arXiv subjects

Haibo Chen

Publications and source records attributed to Haibo Chen.

At least 127 records · Page 7Linked to original sources

arXiv2020

Semiclassical solutions for critical Schrödinger-Poisson systems involving multiple competing potentials

In this paper, a class of Schrödinger-Poisson system involving multiple competing potentials and critical Sobolev exponent is considered. Such a problem cannot be studied with the same argument of the nonlinear term with only a positive potential, because the weight potentials set $\{Q_i(x)|1\le i \le m\}$ contains nonpositive, sign-changing, and nonnegative elements. By introducing the ground energy function and subtle analysis, we first prove the existence of ground state solution $v_\varepsilon$ in the semiclassical limit via the Nehari manifold and concentration-compactness principle. Then we show that $v_\varepsilon$ converges to the ground state solution of the associated limiting problem and concentrates at a concrete set characterized by the potentials. At the same time, some properties for the ground state solution are also studied. Moreover, a sufficient condition for the nonexistence of the ground state solution is obtained.

math.AP↗

arXiv2020

Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(α,β,p)$

In this paper, we introduce a class of infinite Lie conformal algebras $\mathfrak{B}(α,β,p)$, which are the semi-direct sums of Block type Lie conformal algebra $\mathfrak{B}(p)$ and its non-trivial conformal modules of $\Z$-graded free intermediate series. The annihilation algebras are a class of infinite-dimensional Lie algebras, which include a lot of interesting subalgebras: Virasoro algebra, Block type Lie algebra, twisted Heisenberg-Virasoro algebra and so on. We give a complete classification of all finite non-trivial irreducible conformal modules of $\mathfrak{B}(α,β,p)$ for $α,β\in\C, p\in\C^*$. As an application, the classifications of finite irreducible conformal modules over a series of finite Lie conformal algebras $\mathfrak{b}(n)$ for $n\geq1$ are given.

math.RT↗

arXiv2020

A Survey on Adaptive Random Testing

Random testing (RT) is a well-studied testing method that has been widely applied to the testing of many applications, including embedded software systems, SQL database systems, and Android applications. Adaptive random testing (ART) aims to enhance RT's failure-detection ability by more evenly spreading the test cases over the input domain. Since its introduction in 2001, there have been many contributions to the development of ART, including various approaches, implementations, assessment and evaluation methods, and applications. This paper provides a comprehensive survey on ART, classifying techniques, summarizing application areas, and analyzing experimental evaluations. This paper also addresses some misconceptions about ART, and identifies open research challenges to be further investigated in the future work.

cs.SE↗

arXiv2020

Diversified Arbitrary Style Transfer via Deep Feature Perturbation

Image style transfer is an underdetermined problem, where a large number of solutions can satisfy the same constraint (the content and style). Although there have been some efforts to improve the diversity of style transfer by introducing an alternative diversity loss, they have restricted generalization, limited diversity and poor scalability. In this paper, we tackle these limitations and propose a simple yet effective method for diversified arbitrary style transfer. The key idea of our method is an operation called deep feature perturbation (DFP), which uses an orthogonal random noise matrix to perturb the deep image feature maps while keeping the original style information unchanged. Our DFP operation can be easily integrated into many existing WCT (whitening and coloring transform)-based methods, and empower them to generate diverse results for arbitrary styles. Experimental results demonstrate that this learning-free and universal method can greatly increase the diversity while maintaining the quality of stylization.

cs.CV↗

arXiv2019

Deep Learning Decoding of Mental State in Non-invasive Brain Computer Interface

Brain computer interface (BCI) has been popular as a key approach to monitor our brains recent year. Mental states monitoring is one of the most important BCI applications and becomes increasingly accessible. However, the mental state prediction accuracy and generality through encephalogram (EEG) are not good enough for everyday use. Here in this paper we present a deep learning-based EEG decoding method to read mental states. We propose a novel 1D convolutional neural network with different filter lengths to capture different frequency bands information. To improve the prediction accuracy, we also used a resnet-like structure to train a relatively deep convolutional neural network to promote feature extraction. Compared with traditional ways of predictions such as KNN and SVM, we achieved a significantly better result with an accuracy of 96.40%. Also, in contrast with some already published open source deep neural network structures, our methods achieved the state of art prediction accuracy on a mental state recognition dataset. Our results demonstrate using only 1D convolution could extract the features of EEG and the possibility of mental state prediction using portable EEG devices.

