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Feng Zhou

Publications and source records attributed to Feng Zhou.

233 records · Page 13Linked to original sources
arXiv2017

Isolated singularities for elliptic equations with Hardy operator and source nonlinearity

In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -Δu+\fracμ{|x|^2} u=u^p\quad {\rm in}\quad Ω\setminus\{0\},\qquad u=0\quad{\rm on}\quad \partialΩ. \end{equation} We classify the isolated singularities and obtain the existence, the stability of positive solutions of (\ref{0}). Our results are based on the study of nonhomogeneous Hardy problem in a new distributional sense.

math.AP↗
arXiv2017

Frequency manipulation of light by photonic gauge potentials

The ability to manipulate the frequency of light is of great importance in both fundamental quantum sciences and practical applications. Traditional method for frequency conversion relies on nonlinear optical processes, which are faced with the obstacles of low efficiency and limited bandwidth. Recent developments of topological photonics introduce the concepts of gauge potentials and magnetic fields to the realm of photons. Here, we demonstrate versatile frequency manipulation of light via photonic gauge potentials in a fiber-optic communication system. The gauge potential of frequency dimension is realized by controlling the initial phase of electro-optic phase modulation. A maximum 50 GHz frequency shift and three-fold bandwidth expansion for frequency combs are achieved by choosing different gauge potentials. By adopting two cascaded phase modulators with different gauge potentials, we also realize "negative refraction" for frequency combs and frequency "perfect imaging"for arbitrarily input spectra. These results may pave the way towards versatile frequency management in quantum optics and classical optical communications.

physics.optics↗
arXiv2017

Bidirectional-Convolutional LSTM Based Spectral-Spatial Feature Learning for Hyperspectral Image Classification

This paper proposes a novel deep learning framework named bidirectional-convolutional long short term memory (Bi-CLSTM) network to automatically learn the spectral-spatial feature from hyperspectral images (HSIs). In the network, the issue of spectral feature extraction is considered as a sequence learning problem, and a recurrent connection operator across the spectral domain is used to address it. Meanwhile, inspired from the widely used convolutional neural network (CNN), a convolution operator across the spatial domain is incorporated into the network to extract the spatial feature. Besides, to sufficiently capture the spectral information, a bidirectional recurrent connection is proposed. In the classification phase, the learned features are concatenated into a vector and fed to a softmax classifier via a fully-connected operator. To validate the effectiveness of the proposed Bi-CLSTM framework, we compare it with several state-of-the-art methods, including the CNN framework, on three widely used HSIs. The obtained results show that Bi-CLSTM can improve the classification performance as compared to other methods.

cs.CV↗
arXiv2017

Fully Convolutional Attention Networks for Fine-Grained Recognition

Fine-grained recognition is challenging due to its subtle local inter-class differences versus large intra-class variations such as poses. A key to address this problem is to localize discriminative parts to extract pose-invariant features. However, ground-truth part annotations can be expensive to acquire. Moreover, it is hard to define parts for many fine-grained classes. This work introduces Fully Convolutional Attention Networks (FCANs), a reinforcement learning framework to optimally glimpse local discriminative regions adaptive to different fine-grained domains. Compared to previous methods, our approach enjoys three advantages: 1) the weakly-supervised reinforcement learning procedure requires no expensive part annotations; 2) the fully-convolutional architecture speeds up both training and testing; 3) the greedy reward strategy accelerates the convergence of the learning. We demonstrate the effectiveness of our method with extensive experiments on four challenging fine-grained benchmark datasets, including CUB-200-2011, Stanford Dogs, Stanford Cars and Food-101.

cs.CV↗
arXiv2017

Isolated singularities of positive solutions for Choquard equations in sublinear case

Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case $q \in (0,1)$ $$\displaystyle \ \ -Δu+ u =I_α[u^p] u^q\;\; {\rm in}\; \mathbb{R}^N\setminus\{0\}, % [2mm] \phantom{ } \;\; \displaystyle \lim_{|x|\to+\infty}u(x)=0, $$ where $p >0, N \geq 3, α\in (0,N)$ and $I_α[u^p](x) = \int_{\mathbb{R}^N} \frac{u^p(y)}{|x-y|^{N-α}}dy$ is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquard equation under different range of the pair of exponent $(p,q)$. Furthermore, we obtain qualitative properties for the minimal singular solutions of the equation.

math.AP↗
arXiv2017

Interbank Credit and the Money Manufacturing Process. A Systemic Perspective on Financial Stability

Interbank lending and borrowing occur when financial institutions seek to settle and refinance their mutual positions over time and circumstances. This interactive process involves money creation at the aggregate level. Coordination mismatch on interbank credit may trigger systemic crises. This happened when, since summer 2007, interbank credit coordination did not longer work smoothly across financial institutions, eventually requiring exceptional monetary policies by central banks, and guarantee and bailout interventions by governments. Our article develops an interacting heterogeneous agents-based model of interbank credit coordination under minimal institutions. First, we explore the link between interbank credit coordination and the money generation process. Contrary to received understanding, interbank credit has the capacity to make the monetary system unbound. Second, we develop simulation analysis on imperfect interbank credit coordination, studying impact of interbank dynamics on financial stability and resilience at individual and aggregate levels. Systemically destabilizing forces prove to be related to the working of the banking system over time, especially interbank coordination conditions and circumstances.

