arXiv subjects
Publications and source records attributed to Liu Yang.
We discuss how to determine and combine upper limits based on observed events and estimated backgrounds with a Bayesian method, when insignificant signals are observed in independent measurements. In addition to some general features deduced from the analytical formulae, systematic numerical results are obtained by a C$++$ program (CULBA) for low-count experiments, which can be used as a reference to combine two upper limits.
We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates.
We study the optimal rates of convergence for estimating a prior distribution over a VC class from a sequence of independent data sets respectively labeled by independent target functions sampled from the prior. We specifically derive upper and lower bounds on the optimal rates under a smoothness condition on the correct prior, with the number of samples per data set equal the VC dimension. These results have implications for the improvements achievable via transfer learning. We additionally extend this setting to real-valued function, where we establish consistency of an estimator for the prior, and discuss an additional application to a preference elicitation problem in algorithmic economics.
The paper develops and studies a very general notion of dichotomy, referred to as "nonuniform $(h,k,μ,ν)$-dichotomy". The new notion contains as special cases most versions of dichotomy existing in the literature. The paper then provides corresponding new versions of robustness, Hartman-Grobman theorem, and stable manifold theorem for nonautonomous dynamical systems in Banach spaces in term of the nonuniform $(h,k,μ,ν)$-dichotomy.
In this paper, a new notion called the general nonuniform $(h,k,μ,ν)$-dichotomy for a sequence of linear operators is proposed, which occurs in a more natural way and is related to nonuniform hyperbolicity. Then, sufficient criteria are established for the existence of nonuniform $(h,k,μ,ν)$-dichotomy in terms of appropriate Lyapunov exponents for the sequence of linear operators. Moreover, we investigate the stability theory of sequences of non uniformly hyperbolic linear operators in Banach spaces, which admit a nonuniform $(h,k,μ,ν)$-dichotomy. In the case of linear perturbations, we investigate parameter dependence of robustness or roughness of the nonuniform $(h,k,μ,ν)$-dichotomies and show that the stable and unstable subspaces of nonuniform $(h,k,μ,ν)$-dichotomies for the linear perturbed system are Lipschitz continuous for the parameters. In the case of nonlinear perturbations, we construct a new version of the Grobman-Hartman theorem and explore the existence of parameter dependence of stable Lipschitz invariant manifolds when the nonlinear perturbation is of Lipschitz type.
We study the coupled even number of microcavities with the balanced gain and loss between any pair of their neighboring components. The effective non-Hermitian Hamiltonian for such structure has the cyclic permutation-time symmetry with respect to the cavity modes, and this symmetry determines the patterns of the dynamical evolutions of the cavity modes. The systems also have multiple exceptional points for the degeneracy of the existing supermodes, exhibiting the "phase transition" of system dynamics across these exceptional points. We illustrate the quantum dynamical properties of the systems with the evolutions of cavity photon numbers and correlation functions. Moreover, we demonstrate the effects of the quantum noises accompanying the amplification and dissipation of the cavity modes. The reciprocal light transportation predicted with the effective non-Hermitian models for the similar couplers is violated by the unavoidable quantum noises.
Spin torque from spin current applied to a nanoscale region of a ferromagnet can act as negative magnetic damping and thereby excite self-oscillations of its magnetization. In contrast, spin torque uniformly applied to the magnetization of an extended ferromagnetic film does not generate self-oscillatory magnetic dynamics but leads to reduction of the saturation magnetization. Here we report studies of the effect of spin torque on a system of intermediate dimensionality - a ferromagnetic nanowire. We observe coherent self-oscillations of magnetization in a ferromagnetic nanowire serving as the active region of a spin torque oscillator driven by spin orbit torques. Our work demonstrates that magnetization self-oscillations can be excited in a one-dimensional magnetic system and that dimensions of the active region of spin torque oscillators can be extended beyond the nanometer length scale.
This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise model of Tsybakov (2004), the minimax label complexity of active learning with a VC class is always asymptotically smaller than that of passive learning, and is typically significantly smaller than the best previously-published upper bounds in the active learning literature. In high-noise regimes, it turns out that all active learning problems of a given VC dimension have roughly the same minimax label complexity, which contrasts with well-known results for bounded noise. In low-noise regimes, we find that the label complexity is well-characterized by a simple combinatorial complexity measure we call the star number. Interestingly, we find that almost all of the complexity measures previously explored in the active learning literature have worst-case values exactly equal to the star number. We also propose new active learning strategies that nearly achieve these minimax label complexities.
Electromagnetic absorbers have drawn increasing attention in many areas. A series of plasmonic and metamaterial structures can work as efficient narrow band absorbers due to the excitation of plasmonic or photonic resonances, providing a great potential for applications in designing selective thermal emitters, bio-sensing, etc. In other applications such as solar energy harvesting and photonic detection, the bandwidth of light absorbers is required to be quite broad. Under such a background, a variety of mechanisms of broadband/multiband absorption have been proposed, such as mixing multiple resonances together, exciting phase resonances, slowing down light by anisotropic metamaterials, employing high loss materials and so on.
We propose a polarization-insensitive and high-efficiency plasmonic silicon Schottky diode for detection of sub-bandgap photons in the optical communication wavelength range through internal photoemission. Our photodiode is based on a hybrid plasmonic silicon waveguide. It has a gold film covering both the top and the sidewalls of a dielectric silicon waveguide with the Schottky contact formed at the gold-silicon interface. An extensive physical model is presented in detail and applied to calculate and analyze the performance of our detector. By comparison with a diode with only top contact of gold, the polarization sensitivity of responsivity is greatly minimized in our photodetector with sidewall coverage of gold. Much higher responsivities for both polarizations are also achieved in a very broad wavelength range of 1.2-1.5 μm. Moreover, the Schottky contact is only 4 μm long, leading to a very small dark current. Our design is very promising for practical applications in high-density silicon photonic integration.
