The rainbow vertex-index of complementary graphs

A vertex-colored graph $G$ is \emph{rainbow vertex-connected} if two vertices are connected by a path whose internal vertices have distinct colors. The \emph{rainbow vertex-connection number} of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow vertex-connected. If for every pair $u,v$ of distinct vertices, $G$ contains a vertex-rainbow $u-v$ geodesic, then $G$ is \emph{strongly rainbow vertex-connected}. The minimum $k$ for which there exists a $k$-coloring of $G$ that results in a strongly rainbow-vertex-connected graph is called the \emph{strong rainbow vertex number} $srvc(G)$ of $G$. Thus $rvc(G)\leq srvc(G)$ for every nontrivial connected graph $G$. A tree $T$ in $G$ is called a \emph{rainbow vertex tree} if the internal vertices of $T$ receive different colors. For a graph $G=(V,E)$ and a set $S\subseteq V$ of at least two vertices, \emph{an $S$-Steiner tree} or \emph{a Steiner tree connecting $S$} (or simply, \emph{an $S$-tree}) is a such subgraph $T=(V',E')$ of $G$ that is a tree with $S\subseteq V'$. For $S\subseteq V(G)$ and $|S|\geq 2$, an $S$-Steiner tree $T$ is said to be a \emph{rainbow vertex $S$-tree} if the internal vertices of $T$ receive distinct colors. The minimum number of colors that are needed in a vertex-coloring of $G$ such that there is a rainbow vertex $S$-tree for every $k$-set $S$ of $V(G)$ is called the {\it $k$-rainbow vertex-index} of $G$, denoted by $rvx_k(G)$. In this paper, we first investigate the strong rainbow vertex-connection of complementary graphs. The $k$-rainbow vertex-index of complementary graphs are also studied

Deep Joint Source-Channel Coding for Efficient and Reliable Cross-Technology Communication

Cross-technology communication (CTC) is a promising technique that enables direct communications among incompatible wireless technologies without needing hardware modification. However, it has not been widely adopted in real-world applications due to its inefficiency and unreliability. To address this issue, this paper proposes a deep joint source-channel coding (DJSCC) scheme to enable efficient and reliable CTC. The proposed scheme builds a neural-network-based encoder and decoder at the sender side and the receiver side, respectively, to achieve two critical tasks simultaneously: 1) compressing the messages to the point where only their essential semantic meanings are preserved; 2) ensuring the robustness of the semantic meanings when they are transmitted across incompatible technologies. The scheme incorporates existing CTC coding algorithms as domain knowledge to guide the encoder-decoder pair to learn the characteristics of CTC links better. Moreover, the scheme constructs shared semantic knowledge for the encoder and decoder, allowing semantic meanings to be converted into very few bits for cross-technology transmissions, thus further improving the efficiency of CTC. Extensive simulations verify that the proposed scheme can reduce the transmission overhead by up to 97.63\% and increase the structural similarity index measure by up to 734.78%, compared with the state-of-the-art CTC scheme

Robust Control of Automotive Active Seat-Suspension System Subject to Actuator Saturation

This paper deals with the problem of robust sampled-data control for an automotive seatsuspension system subject to control input saturation. By using the nature of the sector nonlinearity, a sampled-data based control input saturation in the control design is studied. A passenger dynamic behavior is considered in the modeling of seat-suspension system, which makes the model more precisely and brings about uncertainties as well in the developed model. Robust output feedback control strategy is adopted since some state variables, such as, body acceleration and body deflection, are unavailable. The desired controller can be achieved by solving the corresponding linear matrix inequalities (LMIs). Finally, a design example has been given to demonstrate the effectiveness and advantages of the proposed controller design approach