q-fin.GN↗
arXiv2017

Conformal scalar curvature equation on S^n: functions with two close critical points (twin pseudo-peaks)

By using the Lyapunov-Schmidt reduction method without perturbation, we consider existence results for the conformal scalar curvature on S^n (n greater or equal to 3) when the prescribed function (after being projected to R^n) has two close critical points, which have the same value (positive), equal "flatness" (twin, flatness < n - 2), and exhibit maximal behavior in certain directions (pseudo-peaks). The proof relies on a balance between the two main contributions to the reduced functional - one from the critical points and the other from the interaction of the two bubbles.

math.AP↗
arXiv2016

Symmetry-Breaking Zeeman-Coherence Parametric Wave Mixing Magnetometry

The nonlinear magneto-optical effect has significantly impacted modern society with prolific applications ranging from precision mapping of the Earth's magnetic field to bio-magnetic sensing. Pioneering works on collisional spin-exchange effects have led to ultra-high magnetic field detection sensitivities at the level of $fT/\sqrt{Hz}$ using a single linearly-polarized probe light field. Here we demonstrate a nonlinear Zeeman-coherence parametric wave-mixing optical-atomic magnetometer using room temperature rubidium vapor that results in more than a three-order-of-magnitude optical signal-to-noise ratio (SNR) enhancement for extremely weak magnetic field sensing. This unprecedented enhancement was achieved with nearly a two-order-of-magnitude reduction in laser power while preserving the sensitivity of the widely-used single-probe beam optical-atomic magnetometry method. This new method opens a myriad of applications ranging from bio-magnetic imaging to precision measurement of the magnetic properties of subatomic particles.

physics.optics↗
arXiv2016

Deep Deformation Network for Object Landmark Localization

We propose a novel cascaded framework, namely deep deformation network (DDN), for localizing landmarks in non-rigid objects. The hallmarks of DDN are its incorporation of geometric constraints within a convolutional neural network (CNN) framework, ease and efficiency of training, as well as generality of application. A novel shape basis network (SBN) forms the first stage of the cascade, whereby landmarks are initialized by combining the benefits of CNN features and a learned shape basis to reduce the complexity of the highly nonlinear pose manifold. In the second stage, a point transformer network (PTN) estimates local deformation parameterized as thin-plate spline transformation for a finer refinement. Our framework does not incorporate either handcrafted features or part connectivity, which enables an end-to-end shape prediction pipeline during both training and testing. In contrast to prior cascaded networks for landmark localization that learn a mapping from feature space to landmark locations, we demonstrate that the regularization induced through geometric priors in the DDN makes it easier to train, yet produces superior results. The efficacy and generality of the architecture is demonstrated through state-of-the-art performances on several benchmarks for multiple tasks such as facial landmark localization, human body pose estimation and bird part localization.

cs.CV↗
arXiv2016

Fine-grained Categorization and Dataset Bootstrapping using Deep Metric Learning with Humans in the Loop

Existing fine-grained visual categorization methods often suffer from three challenges: lack of training data, large number of fine-grained categories, and high intraclass vs. low inter-class variance. In this work we propose a generic iterative framework for fine-grained categorization and dataset bootstrapping that handles these three challenges. Using deep metric learning with humans in the loop, we learn a low dimensional feature embedding with anchor points on manifolds for each category. These anchor points capture intra-class variances and remain discriminative between classes. In each round, images with high confidence scores from our model are sent to humans for labeling. By comparing with exemplar images, labelers mark each candidate image as either a "true positive" or a "false positive". True positives are added into our current dataset and false positives are regarded as "hard negatives" for our metric learning model. Then the model is retrained with an expanded dataset and hard negatives for the next round. To demonstrate the effectiveness of the proposed framework, we bootstrap a fine-grained flower dataset with 620 categories from Instagram images. The proposed deep metric learning scheme is evaluated on both our dataset and the CUB-200-2001 Birds dataset. Experimental evaluations show significant performance gain using dataset bootstrapping and demonstrate state-of-the-art results achieved by the proposed deep metric learning methods.

cs.CV↗
arXiv2016

Embedding Label Structures for Fine-Grained Feature Representation

Recent algorithms in convolutional neural networks (CNN) considerably advance the fine-grained image classification, which aims to differentiate subtle differences among subordinate classes. However, previous studies have rarely focused on learning a fined-grained and structured feature representation that is able to locate similar images at different levels of relevance, e.g., discovering cars from the same make or the same model, both of which require high precision. In this paper, we propose two main contributions to tackle this problem. 1) A multi-task learning framework is designed to effectively learn fine-grained feature representations by jointly optimizing both classification and similarity constraints. 2) To model the multi-level relevance, label structures such as hierarchy or shared attributes are seamlessly embedded into the framework by generalizing the triplet loss. Extensive and thorough experiments have been conducted on three fine-grained datasets, i.e., the Stanford car, the car-333, and the food datasets, which contain either hierarchical labels or shared attributes. Our proposed method has achieved very competitive performance, i.e., among state-of-the-art classification accuracy. More importantly, it significantly outperforms previous fine-grained feature representations for image retrieval at different levels of relevance.