Purpose: CT image reconstruction techniques have two major categories: analytical reconstruction (AR) method and iterative reconstruction (IR) method. AR reconstructs images through analytical formulas, such as filtered backprojection (FBP) in 2D and Feldkamp-Davis-Kress (FDK) method in 3D, which can be either mathematically exact or approximate. On the other hand, IR is often based on the discrete forward model of X-ray transform and formulated as a minimization problem with some appropriate image regularization method, so that the reconstructed image corresponds to the minimizer of the optimization problem. This work is to investigate the fused analytical and iterative reconstruction (AIR) method. Methods: Based on IR with L1-type image regularization, AIR is formulated with a AR-specific preconditioner in the data fidelity term, which results in the minimal change of the solution algorithm that replaces the adjoint X-ray transform by the filtered X-ray transform. As a proof-of-concept 2D example of AIR, FBP is incorporated into tensor framelet (TF) regularization based IR, and the formulated AIR minimization problem is then solved through split Bregman method with GPU-accelerated X-ray transform and filtered adjoint X-ray transform. Conclusion: AIR, the fused Analytical and Iterative Reconstruction method, is proposed with a proof-of-concept 2D example to synergize FBP and TF-regularized IR, with improved image resolution and contrast for experimental data. The potential impact of AIR is that it offers a general framework to develop various AR enhanced IR methods, when neither AR nor IR alone is sufficient.
This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle coefficients are assumed to be strictly positive definite, the mathematical model discussed in the paper belongs to the second order parabolic equations with non-negative characteristic form, namely that there exists degeneracy on the lateral boundaries of the domain. The uniqueness of the solution is obtained by the contraction mapping principle. Based on the optimal control framework, the problem is transformed into an optimization problem and the existence of the minimizer is established. After the necessary conditions which must be satisfied by the minimizer are deduced, the uniqueness and stability of the minimizer are proved. By minor modification of the cost functional and some \emph{a-priori} regularity conditions imposed on the forward operator, the convergence of the minimizer for the noisy input data is obtained in the paper. The results obtained in the paper are interesting and useful, and can be extended to more general degenerate parabolic equations.
In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multi-hop routing is more advantageous than single-hop routing.
In this paper, we give the Hörmander's $L^2$ theorem for Dirac operator over an open subset $Ω\in\R^{n+1}$ with Clifford algebra. Some sufficient condition on the existence of the weak solutions for Dirac operator has been found in the sense of Clifford analysis. In particular, if $Ω$ is bounded, then we prove that for any $f$ in $L^2$ space with value in Clifford algebra, there exists a weak solution of Dirac operator such that $$\bar{D}u=f$$ with $u$ in the $L^2$ space as well. The method is based on Hörmander's $L^2$ existence theorem in complex analysis and the $L^2$ weighted space is utilised.
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two major problems. First, most algorithms only offer point estimation of the distance metric and can therefore be unreliable when the number of training examples is small. Second, since these algorithms generally select their training examples at random, they can be inefficient if labeling effort is limited. This paper presents a Bayesian framework for distance metric learning that estimates a posterior distribution for the distance metric from labeled pairwise constraints. We describe an efficient algorithm based on the variational method for the proposed Bayesian approach. Furthermore, we apply the proposed Bayesian framework to active distance metric learning by selecting those unlabeled example pairs with the greatest uncertainty in relative distance. Experiments in classification demonstrate that the proposed framework achieves higher classification accuracy and identifies more informative training examples than the non-Bayesian approach and state-of-the-art distance metric learning algorithms.
One of the motivations for property testing of boolean functions is the idea that testing can serve as a preprocessing step before learning. However, in most machine learning applications, it is not possible to request for labels of fictitious examples constructed by the algorithm. Instead, the dominant query paradigm in applied machine learning, called active learning, is one where the algorithm may query for labels, but only on points in a given polynomial-sized (unlabeled) sample, drawn from some underlying distribution D. In this work, we bring this well-studied model in learning to the domain of testing. We show that for a number of important properties, testing can still yield substantial benefits in this setting. This includes testing unions of intervals, testing linear separators, and testing various assumptions used in semi-supervised learning. In addition to these specific results, we also develop a general notion of the testing dimension of a given property with respect to a given distribution. We show this dimension characterizes (up to constant factors) the intrinsic number of label requests needed to test that property. We develop such notions for both the active and passive testing models. We then use these dimensions to prove a number of lower bounds, including for linear separators and the class of dictator functions. Our results show that testing can be a powerful tool in realistic models for learning, and further that active testing exhibits an interesting and rich structure. Our work in addition brings together tools from a range of areas including U-statistics, noise-sensitivity, self-correction, and spectral analysis of random matrices, and develops new tools that may be of independent interest.
Microbond tests composed of single fibre and matrix droplet are often used to determine the properties of fibre reinforced composites. Interfacial shear strength is quantified by the maximum pull-out force assuming a uniform stress distribution along the fibre. Here, nonlinear finite element analyses are performed to investigate the validity of this assumption.
An approach is presented for the atomistic study of phonon transport in real dielectric nanowires via Green functions. The formalism is applied to investigate the phonon flow through nanowires coated by an amorphous material. Examples for a simple model system, and for real Si nanowires coated by silica are given. New physical results emerge for these systems, regarding the character of the transition from ballistic to diffusive transport, the low temperature thermal conductance, and the influence of the wire-coating interface on the thermal transport. An efficient treatment of phonon scattering by the amorphous coating is also developed, representing a valuable tool for the investigation of thermal conduction through amorphous-coated nanowires.