20,048 research outputs found
Cluster algebra structure on the finite dimensional representations of for =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 . 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 for some with
, where is
the first eigenvalue of discrete Laplacian , 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 . 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 and is a bounded domain of
with smooth boundary . 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 with
, where is the first eigenvalue of p-Laplacian , 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 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 is a
bounded domain of with smooth boundary
. The main contribution of our work is to introduce a new
condition for some with
, where is
the first eigenvalue of Laplacian , 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
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