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We investigate the computability (in the sense of computable analysis) of the topological pressure $P_{\rm top}(\phi)$ on compact shift spaces $X$ for continuous potentials $\phi:X\to {\mathbb R}$. This question has recently been studied for subshifts of finite type (SFTs) and their factors (Sofic shifts). We develop a framework to address the computability of the topological pressure on general shift spaces and apply this framework to coded shifts. In particular, we prove the computability of the topological pressure for all continuous potentials on S-gap shifts, generalized gap shifts, and particular Beta-shifts. We also construct shift spaces which, depending on the potential, exhibit computability and non-computability of the topological pressure. We further prove that the generalized pressure function $(X,\phi)\mapsto P_{\rm top}(X,\phi\vert_{X})$ is not computable for a large set of shift spaces $X$ and potentials $\phi$. In particular, the entropy map $X\mapsto h_{\rm top}(X)$ is computable at a shift space $X$ if and only if $X$ has zero topological entropy. Along the way of developing these computability results, we derive several ergodic-theoretical properties of coded shifts which are of independent interest beyond the realm of computability., Comment: The statement of Theorem A has been updated. In particular, Theorem A holds now for all coded shifts. This follows from recent work by Beal, Perrin and Restivo (reference [3]) who show that every coded shift is uniquely representable. Further, we revised the proof of Theorem A fixing a mistake in the previous version

Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security, etc. Most existing MCE algorithms focus on improving the efficiency rather than reducing the output size. The output unfortunately could consist of a large number of maximal cliques. In this paper, we study how to report a summary of less overlapping maximal cliques. The problem was studied before, however, after examining the pioneer approach, we consider it still not satisfactory. To advance the research along this line, our paper attempts to make four contributions: (a) we propose a more effective sampling strategy, which produces a much smaller summary but still ensures that the summary can somehow witness all the maximal cliques and the expectation of each maximal clique witnessed by the summary is above a predefined threshold; (b) we prove that the sampling strategy is optimal under certain optimality conditions; (c) we apply clique-size bounding and design new enumeration order to approach the optimality conditions; and (d) to verify experimentally, we test eight real benchmark datasets that have a variety of graph characteristics. The results show that our new sampling strategy consistently outperforms the state-of-the-art approach by producing smaller summaries and running faster on all the datasets., Comment: 20 pages, 80 figures

Recent outbreak of COVID-19 has led a rapid global spread around the world. Many countries have implemented timely intensive suppression to minimize the infections, but resulted in high case fatality rate (CFR) due to critical demand of health resources. Other country-based factors such as sociocultural issues, ageing population etc., has also influenced practical effectiveness of taking interventions to improve morality in early phase. To better understand the relationship of these factors across different countries with COVID-19 CFR is of primary importance to prepare for potentially second wave of COVID-19 infections. In the paper, we propose a novel regularized multi-task learning based factor analysis approach for quantifying country-based factors affecting CFR in early phase of COVID-19 epidemic. We formulate the prediction of CFR progression as a ML regression problem with observed CFR and other countries-based factors. In this formulation, all CFR related factors were categorized into 6 sectors with 27 indicators. We proposed a hybrid feature selection method combining filter, wrapper and tree-based models to calibrate initial factors for a preliminary feature interaction. Then we adopted two typical single task model (Ridge and Lasso regression) and one state-of-the-art MTFL method (fused sparse group lasso) in our formulation. The fused sparse group Lasso (FSGL) method allows the simultaneous selection of a common set of country-based factors for multiple time points of COVID-19 epidemic and also enables incorporating temporal smoothness of each factor over the whole early phase period. Finally, we proposed one novel temporal voting feature selection scheme to balance the weight instability of multiple factors in our MTFL model.

Depth cues with affluent spatial information have been proven beneficial in boosting salient object detection (SOD), while the depth quality directly affects the subsequent SOD performance. However, it is inevitable to obtain some low-quality depth cues due to limitations of its acquisition devices, which can inhibit the SOD performance. Besides, existing methods tend to combine RGB images and depth cues in a direct fusion or a simple fusion module, which makes they can not effectively exploit the complex correlations between the two sources. Moreover, few methods design an appropriate module to fully fuse multi-level features, resulting in cross-level feature interaction insufficient. To address these issues, we propose a novel Multi-level Cross-modal Interaction Network (MCINet) for RGB-D based SOD. Our MCI-Net includes two key components: 1) a cross-modal feature learning network, which is used to learn the high-level features for the RGB images and depth cues, effectively enabling the correlations between the two sources to be exploited; and 2) a multi-level interactive integration network, which integrates multi-level cross-modal features to boost the SOD performance. Extensive experiments on six benchmark datasets demonstrate the superiority of our MCI-Net over 14 state-of-the-art methods, and validate the effectiveness of different components in our MCI-Net. More important, our MCI-Net significantly improves the SOD performance as well as has a higher FPS.

