arXiv subjects
Publications and source records attributed to Yue Wang.
We study asymptotic behaviors of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries under the assumption that the boundaries are piecewise regular with positive curvatures. We derive an estimate of such solutions by the corresponding solutions in the intersections of interior tangent balls. The positivity of curvatures plays an important role.
Spin-orbit coupling (SOC) is expected to partly determine the topologically nontrivial electronic structure of heavy half-Heusler ternary compounds. However, to date, attempts to experimentally observe either the strength of SOC or how it modifies the bulk band structure have been unsuccessful. By using bulk-sensitive nuclear magnetic resonance (NMR) spectroscopy combined with first-principles calculations, we reveal that 209Bi NMR isotropic shifts scale with relativity in terms of the strength of SOC and average atomic numbers, indicating strong relativistic effects on NMR parameters. According to first-principles calculations, we further claim that nuclear magnetic shieldings from relativistic p1/2 states and paramagnetic contributions from low-lying unoccupied p3/2 states are both sensitive to the details of band structures tuned by relativity, which explains why the hidden relativistic effects on band structure can be revealed by 209Bi NMR isotropic shifts in topologically nontrivial half-Heusler compounds. Used in complement to surface-sensitive methods, such as angle resolved photon electron spectroscopy and scanning tunneling spectroscopy, NMR can provide valuable information on bulk electronic states.
In the centenary year of Einstein's General Theory of Relativity, this paper reviews the current status of gravitational wave astronomy across a spectrum which stretches from attohertz to kilohertz frequencies. Sect. 1 of this paper reviews the historical development of gravitational wave astronomy from Einstein's first prediction to our current understanding the spectrum. It is shown that detection of signals in the audio frequency spectrum can be expected very soon, and that a north-south pair of next generation detectors would provide large scientific benefits. Sect. 2 reviews the theory of gravitational waves and the principles of detection using laser interferometry. The state of the art Advanced LIGO detectors are then described. These detectors have a high chance of detecting the first events in the near future. Sect. 3 reviews the KAGRA detector currently under development in Japan, which will be the first laser interferometer detector to use cryogenic test masses. Sect. 4 of this paper reviews gravitational wave detection in the nanohertz frequency band using the technique of pulsar timing. Sect. 5 reviews the status of gravitational wave detection in the attohertz frequency band, detectable in the polarisation of the cosmic microwave background, and discusses the prospects for detection of primordial waves from the big bang. The techniques described in sects. 1-5 have already placed significant limits on the strength of gravitational wave sources. Sects. 6 and 7 review ambitious plans for future space based gravitational wave detectors in the millihertz frequency band. Sect. 6 presents a roadmap for development of space based gravitational wave detectors by China while sect. 7 discusses a key enabling technology for space interferometry known as time delay interferometry.
In this paper, our objective is to find out the determining factors of Chernoff information in distinguishing a set of Gaussian trees. In this set, each tree can be attained via an edge removal and grafting operation from another tree. This is equivalent to asking for the Chernoff information between the most-likely confused, i.e. "bottleneck", Gaussian trees, as shown to be the case in ML estimated Gaussian tree graphs lately. We prove that the Chernoff information between two Gaussian trees related through an edge removal and a grafting operation is the same as that between two three-node Gaussian trees, whose topologies and edge weights are subject to the underlying graph operation. In addition, such Chernoff information is shown to be determined only by the maximum generalized eigenvalue of the two Gaussian covariance matrices. The Chernoff information of scalar Gaussian variables as a result of linear transformation (LT) of the original Gaussian vectors is also uniquely determined by the same maximum generalized eigenvalue. What is even more interesting is that after incorporating the cost of measurements into a normalized Chernoff information, Gaussian variables from LT have larger normalized Chernoff information than the one based on the original Gaussian vectors, as shown in our proved bounds
Part of a review paper entitled "Gravitational wave astronomy: the current status.", appeared in " Science China Physics, Mechanics & Astronomy 58.12 (2015): 1-41.
Blind Source Separation (BSS) has proven to be a powerful tool for the analysis of composite patterns in engineering and science. We introduce Convex Analysis of Mixtures (CAM) for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the convex data scatter plot. We prove a sufficient and necessary condition for identifying the mixing matrix through edge detection, which also serves as the foundation for CAM to be applied not only to the exact-determined and over-determined cases, but also to the under-determined case. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric convex analysis scheme, and stability-based model order selection. We demonstrate the principle of CAM on simulated data and numerically mixed natural images. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data. We then apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.
