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Shun Zhang

Publications and source records attributed to Shun Zhang.

At least 127 records · Page 7Linked to original sources

Tracking Persons-of-Interest via Unsupervised Representation Adaptation

Multi-face tracking in unconstrained videos is a challenging problem as faces of one person often appear drastically different in multiple shots due to significant variations in scale, pose, expression, illumination, and make-up. Existing multi-target tracking methods often use low-level features which are not sufficiently discriminative for identifying faces with such large appearance variations. In this paper, we tackle this problem by learning discriminative, video-specific face representations using convolutional neural networks (CNNs). Unlike existing CNN-based approaches which are only trained on large-scale face image datasets offline, we use the contextual constraints to generate a large number of training samples for a given video, and further adapt the pre-trained face CNN to specific videos using discovered training samples. Using these training samples, we optimize the embedding space so that the Euclidean distances correspond to a measure of semantic face similarity via minimizing a triplet loss function. With the learned discriminative features, we apply the hierarchical clustering algorithm to link tracklets across multiple shots to generate trajectories. We extensively evaluate the proposed algorithm on two sets of TV sitcoms and YouTube music videos, analyze the contribution of each component, and demonstrate significant performance improvement over existing techniques.

cs.CV↗

Reproducing Kernels of Sobolev Spaces on $\mathbb{R}^d$ and Applications to Embedding Constants and Tractability

The standard Sobolev space $W^s_2(\mathbb{R}^d)$, with arbitrary positive integers $s$ and $d$ for which $s>d/2$, has the reproducing kernel $$ K_{d,s}(x,t)=\int_{\mathbb{R}^d}\frac{\prod_{j=1}^d\cos\left(2π\,(x_j-t_j)u_j\right)} {1+\sum_{0<|α|_1\le s}\prod_{j=1}^d(2π\,u_j)^{2α_j}}\,{\rm d}u $$ for all $x,t\in\mathbb{R}^d$, where $x_j,t_j,u_j,α_j$ are components of $d$-variate $x,t,u,α$, and $|α|_1=\sum_{j=1}^dα_j$ with non-negative integers $α_j$. We obtain a more explicit form for the reproducing kernel $K_{1,s}$ and find a closed form for the kernel $K_{d, \infty}$. Knowing the form of $K_{d,s}$, we present applications on the best embedding constants between the Sobolev space $W^s_2(\mathbb{R}^d)$ and $L_\infty(\mathbb{R}^d)$, and on strong polynomial tractability of integration with an arbitrary probability density. We prove that the best embedding constants are exponentially small in $d$, whereas worst case integration errors of algorithms using $n$ function values are also exponentially small in $d$ and decay at least like $n^{-1/2}$. This yields strong polynomial tractability in the worst case setting for the absolute error criterion.

math.NA↗

Interference-Alignment and Soft-Space-Reuse Based Cooperative Transmission for Multi-cell Massive MIMO Networks

As a revolutionary wireless transmission strategy, interference alignment (IA) can improve the capacity of the cell-edge users. However, the acquisition of the global channel state information (CSI) for IA leads to unacceptable overhead in the massive MIMO systems. To tackle this problem, in this paper, we propose an IA and soft-space-reuse (IA-SSR) based cooperative transmission scheme under the two-stage precoding framework. Specifically, the cell-center and the cell-edge users are separately treated to fully exploit the spatial degrees of freedoms (DoF). Then, the optimal power allocation policy is developed to maximize the sum-capacity of the network. Next, a low-cost channel estimator is designed for the proposed IA-SSR framework. Some practical issues in IA-SSR implementation are also discussed. Finally, plenty of numerical results are presented to show the efficiency of the proposed algorithm.

cs.IT↗

Base Station Selection for Massive MIMO Networks with Two-stage Precoding

The two-stage precoding has been proposed to reduce the overhead of both the channel training and the channel state information (CSI) feedback for the massive multiple-input multiple-output (MIMO) system. But the overlap of the angle-spreading-ranges (ASR) for different user clusters may seriously degrade the performance of the two-stage precoding. In this letter, we propose one ASR overlap mitigating scheme through the base station (BS) selection. Firstly, the BS selection is formulated as a sum signal-to-interference-plus-noise ratio (SINR) maximization problem. Then, the problem is solved by a low-complex algorithm through maximizing signal-to-leakage-plus-noise ratio (SLNR). In addition, we propose one low-overhead algorithm with the lower bound on the average SLNR as the objective function. Finally, we demonstrate the efficacy of the proposed schemes through the numerical simulations.

