On ends of finite-volume noncompact mainfolds of nonpositive curvature

In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold $M$ of finite volume with sectional curvature $-1 \leq K \leq 0$, if the universal cover of $M$ is a visibility manifold, then the fundamental group of each end of $M$ is almost nilpotent. Applications on the geometry and topology of noncompact nonpositively curved manifolds will be discussed.Comment: 35 pages, 2 figures. Comments are welcom

Log-Sobolev, isoperimetry and transport inequalities on graphs

In this paper, we study some functional inequalities (such as Poincar\'e inequalities, logarithmic Sobolev inequalities, generalized Cheeger isoperimetric inequalities, transportation-information inequalities and transportation-entropy inequalities) for reversible nearest-neighbor Markov processes on a connected finite graph by means of (random) path method. We provide estimates of the involved constants

Differential Variable Speed Limits Control for Freeway Recurrent Bottlenecks via Deep Reinforcement learning

Variable speed limits (VSL) control is a flexible way to improve traffic condition,increase safety and reduce emission. There is an emerging trend of using reinforcement learning technique for VSL control and recent studies have shown promising results. Currently, deep learning is enabling reinforcement learning to develope autonomous control agents for problems that were previously intractable. In this paper, we propose a more effective deep reinforcement learning (DRL) model for differential variable speed limits (DVSL) control, in which the dynamic and different speed limits among lanes can be imposed. The proposed DRL models use a novel actor-critic architecture which can learn a large number of discrete speed limits in a continues action space. Different reward signals, e.g. total travel time, bottleneck speed, emergency braking, and vehicular emission are used to train the DVSL controller, and comparison between these reward signals are conducted. We test proposed DRL baased DVSL controllers on a simulated freeway recurrent bottleneck. Results show that the efficiency, safety and emissions can be improved by the proposed method. We also show some interesting findings through the visulization of the control policies generated from DRL models.Comment: 24 pages, 7 figures, 1 tabl

Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit

In this paper, we prove Morse index theorem of Lagrangian system with any self-adjoint boundary conditions. Based on it, we give some nontrivial estimation on the difference of Morse indices. As an application, we get a new criterion for the stability problem of brake periodic orbit.Comment: 24 page

Adversarial Discriminative Heterogeneous Face Recognition

The gap between sensing patterns of different face modalities remains a challenging problem in heterogeneous face recognition (HFR). This paper proposes an adversarial discriminative feature learning framework to close the sensing gap via adversarial learning on both raw-pixel space and compact feature space. This framework integrates cross-spectral face hallucination and discriminative feature learning into an end-to-end adversarial network. In the pixel space, we make use of generative adversarial networks to perform cross-spectral face hallucination. An elaborate two-path model is introduced to alleviate the lack of paired images, which gives consideration to both global structures and local textures. In the feature space, an adversarial loss and a high-order variance discrepancy loss are employed to measure the global and local discrepancy between two heterogeneous distributions respectively. These two losses enhance domain-invariant feature learning and modality independent noise removing. Experimental results on three NIR-VIS databases show that our proposed approach outperforms state-of-the-art HFR methods, without requiring of complex network or large-scale training dataset

Scalar waves from a star orbiting a BTZ black hole

In this paper we compute the decay rates of massless scalar waves excited by a star circularly orbiting around the non-extremal (general) and extremal BTZ black holes. These decay rates are compared with the corresponding quantities computed in the corresponding dual conformal field theories respectively. We find that matches are achieved in both cases.Comment: In v2, 17 pages, title changed (contents not changed), discussion of the isometry group of the near-horizon-extremal BTZ geometry and its effects on the solutions is added, references added. V3, minor corrections, several more references adde

Coupled Deep Learning for Heterogeneous Face Recognition

Heterogeneous face matching is a challenge issue in face recognition due to large domain difference as well as insufficient pairwise images in different modalities during training. This paper proposes a coupled deep learning (CDL) approach for the heterogeneous face matching. CDL seeks a shared feature space in which the heterogeneous face matching problem can be approximately treated as a homogeneous face matching problem. The objective function of CDL mainly includes two parts. The first part contains a trace norm and a block-diagonal prior as relevance constraints, which not only make unpaired images from multiple modalities be clustered and correlated, but also regularize the parameters to alleviate overfitting. An approximate variational formulation is introduced to deal with the difficulties of optimizing low-rank constraint directly. The second part contains a cross modal ranking among triplet domain specific images to maximize the margin for different identities and increase data for a small amount of training samples. Besides, an alternating minimization method is employed to iteratively update the parameters of CDL. Experimental results show that CDL achieves better performance on the challenging CASIA NIR-VIS 2.0 face recognition database, the IIIT-D Sketch database, the CUHK Face Sketch (CUFS), and the CUHK Face Sketch FERET (CUFSF), which significantly outperforms state-of-the-art heterogeneous face recognition methods.Comment: AAAI 201

