arXiv subjects

Li Wang

Publications and source records attributed to Li Wang.

At least 541 records · Page 30Linked to original sources

arXiv2017

Stability of Stationary Inverse Transport Equation in Diffusion Scaling

We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales characterized by the magnitude of a dimensionless parameter---the Knudsen number ($K_n$). In the diffusive scaling ($K_n \ll 1$), the stationary RTE is well approximated by an elliptic equation in the forward setting. However, the inverse problem for the elliptic equation is acknowledged to be severely ill-posed as compared to the well-posedness of inverse transport equation, which raises the question of how uniqueness being lost as $K_n \rightarrow 0$. We tackle this problem by examining the stability of inverse problem with varying $K_n$. We show that, the discrepancy in two measurements is amplified in the reconstructed parameters at the order of $K_n^p~ (p = 1\text{ or} ~2)$, and as a result lead to ill-posedness in the zero limit of $K_n$. Our results apply to both continuous and discrete settings. Some numerical tests are performed in the end to validate these theoretical findings.

math.NA↗

arXiv2017

An accurate front capturing scheme for tumor growth models with a free boundary limit

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure $p$ and density $ρ$ is $p(ρ)=\frac{m}{m-1} ρ^{m-1}$, and when $m \gg 1$, the cell density $ρ$ may evolve its support due to a pressure-driven geometric motion with sharp interface along the boundary of its support. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations, let alone the capturing of the singular free boundary limit. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as $m\gg 1$. In this paper, we develope a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as $m \rightarrow \infty$, and with proper spacial discretization, the fully discrete scheme has improved stability, preserves positivity, and implements without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties and showcase good performance in various applications.

math.NA↗

arXiv2017

Realization of Flat Band with Possible Nontrivial Topology in Electronic Kagome Lattice

The energy dispersion of fermions or bosons vanishes in momentum space if destructive quantum interference occurs in a frustrated Kagome lattice with only nearest-neighbour (NN) hopping. A discrete flat band (FB) without any dispersion is consequently formed, promising emergence of fractional quantum Hall states (FQHS) at high temperatures. Here, we report experimental realization of a FB with possible nontrivial topology in an electronic Kagome lattice on a twisted multilayer silicene. The electrons are localized in the Kagome lattice due to quantum destructive interference, and thus, their kinetic energy is quenched, which gives rise to a FB peak in density of states. A robust and pronounced one-dimensional edge state has been revealed at Kagome edge, which resides at higher energy than the FB. Our observations of the FB and the exotic edge state in electronic Kagome lattice open up the possibility towards the realization of fractional Chern insulators in two-dimensional materials.

cond-mat.mtrl-sci↗

arXiv2017

Stability of inverse transport equation in diffusion scaling and Fokker-Planck limit

We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both experimental and computational, an important question is to quantify how the error is amplified in the process of reconstruction. In the forward setting, the solution to the RTE behaves differently in different regimes, and the stability of the inverse problem vary accordingly. In particular, we consider two scalings in this paper. The first one concerns with a diffusive scaling whose macroscopic limit is a diffusion equation. In this case, we showed, following the similar approach as in [Chen, Li and Wang, arXiv:1703.00097], that the stability degrades when the limit is taken. The second one considers a highly forward peaked scattering, wherein the scattering operator is approximated by a Fokker-Planck operator as a limit. In this case, we showed that a fully recover of the scattering coefficient is less possible in the limit, whereas obtaining a rescaled version of the scattering coefficient becomes more practice friendly.

math.NA↗

arXiv2017

A new numerical approach to inverse transport equation with error analysis

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering coefficient of the media, through the source-measurement pairs. A typical computational approach is to form the inverse problem as a PDE-constraint optimization, with the minimizer being the to-be-recovered coefficients. The method is tested to be efficient in practice, but lacks analytical justification: there is no guarantee of the existence or uniqueness of the minimizer, and the error is hard to quantify. In this paper, we provide a different algorithm by levering the ideas from singular decomposition analysis. Our approach is to decompose the measurements into three components, two out of which encode the information of the two coefficients respectively. We then split the optimization problem into two subproblems and use those two components to recover the absorption and scattering coefficients separately. In this regard, we prove the well-posedness of the new optimization, and the error could be quantified with better precision. In the end, we incorporate the diffusive scaling and show that the error is harder to control in the diffusive limit.

