Properties of positive solutions of an Elliptic Equation with negative exponents

In this paper, we study the existence and non-existence result of positive solutions to a singular elliptic equation with negative power on the bounded smooth domain or in the whole Euclidean space. Our model arises in the study of the steady states of thin films and other applied physics. We can get some useful local gradient estimate and L1 lower bound for positive solutions of the elliptic equation. A uniform positive lower bound for convex positive solutions is also obtained. We show that in lower dimensions, there is no stable positive solutions in the whole space. In the whole space of dimension two, we can show that there is no positive smooth solution with finite Morse index. Symmetry properties of related integral equations are also given

Multi-bump solutions of −Δu=K(x)un+2n−2-\Delta u=K(x)u^{\frac{n+2}{n-2}} on lattices in RnR^n

We consider critical exponent semi-linear elliptic equation with coefficient K(x) periodic in its first k variables, with 2k smaller than n-2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in Rk, including infinite lattices. We also show that for 2k greater than or equal to n-2, no such solutions exist.Comment: Final version. Some typo corrected. To appear inJournal fur die reine und angewandte Mathematik (Crelle's Journal

A Comparison of Five Multiple Instance Learning Pooling Functions for Sound Event Detection with Weak Labeling

Sound event detection (SED) entails two subtasks: recognizing what types of sound events are present in an audio stream (audio tagging), and pinpointing their onset and offset times (localization). In the popular multiple instance learning (MIL) framework for SED with weak labeling, an important component is the pooling function. This paper compares five types of pooling functions both theoretically and experimentally, with special focus on their performance of localization. Although the attention pooling function is currently receiving the most attention, we find the linear softmax pooling function to perform the best among the five. Using this pooling function, we build a neural network called TALNet. It is the first system to reach state-of-the-art audio tagging performance on Audio Set, while exhibiting strong localization performance on the DCASE 2017 challenge at the same time

Towards Efficient and Secure Delivery of Data for Training and Inference with Privacy-Preserving

Privacy recently emerges as a severe concern in deep learning, that is, sensitive data must be prohibited from being shared with the third party during deep neural network development. In this paper, we propose Morphed Learning (MoLe), an efficient and secure scheme to deliver deep learning data. MoLe has two main components: data morphing and Augmented Convolutional (Aug-Conv) layer. Data morphing allows data providers to send morphed data without privacy information, while Aug-Conv layer helps deep learning developers to apply their networks on the morphed data without performance penalty. MoLe provides stronger security while introducing lower overhead compared to GAZELLE (USENIX Security 2018), which is another method with no performance penalty on the neural network. When using MoLe for VGG-16 network on CIFAR dataset, the computational overhead is only 9% and the data transmission overhead is 5.12%. As a comparison, GAZELLE has computational overhead of 10,000 times and data transmission overhead of 421,000 times. In this setting, the attack success rate of adversary is 7.9 x 10^{-90} for MoLe and 2.9 x 10^{-30} for GAZELLE, respectively

Progressive Feature Fusion Network for Realistic Image Dehazing

Single image dehazing is a challenging ill-posed restoration problem. Various prior-based and learning-based methods have been proposed. Most of them follow a classic atmospheric scattering model which is an elegant simplified physical model based on the assumption of single-scattering and homogeneous atmospheric medium. The formulation of haze in realistic environment is more complicated. In this paper, we propose to take its essential mechanism as "black box", and focus on learning an input-adaptive trainable end-to-end dehazing model. An U-Net like encoder-decoder deep network via progressive feature fusions has been proposed to directly learn highly nonlinear transformation function from observed hazy image to haze-free ground-truth. The proposed network is evaluated on two public image dehazing benchmarks. The experiments demonstrate that it can achieve superior performance when compared with popular state-of-the-art methods. With efficient GPU memory usage, it can satisfactorily recover ultra high definition hazed image up to 4K resolution, which is unaffordable by many deep learning based dehazing algorithms.Comment: 14 pages, 7 figures, 1 tables, accepted by ACCV201

Adversarial camera stickers: A physical camera-based attack on deep learning systems

