arXiv subjects

Bin Wang

Publications and source records attributed to Bin Wang.

At least 829 records · Page 46Linked to original sources

arXiv2018

Exponential collocation methods for conservative or dissipative systems

In this paper, we propose and analyse a novel class of exponential collocation methods for solving conservative or dissipative systems based on exponential integrators and collocation methods. It is shown that these novel methods can be of arbitrarily high order and exactly or nearly preserve first integrals or Lyapunov functions. We also consider order estimates of the new methods. Furthermore, we explore and discuss the application of our methods in important stiff gradient systems, and it turns out that our methods are unconditionally energy-diminishing and strongly damped even for very stiff gradient systems. Practical examples of the new methods are derived and the efficiency and superiority are confirmed and demonstrated by three numerical experiments including a nonlinear Schrödinger equation. As a byproduct of this paper, arbitrary-order trigonometric/RKN collocation methods are also presented and analysed for second-order highly oscillatory/general systems. The paper is accompanied by numerical results that demonstrate the great potential of this work.

math.NA↗

arXiv2018

A sharp threshold of propagation connectivity for mixed random hypergraphs

This paper studies the propagation connectivity of a random hypergraph $\mathbb{G}$ containing both 2-edges and 3-hyperedges. We find an exact threshold of the propagation connectivity of $\mathbb{G}$: If $I_{ε,r}<-1$, then $\mathbb{G}$ is not propagation connected with high probability; while if $I_{ε,r}>-1$, then $\mathbb{G}$ is propagation connected with high probability, where $I_{ε,r}$ is a constant dependent on the parameters of 2 and 3-edge probabilities.

math.CO↗

arXiv2018

Interacting Dark Energy: Possible Explanation for 21-cm Absorption at Cosmic Dawn

A recent observation points to an excess in the expected 21-cm brightness temperature from cosmic dawn. In this paper, we present an alternative explanation of this phenomenon, an interaction in the dark sector. Interacting dark energy models have been extensively studied recently and there is a whole variety of such in the literature. Here we particularize to a specific model in order to make explicit the effect of an interaction.

astro-ph.CO↗

arXiv2018

Proximal-Free ADMM for Decentralized Composite Optimization via Graph Simplification

We consider the problem of decentralized composite optimization over a symmetric connected graph, in which each node holds its own agent-specific private convex functions, and communications are only allowed between nodes with direct links. A variety of algorithms have been proposed to solve such a problem in an alternating direction method of multiplier (ADMM) framework. Many of these algorithms, however, need to include some proximal term in the augmented Lagrangian function such that the resulting algorithm can be implemented in a decentralized manner. The use of the proximal term slows down the convergence speed because it forces the current solution to stay close to the solution obtained in the previous iteration. To address this issue, in this paper, we first introduce the notion of simplest bipartite graph, which is defined as a bipartite graph that has a minimum number of edges to keep the graph connected. A simple two-step message passing-based procedure is proposed to find a simplest bipartite graph associated with the original graph. We show that the simplest bipartite graph has some interesting properties. By utilizing these properties, an ADMM without involving any proximal terms can be developed to perform decentralized composite optimization over the simplest bipartite graph. Simulation results show that our proposed method achieves a much faster convergence speed than existing state-of-the-art decentralized algorithms.

math.OC↗

arXiv2018

Graph-based Deep-Tree Recursive Neural Network (DTRNN) for Text Classification

A novel graph-to-tree conversion mechanism called the deep-tree generation (DTG) algorithm is first proposed to predict text data represented by graphs. The DTG method can generate a richer and more accurate representation for nodes (or vertices) in graphs. It adds flexibility in exploring the vertex neighborhood information to better reflect the second order proximity and homophily equivalence in a graph. Then, a Deep-Tree Recursive Neural Network (DTRNN) method is presented and used to classify vertices that contains text data in graphs. To demonstrate the effectiveness of the DTRNN method, we apply it to three real-world graph datasets and show that the DTRNN method outperforms several state-of-the-art benchmarking methods.

cs.CL↗

arXiv2018

Scalar field condensation behaviors around reflecting shells in Anti-de Sitter spacetimes

We study scalar condensations around asymptotically Anti-de Sitter(AdS) regular reflecting shells. We show that the charged scalar field can condense around charged reflecting shells with both Dirichlet and Neumann boundary conditions. In particular, the radii of the asymptotically AdS hairy shells are discrete, which is similar to cases in asymptotically flat spacetimes. We also provide upper bounds for the radii of the hairy Dirichlet reflecting shells and above the bound, the scalar field cannot condense around the shell.

gr-qc↗

arXiv2018

Rational curves on hypersurfaces of a projective variety

In this paper, we extend our result in [3] to hypersurfaces of any smooth projective variety $Y$. Precisely we let $X_0$ be a generic hypersurface of $Y$ and $c_0:\mathbf P^1\to X_0$ be a generic birational morphism to its image, i.e. $c_0\in Hom_{bir}(\mathbf P^1, X_0)$ is generic, such that (1) $dim(X_0)\geq 3$, (2) $H^1( N_{c_0/Y})=0$. Then \begin{equation} H^1(N_{c_0/X_0})=0. \end{equation} As an application we prove that the Clemens' conjecture holds for Calabi-Yau complete intersections of dimension 3.

