prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the name of the generative interactive model used in the method?

Read the following text and answer briefly.

Context 1: \section{Introduction}
In recent years, vehicular technology has attracted significant attention from the automotive and telecommunication industries, leading to the emergence of vehicle-to-everything (V2X) communications for improving road safety, traffic management services and driving comfort 
V2X supported by the sixth generation (6G) is envisioned to be a key enabler of future connected autonomous vehicles \cite{9779322}  Although its transformative benefits for leveraging intelligent transportation systems, V2X still face several technical issues mainly related to performance and security 

The integration of sensing and communication (ISAC) has emerged very recently as a revolutionary element of 6G that could potentially help enabling adaptive learning and intelligent decision-making in future V2X applications 
The combination of sensing and communication allows vehicles to perceive their surroundings better, predict manoeuvres from nearby users and make intelligent decisions, thus paving the way toward a safer transportation system \cite{9665433} 
Modernized vehicles are augmented with various types of sensors divided into exteroceptive to observe their surrounding environment and proprioceptive to observe their internal states 
The former like GPS, Lidar, and Cameras are conveyed to improve situational awareness, while latter sensors, such as steering, pedal, and wheel speed, convey to improve self-awareness  

While sensing the environment, vehicles can exchange messages that assist in improving situational- and self-awareness and in coordinating maneuvers with other vehicles 
Those messages like the basic safety (BSMs) and cooperative awareness messages (CAMs) are composed of transmitting vehicle's states such as position and velocity and other vehicles' states in the vicinity  Vehicles might use their sensors, such as cameras and Lidar, to detect road users (e g , pedestrians), which can be communicated with other road users via the V2X messages to improve the overall performance  However, V2X communication links carrying those messages are inherently vulnerable to malicious attacks due to the open and shared nature of the wireless spectrum among vehicles and other cellular users \cite{8336901}  For instance, a jammer in the vicinity might alter the information to be communicated to nearby vehicles/users or can intentionally disrupt communication between a platoon of vehicles making the legitimate signals unrecognizable for on-board units (OBUs) and/or road side units (RSUs) that endanger vehicular safety 
\cite{8553649} 

In addition, the integrity of GPS signals and the correct acquisition of navigation data to compute position, velocity and time information is critical in V2X applications for their safe operation  However, since civil GPS receivers rely on unencrypted satellite signals, spoofers can easily replicate them by deceiving the GPS receiver to compute falsified positions \cite{9226611} 
Also, the long distance between satellites and terrestrial GPS receivers leads to an extremely weak signal that can be easily drowned out by a spoofer  
Thus, GPS sensors' vulnerability to spoofing attacks poses a severe threat that might be causing vehicles to be out of control or even hijacked and endanger human life \cite{9881548} 
Therefore, GPS spoofing attacks and jamming interference needs to be controlled and detected in real-time to reach secured vehicular communications allowing vehicles to securely talk to each other and interact with the infrastructure (e g , roadside terminals, base stations) \cite{9860410} 

Existing methods for GPS spoofing detection include GPS signal analysis methods and GPS message encryption methods \cite{9845684}  However, the former requires the ground truth source during the detection process, which is not always possible to collect  In contrast, the latter involves support from a secured infrastructure and advanced computing resources on GPS receivers, which hinders their adoption in V2X applications  On the other hand, existing methods for jammer detection in vehicular networks are based on analysing the packet drop rate as in \cite{9484071}, making it difficult to detect an advanced jammer manipulating the legitimate signal instead of disrupting it 
In this work, we propose a method to jointly detect GPS spoofing and jamming attacks in the V2X network  A coupled generalized dynamic Bayesian network (C-GDBN) is employed to learn the interaction between RF signals received by the RSU from multiple vehicles and their corresponding trajectories  This integration of vehicles' positional information with vehicle-to-infrastructure (V2I) communications allows semantic learning while mapping RF signals with vehicles' trajectories and enables the RSU to jointly predict the RF signals it expects to receive from the vehicles from which it can anticipate the expected trajectories 

