arXiv subjects

Fei Yang

Publications and source records attributed to Fei Yang.

At least 127 records · Page 7Linked to original sources

arXiv2019

Area and Hausdorff dimension of Sierpiński carpet Julia sets

We prove the existence of rational maps whose Julia sets are Sierpiński carpets having positive area. Such rational maps can be constructed such that they either contain a Cremer fixed point, a Siegel disk or are infinitely renormalizable. We also construct some Sierpiński carpet Julia sets with zero area but with Hausdorff dimension two. Moreover, for any given number $s\in(1,2)$, we prove the existence of Sierpiński carpet Julia sets having Hausdorff dimension exactly $s$.

math.DS↗

arXiv2018

In-the-wild Facial Expression Recognition in Extreme Poses

In the computer research area, facial expression recognition is a hot research problem. Recent years, the research has moved from the lab environment to in-the-wild circumstances. It is challenging, especially under extreme poses. But current expression detection systems are trying to avoid the pose effects and gain the general applicable ability. In this work, we solve the problem in the opposite approach. We consider the head poses and detect the expressions within special head poses. Our work includes two parts: detect the head pose and group it into one pre-defined head pose class; do facial expression recognize within each pose class. Our experiments show that the recognition results with pose class grouping are much better than that of direct recognition without considering poses. We combine the hand-crafted features, SIFT, LBP and geometric feature, with deep learning feature as the representation of the expressions. The handcrafted features are added into the deep learning framework along with the high level deep learning features. As a comparison, we implement SVM and random forest to as the prediction models. To train and test our methodology, we labeled the face dataset with 6 basic expressions.

cs.CV↗

arXiv2018

EAST Real-Time VOD System Based on MDSplus

As with EAST (Experimental Advanced Superconducting Tokamak) experimental data analyzed by more and more collaborators, the experimental videos which directly reflect the real status of vacuum attract more and more researchers' attention. The real time VOD (Video On Demand) system based on MDSplus allows users reading the video frames in real time as same as the signal data which is also stored in the MDSplus database. User can display the plasma discharge videos and analyze videos frame by frame through jScope or our VOD web station. The system mainly includes the frames storing and frames displaying. The frames storing application accepts shot information by using socket TCP communication firstly, then reads video frames through disk mapping, finally stores them into MDSplus. The displaying process is implemented through B/S (Browser/Server) framework, it uses PHP and JavaScript to realize VOD function and read frames information from MDSplus. The system offers a unit way to access and backup experimental data and video during the EAST experiment, which is of great benefit to EAST experimenter than the formal VOD system in VOD function and real time performance.

cs.MM↗

arXiv2018

Jointly Optimize Data Augmentation and Network Training: Adversarial Data Augmentation in Human Pose Estimation

Random data augmentation is a critical technique to avoid overfitting in training deep neural network models. However, data augmentation and network training are usually treated as two isolated processes, limiting the effectiveness of network training. Why not jointly optimize the two? We propose adversarial data augmentation to address this limitation. The main idea is to design an augmentation network (generator) that competes against a target network (discriminator) by generating `hard' augmentation operations online. The augmentation network explores the weaknesses of the target network, while the latter learns from `hard' augmentations to achieve better performance. We also design a reward/penalty strategy for effective joint training. We demonstrate our approach on the problem of human pose estimation and carry out a comprehensive experimental analysis, showing that our method can significantly improve state-of-the-art models without additional data efforts.

cs.CV↗

arXiv2018

Area of the complement of the fast escaping sets of a family of entire functions

Let $f$ be an entire function with the form $f(z)=P(e^z)/e^z$, where $P$ is a polynomial with degree at least $2$ and $P(0)\neq 0$. We prove that the area of the complement of the fast escaping set (hence the Fatou set) of $f$ in a horizontal strip of width $2π$ is finite. In particular, the corresponding result can be applied to the sine family $α\sin(z+β)$, where $α\neq 0$ and $β\in\mathbb{C}$.

math.DS↗

arXiv2018

Quasisymmetric geometry of Sierpinski carpet Julia sets

In this paper, the main focus is on the Sierpinski carpet Julia sets of the rational maps with non-recurrent critical points. We study the uniform quasicircle property of the peripheral circles, the relatively separated property of the peripheral circles and the locally porous property of these carpets. We also establish some quasisymmetric rigidities of these carpets, which generalizes the main results of Bonk-Lyubich-Merenkov to the postcritically infinite case. In the end we give a strategy to construct a class of postcritically infinite rational maps whose Julia sets are quasisymetrically equivalent to some round carpets.

