Roadmap for gravitational wave detection in space - a preliminary study
Part of a review paper entitled "Gravitational wave astronomy: the current status.", appeared in " Science China Physics, Mechanics & Astronomy 58.12 (2015): 1-41.
astro-ph.IM↗
arXiv subjects
Wei Gao
Publications and source records attributed to Wei Gao.
Observation of reversible orbital angular momentum transfer based on photon-phonon coupling
Orbital angular momentum (OAM) has gained great interest due to its most attractive feature of high dimensionality, and several ground-breaking demonstrations in communication based on OAM multiplexing have been carried out. Accordingly, a rapid data-density growth from OAM multiplexing has posed a great challenge to the signal-processing layer. Meanwhile, in another area, optical signal-processing circuit based on photon-phonon conversion has received considerable attention and made rapid progress. Here, with an aim of finding the intersection between OAM multiplexing and photon-phonon conversion, we report on the observation of reversible OAM photon-phonon conversion. A specific OAM state can be flexibly and controllably interconverted between photonic and phononic domains via Brillouin photon-phonon coupling within the decay time of acoustic signal, in which OAM and spin angular momentum are independently conserved. Our result demonstrates the controllable OAM transfer between photons and phonons, shows the potential of using OAM multiplexing to extend the capacity of photon-phonon conversion based signal-processing scheme, and may trigger the development of OAM-multiplexed photon-phonon circuit.
physics.optics↗
Mouse Pose Estimation From Depth Images
We focus on the challenging problem of efficient mouse 3D pose estimation based on static images, and especially single depth images. We introduce an approach to discriminatively train the split nodes of trees in random forest to improve their performance on estimation of 3D joint positions of mouse. Our algorithm is capable of working with different types of rodents and with different types of depth cameras and imaging setups. In particular, it is demonstrated in this paper that when a top-mounted depth camera is combined with a bottom-mounted color camera, the final system is capable of delivering full-body pose estimation including four limbs and the paws. Empirical examinations on synthesized and real-world depth images confirm the applicability of our approach on mouse pose estimation, as well as the closely related task of part-based labeling of mouse.
cs.CV↗
Entropic Effects of Thermal Rippling on van der Waals Interactions between Monolayer Graphene and a Rigid Substrate
Graphene monolayer, with extremely low flexural stiffness, displays spontaneous rippling due to thermal fluctuations at a finite temperature. When a graphene membrane is placed on a solid substrate, the adhesive interactions between graphene and the substrate could considerably suppress thermal rippling. On the other hand, the statistical nature of thermal rippling adds an entropic contribution to the graphene-substrate interactions. In this paper we present a statistical mechanics analysis on thermal rippling of monolayer graphene supported on a rigid substrate, assuming a generic form of van der Waals interactions between graphene and substrate at T = 0 K. The rippling amplitude, the equilibrium average separation, and the average interaction energy are predicted simultaneously and compared with molecular dynamics (MD) simulations. While the amplitude of thermal rippling is reduced by adhesive interactions, the entropic contribution leads to an effective repulsion. As a result, the equilibrium average separation increases and the effective adhesion energy decreases with increasing temperature. Moreover, the effect of a biaxial pre-strain in graphene is considered, and a buckling instability is predicted at a critical compressive strain that depends on both the temperature and the adhesive interactions. Limited by the harmonic approximations, the theoretical predictions agree with MD simulations only for relatively small rippling amplitudes but can be extended to account for the anharmonic effects.
cond-mat.mes-hall↗
On the distance spectra of graphs
The distance matrix of a graph $G$ is the matrix containing the pairwise distances between vertices. The distance eigenvalues of $G$ are the eigenvalues of its distance matrix and they form the distance spectrum of $G$. We determine the distance spectra of halved cubes, double odd graphs, and Doob graphs, completing the determination of distance spectra of distance regular graphs having exactly one positive distance eigenvalue. We characterize strongly regular graphs having more positive than negative distance eigenvalues. We give examples of graphs with few distinct distance eigenvalues but lacking regularity properties. We also determine the determinant and inertia of the distance matrices of lollipop and barbell graphs.
math.CO↗
Minimum codegree threshold for $C_6^3$-factors in $3$-uniform Hypergraphs
Let $C_6^3$ be the 3-uniform hypergraph on $\{1,\dots, 6\}$ with edges $123, 345,561$, which can be seen as the triangle in 3-uniform hypergraphs. For sufficiently large $n$ divisible by 6, we show that every $n$-vertex 3-uniform hypergraph $H$ with minimum codegree at least $n/3$ contains a $C_6^3$-factor, i.e., a spanning subhypergraph consisting of vertex-disjoint copies of $C_6^3$. The minimum codegree condition is best possible. This improves the asymptotical result obtained by Mycroft and answers a question of Rödl and Ruciński exactly.