The main contributions of this paper can be summarized as follows: \textit{i)} A joint GPS spoofing and jamming detection method is proposed for the V2X scenario, which is based on learning a generative interactive model as the C-GDBN  Such a model encodes the cross-correlation between the RF signals transmitted by multiple vehicles and their trajectories, where their semantic meaning is coupled stochastically at a high abstraction level  \textit{ii)} A cognitive RSU equipped with the acquired C-GDBN can predict and estimate vehicle positions based on real-time RF signals  This allows RSU to evaluate whether both RF signals and vehicles' trajectories are evolving according to the dynamic rules encoded in the C-GDBN and, consequently, to identify the cause (i e , a jammer attacking the V2I or a spoofer attacking the satellite link) of the abnormal behaviour that occurred in the V2X environment  \textit{iii)} Extensive simulation results demonstrate that the proposed method accurately estimates the vehicles' trajectories from the predicted RF signals, effectively detect any abnormal behaviour and identify the type of abnormality occurring with high detection probabilities 
To our best knowledge, this is the first work that studies the joint detection of jamming and spoofing in V2X systems 

\section{System model and problem formulation}
The system model depicted in Fig ~\ref{fig_SystemModel}, includes a single cell vehicular network consisting of a road side unit (RSU) located at $\mathrm{p}_{R}=[{x}_{R},{y}_{R}]$, a road side jammer (RSJ) located at $\mathrm{p}_{J}=[{x}_{J},{y}_{J}]$, a road side spoofer (RSS) located at $\mathrm{p}_{s}=[{x}_{s},{y}_{s}]$ and $N$ vehicles moving along multi-lane road in an urban area  The time-varying positions of the $n$-th vehicle is given by $\mathrm{p}_{n,t}=[{x}_{n,t},{y}_{n,t}]$ where $n \in N$  Among the $K$ orthogonal subchannels available for the Vehicle-to-Infrastructure (V2I) communications, RSU assigns one V2I link to each vehicle  Each vehicle exchanges messages composed of the vehicle's state (i e , position and velocity) with RSU through the $k$-th V2I link by transmitting a signal $\textrm{x}_{t,k}$ carrying those messages at each time instant $t$ where $k \in K$  We consider a reactive RSJ that aims to attack the V2I link by injecting intentional interference to the communication link between vehicles and RSU to alter the transmitted signals by the vehicles  In contrast, the RSS purposes to mislead the vehicles by spoofing the GPS signal and so registering wrong GPS positions  RSU aims to detect both the spoofer on the satellite link and the jammer on multiple V2I links in order to take effective actions and protect the vehicular network  
The joint GPS spoofing and jamming detection problem can be formulated as the following ternary hypothesis test:
\begin{equation}
    \begin{cases}
        \mathcal{H}_{0}: \mathrm{z}_{t,k} = \mathrm{g}_{t,k}^{nR} \mathrm{x}_{t,k} + \mathrm{v}_{t,k}, \\
        \mathcal{H}_{1}: \mathrm{z}_{t,k} = \mathrm{g}_{t,k}^{nR} \mathrm{x}_{t,k} + \mathrm{g}_{t,k}^{JR} \mathrm{x}_{t,k}^{j} + \mathrm{v}_{t,k}, \\
        \mathcal{H}_{2}: \mathrm{z}_{t,k} = \mathrm{g}_{t,k}^{nR} \mathrm{x}_{t,k}^{*} + \mathrm{v}_{t,k},
    \end{cases}
\end{equation}
where $\mathcal{H}_{0}$, $\mathcal{H}_{1}$ and $\mathcal{H}_{2}$ denote three hypotheses corresponding to the absence of both jammer and spoofer, the presence of the jammer, and the presence of the spoofer, respectively  $\textrm{z}_{t,k}$ is the received signal at the RSU at $t$ over the $k$-th V2I link, $\textrm{g}_{t,k}^{nR}$ is the channel power gain from vehicle $n$ to the RSU formulated as: $\textrm{g}_{t,k}^{nR} = \alpha_{t,k}^{nR} \mathrm{h}_{t,k}^{nR}$, where $\alpha_{t,k}^{nR}$ is the large-scale fading including path-loss and shadowing modeled as \cite{8723178}: $\alpha_{t,k}^{nR}=G\beta d_{t,nR}^{-\gamma}$ 
\begin{figure}[t!]
    \centering
    \includegraphics[height=5 3cm]{Figures/SystemModel_V1 pdf}
    \caption{An illustration of the system model }
    \label{fig_SystemModel}
\end{figure}
$G$ is the pathloss constant, $\beta$ is a log normal shadow fading random variable, $d_{t,nR}=\sqrt{({x}_{n,t}-x_{R})^{2}+({y}_{n,t}-y_{R})^{2}}$ is the distance between the $n$-th vehicle and the RSU  $\gamma$ is the power decay exponent and
$\mathrm{h}_{t,k}$ is the small-scale fading component distributed according to $\mathcal{CN}(0,1)$  In addition, $\mathrm{x}_{t,k}$ is the desired signal transmitted by the $n$-th vehicle, and $\mathrm{v}_{t,k}$ is an additive white Gaussian noise with variance $\sigma_{n}^{2}$  $\mathrm{x}_{t,k}^{J}$ is the jamming signal, $\mathrm{x}_{t,k}^{*}$ is the spoofed signal (i e , the signal that carries the bits related to the wrong GPS positions), $\mathrm{g}_{t,k}^{JR} = \alpha_{t,k}^{JR} \mathrm{h}_{t,k}^{JR}$ is the channel power gain from RSJ to RSU where $\alpha_{t,k}^{JR}=G\beta d_{t,JR}^{-\gamma}$ such that $d_{t,JR}=\sqrt{({x}_{J}-x_{R})^{2}+({y}_{J}-y_{R})^{2}}$ 
We assume that the channel state information (CSI) of V2I links is known and can be estimated at the RSU as in \cite{8345717}  
The RSU is equipped with an RF antenna which can track the vehicles' trajectories after decoding the received RF signals  RSU aims to learn the interaction between the RF signals received from multiple vehicles and their corresponding trajectories 