High-quality nonmagnetic half-Heusler ScPtBi single crystals were synthesized by a Bi self-flux method. This compound was revealed to be a hole-dominated semimetal with a large low-field magnetoresistance up to 240% at 2K in a magnetic field of 1T. Magneto-transport measurements demonstrated that the large low-field magnetoresistance effect resulted from the coexistence of field-induced metal-semiconductor transition and weak-antilocalization effect. Moreover, Hall measurements indicated that ScPtBi single crystal showed a high mobility over a wide temperature region even up to room temperature (4050 cm2V-1s-1 at 2K - 2016 cm2V-1s-1 at 300K). These findings not only suggest the nonmagnetic ScPtBi semimetal a potential material candidate for applications in high-sensitivity magnetic sensors, but also are of great significance to comprehensively understand the rare-earth based half-Heusler compounds.
We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $Ω\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\barΩ)$. We can improve the Hölder exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.
The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples.
Scene classification is a fundamental perception task for environmental understanding in today's robotics. In this paper, we have attempted to exploit the use of popular machine learning technique of deep learning to enhance scene understanding, particularly in robotics applications. As scene images have larger diversity than the iconic object images, it is more challenging for deep learning methods to automatically learn features from scene images with less samples. Inspired by human scene understanding based on object knowledge, we address the problem of scene classification by encouraging deep neural networks to incorporate object-level information. This is implemented with a regularization of semantic segmentation. With only 5 thousand training images, as opposed to 2.5 million images, we show the proposed deep architecture achieves superior scene classification results to the state-of-the-art on a publicly available SUN RGB-D dataset. In addition, performance of semantic segmentation, the regularizer, also reaches a new record with refinement derived from predicted scene labels. Finally, we apply our SUN RGB-D dataset trained model to a mobile robot captured images to classify scenes in our university demonstrating the generalization ability of the proposed algorithm.
The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still question able if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) of cancer cells. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas thereversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments, and it also fails to capture the overshoot of CSCs. By comparison, it is more likely for the reversible model to correctly describe the stability of the phenotypic mixture and various types of overshoot behavior.
Place classification is a fundamental ability that a robot should possess to carry out effective human-robot interactions. It is a nontrivial classification problem which has attracted many research. In recent years, there is a high exploitation of Artificial Intelligent algorithms in robotics applications. Inspired by the recent successes of deep learning methods, we propose an end-to-end learning approach for the place classification problem. With the deep architectures, this methodology automatically discovers features and contributes in general to higher classification accuracies. The pipeline of our approach is composed of three parts. Firstly, we construct multiple layers of laser range data to represent the environment information in different levels of granularity. Secondly, each layer of data is fed into a deep neural network model for classification, where a graph regularization is imposed to the deep architecture for keeping local consistency between adjacent samples. Finally, the predicted labels obtained from all the layers are fused based on confidence trees to maximize the overall confidence. Experimental results validate the effective- ness of our end-to-end place classification framework in which both the multi-layer structure and the graph regularization promote the classification performance. Furthermore, results show that the features automatically learned from the raw input range data can achieve competitive results to the features constructed based on statistical and geometrical information.
In this paper, we consider the problem of partitioning active users in a manner that facilitates multi-access without collision. The setting is of a noisy, synchronous, Boolean, multi-access channel where $K$ active users (out of a total of $N$ users) seek to access. A solution to the partition problem places each of the $N$ users in one of $K$ groups (or blocks) such that no two active nodes are in the same block. We consider a simple, but non-trivial and illustrative case of $K=2$ active users and study the number of steps $T$ used to solve the partition problem. By random coding and a suboptimal decoding scheme, we show that for any $T\geq (C_1 +ξ_1)\log N$, where $C_1$ and $ξ_1$ are positive constants (independent of $N$), and $ξ_1$ can be arbitrary small, the partition problem can be solved with error probability $P_e^{(N)} \to 0$, for large $N$. Under the same scheme, we also bound $T$ from the other direction, establishing that, for any $T \leq (C_2 - ξ_2) \log N$, the error probability $P_e^{(N)} \to 1$ for large $N$; again $C_2$ and $ξ_2$ are constants and $ξ_2$ can be arbitrarily small. These bounds on the number of steps are lower than the tight achievable lower-bound in terms of $T \geq (C_g +ξ)\log N $ for group testing (in which all active users are identified, rather than just partitioned). Thus, partitioning may prove to be a more efficient approach for multi-access than group testing.