eess.SP↗

arXiv2019

On a class of infinite simple Lie conformal algebras

In this paper, we study a class of infinite simple Lie conformal algebras associated to a class of generalized Block type Lie algebras. The central extensions, conformal derivations and free intermediate series modules of this class of Lie conformal algebras are determined. Moreover, we also show that these Lie conformal algebras do not have any non-trivial finite conformal modules. Consequently, these Lie conformal algebras cannot be embedded into $gc_N$ for any positive integer $N$.

math.RT↗

arXiv2019

Existence and multiplicity of positive solutions for fractional Laplacian systems with nonlinear coupling

It is well known that a single nonlinear fractional Schrödinger equation with a potential $V(x)$ and a small parameter $\varepsilon $ may have a positive solution that is concentrated at the nondegenerate minimum point of $V(x)$. In this paper, we can find two different positive solutions for two weakly coupled fractional Schrödinger systems with a small parameter $\varepsilon $ and two potentials $V_{1}(x)$ and $V_{2}(x)$ having the same minimum point are concentrated at the same point minimum point of $V_{1}(x)$ and $V_{2}\left(x\right) $. In fact that by using the energy estimates, Nehari manifold technique and the Lusternik-Schnirelmann theory of critical points, we obtain the multiplicity results for a class of fractional Laplacian system. Furthermore, the existence and nonexistence of least energy positive solutions are also explored.

math.AP↗

arXiv2019

On the parallels between Paxos and Raft, and how to port optimizations

In recent years, Raft has overtaken Paxos as the consensus algorithm of choice. [53] While many have pointed out similarities between the two protocols, no one has formally mapped out their relationships. In this paper, we show how Raft and Paxos are formally related despite their surface differences. Based on the formal mapping between the two protocols, we show how to automatically port a certain class of optimizations from Paxos to Raft with guaranteed correctness. As case studies, we port and evaluate two optimizations, Mencius and Paxos Quorum Lease to Raft.

cs.DC↗

arXiv2019

Irreducible twisted Heisenberg-Virasoro modules from tensor products

In this paper, we realize polynomial $\H$-modules $Ω(λ,α,β)$ from irreducible twisted Heisenberg-Virasoro modules $\A_{α,β}$. It follows from $\H$-modules $Ω(λ,α,β)$ and $\mathrm{Ind}(M)$ that we obtain a class of natural non-weight tensor product modules $\big(\bigotimes_{i=1}^mΩ(λ_i,α_i,β_i)\big)\otimes \mathrm{Ind}(M)$. Then we give the necessary and sufficient conditions under which these modules are irreducible and isomorphic, and also give that the irreducible modules in this class are new.

math.RT↗

arXiv2019

Learned Indexes for Dynamic Workloads

The recent proposal of learned index structures opens up a new perspective on how traditional range indexes can be optimized. However, the current learned indexes assume the data distribution is relatively static and the access pattern is uniform, while real-world scenarios consist of skew query distribution and evolving data. In this paper, we demonstrate that the missing consideration of access patterns and dynamic data distribution notably hinders the applicability of learned indexes. To this end, we propose solutions for learned indexes for dynamic workloads (called Doraemon). To improve the latency for skew queries, Doraemon augments the training data with access frequencies. To address the slow model re-training when data distribution shifts, Doraemon caches the previously-trained models and incrementally fine-tunes them for similar access patterns and data distribution. Our preliminary result shows that, Doraemon improves the query latency by 45.1% and reduces the model re-training time to 1/20.