\section{Proposed method for joint detection of GPS spoofing and jamming}

\subsection{Environment Representation}
The RSU is receiving RF signals from each vehicle and tracking its trajectory (which we refer to as GPS signal) by decoding and demodulating the received RF signals  
The Generalized state-space model describing the $i$-th signal evolvement at multiple levels embodies the following equations: 
\begin{equation} \label{eq_discreteLevel}
    \mathrm{\Tilde{S}_{t}}^{(i)} = \mathrm{f}(\mathrm{\Tilde{S}_{t-1}}^{(i)}) + \mathrm{\tilde{w}}_{t},
\end{equation}
\begin{equation} \label{eq_continuousLevel}
    \mathrm{\Tilde{X}_{t}}^{(i)} = \mathrm{A} \mathrm{\Tilde{X}_{t-1}}^{(i)} + \mathrm{B} \mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}} + \mathrm{\tilde{w}}_{t},
\end{equation}
\begin{equation} \label{eq_observationLevel}
    \mathrm{\Tilde{Z}_{t}}^{(i)} = \mathrm{H} \mathrm{\Tilde{X}_{t}}^{(i)} + \mathrm{\tilde{v}}_{t},
\end{equation}
where $i \in \{$RF, GPS$\}$ indicates the type of signal received by the RSU  The transition system model defined in \eqref{eq_discreteLevel} explains the evolution of the discrete random variables $\mathrm{\Tilde{S}_{t}}^{(i)}$ representing the clusters of the RF (or GPS) signal dynamics, $\mathrm{f}( )$ is a non linear function of its argument and the additive term $\mathrm{\tilde{w}}_{t}$ denotes the process noise  The dynamic model defined in \eqref{eq_continuousLevel} explains the RF signal dynamics evolution or the motion dynamics evolution of the $n$-th vehicle, where $\mathrm{\Tilde{X}_{t}}^{(i)}$ are hidden continuous variables generating sensory signals, $\mathrm{A} \in \mathbb{R}^{2d}$ and $\mathrm{B} \in \mathbb{R}^{2d}$ are the dynamic and control matrices, respectively, and $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}}$ is the control vector representing the dynamic rules of how the signals evolve with time  The measurement model defined in \eqref{eq_observationLevel} describes dependence of the sensory signals $\mathrm{\Tilde{Z}_{t}}^{(i)}$ on the hidden states $\mathrm{\Tilde{X}_{t}}^{(i)}$ that is parametrized by the measurement matrix $\mathrm{B} \in \mathbb{R}^{2d}$ where $d$ stands for the data dimensionality and $\mathrm{\tilde{v}}_{t}$ is a random noise  