We develop a cross-platform open-source Java application (BACOM2) with graphic user interface (GUI), and users also can use a XML file to set the parameters of algorithm model, file paths and the dataset of paired samples. BACOM2 implements the new entire pipeline of copy number change analysis for heterogeneous cancer tissues, including extraction of raw copy number signals from CEL files of paired samples, attenuation correction, identification of balanced AB-genotype loci, copy number detection and segmentation, global baseline calculation and absolute normalization, differentiation of deletion types, estimation of the normal tissue fraction and correction of normal tissue contamination. BACOM2 focuses on the common tools for data preparation and absolute normalization for copy number analysis of heterogeneous cancer tissues. The software provides an additional choice for scientists who require a user-friendly, high-speed processing, cross-platform computing environment for large copy number data analysis.
Detecting complex interactions among risk factors in case-control studies is a fundamental task in clinical and population research. However, though hypothesis testing using logistic regression (LR) is a convenient solution, the LR framework is poorly powered and ill-suited under several common circumstances in practice including missing or unmeasured risk factors, imperfectly correlated "surrogates", and multiple disease sub-types. The weakness of LR in these settings is related to the way in which the null hypothesis is defined. Here we propose the Asymmetric Independence Model (AIM) as a biologically-inspired alternative to LR, based on the key observation that the mechanisms associated with acquiring a "disease" versus maintaining "health" are asymmetric. We prove mathematically that, unlike LR, AIM is a robust model under the abovementioned confounding scenarios. Further, we provide a mathematical definition of a "synergistic" interaction, and prove that theoretically AIM has better power than LR for such interactions. We then experimentally show the superior performance of AIM as compared to LR on both simulations and four real datasets. While the principal application here involves genetic or environmental variables in the life sciences, our methodology is readily applied to other types of measurements and inferences, e.g. in the social sciences.
High quality half-Heusler single crystals of LuPtSb have been synthesized by a Pb flux method. The temperature dependent resistivity and Hall effects indicate that the LuPtSb crystal is a p-type gapless semiconductor showing a transition from semiconducting to metallic conducting at 150 K. Moreover, a weakly temperature-dependent positive magnetoresistance (MR) as large as 109 % and high carrier mobility up to 2950 cm2/Vs are experimentally observed at temperatures below 150 K. The low-field MR data shows evidence for weak antilocalization (WAL) effect at temperatures even up to 150 K. Analysis of the temperature and angle dependent magnetoconductance manifests that the WAL effect originates from the bulk contribution owing to the strong spin-orbital coupling.
We show that the Dirichlet problem at infinity is unsolvable for the p-Laplace equation for any nonconstant continuous boundary data, for certain range of p>n, on an n-dimensional Cartan-Hadamard manifold constructed from a complete noncompact shrinking gradient Ricci soliton. Using the steady gradient Ricci soliton, we find an incomplete Riemannian metric on ${\mathbb R}^2$ with positive Gauss curvature such that every positive p-harmonic function must be constant for $p\geq 4$.
Several models compete to explain the abundance properties of stellar populations in globular clusters. One of the main constraints is the present-day ratio of first- and second-generation stars that are currently identified based on their sodium content. We propose an alternative interpretation of the observed sodium distribution, and suggest that stars with low sodium abundance that are counted as members of the first stellar generation could actually be second-generation stars. We compute the number ratio of second-generation stars along the Na distribution following the fast rotating massive star model using the same constraints from the well-documented case of NGC 6752 as in our previous developments. We reproduce the typical percentage of low-sodium stars usually classified as first-generation stars by invoking only secondary star formation from material ejected by massive stars and mixed with original globular cluster material in proportions that account for the Li-Na anti-correlation in this cluster. Globular clusters could be totally devoid of first-generation low-mass stars today. This can be tested with the determination of the carbon isotopic ratio and nitrogen abundance in turn-off globular cluster stars. Consequences and related issues are briefly discussed.