cs.CV↗
arXiv2015

Fine-grained Image Classification by Exploring Bipartite-Graph Labels

Given a food image, can a fine-grained object recognition engine tell "which restaurant which dish" the food belongs to? Such ultra-fine grained image recognition is the key for many applications like search by images, but it is very challenging because it needs to discern subtle difference between classes while dealing with the scarcity of training data. Fortunately, the ultra-fine granularity naturally brings rich relationships among object classes. This paper proposes a novel approach to exploit the rich relationships through bipartite-graph labels (BGL). We show how to model BGL in an overall convolutional neural networks and the resulting system can be optimized through back-propagation. We also show that it is computationally efficient in inference thanks to the bipartite structure. To facilitate the study, we construct a new food benchmark dataset, which consists of 37,885 food images collected from 6 restaurants and totally 975 menus. Experimental results on this new food and three other datasets demonstrates BGL advances previous works in fine-grained object recognition. An online demo is available at http://www.f-zhou.com/fg_demo/.

cs.CV↗
arXiv2015

On semi-linear elliptic equation arising from Micro-Electromechanical Systems with contacting elastic membrane

This paper is concerned with the nonlinear elliptic problem $-Δu=\frac{λ}{(a-u)^2}$ on a bounded domain $Ω$ of $\mathbb{R}^N$ with Dirichlet boundary conditions. This problem arises from Micro-Electromechanical Systems devices in the case that the elastic membrane contacts the ground plate on the boundary. We analyze the properties of minimal solutions to this equation when $λ>0$ and the function $a:\barΩ\to[0,1]$ satisfying $a(x)\ge κ{\rm dist}(x,\partialΩ)^γ$ for some $κ>0$ and $γ\in(0,1)$. Our results show how the boundary decay of the membrane works on the solutions and pull-in voltage $λ$.

math.AP↗
arXiv2011

Semigroups and sequential importance sampling for multiway tables and beyond

When an interval of integers between the lower bound l_i and the upper bounds u_i is the support of the marginal distribution n_i|(n_{i-1}, ...,n_1), Chen et al. 2005 noticed that sampling from the interval at each step, for n_i during the sequential importance sampling (SIS) procedure, always produces a table which satisfies the marginal constraints. However, in general, the interval may not be equal to the support of the marginal distribution. In this case, the SIS procedure may produce tables which do not satisfy the marginal constraints, leading to rejection [Chen et al. 2006]. Rejecting tables is computationally expensive and incorrect proposal distributions result in biased estimators for the number of tables given its marginal sums. This paper has two focuses; (1) we propose a correction coefficient which corrects an interval of integers between the lower bound l_i and the upper bounds u_i to the support of the marginal distribution asymptotically even with rejections and with the same time complexity as the original SIS procedure (2) using univariate and bivariate logistic regression models, we present extensive experiments on simulated data sets for estimating the number of tables, and (3) we applied the volume test proposed by Diaconis and Efron 1985 on 2x2x6 randomly generated tables to compare the performance of SIS versus MCMC. When estimating the number of tables in our simulation study, we used univariate and bivariate logistic regression models since under these models the SIS procedure seems to have higher rate of rejections even with small tables. We also apply our correction coefficients to data sets on coronary heart disease and occurrence of esophageal cancer.

math.ST↗
arXiv2011

Regularity of the extremal solution for some elliptic problems with advection

In this note, we investigate the regularity of extremal solution $u^*$ for semilinear elliptic equation $-\triangle u+c(x)\cdot\nabla u=λf(u)$ on a bounded smooth domain of $\mathbb{R}^n$ with Dirichlet boundary condition. Here $f$ is a positive nondecreasing convex function, exploding at a finite value $a\in (0, \infty)$. We show that the extremal solution is regular in low dimensional case. In particular, we prove that for the radial case, all extremal solution is regular in dimension two.

math.AP↗
arXiv2010

Films with the discrete nano-DLC-particles as the field emission cascade

The films with the discrete diamond-like-carbon nanoparticles were prepared by the deposition of the carbon nanoparticle beam. Their morphologies were imaged by Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM). The nanoparticles were found distributed on the silicon (100) substrate discretely. The semisphere shapes of the nanoparticles were demonstrated by the AFM line profile. EELS was measured and the sp3 ratio as high as 86% was found. The field-induced electron emission of the as-prepared cascade (nanoDLC/ Si) was tested and the current density of 1mA/cm2 was achieved at 10.2V/μm.

cond-mat.mes-hall↗