math.CO↗
Parametric amplification of orbital angular momentum beams based on light-acoustic interaction
A high fidelity amplification of beams carrying orbital angular momentum (OAM) is very crucial for OAM multiplexing and other OAM-based applications. Here, we report the first study of stimulated Brillouin amplification (SBA) for OAM beams, the energy conversion efficiency of photon-phonon coupling and the phase structure of amplified signals are investigated in collinear and noncollinear frame systems, respectively. Our results demonstrate that the OAM signals can be efficiently amplified without obvious noise introduced, and the modes of output signal are independent of the pump modes or the geometrical frames. Meanwhile, an OAM state depending on the optical modes and the geometrical frames is loaded into phonons by coherent light-acoustic interaction, which reveals more fundamental significance and a great application potential in OAM-multiplexing.
physics.optics↗
Descope of the ALIA mission
The present work reports on a feasibility study commissioned by the Chinese Academy of Sciences of China to explore various possible mission options to detect gravitational waves in space alternative to that of the eLISA/LISA mission concept. Based on the relative merits assigned to science and technological viability, a few representative mission options descoped from the ALIA mission are considered. A semi-analytic Monte Carlo simulation is carried out to understand the cosmic black hole merger histories starting from intermediate mass black holes at high redshift as well as the possible scientific merits of the mission options considered in probing the light seed black holes and their coevolution with galaxies in early Universe. The study indicates that, by choosing the armlength of the interferometer to be three million kilometers and shifting the sensitivity floor to around one-hundredth Hz, together with a very moderate improvement on the position noise budget, there are certain mission options capable of exploring light seed, intermediate mass black hole binaries at high redshift that are not readily accessible to eLISA/LISA, and yet the technological requirements seem to within reach in the next few decades for China.
gr-qc↗
Estimation for Dynamic and Static Panel Probit Models with Large Individual Effects
For discrete panel data, the dynamic relationship between successive observations is often of interest. We consider a dynamic probit model for short panel data. A problem with estimating the dynamic parameter of interest is that the model contains a large number of nuisance parameters, one for each individual. Heckman proposed to use maximum likelihood estimation of the dynamic parameter, which, however, does not perform well if the individual effects are large. We suggest new estimators for the dynamic parameter, based on the assumption that the individual parameters are random and possibly large. Theoretical properties of our estimators are derived and a simulation study shows they have some advantages compared to Heckman's estimator.
stat.ME↗
Free vibration and mechanical buckling of plates with in-plane material inhomogeneity - a three dimensional consistent approach
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by two-dimensional higher order spectral element. The solution through the thickness is expressed analytically with Pade expansion. The stiffness matrix is derived directly from the three dimensional solutions and by employing the spectral element, a diagonal mass matrix is obtained. The formulation does not require ad hoc shear correction factors and no numerical locking arises. The material properties are assumed to be temperature independent and graded only in the in-plane direction by a simple power law. The effective material properties are estimated using the rule of mixtures. The influence of the material gradient index, the boundary conditions and the geometry of the plate on the fundamental frequencies and critical buckling load are numerically investigated.
math.NA↗
On the Consistency of AUC Pairwise Optimization
AUC (area under ROC curve) is an important evaluation criterion, which has been popularly used in many learning tasks such as class-imbalance learning, cost-sensitive learning, learning to rank, etc. Many learning approaches try to optimize AUC, while owing to the non-convexity and discontinuousness of AUC, almost all approaches work with surrogate loss functions. Thus, the consistency of AUC is crucial; however, it has been almost untouched before. In this paper, we provide a sufficient condition for the asymptotic consistency of learning approaches based on surrogate loss functions. Based on this result, we prove that exponential loss and logistic loss are consistent with AUC, but hinge loss is inconsistent. Then, we derive the $q$-norm hinge loss and general hinge loss that are consistent with AUC. We also derive the consistent bounds for exponential loss and logistic loss, and obtain the consistent bounds for many surrogate loss functions under the non-noise setting. Further, we disclose an equivalence between the exponential surrogate loss of AUC and exponential surrogate loss of accuracy, and one straightforward consequence of such finding is that AdaBoost and RankBoost are equivalent.
cs.LG↗
Dropout Rademacher Complexity of Deep Neural Networks
Great successes of deep neural networks have been witnessed in various real applications. Many algorithmic and implementation techniques have been developed, however, theoretical understanding of many aspects of deep neural networks is far from clear. A particular interesting issue is the usefulness of dropout, which was motivated from the intuition of preventing complex co-adaptation of feature detectors. In this paper, we study the Rademacher complexity of different types of dropout, and our theoretical results disclose that for shallow neural networks (with one or none hidden layer) dropout is able to reduce the Rademacher complexity in polynomial, whereas for deep neural networks it can amazingly lead to an exponential reduction of the Rademacher complexity.
cs.NE↗
Interfacial adhesion between graphene and silicon dioxide by density functional theory with van der Waals corrections
Interfacial adhesion between graphene and a SiO2 substrate is studied by density functional theory (DFT) with dispersion corrections. The results demonstrate the van der Waals (vdW) interaction as the predominate mechanism for the graphene/SiO2 interface. It is found that the interaction strength is strongly influenced by changes of the SiO2 surface structures due to surface reactions with water. The adhesion energy is reduced when the reconstructed SiO2 surface is hydroxylated, and further reduced when covered by a monolayer of adsorbed water molecules. Thus, the effect of humidity may help explain the wide variation of adhesion energies measured in recent experiments between graphene and SiO2. Moreover, it is noted that vdW forces are required to accurately model the graphene/SiO2 interface with DFT and that the adhesion energy is underestimated by empirical force fields commonly used in atomistic simulations.
