Cluster algebra structure on the finite dimensional representations of Uq(A3^)U_q(\widehat{A_{3}}) for ll=2

In this paper, we prove one case of the conjecture given by Hernandez and Leclerc\cite{HL0}. Specifically, we give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of a simply-laced quantum affine algebra U_q(\widehat{\g}). In the procedure, we also give a specific description of compatible subsets of type $E_{6}$. As a conclusion, for every exchange relation of cluster algebra there exists a exact sequence of the full subcategory corresponding to it.Comment: 58 pages, 2 figures. Correct some typoes and add a new example. arXiv admin note: text overlap with arXiv:0903.1452 by other author

A New Condition for Blow-up Solutions to Discrete Semilinear Heat Equations on Networks

The purpose of this paper is to introduce a new condition $$\hbox{(C)$\hspace{1cm} \alpha \int_{0}^{u}f(s)ds \leq uf(u)+\beta u^{2}+\gamma,\,\,u>0$}$$ for some $\alpha, \beta, \gamma>0$ with $0<\beta\leq\frac{\left(\alpha-2\right)\lambda_{0}}{2}$, where $\lambda_{0}$ is the first eigenvalue of discrete Laplacian $\Delta_{\omega}$, with which we obtain blow-up solutions to discrete semilinear heat equations \begin{equation*} \begin{cases} u_{t}\left(x,t\right)=\Delta_{\omega}u\left(x,t\right)+f(u(x,t)), & \left(x,t\right)\in S\times\left(0,+\infty\right),\\ u\left(x,t\right)=0, & \left(x,t\right)\in\partial S\times\left[0,+\infty\right),\\ u\left(x,0\right)=u_{0}\geq0(nontrivial), & x\in\overline{S} \end{cases} \end{equation*} on a discrete network $S$. In fact, it will be seen that the condition (C) improves the conditions known so far.Comment: 19 page

Wearable Affective Robot

With the development of the artificial intelligence (AI), the AI applications have influenced and changed people's daily life greatly. Here, a wearable affective robot that integrates the affective robot, social robot, brain wearable, and wearable 2.0 is proposed for the first time. The proposed wearable affective robot is intended for a wide population, and we believe that it can improve the human health on the spirit level, meeting the fashion requirements at the same time. In this paper, the architecture and design of an innovative wearable affective robot, which is dubbed as Fitbot, are introduced in terms of hardware and algorithm's perspectives. In addition, the important functional component of the robot-brain wearable device is introduced from the aspect of the hardware design, EEG data acquisition and analysis, user behavior perception, and algorithm deployment, etc. Then, the EEG based cognition of user's behavior is realized. Through the continuous acquisition of the in-depth, in-breadth data, the Fitbot we present can gradually enrich user's life modeling and enable the wearable robot to recognize user's intention and further understand the behavioral motivation behind the user's emotion. The learning algorithm for the life modeling embedded in Fitbot can achieve better user's experience of affective social interaction. Finally, the application service scenarios and some challenging issues of a wearable affective robot are discussed

Non-Markovian entanglement dynamics of noisy continuous variable quantum channels

We investigate the entanglement dynamics of continuous-variable quantum channels in terms of an entangled squeezed state of two cavity fields in a general non-Markovian environment. Using the Feynman-Vernon influence functional theory in the coherent-state representation, we derive an exact master equation with time-dependent coefficients reflecting the non-Markovian influence of the environment. The influence of environments with different spectral densities, e.g., Ohmic, sub-Ohmic, and super-Ohmic, is numerically studied. The non-Markovian process shows its remarkable influences on the entanglement dynamics due to the sensitive time-dependence of the dissipation and noise functions within the typical time scale of the environment. The Ohmic environment shows a weak dissipation-noise effect on the entanglement dynamics, while the sub-Ohmic and super-Ohmic environments induce much more severe noise. In particular, the memory of the system interacting with the environment contributes a strong decoherence effect to the entanglement dynamics in the super-Ohmic case.Comment: The final versio

QANUS: An Open-source Question-Answering Platform

In this paper, we motivate the need for a publicly available, generic software framework for question-answering (QA) systems. We present an open-source QA framework QANUS which researchers can leverage on to build new QA systems easily and rapidly. The framework implements much of the code that will otherwise have been repeated across different QA systems. To demonstrate the utility and practicality of the framework, we further present a fully functioning factoid QA system QA-SYS built on top of QANUS.Comment: 6 pages, 3 figures, demo paper describing QANU

A New Condition for the Concavity Method of Blow-up Solutions to p-Laplacian Parabolic Equations