math.NA↗

arXiv2017

Counting statistics of chaotic resonances at optical frequencies: theory and experiments

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang, D. Lippolis, Z.-Y. Li, X.-F. Jiang, Q. Gong, and Y.-F. Xiao, Phys. Rev. E 93, 040201(R) (2016)].

nlin.CD↗

arXiv2017

Theoretical and computational aspects of entanglement

We show that the two notions of entanglement: the maximum of the geometric measure of entanglement and the maximum of the nuclear norm is attained for the same states. We affirm the conjecture of Higuchi-Sudberry on the maximum entangled state of four qubits. We introduce the notion of d-density tensor for mixed d-partite states. We show that d-density tensor is separable if and only if its nuclear norm is $1$. We suggest an alternating method for computing the nuclear norm of tensors. We apply the above results to symmetric tensors. We give many numerical examples.

quant-ph↗

arXiv2017

Uniform regularity for linear kinetic equations with random input based on hypocoercivity

In this paper we study the effect of randomness in kinetic equations that preserve mass. Our focus is in proving the analyticity of the solution with respect to the randomness, which naturally leads to the convergence of numerical methods. The analysis is carried out in a general setting, with the regularity result not depending on the specific form of the collision term, the probability distribution of the random variables, or the regime the system is in, and thereby termed "uniform". Applications include the linear Boltzmann equation, BGK model, Carlemann model, among many others; and the results hold true in kinetic, parabolic and high field regimes. The proof relies on the explicit expression of the high order derivatives of the solution in the random space, and the convergence in time is mainly based on hypocoercivity, which, despite the popularity in PDE analysis of kinetic theory, has rarely been used for numerical algorithms.

math.NA↗

arXiv2017

Evolving Boxes for Fast Vehicle Detection

We perform fast vehicle detection from traffic surveillance cameras. A novel deep learning framework, namely Evolving Boxes, is developed that proposes and refines the object boxes under different feature representations. Specifically, our framework is embedded with a light-weight proposal network to generate initial anchor boxes as well as to early discard unlikely regions; a fine-turning network produces detailed features for these candidate boxes. We show intriguingly that by applying different feature fusion techniques, the initial boxes can be refined for both localization and recognition. We evaluate our network on the recent DETRAC benchmark and obtain a significant improvement over the state-of-the-art Faster RCNN by 9.5% mAP. Further, our network achieves 9-13 FPS detection speed on a moderate commercial GPU.

cs.CV↗

arXiv2017

Geometric measure of entanglement of symmetric d-qubits is polynomial-time computable

We give a simple formula for finding the spectral norm of d-mode symmetric tensor in two variables over the complex or real numbers in terms of the complex or real roots of a corresponding polynomial in one complex variable. This result implies that the geometric measure of entanglement of symmetric d-qubits is polynomial-time computable. We discuss a generalization to d-mode symmetric tensor in more than two variables.

math.RA↗

arXiv2017

The first result on 76Ge neutrinoless double beta decay from CDEX-1 experiment

We report the first result on Ge-76 neutrinoless double beta decay from CDEX-1 experiment at China Jinping Underground Laboratory. A mass of 994 g p-type point-contact high purity germanium detector has been installed to search the neutrinoless double beta decay events, as well as to directly detect dark matter particles. An exposure of 304 kg*day has been analyzed. The wideband spectrum from 500 keV to 3 MeV was obtained and the average event rate at the 2.039 MeV energy range is about 0.012 count per keV per kg per day. The half-life of Ge-76 neutrinoless double beta decay has been derived based on this result as: T 1/2 > 6.4*10^22 yr (90% C.L.). An upper limit on the effective Majorana-neutrino mass of 5.0 eV has been achieved. The possible methods to further decrease the background level have been discussed and will be pursued in the next stage of CDEX experiment.

hep-ex↗

arXiv2017

Safe Certificate-Based Maneuvers for Teams of Quadrotors Using Differential Flatness

