arXiv subjects
Publications and source records attributed to Chao Gao.
We present a new technique, iterative fluctuation ghost imaging (IFGI) which dramatically enhances the resolution of ghost imaging (GI). It is shown that, by the fluctuation characteristics of the second-order correlation function, the imaging information with the narrower point spread function (PSF) than the original information can be got. The effects arising from the PSF and the iteration times also be discussed.
Observation of strong correlations and superconductivity in twisted-bilayer-graphene have stimulated tremendous interest in fundamental and applied physics. In this system, the superposition of two twisted honeycomb lattices, generating a Moir$\acute{\mathrm{e}}$ pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states. Despite these observations, a full understanding of the emerging superconductivity from the coupled insulating layers and the appearance of a small magic angle remain a hot topic of research. Here, we demonstrate a quantum simulation platform to study superfluids in twisted bilayer lattices based on Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension of the two layers. The twisted angle of the two lattices is controlled by the relative angle of the laser beams. We show that atoms in each spin state only feel one set of the lattice and the interlayer coupling can be controlled by microwave coupling between the spin states. Our system allows for flexible control of both the inter- and intralayer couplings. Furthermore we directly observe the spatial Moir$\acute{\mathrm{e}}$ pattern and the momentum diffraction, which confirm the presence of atomic superfluid in the bilayer lattices. Our system constitutes a powerful platform to investigate the physics underlying the superconductivity in twisted-bilayer-graphene and to explore other novel quantum phenomena difficult to realize in materials.
People are likely to engage in collective behaviour online during extreme events, such as the COVID-19 crisis, to express their awareness, actions and concerns. Hong Kong has implemented stringent public health and social measures (PHSMs) to curb COVID-19 epidemic waves since the first COVID-19 case was confirmed on 22 January 2020. People are likely to engage in collective behaviour online during extreme events, such as the COVID-19 crisis, to express their awareness, actions and concerns. Here, we offer a framework to evaluate interactions among individuals emotions, perception, and online behaviours in Hong Kong during the first two waves (February to June 2020) and found a strong correlation between online behaviours of Google search and the real-time reproduction numbers. To validate the model output of risk perception, we conducted 10 rounds of cross-sectional telephone surveys from February 1 through June 20 in 2020 to quantify risk perception levels over time. Compared with the survey results, the estimates of the risk perception of individuals using our network-based mechanistic model capture 80% of the trend of people risk perception (individuals who worried about being infected) during the studied period. We may need to reinvigorate the public by engaging people as part of the solution to live their lives with reduced risk.
In this paper, we test whether two datasets share a common clustering structure. As a leading example, we focus on comparing clustering structures in two independent random samples from two mixtures of multivariate normal distributions. Mean parameters of these normal distributions are treated as potentially unknown nuisance parameters and are allowed to differ. Assuming knowledge of mean parameters, we first determine the phase diagram of the testing problem over the entire range of signal-to-noise ratios by providing both lower bounds and tests that achieve them. When nuisance parameters are unknown, we propose tests that achieve the detection boundary adaptively as long as ambient dimensions of the datasets grow at a sub-linear rate with the sample size.
The Bradley-Terry-Luce (BTL) model is a benchmark model for pairwise comparisons between individuals. Despite recent progress on the first-order asymptotics of several popular procedures, the understanding of uncertainty quantification in the BTL model remains largely incomplete, especially when the underlying comparison graph is sparse. In this paper, we fill this gap by focusing on two estimators that have received much recent attention: the maximum likelihood estimator (MLE) and the spectral estimator. Using a unified proof strategy, we derive sharp and uniform non-asymptotic expansions for both estimators in the sparsest possible regime (up to some poly-logarithmic factors) of the underlying comparison graph. These expansions allow us to obtain: (i) finite-dimensional central limit theorems for both estimators; (ii) construction of confidence intervals for individual ranks; (iii) optimal constant of $\ell_2$ estimation, which is achieved by the MLE but not by the spectral estimator. Our proof is based on a self-consistent equation of the second-order remainder vector and a novel leave-two-out analysis.
We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + σW_{ij}\in\mathbb{R}^{d\times d}$ where $W_{ij}$ is a Gaussian random matrix and $Z_i^*$ is either an orthogonal matrix or a rotation matrix, and each $Y_{ij}$ is observed independently with probability $p$. We analyze an iterative polar decomposition algorithm for the estimation of $Z^*$ and show it has an error of $(1+o(1))\frac{σ^2 d(d-1)}{2np}$ when initialized by spectral methods. A matching minimax lower bound is further established which leads to the optimality of the proposed algorithm as it achieves the exact minimax risk.