math.DS↗

arXiv2018

Cantor Julia sets with Hausdorff dimension two

We prove the existence of Cantor Julia sets with Hausdorff dimension two. In particular, such examples can be found in cubic polynomials. The proof is based on the characterization of the parameter spaces and dynamical planes of cubic polynomials by Branner-Hubbard, and the parabolic bifurcation theory developed by Shishikura in 1990s.

math.DS↗

arXiv2018

Quality Classified Image Analysis with Application to Face Detection and Recognition

Motion blur, out of focus, insufficient spatial resolution, lossy compression and many other factors can all cause an image to have poor quality. However, image quality is a largely ignored issue in traditional pattern recognition literature. In this paper, we use face detection and recognition as case studies to show that image quality is an essential factor which will affect the performances of traditional algorithms. We demonstrated that it is not the image quality itself that is the most important, but rather the quality of the images in the training set should have similar quality as those in the testing set. To handle real-world application scenarios where images with different kinds and severities of degradation can be presented to the system, we have developed a quality classified image analysis framework to deal with images of mixed qualities adaptively. We use deep neural networks first to classify images based on their quality classes and then design a separate face detector and recognizer for images in each quality class. We will present experimental results to show that our quality classified framework can accurately classify images based on the type and severity of image degradations and can significantly boost the performances of state-of-the-art face detector and recognizer in dealing with image datasets containing mixed quality images.

cs.CV↗

arXiv2017

Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)

The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between context-free and pushdown processes fails modulo bisimilarity, and it is not clear how to specify an always terminating half counter. We propose a revised operational semantics for the sequential composition operator in the context of intermediate termination. With the revised operational semantics, we eliminate transparency, allowing us to establish a close correspondence between context-free processes and pushdown processes. Moreover, we prove the reactive Turing powerfulness of TCP with iteration and nesting with the revised operational semantics for sequential composition.

cs.LO↗

arXiv2017

A criterion to generate carpet Julia sets

It was known that the Sierpiński carpets can appear as the Julia sets in the families of some rational maps. In this article we present a criterion that guarantees the existence of the carpet Julia sets in some rational maps having exactly one fixed (super-) attracting or parabolic basin. We show that this criterion can be applied to some well known rational maps, such as McMullen maps and Morosawa-Pilgrim family. Moreover, we give also some special examples whose Julia sets are Sierpiński carpets.

math.DS↗

arXiv2017

Sequential Composition in the Presence of Intermediate Termination

The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between context-free and pushdown processes fails modulo bisimilarity, and it is not clear how to specify an always terminating half counter. We propose a revised operational semantics for the sequential composition operator in the context of intermediate termination. With the revised operational semantics, we eliminate transparency. As a consequence, we establish a correspondence between context-free processes and pushdown processes. Moreover, we prove the reactive Turing powerfulness of TCP with iteration and nesting with the revised operational semantics for sequential composition.

cs.LO↗

arXiv2017

Rigidity of Gradient Shrinking Ricci Solitons

We prove that a gradient shrinking Ricci soliton with fourth order divergence-free Riemannian tensor is rigid. For the $4$-dimensional case, we show that any gradient shrinking Ricci soliton with fourth order divergence-free Riemannian tensor is either Einstein, or a finite quotient of the Gaussian shrinking soliton $\mathbb{R}^4$, $\mathbb{R}^2\times\mathbb{S}^2$ or the round cylinder $\mathbb{R}\times\mathbb{S}^3$. Under the condition of fourth order divergence-free Weyl tensor, we have the same results.