\subsection{Learning GDBN}
The hierarchical dynamic models defined in \eqref{eq_discreteLevel}, \eqref{eq_continuousLevel} and \eqref{eq_observationLevel} are structured in a Generalized Dynamic Bayesian Network (GDBN) \cite{9858012} as shown in Fig ~\ref{fig_GDBN_CGDBN}-(a) that provides a probabilistic graphical model expressing the conditional dependencies among random hidden variables and observable states  The generative process explaining how sensory signals have been generated can be factorized as:
\begin{equation} \label{eq_generative_process}
\begin{split}
    \mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}, \mathrm{\tilde{X}}_{t}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}) = \mathrm{P}(\mathrm{\tilde{S}}_{0}^{(i)}) \mathrm{P}(\mathrm{\tilde{X}}_{0}^{(i)}) \\ \bigg[ \prod_{t=1}^{\mathrm{T}} \mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t}^{(i)}) \mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}) \mathrm{P}(\mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t-1}^{(i)}) \bigg],
\end{split}
\end{equation}
where $\mathrm{P}(\mathrm{\tilde{S}}_{0}^{(i)})$ and $\mathrm{P}(\mathrm{\tilde{X}}_{0}^{(i)})$ are initial prior distributions, $\mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t}^{(i)})$ is the likelihood, $\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)})$ and $\mathrm{P}(\mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t-1}^{(i)})$ are the transition densities describing the temporal and hierarchical dynamics of the generalized state-space model 
The generative process defined in \eqref{eq_generative_process} indicates the cause-effect relationships the model impose on the random variables $\mathrm{\tilde{S}}_{t}^{(i)}$, $\mathrm{\tilde{X}}_{t}^{(i)}$ and $\mathrm{\tilde{Z}}_{t}^{(i)}$ forming a chain of causality describing how one state contributes to the production of another state which is represented by the link $\mathrm{\tilde{S}}_{t}^{(i)} \rightarrow \mathrm{\tilde{X}}_{t}^{(i)} \rightarrow \mathrm{\tilde{Z}}_{t}^{(i)}$ 

The RSU starts perceiving the environment using a static assumption about the environmental states evolution by assuming that sensory signals are only subject to random noise  Hence, RSU predicts the RF signal (or vehciles trajectory) using the following simplified model:
$\mathrm{\tilde{X}}_{t}^{(i)} = \mathrm{A} \mathrm{\tilde{X}}_{t-1}^{(i)} + \mathrm{\tilde{w}}_{t}$, 
that differs from \eqref{eq_continuousLevel} in the control vector $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}}$ which is supposed to be null, i e , $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}} = 0$ as the dynamic rules explaining how the environmental states evolve with time are not discovered yet 
Those rules can be discovered by exploiting the generalized errors (GEs), i e , the difference between predictions and observations  The GEs projected into the measurement space are calculated as:
$\tilde{\varepsilon}_{\mathrm{\tilde{Z}}_{t}^{(i)}}^{} = \mathrm{\tilde{Z}}_{t}^{(i)} - \mathrm{H} \mathrm{\tilde{X}}_{t}^{(i)}$ 
Projecting $\tilde{\varepsilon}_{\mathrm{\tilde{Z}}_t}^{}$ back into the generalized state space can be done as follows:
\begin{equation}\label{GE_continuousLevel_initialModel}
    \tilde{\varepsilon}_{\mathrm{\tilde{X}}_t}^{(i)} = \mathrm{H}^{-1}\tilde{\varepsilon}_{\mathrm{\tilde{Z}}_{t}^{(i)}}^{}=\mathrm{H}^{-1}(\mathrm{\tilde{Z}}_{t}^{(i)}-\mathrm{H}\mathrm{\tilde{X}}_{t}^{(i)}) = \mathrm{H}^{-1}\mathrm{\tilde{Z}}_{t}^{(i)} - \mathrm{\tilde{X}}_{t}^{(i)} 
\end{equation}
The GEs defined in \eqref{GE_continuousLevel_initialModel} can be grouped into discrete clusters in an unsupervised manner by employing the Growing Neural Gas (GNG)  The latter produces a set of discrete variables (clusters) denoted by:
$\mathbf{\tilde{S}^{(i)}}=\{\mathrm{\tilde{S}}_{1}^{(i)},\mathrm{\tilde{S}}_{2}^{(i)},\dots,\mathrm{\tilde{S}}_{M_{i}}^{(i)}\}$,
where $M_{i}$ is the total number of clusters and each cluster $\mathrm{\tilde{S}}_{m}^{(i)} \in \mathbf{\tilde{S}^{(i)}}$ follows a Gaussian distribution composed of GEs with homogeneous properties, such that $\mathrm{\tilde{S}}_{m}^{(i)} \sim \mathcal{N}(\tilde{\mu}_{\mathrm{\tilde{S}}_{m}^{(i)}}=[\mu_{\tilde{S}_{m}^{(i)}}, \Dot{\mu}_{\tilde{S}_{m}^{(i)}}], \Sigma_{\mathrm{\tilde{S}}_{m}^{(i)}})$ 
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 40\linewidth}
        \centering
           \includegraphics[width=2 5cm]{Figures/GDBN pdf}
        \\[-1 0mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 50\linewidth}
            \centering
            \includegraphics[width=5 0cm]{Figures/C_GDBN pdf}
           
