m\to -m$), which makes the KG equation a self-consistent theory. Dirac equation is also discussed accordingly. Various applications of this discrete symmetry are discussed, including the prediction of antigravity between matter and antimatter as well as the reason why we believe neutrinos are likely the tachyons.

physics.gen-ph↗

arXiv2012

Evolution of the CPT Invariance into a Basic Postulate in Physics

Einstein-Podolsky-Rosen's paper in 1935 is discussed in parallel with an EPR experiment on $K^0\bar{K}^0$ system in 1998, yielding a strong hint of distinction in both wave-function and operators between particle and antiparticle at the level of quantum mechanics (QM). Then it is proposed that the CPT invariance in particle physics leads naturally to a basic postulate that the (newly defined) space-time inversion (${\bf x}\to -{\bf x},t\to -t$) is equivalent to the transformation between particle and its antiparticle. The evolution of this postulate from nonrelativistic QM via relativistic QM till the quantum field theory is discussed in some detail. The Klein paradox for both Klein-Gordon equation and Dirac equation is also discussed. Keywords: CPT invariance, Antiparticle, Quantum mechanics, Quantum field theory

physics.gen-ph↗

arXiv2010

Essence of Special Relativity, Reduced Dirac Equation and Antigravity

The essence of special relativity is hiding in the equal existence of particle and antiparticle, which can be expressed by two discrete symmetries within one inertial frame --- the invariance under the (newly defined) space-time inversion (${\bf x}\to -{\bf x},t\to -t$), or equivalently, the invariance under a mass inversion ($m\to -m$). The problems discussed are: the evolution of the $CPT$ invariance into a basic postulate, an unique solution to the original puzzle in Einstein-Podolsky-Rosen paradox, the reduced Dirac equation for hydrogenlike atoms, and the negative mass paradox leading to the prediction of antigravity between matter and antimatter. {\bf Keywords}: Special relativity, Reduced Dirac Equation, Antiparticle, Antigravity

physics.gen-ph↗

arXiv2010

Puzzles of Divergence and Renormalization in Quantum Field Theory

A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times, rendering it just convergent. Then integrate it back into $I$ with some arbitrary constants appeared. Third, the renormalization is nothing but a process of reconfirmation to fix relevant parameters (mass, charge, \etc) by experimental data via suitable choices of these constants. Various $QFT$ problems, including the Lamb shift, the running coupling constants in $QED$ and $QCD$, the $λϕ^4$ model as well as Higgs mass in the standard model of particle physics, are discussed. Hence the calculation, though still approximate and limited in accuracy, can be performed in an unambiguous way with no explicit divergence, no counter term, no bare parameter and no arbitrarily running mass scale (like the $μ$ in $QCD$).

quant-ph↗

arXiv2010

Reduced Dirac Equation and Lamb Shift as an Off-mass-shell effect in Quantum Electrodynamics

Based on the precision experimental data of energy-level differences in hydrogenlike atoms, especially the 1S-2S transition of hydrogen and deuterium, the necessity of establishing a reduced Dirac equation (RDE) with reduced mass as the substitution of original electron mass is stressed. The theoretical basis of RDE lies on two symmetries, the invariance under the space-time inversion and that under the pure space inversion. Based on RDE and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state--a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.

quant-ph↗

arXiv2000

The Stability of Radiatively Cooled Jets in Three Dimensions

The effect of optically thin radiative cooling on the Kelvin-Helmholtz instability of three dimensional jets is investigated via linear stability theory and nonlinear hydrodynamical simulation. Two different cooling functions are considered: radiative cooling is found to have a significant effect on the stability of the jet in each case. The wavelengths and growth rates of unstable modes in the numerical simulations are found to be in good agreement with theoretical predictions. Disruption of the jet is found to be sensitive to the precessional frequency at the origin with lower frequencies leading to more rapid disruption. Strong nonlinear effects are observed as the result of the large number of normal modes in three dimensions which provide rich mode-mode interactions. These mode-mode interactions provide new mechanisms for the formation of knots in the flows. Significant structural features found in the numerical simulations appear similar to structures observed on protostellar jets.

astro-ph↗