cond-mat.mtrl-sci↗
Sign patterns with minimum rank 3 and point-line configurations
A \emph{sign pattern (matrix)} is a matrix whose entries are from the set $\{+, -, 0\}$. The \emph{minimum rank} (respectively, \emph{rational minimum rank}) of a sign pattern matrix $\cal A$ is the minimum of the ranks of the real (respectively, rational) matrices whose entries have signs equal to the corresponding entries of $\cal A$. A sign pattern $\cal A$ is said to be \emph{condensed} if $\cal A$ has no zero row or column and no two rows or columns are identical or negatives of each other. In this paper, a new direct connection between condensed $m \times n $ sign patterns with minimum rank $r$ and $m$ point--$n$ hyperplane configurations in ${\mathbb R}^{r-1}$ is established. In particular, condensed sign patterns with minimum rank 3 are closed related to point--line configurations on the plane. It is proved that for any sign pattern $\cal A$ with minimum rank $r\geq 3$, if the number of zero entries on each column of $\cal A$ is at most $r-1$, then the rational minimum rank of $\cal A$ is also $r$. Furthermore, we construct the smallest known sign pattern whose minimum rank is 3 but whose rational minimum rank is greater than 3.
math.CO↗
Convergence analysis of kernel LMS algorithm with pre-tuned dictionary
The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a KLMS adaptive filter requires to select a so-called dictionary in order to get a finite-order model. This dictionary has a significant impact on performance, and requires careful consideration. Theoretical analysis of KLMS as a function of dictionary setting has rarely, if ever, been addressed in the literature. In an analysis previously published by the authors, the dictionary elements were assumed to be governed by the same probability density function of the input data. In this paper, we modify this study by considering the dictionary as part of the filter parameters to be set. This theoretical analysis paves the way for future investigations on KLMS dictionary design.
stat.ML↗
Efficient Computational Algorithm for Optimal Allocation in Regression Models
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been discussed in the literature. Here, we provide an alternate proof of the monotonic convergence for $D$-criterion with a simple computational algorithm and furthermore show it converges to the $D$-optimality. We also discuss an algorithm as well as a conjecture of the monotonic convergence for $A$-criterion. Monte Carlo simulations are used to demonstrate the reliability, efficiency and usefulness of the proposed algorithms.
stat.CO↗
On the Doubt about Margin Explanation of Boosting
Margin theory provides one of the most popular explanations to the success of \texttt{AdaBoost}, where the central point lies in the recognition that \textit{margin} is the key for characterizing the performance of \texttt{AdaBoost}. This theory has been very influential, e.g., it has been used to argue that \texttt{AdaBoost} usually does not overfit since it tends to enlarge the margin even after the training error reaches zero. Previously the \textit{minimum margin bound} was established for \texttt{AdaBoost}, however, \cite{Breiman1999} pointed out that maximizing the minimum margin does not necessarily lead to a better generalization. Later, \cite{Reyzin:Schapire2006} emphasized that the margin distribution rather than minimum margin is crucial to the performance of \texttt{AdaBoost}. In this paper, we first present the \textit{$k$th margin bound} and further study on its relationship to previous work such as the minimum margin bound and Emargin bound. Then, we improve the previous empirical Bernstein bounds \citep{Maurer:Pontil2009,Audibert:Munos:Szepesvari2009}, and based on such findings, we defend the margin-based explanation against Breiman's doubts by proving a new generalization error bound that considers exactly the same factors as \cite{Schapire:Freund:Bartlett:Lee1998} but is sharper than \cite{Breiman1999}'s minimum margin bound. By incorporating factors such as average margin and variance, we present a generalization error bound that is heavily related to the whole margin distribution. We also provide margin distribution bounds for generalization error of voting classifiers in finite VC-dimension space.
cs.LG↗
Online dictionary learning for kernel LMS. Analysis and forward-backward splitting algorithm
Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification. Unfortunately, an undesirable characteristic of these methods is that the order of the filters grows linearly with the number of input data. This dramatically increases the computational burden and memory requirement. A variety of strategies based on dictionary learning have been proposed to overcome this severe drawback. Few, if any, of these works analyze the problem of updating the dictionary in a time-varying environment. In this paper, we present an analytical study of the convergence behavior of the Gaussian least-mean-square algorithm in the case where the statistics of the dictionary elements only partially match the statistics of the input data. This allows us to emphasize the need for updating the dictionary in an online way, by discarding the obsolete elements and adding appropriate ones. We introduce a kernel least-mean-square algorithm with L1-norm regularization to automatically perform this task. The stability in the mean of this method is analyzed, and its performance is tested with experiments.
stat.ML↗