Searcharxiv⌕ Search

arXiv subjects

Zipeng Wang

Publications and source records attributed to Zipeng Wang.

101 records · Page 6Linked to original sources
arXiv2019

Hyper-positive definite functions I: scalar case, branching-type stationary stochastic processes

We propose a definition of branching-type stationary stochastic processes on rooted trees and related definitions of hyper-positivity for functions on the unit circle and functions on the set of non-negative integers. We then obtain (1) a necessary and sufficient condition on a rooted tree for the existence of non-trivial branching-type stationary stochastic processes on it, (2) a complete criterion of the hyper-positive functions in the setting of rooted homogeneous trees in terms of a variant of the classical Herglotz-Bochner Theorem, (3) a prediction theory result for branching-type stationary stochastic processes. As an unexpected application, we obtain natural hypercontractive inequalities for Hankel operators with hyper-positive symbols.

math.PR↗
arXiv2019

Video synthesis of human upper body with realistic face

This paper presents a generative adversarial learning-based human upper body video synthesis approach to generate an upper body video of target person that is consistent with the body motion, face expression, and pose of the person in source video. We use upper body keypoints, facial action units and poses as intermediate representations between source video and target video. Instead of directly transferring the source video to the target video, we firstly map the source person's facial action units and poses into the target person's facial landmarks, then combine the normalized upper body keypoints and generated facial landmarks with spatio-temporal smoothing to generate the corresponding target video's image. Experimental results demonstrated the effectiveness of our method.

cs.CV↗
arXiv2019

A Neural Virtual Anchor Synthesizer based on Seq2Seq and GAN Models

This paper presents a novel framework to generate realistic face video of an anchor, who is reading certain news. This task is also known as Virtual Anchor. Given some paragraphs of words, we first utilize a pretrained Word2Vec model to embed each word into a vector; then we utilize a Seq2Seq-based model to translate these word embeddings into action units and head poses of the target anchor; these action units and head poses will be concatenated with facial landmarks as well as the former $n$ synthesized frames, and the concatenation serves as input of a Pix2PixHD-based model to synthesize realistic facial images for the virtual anchor. The experimental results demonstrate our framework is feasible for the synthesis of virtual anchor.

cs.CV↗
arXiv2019

How Old Are You? Face Age Translation with Identity Preservation Using GANs

We present a novel framework to generate images of different age while preserving identity information, which is known as face aging. Different from most recent popular face aging networks utilizing Generative Adversarial Networks(GANs) application, our approach do not simply transfer a young face to an old one. Instead, we employ the edge map as intermediate representations, firstly edge maps of young faces are extracted, a CycleGAN-based network is adopted to transfer them into edge maps of old faces, then another pix2pixHD-based network is adopted to transfer the synthesized edge maps, concatenated with identity information, into old faces. In this way, our method can generate more realistic transfered images, simultaneously ensuring that face identity information be preserved well, and the apparent age of the generated image be accurately appropriate. Experimental results demonstrate that our method is feasible for face age translation.

cs.CV↗
arXiv2018

Three Remarks on Carleson Measures for Dirichlet Space

In this paper, we prove that all doubling measures on the unit disk $\mathbb{D}$ are Carleson measures for the standard Dirichlet space $\mathcal{D}$. The proof has three ingredients. The first one is a characterization of Carleson measures which holds true for general reproducing kernel Hilbert spaces. The second one is another new equivalent condition for Carleson measures, which holds true only for the standard Dirichlet space. The third one is an application of the dyadic method to our settings.

math.FA↗
arXiv2018

Composition Operators with Quasiconformal Symbols

This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In particular, we present a thorough analysis of $L^p$-estimates of a class of singular integral operators $P_φ$ associated with a quasiconformal mapping $φ$.

math.FA↗
arXiv2018

Weighted inequalities for product fractional integrals

We investigate one and two weight norm inequalities for product fractional integrals. We show that in the one weight case, most of the 1 parameter theory carries over to the 2 parameter setting. However, in the two weight case, apart from the trivial case of product weights, the rectangle characteristic never controls the operator norm without side conditions. The Stein-Weiss extension of the classical Hardy-Littlewood-Sobolev inequality carries over to the setting of 2 parameters with nonproduct power weights using a sandwiching technique.

math.CA↗
arXiv2017

On the Controllability of Lagrangian Systems by Active Constraints

We consider a mechanical system which is controlled by means of moving constraints. Namely, we assume that some of the coordinates can be directly assigned as functions of time by means of frictionless constraints. This leads to a system of ODE's whose right hand side depends quadratically on the time derivative of the control. In this paper we introduce a simplified dynamics, described by a differential inclusion. We prove that every trajectory of the differential inclusion can be uniformly approximated by a trajectory of the original system, on a sufficiently large time interval, starting at rest. Under a somewhat stronger assumption, we show this second trajectory reaches exactly the same terminal point.

math.CA↗
arXiv2016

Generalized Dirichlet to Neumann Maps for Linear Dispersive Equations on Half-Line

A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized Dirichlet to Neumann maps. Namely, the determination of the unknown boundary values in terms of an essential set of given data.

math.AP↗
arXiv2016

Toeplitz operators on the weighted harmonic Bergman spaces

In this paper, we study Toeplitz operators on the weighted harmonic Bergman spaces with nonnegative symbols, the weights we choose here are Muckenhoupt A_2 weights. Results obtained include characterizations of bounded Toeplitz operators, compact Toeplitz operators, invertible Toeplitz operators and Toeplitz operators in the Schatten classes.

math.FA↗