            {\scriptsize (b)}
        \end{minipage}
        \caption{(a) The GDBN  (b) The coupled GDBN (C-GDBN) composed of two GDBNs representing the two signals received at the RSU where their discrete hidden variables are stochastically coupled }
        \label{fig_GDBN_CGDBN}
    \end{center}
\end{figure}
The dynamic transitions of the sensory signals among the available clusters can be captured in a time-varying transition matrix ($\Pi_{\tau}$) by estimating the time-varying transition probabilities $\pi_{ij}=\mathrm{P}(\mathrm{\tilde{S}}_{t}^{(i)}=i|\mathrm{\tilde{S}}_{t-1}^{(i)}=j, \tau)$ where $\tau$ is the time spent in $\mathrm{\tilde{S}}_{t-1}^{(i)}=j$ before transition to $\mathrm{\tilde{S}}_{t}^{(i)}=i$ 

\subsection{Learning Coupled GDBN (C-GDBN)}
The learning procedure described in the previous section can be executed for each signal type, i e , RF and GPS  After learning a separated GDBN model for each signal type, we analyse the interaction behaviour between RF signal and GPS signal received at the RSU by tracking the cluster firing among $\mathbf{\tilde{S}^{(1)}}$ and $\mathbf{\tilde{S}^{(2)}}$ during a certain experience  Such an interaction can be encoded in a Coupled GDBN (C-GDBN) as shown in Fig \ref{fig_GDBN_CGDBN}-(b) composed of the two GDBNs representing the two signals where their hidden variables at the discrete level are stochastically coupled (in $\mathrm{\tilde{C}}_{t}{=}[\mathrm{\tilde{S}}_{t}^{(1)},\mathrm{\tilde{S}}_{t}^{(2)}]$) as those variables are uncorrelated but have coupled means 
The interactive matrix $\Phi \in \mathbb{R}^{M_{1},M_{2}}$ encodes the firing cluster pattern allowing to predict the GPS signal from RF signal is defined as follows:
\begin{equation} \label{interactiveTM_fromRFtoGPS}
\Phi = 
        \begin{bmatrix} 
            \mathrm{P}(\mathrm{\Tilde{S}_{1}}^{(2)}|\mathrm{\Tilde{S}_{1}}^{(1)}) & \mathrm{P}(\mathrm{\Tilde{S}_{2}}^{(2)}|\mathrm{\Tilde{S}_{1}}^{(1)}) & \dots & \mathrm{P}(\mathrm{\Tilde{S}_{M_{2}}}^{(2)}|\mathrm{\Tilde{S}_{1}}^{(1)}) \\
            \mathrm{P}(\mathrm{\Tilde{S}_{1}}^{(2)}|\mathrm{\Tilde{S}_{2}}^{(1)}) & \mathrm{P}(\mathrm{\Tilde{S}_{2}}^{(2)}|\mathrm{\Tilde{S}_{2}}^{(1)}) & \dots & \mathrm{P}(\mathrm{\Tilde{S}_{M_{2}}}^{(2)}|\mathrm{\Tilde{S}_{2}}^{(1)}) \\
            \vdots & \vdots & \ddots & \vdots \\
            \mathrm{P}(\mathrm{\Tilde{S}_{1}}^{(2)}|\mathrm{\Tilde{S}_{M_{1}}}^{(1)}) & \mathrm{P}(\mathrm{\Tilde{S}_{2}}^{(2)}|\mathrm{\Tilde{S}_{M_{1}}}^{(1)}) & \dots & \mathrm{P}(\mathrm{\Tilde{S}_{M_{2}}}^{(2)}|\mathrm{\Tilde{S}_{M_{1}}}^{(1)}) 
        \end{bmatrix} 
\end{equation}