cs.LG↗

arXiv2019

Taming Distrust in the Decentralized Internet with PIXIU

Decentralized Internet is booming. People are fascinated by its promise that users can truly own their data. However, in a decentralized Internet, completing a task usually involves multiple nodes with mutual distrust. Such distrust might eventually become a major obstacle for the growth of the decentralized Internet. In this paper, we analyze the distrust using a simple model and highlight the properties required to faithfully accomplish one task in a decentralized Internet. We also introduce our draft solution -- PIXIU, a framework to mitigate the distrust among different nodes. In PIXIU, we design and utilize trust-λ and decentralized executor to achieve the above-needed properties.

cs.CR↗

arXiv2018

Hausdorff dimensions of level sets related to moving digit means

In this paper, we will introduce and study the lower moving digit mean $\underline{M}(x)$ and the upper moving digit mean $\overline{M}(x)$ of $x\in[0,1]$ in $p$-adic expansion, where $p\geq2$ is an integer. Moreover, the Hausdorff dimension of level set \[B(α,β)=\left\{x\in [0,1]\colon \underline{M}(x)=α,\overline{M}(x)=β\right\}\] is determined for each pair of numbers $α$ and $β$ satisfying with $0\leqα\leqβ\leq p-1$.

math.NT↗

arXiv2018

Hausdorff dimensions of sets related to Erdös-Rényi averages in beta expansions

Let $β>1$, $I$ be the unite interval $[0,1)$ and $ϕ$ be an integer function defined on $\mathbb{N}\setminus\{0\}$ satisfying $1\leqϕ(n)\leq n$. Denote by $A_ϕ(x,β)$ the Erdös-Rényi average of $x\in I$ associated with the function $ϕ$ in $β$-expansion and $I_β$ the range of $A_ϕ(x,β)$ for $x\in I$. For the level set \begin{align*} ER_ϕ^β(α)=\left\{x\in I\colon A_ϕ(x,β)=α\right\},\quad\text{where}\ α\in I_β, \end{align*} in this paper we will determine its Hausdorff dimension under the assumption $ϕ(n)\to\infty$ as $n\to\infty$ and $ϕ$ is the integer part of some slowly varying sequence. Besides, a generalization to the classic work \cite{Be} of Besicovitch is also given in $β$-expansion.

math.NT↗

arXiv2018

The multifractal spectra of planar waiting sets in beta expansions

Let $β>1$ be a real number. In this paper, the Hausdorff dimension of sets consisting of pairs of numbers with prescribed quantitative waiting time indicators in $β$-expansions are determined. More precisely, let $I$ be the unit interval $[0,1)$ and write $\underline{R}^β(x,y)$ and $\overline{R}^β(x,y)$ as the lower and upper quantitative waiting time indicators of $y$ by $x$ in $β$-expansions, respectively. Define the waiting set on the plane by \[E_β(a,b)=\left\{(x,y)\in I^2\colon\underline{R}^β(x,y)=a,\overline{R}^β(x,y)=b\right\}.\] where $0\leq a\leq b\leq\infty$, then the set $E_β(a,b)$ is always of Hausdorff dimension two for any pair of numbers $a$ and $b$. In addition, some generalizations for this result are also given in the last section.

