On the semicircular law of large dimensional random quaternion matrices

It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a natural idea we want to get more universal results by removing the Gaussian condition. For the first step, in this paper we prove that the empirical spectral distribution of the common quaternion self-dual Hermitian matrices tends to semicircular law. The main tool to establish the universal result is given as a lemma in this paper as well.Comment: 20 page

On the limit of extreme eigenvalues of large dimensional random quaternion matrices

Since E.P.Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin (1988) obtained the necessary and sufficient conditions for the strong convergence of the extreme eigenvalues of a Wigner matrix. In this paper, we consider the case of quaternion self-dual Hermitian matrices. We prove the necessary and sufficient conditions for the strong convergence of extreme eigenvalues of quaternion self-dual Hermitian matrices corresponding to the Wigner case.Comment: 16 pages, 5 figure

Dynamical Variations of the Global COVID-19 Pandemic Based on a SEICR Disease Model: A New Approach of Yi Hua Jie Mu

The ongoing coronavirus disease 2019 (COVID-19) pandemic has caused more than 150 million cases of infection to date and poses a serious threat to global public health. In this study, global COVID-19 data were used to examine the dynamical variations from the perspectives of immunity and contact of 84 countries across the five climate regions: tropical, arid, temperate, and cold. A new approach named Yi Hua Jie Mu is proposed to obtain the transmission rates based on the COVID-19 data between the countries with the same climate region over the Northern Hemisphere and Southern Hemisphere. Our results suggest that the COVID-19 pandemic will persist over a long period of time or enter into regular circulation in multiple periods of 1–2 years. Moreover, based on the simulated results by the COVID-19 data, it is found that the temperate and cold climate regions have higher infection rates than the tropical and arid climate regions, which indicates that climate may modulate the transmission of COVID-19. The role of the climate on the COVID-19 variations should be concluded with more data and more cautions. The non-pharmaceutical interventions still play the key role in controlling and prevention this global pandemic

Magnetic-field control of topological electronic response near room temperature in correlated Kagome magnets

Strongly correlated Kagome magnets are promising candidates for achieving controllable topological devices owing to the rich interplay between inherent Dirac fermions and correlation-driven magnetism. Here we report tunable local magnetism and its intriguing control of topological electronic response near room temperature in the Kagome magnet Fe3Sn2 using small angle neutron scattering, muon spin rotation, and magnetoresistivity measurement techniques. The average bulk spin direction and magnetic domain texture can be tuned effectively by small magnetic fields. Magnetoresistivity, in response, exhibits a measurable degree of anisotropic weak localization behavior, which allows the direct control of Dirac fermions with strong electron correlations. Our work points to a novel platform for manipulating emergent phenomena in strongly-correlated topological materials relevant to future applications

Foot-and-Mouth Disease Virus Persists in the Light Zone of Germinal Centres

Foot-and-mouth disease virus (FMDV) is one of the most contagious viruses of animals and is recognised as the most important constraint to international trade in animals and animal products. Two fundamental problems remain to be understood before more effective control measures can be put in place. These problems are the FMDV “carrier state” and the short duration of immunity after vaccination which contrasts with prolonged immunity after natural infection. Here we show by laser capture microdissection in combination with quantitative real-time reverse transcription polymerase chain reaction, immunohistochemical analysis and corroborate by in situ hybridization that FMDV locates rapidly to, and is maintained in, the light zone of germinal centres following primary infection of naïve cattle. We propose that maintenance of non-replicating FMDV in these sites represents a source of persisting infectious virus and also contributes to the generation of long-lasting antibody responses against neutralising epitopes of the virus

A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test

We establish a joint central limit theorem for sums of squares and the fourth powers of residuals in a high-dimensional regression model. We then apply this CLT to detect the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size n tends to infinity and the number of covariates p may be fixed or tend to infinity.MOE (Min. of Education, S’pore

An Accurate GPS-IMU/DR Data Fusion Method for Driverless Car Based on a Set of Predictive Models and Grid Constraints

A high-performance differential global positioning system (GPS)  receiver with real time kinematics provides absolute localization for driverless cars. However, it is not only susceptible to multipath effect but also unable to effectively fulfill precise error correction in a wide range of driving areas. This paper proposes an accurate GPS–inertial measurement unit (IMU)/dead reckoning (DR) data fusion method based on a set of predictive models and occupancy grid constraints. First, we employ a set of autoregressive and moving average (ARMA) equations that have different structural parameters to build maximum likelihood models of raw navigation. Second, both grid constraints and spatial consensus checks on all predictive results and current measurements are required to have removal of outliers. Navigation data that satisfy stationary stochastic process are further fused to achieve accurate localization results. Third, the standard deviation of multimodal data fusion can be pre-specified by grid size. Finally, we perform a lot of field tests on a diversity of real urban scenarios. The experimental results demonstrate that the method can significantly smooth small jumps in bias and considerably reduce accumulated position errors due to DR. With low computational complexity, the position accuracy of our method surpasses existing state-of-the-arts on the same dataset and the new data fusion method is practically applied in our driverless car