\subsection{Joint Prediction and Perception}
RSU starts predicting the RF signals it expects to receive from each vehicle based on a Modified Markov Jump Particle Filter (M-MJPF) \cite{9858012} that combines Particle filter (PF) and Kalman filter (KF) to perform temporal and hierarchical predictions  Since the acquired C-GDBN allows predicting a certain signal's dynamic evolution based on another's evolution, it requires an interactive Bayesian filter capable of dealing with more complicated predictions  To this purpose, we propose to employ an Interactive M-MJPF (IM-MJPF) on the C-GDBN  The IM-MJPF consists of a PF that propagates a set of $L$ particles equally weighted, such that $\{\mathrm{\tilde{S}}_{t,l}^{(1)}, \mathrm{W}_{t,l}^{(1)}\}{\sim}\{\pi(\mathrm{\tilde{S}}_{t}^{(1)}), \frac{1}{L}\}$, where $\mathrm{\tilde{S}}_{t,l}^{(1)}$, $l \in L$ and $( ^{(1)})$ is the RF signal type  In addition, RSU relies on $\Phi$ defined in \eqref{interactiveTM_fromRFtoGPS} to predict $\mathrm{\tilde{S}}_{t}^{(2)}$ realizing the discrete cluster of vehicle's trajectory starting from the predicted RF signal according to: $\{\mathrm{\tilde{S}}_{t}^{(2)},\mathrm{W}_{t,l}^{(2)}\}{\sim} \{\Phi(\mathrm{\tilde{S}}_{t,l}^{(1)}){=}\mathrm{P}( |\mathrm{\tilde{S}}_{t,l}^{(1)}), \mathrm{W}_{t,l}^{(2)}\}$  For each predicted discrete variable $\mathrm{\tilde{S}}_{t,l}^{(i)}$, a multiple KF is employed to predict multiple continuous variables which guided by the predictions at the higher level as declared in \eqref{eq_continuousLevel} that can be represented probabilistically as $\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)})$  The posterior probability that is used to evaluate expectations is given by:
\begin{multline} \label{piX}
    \pi(\mathrm{\tilde{X}}_{t}^{(i)})=\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)},\mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{Z}}_{t-1}^{(i)})= \\ \int \mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}) \lambda(\mathrm{\tilde{X}}_{t-1}^{(i)})d\mathrm{\tilde{X}}_{t-1}^{(i)},
\end{multline}
where $\lambda(\mathrm{\tilde{X}}_{t-1}^{(i)}){=}\mathrm{P}(\mathrm{\tilde{Z}}_{t-1}^{(i)}|\mathrm{\tilde{X}}_{t-1}^{(i)})$  
The posterior distribution can be updated (and so representing the updated belief) after having seen the new evidence $\mathrm{\tilde{Z}}_{t}^{(i)}$ by exploiting the diagnostic message $\lambda(\mathrm{\tilde{X}}_{t}^{(i)})$ in the following form: $\mathrm{P}(\mathrm{\tilde{X}}_{t}^{(i)}, \mathrm{\tilde{S}}_{t}^{(i)}|\mathrm{\tilde{Z}}_{t}^{(i)}) {=} \pi(\mathrm{\tilde{X}}_{t}^{(i)})\lambda(\mathrm{\tilde{X}}_{t}^{(i)})$  Likewise, belief in discrete hidden variables can be updated according to: $\mathrm{W}_{t,l}^{(i)}{=}\mathrm{W}_{t,l}^{(i)}\lambda (\mathrm{\tilde{S}}_{t}^{(i)})$ where:
$\lambda (\mathrm{\tilde{S}}_{t}^{(i)}) {=} \lambda (\mathrm{\Tilde{X}}_{t}^{(i)})\mathrm{P}(\mathrm{\Tilde{X}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t}^{(i)}) {=} \mathrm{P}(\mathrm{\tilde{Z}}_{t}^{(i)}|\mathrm{\Tilde{X}}_{t}^{(i)})\mathrm{P}(\mathrm{\Tilde{X}}_{t}^{(i)}|\mathrm{\tilde{S}}_{t}^{(i)})$ 

