Topic
Continuous embedding
About: Continuous embedding is a research topic. Over the lifetime, 56 publications have been published within this topic receiving 1877 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1977
TL;DR: In this article, a Harmonic Analysis of Almost Periodic Locally Compact Groups is presented, where the authors show that almost periodic locally compact groups can be represented by almost positive functions.
Abstract: Preliminaries. Almost Periodic Locally Compact Groups.- References and Comments.- I. Harmonic Analysis of Almost Periodic Locally Compact Groups.- 1.1 Measures on a Locally Compact Space.- 1.2 Convolution of Measures on a Locally Compact Group.- 1.3 Fourier Transforms of Bounded Measures.- 1.4 The Theorems of Levy and Bochner.- 1.5 Convolution Semigroups and Negative-Definite Forms.- References and Comments.- II. Convergence of Convolution Sequences of Probability Measures.- 2.1 Convolution Powers on a Compact Group.- 2.2 Equivalence of Types of Convergence.- 2.3 The Normed Convergence Property.- 2.4 Convergence in Variance.- 2.5 Asymptotic Equidistribution.- 2.6 Shifting Iterated Convolutions.- References and Comments.- III. Embedding of Infinitely Divisible Probability Measures.- 3.1 Root Compact Groups.- 3.2 Poisson Measures and Their Characterizations.- 3.3 Submonogeneous Embedding of Infinitely Divisible Measures.- 3.4 Existence of One-Parameter Semigroups.- 3.5 The General Continuous Embedding.- 3.6 Injective Submonogeneous Embeddings.- References and Comments.- IV. Canonical Representations of Convolution Semigroups.- 4.1 Positive Semigroups and Their Generating Functionals.- 4.2 Hunt's Representation Theorem.- 4.3 The Levy-Khintchine Formula for Almost Periodic Groups.- 4.4 The Canonical Representation of Almost Positive Functionals.- 4.5 The Levy-Khintchine Formula for General Locally Compact Groups.- 4.6 Convolution Hemigroups. Generation and Representation.- References and Comments.- V. The Central Limit Problem in the Abelian Case.- 5.1 Convergence of Infinitesimal Systems.- 5.2 Gauss Measures in the Sense of Parthasarathy.- 5.3 Gauss Measures in the Sense of Bernstein.- 5.4 Convergence to Gauss Measures.- 5.5 Symmetric Gauss Semigroups.- 5.6 Additive Processes and Their Decomposition.- References and Comments.- VI. The Central Limit Problem in the General Case.- 6.1 Poisson Embedding and Approximation.- 6.2 Gauss Measures and Their Characterizations.- 6.3 Absolute Continuity and Diffusion of Gauss Semigroups.- 6.4 Central Gauss Semigroups.- 6.5 Convergence of Triangular Systems of Probability Measures.- 6.6 Central Limit Theorems for Totally Disconnected Groups.- References and Comments.- List of Symbols.
640 citations
TL;DR: In this article, a Sobolev-type embedding theorem for generalized Lebesgue-Sobolev space Wk, p(x)(Ω), where Ω is an open domain in RN(N ≥ 2) with cone property, was given.
627 citations
1 Aug 2016
TL;DR: This article proposed a generative topic embedding model to combine word embedding and topic modeling, where topics are represented by embedding vectors and are shared across documents, and the probability of each word is influenced by both its local context and its topic.
Abstract: Word embedding maps words into a lowdimensional continuous embedding space by exploiting the local word collocation patterns in a small context window. On the other hand, topic modeling maps documents onto a low-dimensional topic space, by utilizing the global word collocation patterns in the same document. These two types of patterns are complementary. In this paper, we propose a generative topic embedding model to combine the two types of patterns. In our model, topics are represented by embedding vectors, and are shared across documents. The probability of each word is influenced by both its local context and its topic. A variational inference method yields the topic embeddings as well as the topic mixing proportions for each document. Jointly they represent the document in a low-dimensional continuous space. In two document classification tasks, our method performs better than eight existing methods, with fewer features. In addition, we illustrate with an example that our method can generate coherent topics even based on only one document.
116 citations
Posted Content•
TL;DR: In this paper, several discrete Gagliardo-Nirenberg-Sobolev and Poincar\'e-Solicolev inequalities were proved for some approximations with arbitrary boundary values on finite volume meshes.
Abstract: We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincar\'e-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint of our approach is to use the continuous embedding of the space $BV(\Omega)$ into $L^{N/(N-1)}(\Omega)$ for a Lipschitz domain $ \Omega \subset \mathbb{R}^{N}$, with $N \geq 2$. Finally, we give several applications to discrete duality finite volume (DDFV) schemes which are used for the approximation of nonlinear and non isotropic elliptic and parabolic problems.
82 citations
TL;DR: In this paper, the authors construct a regular and a strongly regular Dirichlet space which are equivalent to a given Diriclet space in the sense that their associated function algebras are isomorphic and isometric.
Abstract: We construct a regular and a strongly regular Dirichlet space which are equivalent to a given Dirichlet space in the sense that their associated function algebras are isomorphic and isometric. There is an appropriate strong Markov process called a Ray process on the underlying space of each strongly regular Dirichlet space.
68 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 6 |
| 2019 | 1 |
| 2018 | 2 |
| 2017 | 6 |
| 2016 | 4 |