Recent work has documented the susceptibility of deep learning systems to adversarial examples, but most such attacks directly manipulate the digital input to a classifier. Although a smaller line of work considers physical adversarial attacks, in all cases these involve manipulating the object of interest, e.g., putting a physical sticker on an object to misclassify it, or manufacturing an object specifically intended to be misclassified. In this work, we consider an alternative question: is it possible to fool deep classifiers, over all perceived objects of a certain type, by physically manipulating the camera itself? We show that by placing a carefully crafted and mainly-translucent sticker over the lens of a camera, one can create universal perturbations of the observed images that are inconspicuous, yet misclassify target objects as a different (targeted) class. To accomplish this, we propose an iterative procedure for both updating the attack perturbation (to make it adversarial for a given classifier), and the threat model itself (to ensure it is physically realizable). For example, we show that we can achieve physically-realizable attacks that fool ImageNet classifiers in a targeted fashion 49.6% of the time. This presents a new class of physically-realizable threat models to consider in the context of adversarially robust machine learning. Our demo video can be viewed at: https://youtu.be/wUVmL33Fx5

Ground States of Two-Component Attractive Bose-Einstein Condensates I: Existence and Uniqueness

We study ground states of two-component Bose-Einstein condensates (BEC) with trapping potentials in $R^2$, where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction $-\beta$ are both attractive, $i.e,$ $a_1$, $a_2$ and $\beta$ are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated $L^2$-critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as $\beta \nearrow \beta ^*=a^*+\sqrt{(a^*-a_1)(a^*-a_2)}$, where $0<a_i<a^*:=\|w\|^2_2$ ($i=1,2$) is fixed and $w$ is the unique positive solution of $\Delta w-w+w^3=0$ in $R^2$. The semi-trivial limit behavior of ground states is tackled in the companion paper [12].Comment: 40 pages, two figure

Ground States of Two-Component Attractive Bose-Einstein Condensates II: Semi-trivial Limit Behavior

As a continuation of [14], we study new pattern formations of ground states $(u_1,u_2)$ for two-component Bose-Einstein condensates (BEC) with homogeneous trapping potentials in $R^2$, where the intraspecies interaction $(-a,-b)$ and the interspecies interaction $-\beta$ are both attractive, $i.e,$ $a$, $b$ and $\beta$ are all positive. If $0<b<a^*:=\|w\|^2_2$ and $0<\beta <a^*$ are fixed, where $w$ is the unique positive solution of $\Delta w-w+w^3=0$ in $R^2$, the semi-trivial behavior of $(u_1,u_2)$ as $a\nearrow a^*$ is proved in the sense that $u_1$ concentrates at a unique point and while $u_2\equiv 0$ in $R^2$. However, if $0<b<a^*$ and $a^*\le\beta <\beta ^*=a^*+\sqrt{(a^*-a)(a^*-b)}$, the refined spike profile and the uniqueness of $(u_1,u_2)$ as $a\nearrow a^*$ are analyzed, where $(u_1,u_2)$ must be unique, $u_1$ concentrates at a unique point, and meanwhile $u_2$ can either blow up or vanish, depending on how $\beta$ approaches to $a^*$.Comment: 45 pages, two figures; Accepted by Trans. Amer. Math. So

Comparing the Max and Noisy-Or Pooling Functions in Multiple Instance Learning for Weakly Supervised Sequence Learning Tasks

Many sequence learning tasks require the localization of certain events in sequences. Because it can be expensive to obtain strong labeling that specifies the starting and ending times of the events, modern systems are often trained with weak labeling without explicit timing information. Multiple instance learning (MIL) is a popular framework for learning from weak labeling. In a common scenario of MIL, it is necessary to choose a pooling function to aggregate the predictions for the individual steps of the sequences. In this paper, we compare the "max" and "noisy-or" pooling functions on a speech recognition task and a sound event detection task. We find that max pooling is able to localize phonemes and sound events, while noisy-or pooling fails. We provide a theoretical explanation of the different behavior of the two pooling functions on sequence learning tasks

A Light-Weight Multimodal Framework for Improved Environmental Audio Tagging

The lack of strong labels has severely limited the state-of-the-art fully supervised audio tagging systems to be scaled to larger dataset. Meanwhile, audio-visual learning models based on unlabeled videos have been successfully applied to audio tagging, but they are inevitably resource hungry and require a long time to train. In this work, we propose a light-weight, multimodal framework for environmental audio tagging. The audio branch of the framework is a convolutional and recurrent neural network (CRNN) based on multiple instance learning (MIL). It is trained with the audio tracks of a large collection of weakly labeled YouTube video excerpts; the video branch uses pretrained state-of-the-art image recognition networks and word embeddings to extract information from the video track and to map visual objects to sound events. Experiments on the audio tagging task of the DCASE 2017 challenge show that the incorporation of video information improves a strong baseline audio tagging system by 5.3\% absolute in terms of $F_1$ score. The entire system can be trained within 6~hours on a single GPU, and can be easily carried over to other audio tasks such as speech sentimental analysis.Comment: 5 pages, 3 figures, Accepted and to appear at ICASSP 201