math.AG↗

arXiv2018

A Hybrid Differential Evolution Approach to Designing Deep Convolutional Neural Networks for Image Classification

Convolutional Neural Networks (CNNs) have demonstrated their superiority in image classification, and evolutionary computation (EC) methods have recently been surging to automatically design the architectures of CNNs to save the tedious work of manually designing CNNs. In this paper, a new hybrid differential evolution (DE) algorithm with a newly added crossover operator is proposed to evolve the architectures of CNNs of any lengths, which is named DECNN. There are three new ideas in the proposed DECNN method. Firstly, an existing effective encoding scheme is refined to cater for variable-length CNN architectures; Secondly, the new mutation and crossover operators are developed for variable-length DE to optimise the hyperparameters of CNNs; Finally, the new second crossover is introduced to evolve the depth of the CNN architectures. The proposed algorithm is tested on six widely-used benchmark datasets and the results are compared to 12 state-of-the-art methods, which shows the proposed method is vigorously competitive to the state-of-the-art algorithms. Furthermore, the proposed method is also compared with a method using particle swarm optimisation with a similar encoding strategy named IPPSO, and the proposed DECNN outperforms IPPSO in terms of the accuracy.

cs.NE↗

arXiv2018

Neural Material: Learning Elastic Constitutive Material and Damping Models from Sparse Data

The accuracy and fidelity of deformation simulations are highly dependent upon the underlying constitutive material model. Commonly used linear or nonlinear constitutive material models only cover a tiny part of possible material behavior. In this work we propose a unified framework for modeling deformable material. The key idea is to use a neural network to correct a nominal model of the elastic and damping properties of the object. The neural network encapsulates a complex function that is hard to explicitly model. It injects force corrections that help the forward simulation to more accurately predict the true behavior of a given soft object, which includes non-linear elastic forces and damping. Attempting to satisfy the requirement from real material interference and animation design scenarios, we learn material models from examples of dynamic behavior of a deformable object's surface. The challenge is that such data is sparse as it is consistently given only on part of the surface. Sparse reduced space-time optimization is employed to gradually generate increasingly accurate training data, which further refines and enhances the neural network. We evaluate our choice of network architecture and show evidence that the modest amount of training data we use is suitable for the problem tackled. Our method is demonstrated with a set of synthetic examples.

cs.GR↗

arXiv2018

Exponential collocation methods for the cubic Schrödinger equation

In this paper we derive and analyse new exponential collocation methods to efficiently solve the cubic Schrödinger Cauchy problem on a $d$-dimensional torus. Energy preservation is a key feature of the cubic Schrödinger equation. It is proved that the novel methods can be of arbitrarily high order which exactly or nearly preserve the continuous energy of the original continuous system. The existence and uniqueness, regularity, global convergence, nonlinear stability of the new methods are studied in detail. Two practical exponential collocation methods are constructed and two numerical experiments are included. The numerical results illustrate the efficiency of the new methods in comparison with existing numerical methods in the literature.

math.NA↗

arXiv2018

Long-time momentum and actions behaviour of energy-preserving methods for semilinear wave equations via spatial spectral semi-discretizations

As is known that wave equations have physically very important properties which should be respected by numerical schemes in order to predict correctly the solution over a long time period. In this paper, the long-time behaviour of momentum and actions for energy-preserving methods is analysed for semilinear wave equations. A full discretisation of wave equations is derived and analysed by firstly using a spectral semi-discretisation in space and then by applying the adopted average vector field (AAVF) method in time. This numerical scheme can exactly preserve the energy of the semi-discrete system. The main theme of this paper is to analyse another important physical property of the scheme. It is shown that this scheme yields near conservation of a modified momentum and modified actions over long times. Both the results are rigorously proved based on the technique of modulated Fourier expansions in two stages. First a multi-frequency modulated Fourier expansion of the AAVF method is constructed and then two almost-invariants of the modulation system are derived.

math.NA↗

arXiv2018

Improved training of neural trans-dimensional random field language models with dynamic noise-contrastive estimation

A new whole-sentence language model - neural trans-dimensional random field language model (neural TRF LM), where sentences are modeled as a collection of random fields, and the potential function is defined by a neural network, has been introduced and successfully trained by noise-contrastive estimation (NCE). In this paper, we extend NCE and propose dynamic noise-contrastive estimation (DNCE) to solve the two problems observed in NCE training. First, a dynamic noise distribution is introduced and trained simultaneously to converge to the data distribution. This helps to significantly cut down the noise sample number used in NCE and reduce the training cost. Second, DNCE discriminates between sentences generated from the noise distribution and sentences generated from the interpolation of the data distribution and the noise distribution. This alleviates the overfitting problem caused by the sparseness of the training set. With DNCE, we can successfully and efficiently train neural TRF LMs on large corpus (about 0.8 billion words) with large vocabulary (about 568 K words). Neural TRF LMs perform as good as LSTM LMs with less parameters and being 5x~114x faster in rescoring sentences. Interpolating neural TRF LMs with LSTM LMs and n-gram LMs can further reduce the error rates.

