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Wenbin Liu

Publications and source records attributed to Wenbin Liu.

27 records · Page 2Linked to original sources

Cell Selection with Deep Reinforcement Learning in Sparse Mobile Crowdsensing

Sparse Mobile CrowdSensing (MCS) is a novel MCS paradigm where data inference is incorporated into the MCS process for reducing sensing costs while its quality is guaranteed. Since the sensed data from different cells (sub-areas) of the target sensing area will probably lead to diverse levels of inference data quality, cell selection (i.e., choose which cells of the target area to collect sensed data from participants) is a critical issue that will impact the total amount of data that requires to be collected (i.e., data collection costs) for ensuring a certain level of quality. To address this issue, this paper proposes a Deep Reinforcement learning based Cell selection mechanism for Sparse MCS, called DR-Cell. First, we properly model the key concepts in reinforcement learning including state, action, and reward, and then propose to use a deep recurrent Q-network for learning the Q-function that can help decide which cell is a better choice under a certain state during cell selection. Furthermore, we leverage the transfer learning techniques to reduce the amount of data required for training the Q-function if there are multiple correlated MCS tasks that need to be conducted in the same target area. Experiments on various real-life sensing datasets verify the effectiveness of DR-Cell over the state-of-the-art cell selection mechanisms in Sparse MCS by reducing up to 15% of sensed cells with the same data inference quality guarantee.

cs.AI↗

Fractional Kirchhoff equation with a general critical nonlinearity

In this paper, we study the fractional Kirchhoff equation with critical nonlinearity \begin{align*} \left(a+b\int_{\mathbb R^N}|(-Δ)^{\frac{s}{2}}u|^2dx\right)(-Δ)^su+u=f(u)\ \ \mbox{in}\ \ \mathbb R^N, \end{align*} where $N>2s$ and $(-Δ)^s$ is the fractional Laplacian with $0<s<1$. By using a perturbation approach, we prove the existence of solutions to the above problem without the Ambrosetti-Rabinowitz condition when the parameter $b$ small. What's more, we obtain the asymptotic behavior of solutions as $b\to 0$.

math.AP↗

Singularly perturbed fractional Schrödinger equation involving a general critical nonlinearity

In this paper, we are concerned with the existence and concentration phenomena of solutions for the following singularly perturbed fractional Schrödinger problem \begin{align*} \varepsilon^{2s}(-Δ)^su+V(x)u=f(u) \ \ \ \mbox{in} \ \ \ \mathbb{R}^N, \end{align*} where $N>2s$ and the nonlinearity $f$ has critical growth. By using the variational approach, we construct a localized bound-state solution concentrating around an isolated component of the positive minimum point of $V$ as $\varepsilon\rightarrow 0$. Our result improves the study made in X. He and W. Zou ({\it Calc. Var. Partial Differential Equations}. 55-91(2016)), in the sense that, in the present paper, the {\it Ambrosetti-Rabinowitz} condition and {\it monotonicity} condition on $f(t)/t$ are not required.

math.AP↗

Ground states of nonlinear fractional Schrödinger equation involving critical growth

In this paper, we are concerned with the ground state solutions of nonlinear fractional Schrödinger equation involving critical growth. Without Ambrosetti-Rabinowitz condition and monotonicity condition on the nonlinearity, we get the existence of ground state solutions of such equation when the potential $V(x)$ is not a constant and not radial.

math.AP↗

Fractional Sobolev Space and Spectral Structure of Fractional Dirichlet Boundary Value Problem

Based on the need of studying the fractional boundary value problems by using variational methods, in this paper, we introduce a fundamental theory framework of fractional Sobolev space in one dimension, study the regularity of weak solutions for a fractional boundary value problem with variational structure, give out the spectral structure of operator ${_t}D_T^α{_0}D_t^α$ with Dirichlet boundary value conditions. Especially, when $α=1$, the operator ${_t}D_T^α{_0}D_t^α=-D^2$. So, the results of this paper are the generalization of corresponding conclusions for integer differential operator to some extent.

math.SP↗

On the Estimation of Directional Returns to Scale via DEA models

Data envelopment analysis (DEA) is one of the most commonly used methods to estimate the returns to scale (RTS) of the public sector (e.g., research institutions). Existing studies are all based on the traditional definition of RTS in economics and assume that multiple inputs and outputs change in the same proportion, which is the starting point to determine the qualitative and quantitative features of RTS of decision making units (DMUs). However, for more complex products, such as the scientific research in institutes, changes of various types of inputs or outputs are often not in proportion. Therefore, the existing definition of RTS in the framework of DEA method may not meet the need to estimate the RTS of research institutions with multiple inputs and outputs. This paper proposes a definition of directional RTS in the DEA framework and estimates the directional RTS of research institutions using DEA models. Further in-depth analysis is conducted for an illustrative example of 16 basic research institutes in Chinese Academy of Sciences (CAS) in 2010.

math.OC↗