Because hyperspectral remote sensing images contain a lot of redundant information and the data structure is highly non-linear, leading to low classification accuracy of traditional machine learning methods. The latest research shows that hyperspectral image classification based on deep convolutional neural network has high accuracy. However, when a small amount of data is used for training, the classification accuracy of deep learning methods is greatly reduced. In order to solve the problem of low classification accuracy of existing algorithms on small samples of hyperspectral images, a multi-scale residual network is proposed. The multi-scale extraction and fusion of spatial and spectral features is realized by adding a branch structure into the residual block and using convolution kernels of different sizes in the branch. The spatial and spectral information contained in hyperspectral images are fully utilized to improve the classification accuracy. In addition, in order to improve the speed and prevent overfitting, the model uses dynamic learning rate, BN and Dropout strategies. The experimental results show that the overall classification accuracy of this method is 99.07% and 99.96% respectively in the data set of Indian Pines and Pavia University, which is better than other algorithms.

In this paper, we give a quantitative estimate for the sum of the first $N$ Lyapunov exponents for random perturbations of a natural class $2N$-dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but noninvariant subset of phase space. Concrete models covered by our setting include systems of coupled standard maps, in both `weak' and `strong' coupling regimes., Comment: 29 pages

Object detection is an important task in remote sensing image analysis. To reduce the computational complexity of redundant information and improve the efficiency of image processing, visual saliency models have been widely applied in this field. In this paper, a novel saliency detection model based on Contrast-weighted Dictionary Learning (CDL) is proposed for remote sensing images. Specifically, the proposed CDL learns salient and non-salient atoms from positive and negative samples to construct a discriminant dictionary, in which a contrast-weighted term is proposed to encourage the contrast-weighted patterns to be present in the learned salient dictionary while discouraging them from being present in the non-salient dictionary. Then, we measure the saliency by combining the coefficients of the sparse representation (SR) and reconstruction errors. Furthermore, by using the proposed joint saliency measure, a variety of saliency maps are generated based on the discriminant dictionary. Finally, a fusion method based on global gradient optimization is proposed to integrate multiple saliency maps. Experimental results on four datasets demonstrate that the proposed model outperforms other state-of-the-art methods.

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine learning problem, principal component analysis (PCA). Despite the massive literature on top eigenvector estimation, much less is presented for the top-$L$-dim ($L>1$) eigenspace estimation, especially in a distributed manner. We propose a novel multi-round algorithm for constructing top-$L$-dim eigenspace for distributed data. Our algorithm takes advantage of shift-and-invert preconditioning and convex optimization. Our estimator is communication-efficient and achieves a fast convergence rate. In contrast to the existing divide-and-conquer algorithm, our approach has no restriction on the number of machines. Theoretically, the traditional Davis-Kahan theorem requires the explicit eigengap assumption to estimate the top-$L$-dim eigenspace. To abandon this eigengap assumption, we consider a new route in our analysis: instead of exactly identifying the top-$L$-dim eigenspace, we show that our estimator is able to cover the targeted top-$L$-dim population eigenspace. Our distributed algorithm can be applied to a wide range of statistical problems based on PCA, such as principal component regression and single index model. Finally, We provide simulation studies to demonstrate the performance of the proposed distributed estimator.

In this paper, we study the differential invariants and the invariant heat flow in centro-affine geometry, proving that the latter is equivalent to the inviscid Burgers' equation. Furthermore, we apply the centro-affine invariants to develop an invariant algorithm to match features of objects appearing in images. We show that the resulting algorithm compares favorably with the widely applied scale-invariant feature transform (SIFT), speeded up robust features (SURF), and affine-SIFT (ASIFT) methods.

Given an integer $k \geq 5$, and a $C^k$ Anosov flow $\Phi$ on some compact connected $3$-manifold preserving a smooth volume, we show that the measure of maximal entropy (MME) is the volume measure if and only if $\Phi$ is $C^{k-\varepsilon}$-conjugate to an algebraic flow, for $\varepsilon>0$ arbitrarily small. Besides the rigidity, we also study the entropy flexibility, and show that the metric entropy with respect to the volume measure and the topological entropy of suspension flows over Anosov diffeomorphisms on the $2$-torus achieve all possible values subject to natural normalizations. Moreover, in the case of dispersing billiards, we show that if the measure of maximal entropy is the volume measure, then the Birkhoff Normal Form of regular periodic orbits with a homoclinic intersection is linear., Comment: 36 pages, 5 (+2) figures

Deep neural networks (DNNs) are known to be vulnerable to adversarial examples. Existing works have mostly focused on either digital adversarial examples created via small and imperceptible perturbations, or physical-world adversarial examples created with large and less realistic distortions that are easily identified by human observers. In this paper, we propose a novel approach, called Adversarial Camouflage (\emph{AdvCam}), to craft and camouflage physical-world adversarial examples into natural styles that appear legitimate to human observers. Specifically, \emph{AdvCam} transfers large adversarial perturbations into customized styles, which are then "hidden" on-target object or off-target background. Experimental evaluation shows that, in both digital and physical-world scenarios, adversarial examples crafted by \emph{AdvCam} are well camouflaged and highly stealthy, while remaining effective in fooling state-of-the-art DNN image classifiers. Hence, \emph{AdvCam} is a flexible approach that can help craft stealthy attacks to evaluate the robustness of DNNs. \emph{AdvCam} can also be used to protect private information from being detected by deep learning systems., Comment: Accepted to CVPR2020

We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the $K$-means clustering method achieves such sharp threshold for exact recovery without assuming the symmetry of cluster centers.