cs.CL↗

arXiv2018

Long-time oscillatory energy conservation of total energy-preserving methods for highly oscillatory Hamiltonian systems

For an integrator when applied to a highly oscillatory system, the near conservation of the oscillatory energy over long times is an important aspect. In this paper, we study the long-time near conservation of oscillatory energy for the adopted average vector field (AAVF) method when applied to highly oscillatory Hamiltonian systems. This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly. This paper is devoted to analysinganother important property of AAVF method, i.e., the near conservation of its oscillatory energy in a long term. The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion. A similar result of the method in the multi-frequency case is also presented in this paper.

math.NA↗

arXiv2018

A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems

The primary objective of this paper is to present a long-term numerical energy-preserving analysis of one-stage explicit symmetric and/or symplectic extended Runge--Kutta--Nyström (ERKN) integrators for highly oscillatory Hamiltonian systems. We study the long-time numerical energy conservation not only for symmetric integrators but also for symplectic integrators. In the analysis, we neither assume symplecticity for symmetric methods, nor assume symmetry for symplectic methods. It turns out that these both kinds of ERKN integrators have a near conservation of the total and oscillatory energy over a long term. To prove the result for symmetric integrators, a relationship between symmetric ERKN integrators and trigonometric integrators is established by using Strang splitting and based on this connection, the long-time conservation is derived. For the long-term analysis of symplectic ERKN integrators, the above approach does not work anymore and we use the technology of modulated Fourier expansion developed in SIAM J. Numer. Anal. 38 (2000) by Hairer and Lubich. By taking some novel adaptations of this essential technology for non-symmetric methods, we derive the modulated Fourier expansion for symplectic ERKN integrators. Moreover, it is shown that the symplectic ERKN integrators have two almost-invariants and then the near energy conservation over a long term is obtained.

math.NA↗

arXiv2018

Stephani Cosmology: Entropically Viable But Observationally Challenged

Inhomogeneous cosmological models such as the Stephani universes could, in principle, provide an explanation for the observed accelerated expansion of the Universe. Working with a concrete, popular model of the Stephani cosmology -- the Stephani-Dabrowski model, we found that it is entropically viable. We also comment on the energy conditions and the two-sheeted geometry of the spacetime. However, similar to the LTB models, despite satisfying the holographic principle, Stephani cosmology has difficulty satisfying all the constraints from observations.

gr-qc↗

arXiv2018

Volume-preserving exponential integrators

As is known that various dynamical systems including all Hamiltonian systems preserve volume in phase space. This qualitative geometrical property of the analytical solution should be respected in the sense of Geometric Integration. This paper analyses the volume-preserving property of exponential integrators in different vector fields. We derive a necessary and sufficient condition of volume preservation for exponential integrators, and with this condition, volume-preserving exponential integrators are analysed in detail for four kinds of vector fields. It turns out that symplectic exponential integrators can be volume preserving for a much larger class of vector fields than Hamiltonian systems. On the basis of the analysis, novel volume-preserving exponential integrators are derived for solving highly oscillatory second-order systems and extended Runge--Kutta--Nyström (ERKN) integrators of volume preservation are presented for separable partitioned systems. Moreover, the volume preservation of Runge--Kutta--Nyström (RKN) methods is also discussed. Four illustrative numerical experiments are carried out to demonstrate the notable superiority of volume-preserving exponential integrators in comparison with volume-preserving Runge-Kutta methods.

math.NA↗

arXiv2018

Collective diffusion and quantum chaos in holography

We define a particular combination of charge and heat currents that is decoupled with the heat current. This `heat-decoupled' (HD) current can be transported by diffusion at long distances, when some thermo-electric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z=2. In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.

hep-th↗

arXiv2018

Improving Knowledge Graph Embedding Using Simple Constraints

Embedding knowledge graphs (KGs) into continuous vector spaces is a focus of current research. Early works performed this task via simple models developed over KG triples. Recent attempts focused on either designing more complicated triple scoring models, or incorporating extra information beyond triples. This paper, by contrast, investigates the potential of using very simple constraints to improve KG embedding. We examine non-negativity constraints on entity representations and approximate entailment constraints on relation representations. The former help to learn compact and interpretable representations for entities. The latter further encode regularities of logical entailment between relations into their distributed representations. These constraints impose prior beliefs upon the structure of the embedding space, without negative impacts on efficiency or scalability. Evaluation on WordNet, Freebase, and DBpedia shows that our approach is simple yet surprisingly effective, significantly and consistently outperforming competitive baselines. The constraints imposed indeed improve model interpretability, leading to a substantially increased structuring of the embedding space. Code and data are available at https://github.com/iieir-km/ComplEx-NNE_AER.

cs.AI↗