On Gaussian Comparison Inequality and Its Application to Spectral Analysis of Large Random Matrices

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp inference on spectra of large random matrices. In particular, we show that two long-standing problems in random matrix theory can be solved: (i) simple bootstrap inference on sample eigenvalues when true eigenvalues are tied; (ii) conducting two-sample Roy's covariance test in high dimensions. To establish the asymptotic results, a generalized $\epsilon$-net argument regarding the matrix rescaled spectral norm and several new empirical process bounds are developed and of independent interest.Comment: to appear in Bernoull

Nonadiabatic molecular dynamics simulation: An approach based on quantum measurement picture

Mixed-quantum-classical molecular dynamics simulation implies an effective measurement on the electronic states owing to continuously tracking the atomic forces.Based on this insight, we propose a quantum trajectory mean-field approach for nonadiabatic molecular dynamics simulations. The new protocol provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also bridges two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. Excellent agreement with the exact results is illustrated with representative model systems, including the challenging ones for traditional methods

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we can realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed by a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial-linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks and find both the existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure

5-Arc transitive cubic Cayley graphs on finite simple groups

AbstractIn this paper, we determine all connected 5-arc transitive cubic Cayley graphs on the alternating group A47; there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two non-normal connected cubic arc-transitive Cayley graphs for finite nonabelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs

Contextual-Bandit Based Personalized Recommendation with Time-Varying User Interests

A contextual bandit problem is studied in a highly non-stationary environment, which is ubiquitous in various recommender systems due to the time-varying interests of users. Two models with disjoint and hybrid payoffs are considered to characterize the phenomenon that users' preferences towards different items vary differently over time. In the disjoint payoff model, the reward of playing an arm is determined by an arm-specific preference vector, which is piecewise-stationary with asynchronous and distinct changes across different arms. An efficient learning algorithm that is adaptive to abrupt reward changes is proposed and theoretical regret analysis is provided to show that a sublinear scaling of regret in the time length $T$ is achieved. The algorithm is further extended to a more general setting with hybrid payoffs where the reward of playing an arm is determined by both an arm-specific preference vector and a joint coefficient vector shared by all arms. Empirical experiments are conducted on real-world datasets to verify the advantages of the proposed learning algorithms against baseline ones in both settings.Comment: Accepted by AAAI 2

miR-638 is a new biomarker for outcome prediction of non-small cell lung cancer patients receiving chemotherapy.

MicroRNAs (miRNAs), a class of small non-coding RNAs, mediate gene expression by either cleaving target mRNAs or inhibiting their translation. They have key roles in the tumorigenesis of several cancers, including non-small cell lung cancer (NSCLC). The aim of this study was to investigate the clinical significance of miR-638 in the evaluation of NSCLC patient prognosis in response to chemotherapy. First, we detected miR-638 expression levels in vitro in the culture supernatants of the NSCLC cell line SPC-A1 treated with cisplatin, as well as the apoptosis rates of SPC-A1. Second, serum miR-638 expression levels were detected in vivo by using nude mice xenograft models bearing SPC-A1 with and without cisplatin treatment. In the clinic, the serum miR-638 levels of 200 cases of NSCLC patients before and after chemotherapy were determined by quantitative real-time PCR, and the associations of clinicopathological features with miR-638 expression patterns after chemotherapy were analyzed. Our data helped in demonstrating that cisplatin induced apoptosis of the SPC-A1 cells in a dose- and time-dependent manner accompanied by increased miR-638 expression levels in the culture supernatants. In vivo data further revealed that cisplatin induced miR-638 upregulation in the serum derived from mice xenograft models, and in NSCLC patient sera, miR-638 expression patterns after chemotherapy significantly correlated with lymph node metastasis. Moreover, survival analyses revealed that patients who had increased miR-638 levels after chemotherapy showed significantly longer survival time than those who had decreased miR-638 levels. Our findings suggest that serum miR-638 levels are associated with the survival of NSCLC patients and may be considered a potential independent predictor for NSCLC prognosis

Holographic Einstein rings of Non-commutative black holes

With the help of the AdS/CFT correspondence, we easily derive the desired response function of QFT on the boundary. Using the virtual optical system with a convex lens, we are able to obtain the image of the black hole from the response function and further study the Einstein ring of the non-commutative black holes. All the results show that there are some common features and different features compared to the previous study of other background black holes. The common features include that the holographic ring always appears with the concentric stripe surrounded when the observer located at the north pole, and an extremely bright ring when the observer is at the position of the photon sphere of the black hole. And with the change of the observation position, this ring will change into a luminosity-deformed ring, or light points. In addition to these similarities, there are some different features which are due to the singularity of the event horizon temperature. Explicitly, the relation between temperature and the event horizon $T-z_h$ has two branches when the non-commutative parameter $n$ is fixed. These in turn have an effect on the behavior of the response function and the Einstein ring. For example, the amplitude of the response function $|\langle O\rangle|$ increases with the decrease of the non-commutative strength parameter $n$ for both two branches of $T-n$ relation. However, the amplitude of $|\langle O\rangle|$ increases with the decrease of the temperature $T$ for the left branch of $T-z_h$ relation, while the amplitude of $|\langle O\rangle|$ decreases with the decrease of the temperature $T$ for the right branch. These differences are also reflected in the Einstein ring. Therefore, these differences can be used to distinguish different black hole backgrounds. Furthermore, we show that the non-commutative parameter has an effect on the brightness and the position of Einstein ring.Comment: revised version. arXiv admin note: text overlap with arXiv:2307.01973; text overlap with arXiv:1811.12617, arXiv:1906.09113 by other author