Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature and large volume growth. We prove that they have finite topological types under some curvature decay and volume growth conditions. We also generize it to the manifolds with $k$-th asymptotically nonnegative Ricci curvature by using extensions of Abresch-Gromoll's excess function estimate.Comment: 11 page

On the volume of sectional-hyperbolic sets

For a transitive sectional-hypebolic set $\Lambda$ with positive volume on a $d$-dimensional manifold $M$($d\ge3$), we show that $\Lambda=M$ and $\Lambda$ is a uniformly hyperbolic set without singularitiesComment: 6 page

An alternative proof of lower bounds for the first eigenvalue on manifolds

Recently, Andrews and Clutterbuck [AC13] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [AC13]. More precisely, following Ni's method ([Ni13, Section 6]) we give an elliptic proof of this theorem.Comment: All comments are welcom

Paper evolution graph: Multi-view structural retrieval for academic literature

Academic literature retrieval is concerned with the selection of papers that are most likely to match a user's information needs. Most of the retrieval systems are limited to list-output models, in which the retrieval results are isolated from each other. In this work, we aim to uncover the relationships of the retrieval results and propose a method for building structural retrieval results for academic literatures, which we call a paper evolution graph (PEG). A PEG describes the evolution of the diverse aspects of input queries through several evolution chains of papers. By utilizing the author, citation and content information, PEGs can uncover the various underlying relationships among the papers and present the evolution of articles from multiple viewpoints. Our system supports three types of input queries: keyword, single-paper and two-paper queries. The construction of a PEG mainly consists of three steps. First, the papers are soft-clustered into communities via metagraph factorization during which the topic distribution of each paper is obtained. Second, topically cohesive evolution chains are extracted from the communities that are relevant to the query. Each chain focuses on one aspect of the query. Finally, the extracted chains are combined to generate a PEG, which fully covers all the topics of the query. The experimental results on a real-world dataset demonstrate that the proposed method is able to construct meaningful PEGs

DarkRank: Accelerating Deep Metric Learning via Cross Sample Similarities Transfer

We have witnessed rapid evolution of deep neural network architecture design in the past years. These latest progresses greatly facilitate the developments in various areas such as computer vision and natural language processing. However, along with the extraordinary performance, these state-of-the-art models also bring in expensive computational cost. Directly deploying these models into applications with real-time requirement is still infeasible. Recently, Hinton etal. have shown that the dark knowledge within a powerful teacher model can significantly help the training of a smaller and faster student network. These knowledge are vastly beneficial to improve the generalization ability of the student model. Inspired by their work, we introduce a new type of knowledge -- cross sample similarities for model compression and acceleration. This knowledge can be naturally derived from deep metric learning model. To transfer them, we bring the "learning to rank" technique into deep metric learning formulation. We test our proposed DarkRank method on various metric learning tasks including pedestrian re-identification, image retrieval and image clustering. The results are quite encouraging. Our method can improve over the baseline method by a large margin. Moreover, it is fully compatible with other existing methods. When combined, the performance can be further boosted

A Deep Optimization Approach for Image Deconvolution

In blind image deconvolution, priors are often leveraged to constrain the solution space, so as to alleviate the under-determinacy. Priors which are trained separately from the task of deconvolution tend to be instable, or ineffective. We propose the Golf Optimizer, a novel but simple form of network that learns deep priors from data with better propagation behavior. Like playing golf, our method first estimates an aggressive propagation towards optimum using one network, and recurrently applies a residual CNN to learn the gradient of prior for delicate correction on restoration. Experiments show that our network achieves competitive performance on GoPro dataset, and our model is extremely lightweight compared with the state-of-art works.Comment: 12 pages, 16 figure

Visualization of Hyperspectral Images Using Moving Least Squares

Displaying the large number of bands in a hyper spectral image on a trichromatic monitor has been an active research topic. The visualized image shall convey as much information as possible form the original data and facilitate image interpretation. Most existing methods display HSIs in false colors which contradict with human's experience and expectation. In this paper, we propose a nonlinear approach to visualize an input HSI with natural colors by taking advantage of a corresponding RGB image. Our approach is based on Moving Least Squares, an interpolation scheme for reconstructing a surface from a set of control points, which in our case is a set of matching pixels between the HSI and the corresponding RGB image. Based on MLS, the proposed method solves for each spectral signature a unique transformation so that the non linear structure of the HSI can be preserved. The matching pixels between a pair of HSI and RGB image can be reused to display other HSIs captured b the same imaging sensor with natural colors. Experiments show that the output image of the proposed method no only have natural colors but also maintain the visual information necessary for human analysis.Comment: arXiv admin note: text overlap with arXiv:1712.0165

Neural Trojans

While neural networks demonstrate stronger capabilities in pattern recognition nowadays, they are also becoming larger and deeper. As a result, the effort needed to train a network also increases dramatically. In many cases, it is more practical to use a neural network intellectual property (IP) that an IP vendor has already trained. As we do not know about the training process, there can be security threats in the neural IP: the IP vendor (attacker) may embed hidden malicious functionality, i.e. neural Trojans, into the neural IP. We show that this is an effective attack and provide three mitigation techniques: input anomaly detection, re-training, and input preprocessing. All the techniques are proven effective. The input anomaly detection approach is able to detect 99.8% of Trojan triggers although with 12.2% false positive. The re-training approach is able to prevent 94.1% of Trojan triggers from triggering the Trojan although it requires that the neural IP be reconfigurable. In the input preprocessing approach, 90.2% of Trojan triggers are rendered ineffective and no assumption about the neural IP is needed.Comment: The shorth-length version of this paper is to appear in the 2017 IEEE International Conference on Computer Design (ICCD

Positive Geometries and Canonical Forms

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. In this paper we initiate an exploration of "positive geometries" and "canonical forms" as objects of study in their own right in a more general mathematical setting. We give a precise definition of positive geometries and canonical forms, introduce general methods for finding forms for more complicated positive geometries from simpler ones, and present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties. We also illustrate a number of strategies for computing canonical forms which yield interesting representations for the forms associated with wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.Comment: 123 pages, 12 figures, v2: fixed a reference and some minor typo

Constrained Manifold Learning for Hyperspectral Imagery Visualization

Displaying the large number of bands in a hyper- spectral image (HSI) on a trichromatic monitor is important for HSI processing and analysis system. The visualized image shall convey as much information as possible from the original HSI and meanwhile facilitate image interpretation. However, most existing methods display HSIs in false color, which contradicts with user experience and expectation. In this paper, we propose a visualization approach based on constrained manifold learning, whose goal is to learn a visualized image that not only preserves the manifold structure of the HSI but also has natural colors. Manifold learning preserves the image structure by forcing pixels with similar signatures to be displayed with similar colors. A composite kernel is applied in manifold learning to incorporate both the spatial and spectral information of HSI in the embedded space. The colors of the output image are constrained by a corresponding natural-looking RGB image, which can either be generated from the HSI itself (e.g., band selection from the visible wavelength) or be captured by a separate device. Our method can be done at instance-level and feature-level. Instance-level learning directly obtains the RGB coordinates for the pixels in the HSI while feature-level learning learns an explicit mapping function from the high dimensional spectral space to the RGB space. Experimental results demonstrate the advantage of the proposed method in information preservation and natural color visualization