math.DG↗

arXiv2017

Reactive Turing Machines with Infinite Alphabets

The notion of Reactive Turing machine (RTM) was proposed as an orthogonal extension of Turing machines with interaction. RTMs are used to define the notion of executable transition system in the same way as Turing machines are used to define the notion of computable function on natural numbers. RTMs inherited finiteness of all sets involved from Turing machines, and as a consequence, in a single step, an RTM can only communicate elements from a finite set of data. Some process calculi, such as the pi-calculus, essentially depend on an infinite alphabet of actions, and hence it immediately follows that transition systems specified in these calculi are not executable. On closer inspection, however, the pi-calculus does not appear to use the infinite data in a non-computable manner. In this paper, we investigate several ways to relax the finiteness requirement. We start by considering a variant of RTMs in which all sets are allowed to be countable, and we get a notion of infinitary RTM. Infinitary RTMs are extremely expressive such that we can hardly use them as a expressiveness criterion. Then, we refine the model by adding extra restrictions. As a result, we define a notion of RTM with atoms. It is a more restricted variant of RTMs in which the sets of actions and data symbols are still allowed to be infinite. We propose a notion of of nominal executability based on RTMs with atoms, and show that every effective transition system with atoms is nominally executable. It will follow that processes definable in the pi-calculus are nominally executable. In contrast, in the process specification language mCRL2 it is possible to specify processes that are not nominally executable. Thus, nominal executability provides a new expressiveness criterion for process calculi.

cs.LO↗

arXiv2017

Quantum anomalous Hall effect in atomic crystal layers from in-plane magnetization

We theoretically report that, with \textit{in-plane} magnetization, the quantum anomalous Hall effect (QAHE) can be realized in two-dimensional atomic crystal layers with preserved inversion symmetry but broken out-of-plane mirror reflection symmetry. We take the honeycomb lattice as an example, where we find that the low-buckled structure, which makes the system satisfy the symmetric criteria, is crucial to induce QAHE. The topologically nontrivial bulk gap carrying a Chern number of $\mathcal{C}=\pm1$ opens in the vicinity of the saddle points $M$, where the band dispersion exhibits strong anisotropy. We further show that the QAHE with electrically tunable Chern number can be achieved in Bernal-stacked multilayer systems, and the applied interlayer potential differences can dramatically decrease the critical magnetization to make the QAHE experimentally feasible.

cond-mat.mes-hall↗

arXiv2016

Rational maps without Herman rings

Let $f$ be a rational map with degree at least two. We prove that $f$ has at least $2$ disjoint and infinite critical orbits in the Julia set if it has a Herman ring. This result is sharp in the following sense: there exists a cubic rational map having exactly two critical grand orbits but also having a Herman ring. In particular, $f$ has no Herman rings if it has at most one infinite critical orbit in the Julia set. These criterions derive some known results about the rational maps without Herman rings.

math.DS↗

arXiv2016

Singular perturbations with multiple poles of the simple polynomials

In this article, we study the dynamics of the following family of rational maps with one parameter: \begin{equation*} f_λ(z)= z^n+\frac{λ^2}{z^n-λ}, \end{equation*} where $n\geq 3$ and $λ\in\mathbb{C}^*$. This family of rational maps can be viewed as a singular perturbations of the simple polynomial $P_n(z)=z^n$. We give a characterization of the topological properties of the Julia sets of the family $f_λ$ according to the dynamical behaviors of the orbits of the free critical points.

math.DS↗

arXiv2016

Time and Frequency Injection into a Stabilized Fiber Link for Multi-clock Dissemination Network

Owing to the characteristics of ultra-low loss and anti-electromagnetic interference, using optical fiber to deliver time and frequency signal has been a preferred choice for high precise clock dissemination and comparison. As a brilliant idea, one has been able to reproduce ultra-stable signals from one local station to multiple users. In this paper, we take a step further. A concept of multi-clock (in different locations) dissemination for multi-terminals is presented. By injecting frequency signals into one stabilized ring-like fiber network, the relative stabilities of 3.4e-14@1s for a master clock dissemination and 5.1e-14@1s for a slave clock dissemination have been achieved. The proposed scheme can greatly simplify the future 'N' to 'N' time and frequency dissemination network, especially facing a multi-clock comparison situation.

physics.optics↗

arXiv2016

On the Executability of Interactive Computation

The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are reactively executable. In this article we provide a comparison of the two models. We show, on the one hand, that the behaviour exhibited by ITMs is reactively executable, and, on the other hand, that the stream translations naturally associated with RTMs are interactively computable. We conclude from these results that the theory of reactive executability subsumes the theory of interactive computability. Inspired by the existing model of ITMs with advice, which provides a model of evolving computation, we also consider RTMs with advice and we establish that a facility of advice considerably upgrades the behavioural expressiveness of RTMs: every countable transition system can be simulated by some RTM with advice up to a fine notion of behavioural equivalence.

cs.LO↗