We study the phase synchronization problem with noisy measurements $Y=z^*z^{*H}+σW\in\mathbb{C}^{n\times n}$, where $z^*$ is an $n$-dimensional complex unit-modulus vector and $W$ is a complex-valued Gaussian random matrix. It is assumed that each entry $Y_{jk}$ is observed with probability $p$. We prove that an SDP relaxation of the MLE achieves the error bound $(1+o(1))\frac{σ^2}{2np}$ under a normalized squared $\ell_2$ loss. This result matches the minimax lower bound of the problem, and even the leading constant is sharp. The analysis of the SDP is based on an equivalent non-convex programming whose solution can be characterized as a fixed point of the generalized power iteration lifted to a higher dimensional space. This viewpoint unifies the proofs of the statistical optimality of three different methods: MLE, SDP, and generalized power method. The technique is also applied to the analysis of the SDP for $\mathbb{Z}_2$ synchronization, and we achieve the minimax optimal error $\exp\left(-(1-o(1))\frac{np}{2σ^2}\right)$ with a sharp constant in the exponent.
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not known to hold generally with dependent samples, such as in online learning with time series data or distributed computing with Markovian training samples. In this paper, we show that SAA remains tractable when the distribution of unknown parameters is only observable through dependent instances and still enjoys asymptotic consistency and finite sample guarantees. Specifically, we provide a rigorous probability error analysis to derive $1 - β$ confidence bounds for the out-of-sample performance of SAA estimators and show that these estimators are asymptotically consistent. We then, using monotone operator theory, study the performance of a class of stochastic first-order algorithms trained on a dependent source of data. We show that approximation error for these algorithms is bounded and concentrates around zero, and establish deviation bounds for iterates when the underlying stochastic process is $ϕ$-mixing. The algorithms presented can be used to handle numerically inconvenient loss functions such as the sum of a smooth and non-smooth function or of non-smooth functions with constraints. To illustrate the usefulness of our results, we present several stochastic versions of popular algorithms such as stochastic proximal gradient descent (S-PGD), stochastic relaxed Peaceman--Rachford splitting algorithms (S-rPRS), and numerical experiment.
Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between these two limits; that is, there exist situations that the solution to a class of interacting hydrodynamic equations with certain initial conditions can be exactly constructed from the dynamics of noninteracting ideal gases. We analytically provide three such examples. The first two examples focus on scale-invariant systems, which generalize fermionization to the hydrodynamics of strongly interacting systems, and determine specific initial conditions for perfect density oscillations in a harmonic trap. The third example recovers the dark soliton solution in a one-dimensional Bose condensate. The results can explain a recent puzzling experimental observation in ultracold atomic gases by the Paris group and make further predictions for future experiments. We envision that extensive examples of such an ideal-gas approach to hydrodynamics can be found by systematical numerical search, which can find broad applications in different problems in various subfields of physics.
Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network models for classical machine learning. In this work, we combine the ideas of matrix product state (MPS), the simplest tensor network structure, and residual neural network and propose the residual matrix product state (ResMPS). The ResMPS can be treated as a network where its layers map the "hidden" features to the outputs (e.g., classifications), and the variational parameters of the layers are the functions of the features of the samples (e.g., pixels of images). This is different from neural network, where the layers map feed-forwardly the features to the output. The ResMPS can equip with the non-linear activations and dropout layers, and outperforms the state-of-the-art tensor network models in terms of efficiency, stability, and expression power. Besides, ResMPS is interpretable from the perspective of polynomial expansion, where the factorization and exponential machines naturally emerge. Our work contributes to connecting and hybridizing neural and tensor networks, which is crucial to further enhance our understand of the working mechanisms and improve the performance of both models.
We fully characterize the nonasymptotic minimax separation rate for sparse signal detection in the Gaussian sequence model with $p$ equicorrelated observations, generalizing a result of Collier, Comminges, and Tsybakov. As a consequence of the rate characterization, we find that strong correlation is a blessing, moderate correlation is a curse, and weak correlation is irrelevant. Moreover, the threshold correlation level yielding a blessing exhibits phase transitions at the $\sqrt{p}$ and $p-\sqrt{p}$ sparsity levels. We also establish the emergence of new phase transitions in the minimax separation rate with a subtle dependence on the correlation level. Additionally, we study group structured correlations and derive the minimax separation rate in a model including multiple random effects. The group structure turns out to fundamentally change the detection problem from the equicorrelated case and different phenomena appear in the separation rate.
In the conventional ghost imaging (GI), the image is retrieved by correlating the reference intensity fluctuation at a charge-coupled device (CCD) with the signal intensity fluctuation at a bucket detector. In this letter, we present the protocol of GI, it is called Second-order Cumulants ghost imaging (SCGI). The image is retrieved by the fluctuation information of correlating intensity fluctuation at two detectors, and the resolution limit can be enhanced than conventional GI. The experimental results of SCGI agreement with theoretical results.
