Higher-degree Smoothness of Perturbations III
This paper is the continuation of the previous two papers with the same title.
math.SG↗
arXiv subjects
Gang Liu
Publications and source records attributed to Gang Liu.
Higher-degree Smoothness of Perturbations II
In this paper we generalize the higher-degree smoothness results in perturbation theory from the case that the stable maps have the fixed domain $S^2$ to the general genus zero case.
math.SG↗
Extended Dynamical Equations of the Period Vectors of Crystals under Constant External Stress to Many-body Interactions
Since crystals are made of periodic structures in space, predicting their three period vectors starting from any values based on the inside interactions is a basic theoretical physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show that the period vectors are driven by the imbalance between the internal and external stresses. This presents a physical process where when the external stress changes, the crystal structure changes accordingly, since the original internal stress can not balance the external stress. The internal stress has both a full kinetic energy term and a full interaction term. It is extended to many-body interactions in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.
cond-mat.mtrl-sci↗
A geometric interpretation of Kirillov's Conjecture
In this article, we give a natural geometric interpretation of Kirillov's conjecture for tempered representations in the framework of orbit method. This interpretation can also be considered as a first generalization of Duflo's conjecture to non-discrete series representations.
math.RT↗
11,11,12,12-tetracyanonaphtho-2,6-quinodimethane in Contact with Ferromagnetic Electrodes for Organic Spintronics
Spinterface engineering has shown quite important roles in organic spintronics as it can improve spin injection or extraction. In this study, 11,11,12,12-tetracyanonaptho-2,6-quinodimethane (TNAP) is introduced as an interfacial layer for a prototype interface of Fe/TNAP. We report an element-specific investigation of the electronic and magnetic structures of Fe/TNAP system by use of near edge X-Ray absorption fine structure (NEXAFS) and X-ray magnetic circular dichroism (XMCD). Strong hybridization between TNAP and Fe and induced magnetization of N atoms in TNAP molecule are observed. XMCD sum rule analysis demonstrates that the adsorption of TNAP reduces the spin moment of Fe by 12%. In addition, induced magnetization in N K-edge of TNAP has also been found with other commonly used ferromagnets in organic spintronics, such as La0.7Sr0.3MnO3 and permalloy, which makes TNAP a very promising molecule for spinterface engineering in organic spintronics.
cond-mat.mtrl-sci↗
An Ensemble Framework of Voice-Based Emotion Recognition System for Films and TV Programs
Employing voice-based emotion recognition function in artificial intelligence (AI) product will improve the user experience. Most of researches that have been done only focus on the speech collected under controlled conditions. The scenarios evaluated in these research were well controlled. The conventional approach may fail when background noise or nonspeech filler exist. In this paper, we propose an ensemble framework combining several aspects of features from audio. The framework incorporates gender and speaker information relying on multi-task learning. Therefore it is able to dig and capture emotional information as much as possible. This framework is evaluated on multimodal emotion challenge (MEC) 2017 corpus which is close to real world. The proposed framework outperformed the best baseline system by 29.5% (relative improvement).
eess.AS↗
Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm
In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates.
math.CV↗
Advanced LSTM: A Study about Better Time Dependency Modeling in Emotion Recognition
Long short-term memory (LSTM) is normally used in recurrent neural network (RNN) as basic recurrent unit. However,conventional LSTM assumes that the state at current time step depends on previous time step. This assumption constraints the time dependency modeling capability. In this study, we propose a new variation of LSTM, advanced LSTM (A-LSTM), for better temporal context modeling. We employ A-LSTM in weighted pooling RNN for emotion recognition. The A-LSTM outperforms the conventional LSTM by 5.5% relatively. The A-LSTM based weighted pooling RNN can also complement the state-of-the-art emotion classification framework. This shows the advantage of A-LSTM.
cs.LG↗
MetaLDA: a Topic Model that Efficiently Incorporates Meta information
Besides the text content, documents and their associated words usually come with rich sets of meta informa- tion, such as categories of documents and semantic/syntactic features of words, like those encoded in word embeddings. Incorporating such meta information directly into the generative process of topic models can improve modelling accuracy and topic quality, especially in the case where the word-occurrence information in the training data is insufficient. In this paper, we present a topic model, called MetaLDA, which is able to leverage either document or word meta information, or both of them jointly. With two data argumentation techniques, we can derive an efficient Gibbs sampling algorithm, which benefits from the fully local conjugacy of the model. Moreover, the algorithm is favoured by the sparsity of the meta information. Extensive experiments on several real world datasets demonstrate that our model achieves comparable or improved performance in terms of both perplexity and topic quality, particularly in handling sparse texts. In addition, compared with other models using meta information, our model runs significantly faster.