Safety Barrier Certificates that ensure collision-free maneuvers for teams of differential flatness-based quadrotors are presented in this paper. Synthesized with control barrier functions, the certificates are used to modify the nominal trajectory in a minimally invasive way to avoid collisions. The proposed collision avoidance strategy complements existing flight control and planning algorithms by providing trajectory modifications with provable safety guarantees. The effectiveness of this strategy is supported both by the theoretical results and experimental validation on a team of five quadrotors.

cs.RO↗

arXiv2017

Minimum Rate Sampling and Spectrum Blind Reconstruction in Random Equivalent Sampling

The random equivalent sampling (RES) is a well-known sampling technique that can be used to capture a high-speed repetitive waveform with low sampling rate. In this paper, the feasibility of spectrum-blind multiband signal reconstruction for data sampled from RES is investigated. We propose a RES sampling pattern and its corresponding mathematical model that guarantees well-conditioned reconstruction of multiband signal with unknown spectral support. We give the minimum number of RES acquisitions that hold overwhelming probability to successfully reconstruct original signal. We demonstrate that for signal with specific spectral occupation, the number of RES acquisitions and the minimum sampling rate could be approached. The signal reconstruction is studied in the framework of compressive sampling (CS) theory. The eigen-decomposition and minimum description length (MDL) criteria are adopted to adaptively estimate the dimension of signal, and the number of unknowns of reconstruction problem is reduced. Experimental results are reported to indicate that, for a spectrum-blind sparse multiband signal, the proposed reconstruction algorithm for RES is feasible and robust.

physics.ins-det↗

arXiv2016

Central limit theorems for supercritical superprocesses with immigration

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with immigration with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem extends and generalizes the results obtained by Ren, Song and Zhang[2015]. We first give law of large numbers for supercritical superprocesses with immigration since there is few convergence result on immigration superprocesses, then based on these results, we establish the central limit theorem.

math.PR↗

arXiv2016

Cross-model convolutional neural network for multiple modality data representation

A novel data representation method of convolutional neural net- work (CNN) is proposed in this paper to represent data of different modalities. We learn a CNN model for the data of each modality to map the data of differ- ent modalities to a common space, and regularize the new representations in the common space by a cross-model relevance matrix. We further impose that the class label of data points can also be predicted from the CNN representa- tions in the common space. The learning problem is modeled as a minimiza- tion problem, which is solved by an augmented Lagrange method (ALM) with updating rules of Alternating direction method of multipliers (ADMM). The experiments over benchmark of sequence data of multiple modalities show its advantage.

cs.LG↗

arXiv2016

Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations

We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. We show that, this new scheme is unconditionally stable as long as the initial condition does not exceed certain threshold, and it asymptotically preserves the quasi-static limit in the transient regime. Furthermore, we prove that the fully discrete scheme is conservative and positivity preserving, which makes it ideal for simulations. The analogical schemes for the radial symmetric cases and the subcritical degenerate cases are also presented and analyzed. With extensive numerical tests, we verify the claimed properties of the methods and demonstrate their superiority in various challenging applications.

math.NA↗

arXiv2016

Bilevel Polynomial Programs and Semidefinite Relaxation Methods

A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as semi-infinite polynomial programs (SIPPs), using Fritz John conditions and Jacobian representations. Combining the exchange technique and Lasserre type semidefinite relaxations, we propose numerical methods for solving both simple and general BPPs. For simple BPPs, we prove the convergence to global optimal solutions. Numerical experiments are presented to show the efficiency of proposed algorithms.

math.OC↗

arXiv2016

Probabilistic Dimensionality Reduction via Structure Learning

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth skeleton of embedding points in a low-dimensional space from high-dimensional noisy data. The formulation of the new model can be equivalently interpreted as two coupled learning problem, i.e., structure learning and the learning of projection matrix. This interpretation motivates the learning of the embedding points that can directly form an explicit graph structure. We develop a new method to learn the embedding points that form a spanning tree, which is further extended to obtain a discriminative and compact feature representation for clustering problems. Unlike traditional clustering methods, we assume that centers of clusters should be close to each other if they are connected in a learned graph, and other cluster centers should be distant. This can greatly facilitate data visualization and scientific discovery in downstream analysis. Extensive experiments are performed that demonstrate that the proposed framework is able to obtain discriminative feature representations, and correctly recover the intrinsic structures of various real-world datasets.

stat.ML↗