math.DS↗

arXiv2018

Elliptic problem involving finite many critical exponents in $\mathbb{R}^{N}$

In this paper, we consider the following problem $$ -Δu -ζ\frac{u}{|x|^{2}} = \sum_{i=1}^{k} \left( \int_{\mathbb{R}^{N}} \frac{|u|^{2^{*}_{α_{i}}}}{|x-y|^{α_{i}}} \mathrm{d}y \right) |u|^{2^{*}_{α_{i}}-2}u + |u|^{2^{*}-2}u , \mathrm{~in~} \mathbb{R}^{N}, $$ where $N\geqslant3$, $ζ\in(0,\frac{(N-2)^{2}}{4})$, $2^{*}=\frac{2N}{N-2}$ is the critical Sobolev exponent, and $2^{*}_{α_{i}}=\frac{2N-α_{i}}{N-2}$ ($i=1,\ldots,k$) are the critical Hardy--Littlewood--Sobolev upper exponents. The parameters $α_{i}$ ($i=1,\ldots,k$) satisfy some suitable assumptions. By using Coulomb--Sobolev space, endpoint refined Sobolev inequality and variational methods, we establish the existence of nontrivial solutions. Our result generalizes the result obtained by Yang and Wu [Adv. Nonlinear Stud. (2017)].

math.AP↗

arXiv2018

The minimizing problem involving p--Laplacian and Hardy--Littlewood--Sobolev upper critical exponent

In this paper, we study the minimizing problem: $$ S_{p,1,α,μ}:= \inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}} \frac{ \int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x - μ\int_{\mathbb{R}^{N}} \frac{|u|^{p}}{|x|^{p}} \mathrm{d}x} {\left( \int_{\mathbb{R}^{N}} \int_{\mathbb{R}^{N}} \frac{|u(x)|^{p^{*}_α}|u(y)|^{p^{*}_α}}{|x-y|^α} \mathrm{d}x \mathrm{d}y \right)^{\frac{p}{2\cdot p^{*}_α}}}, $$ where $N\geqslant3$, $p\in(1,N)$, $μ\in \left[ 0, \left( \frac{N-p}{p} \right)^{p} \right)$, $α\in(0,N)$ and $p^{*}_α= \frac{p}{2}\left(\frac{2N-α}{N-p}\right)$ is the Hardy--Littlewood--Sobolev upper critical exponent. Firstly, by using refinement of Hardy-Littlewood-Sobolev inequality, we prove that $S_{p,1,α,μ}$ is achieved in $\mathbb{R}^{N}$ by a radially symmetric, nonincreasing and nonnegative function. Secondly, we give a estimation of extremal function.

math.AP↗

arXiv2018

Fractional Elliptic problem with Finite many critical Hardy--Sobolev Exponents

In this paper, we consider the following problem: $$ (-Δ)^{s} u -\frac{ζu}{|x|^{2s}} = \sum_{i=1}^{k} \frac{|u|^{2^{*}_{s,θ_{i}}-2}u} {|x|^{θ_{i}}} , \mathrm{~in~} \mathbb{R}^{N}, $$ where $N\geqslant3$, $s\in(0,1)$, $ζ\in \left[ 0,4^{s}\frac{Γ(\frac{N+2s}{4})}{Γ(\frac{N-2s}{4})} \right)$, $2^{*}_{s,θ_{i}}=\frac{2(N-θ_{i})}{N-2s}$ are the critical Hardy--Sobolev exponents, the parameters $θ_{i}$ satisfy a suitable assumption. By using Morrey space, refinement of Hardy--Sobolev inequality and variational method, we establish the existence of nonnegative solution. Our result generalizes the result obtained by Chen [Electronic J. Differ. Eq. (2018) 1--12].

math.AP↗

arXiv2018

An Attempt at Analyzing the Information Nature of Money

Money was invented to address the difficulty in the double coincidence of wants between the supply and demand when people exchanged their goods and services. There are two information states in society: one is the initial state that people have goods and services due to division of labor; the other is the final state that people have different goods and services with the initial state due to exchange of goods and services between them. The process is that the initial state is changed to the final state with the help of money. Because the direct exchanges of goods and services are difficult to achieve the double coincidence of wants in time and space, it can be achieved with the help of money which is as a medium and bridge. In this paper the changing process of the state information is analyzed through the matrix representation of money, and then the nature of money with a kind of information of reliable ledger is more apparently shown. This paper also analyzes the common characteristics of physical money, electronic money and digital currency, that is, reliable ledger and explores the future trend of money development from the perspective of history and security technology of money.

q-fin.GN↗