Wasserstein CNN: Learning Invariant Features for NIR-VIS Face Recognition

Heterogeneous face recognition (HFR) aims to match facial images acquired from different sensing modalities with mission-critical applications in forensics, security and commercial sectors. However, HFR is a much more challenging problem than traditional face recognition because of large intra-class variations of heterogeneous face images and limited training samples of cross-modality face image pairs. This paper proposes a novel approach namely Wasserstein CNN (convolutional neural networks, or WCNN for short) to learn invariant features between near-infrared and visual face images (i.e. NIR-VIS face recognition). The low-level layers of WCNN are trained with widely available face images in visual spectrum. The high-level layer is divided into three parts, i.e., NIR layer, VIS layer and NIR-VIS shared layer. The first two layers aims to learn modality-specific features and NIR-VIS shared layer is designed to learn modality-invariant feature subspace. Wasserstein distance is introduced into NIR-VIS shared layer to measure the dissimilarity between heterogeneous feature distributions. So W-CNN learning aims to achieve the minimization of Wasserstein distance between NIR distribution and VIS distribution for invariant deep feature representation of heterogeneous face images. To avoid the over-fitting problem on small-scale heterogeneous face data, a correlation prior is introduced on the fully-connected layers of WCNN network to reduce parameter space. This prior is implemented by a low-rank constraint in an end-to-end network. The joint formulation leads to an alternating minimization for deep feature representation at training stage and an efficient computation for heterogeneous data at testing stage. Extensive experiments on three challenging NIR-VIS face recognition databases demonstrate the significant superiority of Wasserstein CNN over state-of-the-art methods

A Light CNN for Deep Face Representation with Noisy Labels

The volume of convolutional neural network (CNN) models proposed for face recognition has been continuously growing larger to better fit large amount of training data. When training data are obtained from internet, the labels are likely to be ambiguous and inaccurate. This paper presents a Light CNN framework to learn a compact embedding on the large-scale face data with massive noisy labels. First, we introduce a variation of maxout activation, called Max-Feature-Map (MFM), into each convolutional layer of CNN. Different from maxout activation that uses many feature maps to linearly approximate an arbitrary convex activation function, MFM does so via a competitive relationship. MFM can not only separate noisy and informative signals but also play the role of feature selection between two feature maps. Second, three networks are carefully designed to obtain better performance meanwhile reducing the number of parameters and computational costs. Lastly, a semantic bootstrapping method is proposed to make the prediction of the networks more consistent with noisy labels. Experimental results show that the proposed framework can utilize large-scale noisy data to learn a Light model that is efficient in computational costs and storage spaces. The learned single network with a 256-D representation achieves state-of-the-art results on various face benchmarks without fine-tuning. The code is released on https://github.com/AlfredXiangWu/LightCNN.Comment: arXiv admin note: text overlap with arXiv:1507.04844. The models are released on https://github.com/AlfredXiangWu/LightCNN, IEEE Transactions on Information Forensics and Security, 201

ES-CTC: A Deep Neuroevolution Model for Cooperative Intelligent Freeway Traffic Control

Cooperative intelligent freeway traffic control is an important application in intelligent transportation systems, which is expected to improve the mobility of freeway networks. In this paper, we propose a deep neuroevolution model, called ES-CTC, to achieve a cooperative control scheme of ramp metering, differential variable speed limits and lane change control agents for improving freeway traffic. In this model, the graph convolutional networks are used to learn more meaningful spatial pattern from traffic sensors, a knowledge sharing layer is designed for communication between different agents. The proposed neural networks structure allows different agents share knowledge with each other and execute action asynchronously. In order to address the delayed reward and action asynchronism issues, the evolutionary strategy is utilized to train the agents under stochastic traffic demands. The experimental results on a simulated freeway section indicate that ES-CTC is a viable approach and outperforms several existing methodsComment: 7 page