cs.IT↗

Self-organized mechano-chemical dynamics in amoeboid locomotion of Physarum fragments

The aim of this work is to quantify the spatio-temporal dynamics of flow-driven amoeboid locomotion in small ($\sim$100 $μ$m) fragments of the true slime mold \phys {\it polycephalum}. In this model organism, cellular contraction drives intracellular flows, and these flows transport the chemical signals that regulate contraction in the first place. As a consequence of these non-linear interactions, a diversity of migratory behaviors can be observed in migrating \phys fragments. To study these dynamics, we measure the spatio-temporal distributions of the velocities of the endoplasm and ectoplasm of each migrating fragment, the traction stresses it generates on the substratum, and the concentration of free intracellular calcium. Using these unprecedented experimental data, we classify migrating \phys fragments according to their dynamics, finding that they often exhibit spontaneously coordinated waves of flow, contractility and chemical signaling. We show that \phys fragments exhibiting symmetric spatio-temporal patterns of endoplasmic flow migrate significantly slower than fragments with asymmetric patterns. In addition, our joint measurements of ectoplasm velocity and traction stress at the substratum suggest that forward motion of the ectoplasm is enabled by a succession of stick-slip transitions, which we conjecture are also organized in the form of waves. Combining our experiments with a simplified convection-diffusion model, we show that the convective transport of calcium ions may be key for establishing and maintaining the spatio-temporal patterns of calcium concentration that regulate the generation of contractile forces.

q-bio.CB↗

Spatial-Temporal BEM and Channel Estimation Strategy for Massive MIMO Time-Varying Systems

This paper proposes a new channel estimation scheme for the multiuser massive multiple-input multiple-output (MIMO) systems in time-varying environment. We introduce a discrete Fourier transform (DFT) aided spatial-temporal basis expansion model (ST-BEM) to reduce the effective dimensions of uplink/downlink channels, such that training overhead and feedback cost could be greatly decreased. The newly proposed ST-BEM is suitable for both time division duplex (TDD) systems and frequency division duplex (FDD) systems thanks to the angle reciprocity, and can be efficiently deployed by fast Fourier transform (FFT). Various numerical results have corroborated the proposed studies.

cs.IT↗

Optimal Quadrature Formulas for the Sobolev Space $H^1$

We study optimal quadrature formulas for arbitrary weighted integrals and integrands from the Sobolev space $H^1([0,1])$. We obtain general formulas for the worst case error depending on the nodes $x_j$. A particular case is the computation of Fourier coefficients, where the oscillatory weight is given by $ρ_k(x) = \exp(- 2 πi k x)$. Here we study the question whether equidistant nodes are optimal or not. We prove that this depends on $n$ and $k$: equidistant nodes are optimal if $n \ge 2.7 |k| +1 $ but might be suboptimal for small $n$. In particular, the equidistant nodes $x_j = j/ |k|$ for $j=0, 1, \dots , |k| = n+1$ are the worst possible nodes and do not give any useful information. To characterize the worst case function we use certain results from the theory of weak solutions of boundary value problems and related quadratic extremal problems.

math.NA↗

Improved ZZ A Posteriori Error Estimators for Diffusion Problems: Conforming Linear Elements

In \cite{CaZh:09}, we introduced and analyzed an improved Zienkiewicz-Zhu (ZZ) estimator for the conforming linear finite element approximation to elliptic interface problems. The estimator is based on the piecewise "constant" flux recovery in the $H(div;Ω)$ conforming finite element space. This paper extends the results of \cite{CaZh:09} to diffusion problems with full diffusion tensor and to the flux recovery both in piecewise constant and piecewise linear $H(div)$ space.

math.NA↗

Finite Element Methods for Interface Problems: Robust Residual-Based A Posteriori Error Estimates

For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the Crouzeix-Raviart nonconforming and the discontinuous Galerkin elements in both two- and three-dimensions, the global reliability bounds are established with constants independent of the jump of the diffusion coefficient. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.

math.NA↗

Residual-based a Posteriori Error Estimate for Interface Problems: Nonconforming Linear Elements

In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach without using the Helmholtz decomposition. It is proved that the estimator is reliable with constant independent of the jump of diffusion coefficients across the interfaces, without the assumption that the diffusion coefficient is quasi-monotone. Numerical results for one test problem with intersecting interfaces are also presented.