Based on the Hugenholtz-Van Hove theorem, six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy $t(k)$, the isospin symmetric and asymmetric parts of the single-nucleon potentials $U_0(ρ,k)$ and $U_{\text{\text{sym,i}}}(ρ,k)$. The six basic quantities include the quadratic symmetry energy $E_{\text{sym,2}}(ρ)$, the quartic symmetry energy $E_{\text{sym,4}}(ρ)$, their corresponding density slopes $L_2(ρ)$ and $L_4(ρ)$, and the incompressibility coefficients $K_2(ρ)$ and $K_4(ρ)$. By using four types of well-known effective nucleon-nucleon interaction models, namely the BGBD, MDI, Skyrme, and Gogny forces, the density- and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density $ρ_0$ are explicitly given. The contributions to these quantities from $t(k)$, $U_0(ρ,k)$, and $U_{\text{sym,i}}(ρ,k)$ are also analyzed at the normal nuclear density $ρ_0$. It is clearly shown that the first-order asymmetric term $U_{\text{sym,1}}(ρ,k)$ (also known as the symmetry potential in Lane potential) plays a vital role in determining the density dependence of the quadratic symmetry energy $E_{\text{sym,2}}(ρ)$. It is also shown that the contributions from high-order asymmetric parts of the single-nucleon potentials ($U_{\text{sym,i}}(ρ,k)$ with $i>1$) cannot be neglected in the calculations of the other five basic quantities. Moreover, by analyzing the properties of asymmetric nuclear matter at the exact saturation density $ρ_{\text{sat}}(δ)$, the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation $K_{\text{sat,2}}=K_{2}(ρ_0)-4.14 L_2(ρ_0)$.
Given partially observed pairwise comparison data generated by the Bradley-Terry-Luce (BTL) model, we study the problem of top-$k$ ranking. That is, to optimally identify the set of top-$k$ players. We derive the minimax rate with respect to a normalized Hamming loss. This provides the first result in the literature that characterizes the partial recovery error in terms of the proportion of mistakes for top-$k$ ranking. We also derive the optimal signal to noise ratio condition for the exact recovery of the top-$k$ set. The maximum likelihood estimator (MLE) is shown to achieve both optimal partial recovery and optimal exact recovery. On the other hand, we show another popular algorithm, the spectral method, is in general sub-optimal. Our results complement the recent work by Chen et al. (2019) that shows both the MLE and the spectral method achieve the optimal sample complexity for exact recovery. It turns out the leading constants of the sample complexity are different for the two algorithms. Another contribution that may be of independent interest is the analysis of the MLE without any penalty or regularization for the BTL model. This closes an important gap between theory and practice in the literature of ranking.
Analyzing human affect is vital for human-computer interaction systems. Most methods are developed in restricted scenarios which are not practical for in-the-wild settings. The Affective Behavior Analysis in-the-wild (ABAW) 2021 Contest provides a benchmark for this in-the-wild problem. In this paper, we introduce a multi-modal and multi-task learning method by using both visual and audio information. We use both AU and expression annotations to train the model and apply a sequence model to further extract associations between video frames. We achieve an AU score of 0.712 and an expression score of 0.477 on the validation set. These results demonstrate the effectiveness of our approach in improving model performance.
This paper investigates the asymptotic BER performance of coherent optical wireless communication systems in Gamma-Gamma turbulence when applying the V-BLAST MIMO scheme. A new method is proposed to quantify the performance of the system and mathematical solutions for asymptotic BER performance are derived. Counterintuitive results are shown since the diversity gain of the V-BLAST MIMO system is equal to the number of the receivers. As a consequence, it is shown that when applying the V-BLAST MIMO scheme, the symbol rate per transmission can be equal to the number of transmitters with some cost to diversity gain. This means that we can simultaneously exploit the spatial multiplexing and diversity properties of the MIMO system to achieve a higher data rate than existing schemes in a channel that displays severe turbulence and moderate attenuation.
AlphaStar, the AI that reaches GrandMaster level in StarCraft II, is a remarkable milestone demonstrating what deep reinforcement learning can achieve in complex Real-Time Strategy (RTS) games. However, the complexities of the game, algorithms and systems, and especially the tremendous amount of computation needed are big obstacles for the community to conduct further research in this direction. We propose a deep reinforcement learning agent, StarCraft Commander (SCC). With order of magnitude less computation, it demonstrates top human performance defeating GrandMaster players in test matches and top professional players in a live event. Moreover, it shows strong robustness to various human strategies and discovers novel strategies unseen from human plays. In this paper, we will share the key insights and optimizations on efficient imitation learning and reinforcement learning for StarCraft II full game.
We discuss the interconnections between AO*, adversarial game-searching algorithms, e.g., proof number search and minimax search. The former was developed in the context of a general AND/OR graph model, while the latter were mostly presented in game-trees which are sometimes modeled using AND/OR trees. It is thus worth investigating to what extent these algorithms are related and how they are connected. In this paper, we explicate the interconnections between these search paradigms. We argue that generalized proof number search might be regarded as a more informed replacement of AO* for solving arbitrary AND/OR graphs, and the minimax principle might also extended to use dual heuristics.