In this paper, we consider an initial-boundary value problem of the p-Laplacian parabolic equations \begin{equation} \begin{cases} u_{t}\left(x,t\right)=\mbox{div}(|\nabla u\left(x,t\right)|^{p-2}\nabla u(x,t))+f(u(x,t)), & \left(x,t\right)\in \Omega\times\left(0,+\infty\right), \newline u\left(x,t\right)=0, & \left(x,t\right)\in\partial \Omega\times\left[0,+\infty\right), \newline u\left(x,0\right)=u_{0}\geq0, & x\in\overline{\Omega}, \end{cases} \end{equation} where $p\geq2$ and $\Omega$ is a bounded domain of $\mathbb{R}^{N}$ $(N\geq1)$ with smooth boundary $\partial\Omega$. The main contribution of this work is to introduce a new condition \mbox{$(C_{p})$$\hspace{1cm} \alpha \int_{0}^{u}f(s)ds \leq uf(u)+\beta u^{p}+\gamma,\,\,u>0$} for some $\alpha, \beta, \gamma>0$ with $0<\beta\leq\frac{\left(\alpha-p\right)\lambda_{1, p}}{p}$, where $\lambda_{1, p}$ is the first eigenvalue of p-Laplacian $\Delta_{p}$, and we use the concavity method to obtain the blow-up solutions to the above equations. In fact, it will be seen that the condition $(C_{p})$ improves the conditions ever known so far.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1706.0349

A New Condition for the Concavity Method of Blow-up Solutions to Semilinear Heat Equations

In this paper, we consider the semilinear heat equations under Dirichlet boundary condition u_{t}\left(x,t\right)=\Delta u\left(x,t\right)+f(u(x,t)), & \left(x,t\right)\in \Omega\times\left(0,+\infty\right), u\left(x,t\right)=0, & \left(x,t\right)\in\partial \Omega\times\left[0,+\infty\right), u\left(x,0\right)=u_{0}\geq0, & x\in\overline{\Omega}, where $\Omega$ is a bounded domain of $\mathbb{R}^{N}$ $(N\geq1)$ with smooth boundary $\partial\Omega$. The main contribution of our work is to introduce a new condition $$(C) \alpha \int_{0}^{u}f(s)ds \leq uf(u)+\beta u^{2}+\gamma,\,\,u>0$$ for some $\alpha, \beta, \gamma>0$ with $0<\beta\leq\frac{\left(\alpha-2\right)\lambda_{0}}{2}$, where $\lambda_{0}$ is the first eigenvalue of Laplacian $\Delta$, and we use the concavity method to obtain the blow-up solutions to the semilinear heat equations. In fact, it will be seen that the condition (C) improves the conditions known so far.Comment: 7 page

Quantitative Comparisons of Linked Color Imaging and White-Light Colonoscopy for Colorectal Polyp Analysis

The performance of imaging techniques has an important influence on the clinical diagnostic strategy of colorectal cancer. Linked color imaging (LCI) by laser endoscopy is a recently developed techniques, and its advantage in improving the analysis accuracy of colorectal polyps over white-light (WL) endoscopy has been demonstrated in previous clinical studies. However, there are no objective criteria to evaluate and compare the aforementioned endoscopy methods. This paper presents a new criterion, namely entropy of color gradients image (ECGI), which is based on color gradients distribution and provides a comprehensive and objective evaluating indicator of the performance of colorectal images. Our method extracts the color gradient image pairs of 143 colonoscopy polyps in the LCI-PairedColon database, which are generated with WL and LCI conditions, respectively. Then, we apply the morphological method to fix the deviation of light-reflecting regions, and the ECGI scores of sample pairs are calculated. Experimental results show that the average ECGI scores of LCI images (5.7071) were significantly higher than that of WL (4.6093). This observation is consistent with the clinical studies. Therefore, the effectiveness of the proposed criterion is demonstrated

Joint Design of Optimal Cooperative Jamming and Power Allocation for Linear Precoding

Linear precoding and cooperative jamming for multiuser broadcast channel is studied to enhance the physical layer security. We consider the system where multiple independent data streams are transmitted from the base station to multiple legitimate users with the help of a friendly jammer. It is assumed that a normalized linear precoding matrix is given at the base station, whereas the power allocated to each user is to be determined. The problem is to jointly design the power allocation across different users for linear precoding and the cooperative jamming at the friendly jammer. The goal is to maximize a lower bound of the secrecy rate, provided that a minimum communication rate to the users is guaranteed. The optimal solution is obtained when the number of antennas at the friendly jammer is no less than the total number of antennas at the users and eavesdropper. Moreover, a suboptimal algorithm is proposed, which can be applied for all the scenarios. Numerical results demonstrate that the proposed schemes are effective for secure communications.Comment: accepted by IEEE Transactions on Communication

Thermal rectification and negative differential thermal conductance in harmonic chains with nonlinear system-bath coupling

Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to the most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [A. Eichler \emph{et al.}, Nat. Nanotech. \textbf{6}, 339 (2011)]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed comparing to the results of weak linear coupling constant.Comment: 27 pages, 8 figure