math.NA↗

A Simple DFT-aided Spatial Basis Expansion Model and Channel Estimation Strategy for TDD/FDD Massive MIMO Systems

This paper proposes a new transmission strategy for the multiuser massive multiple-input multiple-output (MIMO) systems, including uplink/downlink channel estimation and user scheduling for data transmission. A discrete Fourier transform (DFT) aided spatial basis expansion model (SBEM) is first introduced to represent the uplink/downlink channels with much few parameter dimensions by exploiting angle reciprocity and the physical characteristics of the uniform linear array (ULA). With SBEM, both uplink and downlink channel estimation of multiuser can be carried out with very few amount of training resources, which significantly reduces the training overhead and feedback cost. Meanwhile, the pilot contamination problem in the uplink raining is immediately relieved by exploiting the spatial information of users. To enhance the spectral efficiency and to fully utilize the spatial resources, we also design a greedy user scheduling scheme during the data transmission period. Compared to existing low-rank models, the newly proposed SBEM offers an alternative for channel acquisition without need of channel statistics for both TDD and FDD systems based on the angle reciprocity. Moreover, the proposed method can be efficiently deployed by the fast Fourier transform (FFT). Various numerical results are provided to corroborate the proposed studies.

cs.IT↗

Complexity of Oscillatory Integrals on the Real Line

We analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space $H^s({\mathbb{R}})$ and from the space $C^s({\mathbb{R}})$ with an arbitrary integer $s\ge1$. We find tight upper and lower bounds for the worst case error of optimal algorithms that use $n$ function values. More specifically, we study integrals of the form \[ I_k^ρ(f) = \int_{ {\mathbb{R}}} f(x) \,e^{-i\,kx} ρ(x) \, {\rm d} x\ \ \ \mbox{for}\ \ f\in H^s({\mathbb{R}})\ \ \mbox{or}\ \ f\in C^s({\mathbb{R}}) \] with $k\in {\mathbb{R}}$ and a smooth density function $ρ$ such as $ ρ(x) = \frac{1}{\sqrt{2 π}} \exp( -x^2/2) $. The optimal error bounds are $Θ((n+\max(1,|k|))^{-s})$ with the factors in the $Θ$ notation dependent only on $s$ and $ρ$.

math.NA↗

Finite Element Methods for Interface Problems: Robust and Local Optimal A Priori Error Estimates

For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These estimates are robust with respect to the diffusion coefficient and optimal with respect to local regularity of the solution. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.

math.NA↗

An Efficient Implementation of Brezzi-Douglas-Marini (BDM) Mixed Finite Element Method in MATLAB

In this paper, a MATLAB package bdm_mfem for a linear Brezzi-Douglas- Marini (BDM) mixed finite element method is provided for the numerical solution of elliptic diffusion problems with mixed boundary conditions on unstructured grids. BDM basis functions defined by standard barycentric coordinates are used in the paper. Local and global edge ordering are treated carefully. MATLAB build-in functions and vectorizations are used to guarantee the erectness of the programs. The package is simple and efficient, and can be easily adapted for more complicated edge-based finite element spaces. A numerical example is provided to illustrate the usage of the package.

math.NA↗

Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations

The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [10], in order to retain the full efficiency of the L2 norm first-order system least-squares (FOSLS) ap- proach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach in [10] was applied to the div-curl system with added slack vari- ables, and hence it is quite complicated. In this paper, we apply the FOSLL* approach to the div system and establish its well-posedness. For the corresponding finite ele- ment approximation, we obtain a quasi-optimal a priori error bound under the same regularity assumption as the standard Galerkin method, but without the restriction to sufficiently small mesh size. Unlike the FOSLS approach, the FOSLL* approach does not have a free a posteriori error estimator, we then propose an explicit residual error estimator and establish its reliability and efficiency bounds

math.NA↗

Recovery-Based Error Estimators for Diffusion Problems: Explicit Formulas

We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e., requiring solutions of global problems with mass matrices). In this paper, we develop fully explicit recovery-based error estimators for lower order conforming, mixed, and non- conforming finite element approximations to diffusion problems with full coefficient tensor. When the diffusion coefficient is piecewise constant scalar and its distribution is local quasi-monotone, it is shown theoretically that the estimators developed in this paper are robust with respect to the size of jumps. Numerical experiments are also performed to support the theoretical results.

math.NA↗