cs.CL↗
On Harmonic $ν$-Bloch and $ν$-Bloch-type mappings
The aim of this paper is twofold. One is to introduce the class of harmonic $ν$-Bloch-type mappings as a generalization of harmonic $ν$-Bloch mappings and thereby we generalize some recent results of harmonic $1$-Bloch-type mappings investigated recently by Efraimidis et al. \cite{EGHV}. The other is to investigate some subordination principles for harmonic Bloch mappings and then establish Bohr's theorem for these mappings and in a general setting, in some cases.
math.CV↗
Harmonic pre-Schwarzian and its applications
The primary aim of this article is to extend certain inequalities concerning the pre-Schwarzian derivatives from the case of analytic univalent functions to that of univalent harmonic mappings defined on certain domains. This is done in two different ways. One of the ways is to connect with a conjecture on the univalent harmonic mappings. Also, we improve certain known results on the majorization of the Jacobian of functions in the affine and linear invariant family of sense-preserving harmonic mappings. This is achieved as an application of a corresponding distortion theorem in terms of the harmonic pre-Schwarzian derivative.
math.CV↗
Compactification of certain Kähler manifolds with nonnegative Ricci curvature
We prove compactification theorems for some complete Kähler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete noncompact Kähler Ricci flat manifold with maximal volume growth and quadratic curvature decay is a crepant resolution of a normal affine algebraic variety. Furthermore, such affine variety degenerates in two steps to the unique metric tangent cone at infinity.
math.DG↗
On Yau's uniformization conjecture
Let $M^n$ be a complete noncompact Kähler manifold with nonnegative bisectional curvature and maximal volume growth, we prove that $M$ is biholomorphic to $\mathbb{C}^n$. This confirms Yau's uniformization conjecture when M has maximal volume growth.
math.DG↗
Diameter Rigidity for Kähler manifolds with positive bisectional curvature
Let $M^n$ be a compact Kähler manifold with bisectional curvature bounded from below by $1$. If $diam(M) = π/ \sqrt{2}$ and $vol(M)> vol(\mathbb{C}\mathbb{P}^n)/ 2^n$, we prove that $M$ is biholomorphically isometric to $\mathbb{C}\mathbb{P}^n$ with the standard Fubini-Study metric.
math.DG↗
Texture Characterization by Using Shape Co-occurrence Patterns
Texture characterization is a key problem in image understanding and pattern recognition. In this paper, we present a flexible shape-based texture representation using shape co-occurrence patterns. More precisely, texture images are first represented by tree of shapes, each of which is associated with several geometrical and radiometric attributes. Then four typical kinds of shape co-occurrence patterns based on the hierarchical relationship of the shapes in the tree are learned as codewords. Three different coding methods are investigated to learn the codewords, with which, any given texture image can be encoded into a descriptive vector. In contrast with existing works, the proposed method not only inherits the strong ability to depict geometrical aspects of textures and the high robustness to variations of imaging conditions from the shape-based method, but also provides a flexible way to consider shape relationships and to compute high-order statistics on the tree. To our knowledge, this is the first time to use co-occurrence patterns of explicit shapes as a tool for texture analysis. Experiments on various texture datasets and scene datasets demonstrate the efficiency of the proposed method.
cs.CV↗
Linear measure and $K$-quasiconformal harmonic mappings
In this paper, we investigate the relationships between linear measure and harmonic mappings.
math.CV↗
Compositions of polyharmonic mappings
The paper is devoted to the study of compositions of polyharmonic mappings in simply connected domains. More precisely, we determine necessary and sufficient conditions of polyharmonic mapping $f$ such that $f\circ F$ (resp. $F\circ f$) is $l$-harmonic for any analytic function (or harmonic mapping but not analytic, or $q$-harmonic mapping but not $(q-1)$-harmonic) $F$.
math.CV↗
Taming intermittent plasticity at small scales
The extreme miniaturization in modern technology calls for deeper insights into the non-conventional, fluctuation dominated mechanics of materials at micro- to nano-scales. Both experiments and simulations show that sub-micron face-centered-cubic (FCC) crystals exhibit high yield strength, which is, however, compromised by intermittent, power law distributed strain fluctuations, typical of wild plasticity. At macro-scales, the same bulk materials show mild plasticity characterized by bounded, uncorrelated fluctuations. Both anomalous strength and intermittency appear therefore as size effects. While the former is highly desirable, the latter is detrimental because stochastic dislocation avalanches interfere with forming processes and endanger structural stability. In this paper we show that defectiveness, which is used in classical metallurgy to harden materials, can be used at sub-micron scales to suppress intermittent fluctuations. We quantify the coexistence of wild and mild fluctuations in compressed Al alloys micro-pillars, demonstrate that the statistical nature of fluctuations is determined by sample size, and propose quantitative strategies allowing one to temper plastic intermittency by artificially tailored disorder. Our experimental results are rationalized using a theoretical framework which quantifies the competition between external (size related) and internal (disorder related) length scales.
cond-mat.mtrl-sci↗