\subsection{Joint GPS spoofing and jamming detection}
RSU can evaluate the current situation and identify if V2I is under attack, or the satellite link is under spoofing based on a multiple abnormality indicator produced by the IM-MJPF  The first indicator calculates the similarity between the predicted RF signal and the observed one, which is defined as:
\begin{equation}\label{eq_CLA1}
    \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} = -ln \bigg( \mathcal{BC} \big(\pi(\mathrm{\tilde{X}}_{t}^{(1)}),\lambda(\mathrm{\tilde{X}}_{t}^{(1)}) \big) \bigg),
\end{equation}
where $\mathcal{BC}( ){=}\int \sqrt{\pi(\mathrm{\tilde{X}}_{t}^{(1)}),\lambda(\mathrm{\tilde{X}}_{t}^{(1)}})d\mathrm{\tilde{X}}_{t}^{(1)}$ is the Bhattacharyya coefficient 
The second indicator calculates the similarity between the predicted GPS signal (from the RF signal) and the observed one after decoding the RF signal which is defined as:
\begin{equation}\label{eq_CLA2}
    \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} = -ln \bigg( \mathcal{BC} \big(\pi(\mathrm{\tilde{X}}_{t}^{(2)}),\lambda(\mathrm{\tilde{X}}_{t}^{(2)}) \big) \bigg),
\end{equation}
where $\mathcal{BC}( ){=}\int \sqrt{\pi(\mathrm{\tilde{X}}_{t}^{(2)}),\lambda(\mathrm{\tilde{X}}_{t}^{(2)}})d\mathrm{\tilde{X}}_{t}^{(2)}$ 
Different hypotheses can be identified by the RSU to understand the current situation whether there is: a jammer attacking the V2I link, or a spoofer attacking the link between the satellite and the vehicle or both jammer and spoofer are absent according to:
\begin{equation}
    \begin{cases}
        \mathcal{H}_{0}: \text{if} \ \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} < \xi_{1} \ \text{and} \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} < \xi_{2}, \\
        \mathcal{H}_{1}: \text{if} \ \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} \geq \xi_{1} \ \text{and} \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2}, \\
        \mathcal{H}_{2}: \text{if} \ \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}} < \xi_{1} \ \text{and} \ \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2},
    \end{cases}
\end{equation}
where $\xi_{1} = \mathbb{E}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(1)}}] + 3\sqrt{\mathbb{V}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(1)}}]}$, and $\xi_{2} = \mathbb{E}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(2)}}] + 3\sqrt{\mathbb{V}[\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(2)}}]}$  In $\xi_{1}$ and $\xi_{2}$, $\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(1)}}$ and $\Bar{\Upsilon}_{\mathrm{\tilde{X}}_{t}^{(2)}}$ stand for the abnormality signals during training (i e , normal situation when jammer and spoofer are absent) 

\subsection{Evaluation metrics}
In order to evaluate the performance of the proposed method to jointly detect jammer and GPS spoofer, we adopt the jammer detection probability ($\mathrm{P}_{d}^{j}$) and the spoofer detection probability ($\mathrm{P}_{d}^{s}$), respectively, which are defined as:
\begin{equation}
    \mathrm{P}_{d}^{j} = \mathrm{Pr}(\Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}}\geq \xi_{1}, \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2}|\mathcal{H}_{1}),
\end{equation}
\begin{equation}
    \mathrm{P}_{d}^{s} = \mathrm{Pr}(\Upsilon_{\mathrm{\tilde{X}}_{t}^{(1)}}< \xi_{1}, \Upsilon_{\mathrm{\tilde{X}}_{t}^{(2)}} \geq \xi_{2}|\mathcal{H}_{2}) 
\end{equation}
Also, we evaluate the accuracy of the proposed method in predicting and estimating the vehicles' trajectories and the expected RF signals by adopting the root mean square error (RMSE) defined as:
\begin{equation}
    RMSE = \sqrt{ \frac{1}{T} \sum_{t=1}^{T}\bigg( \mathrm{\tilde{Z}}_{t}^{(i)}-\mathrm{\tilde{X}}_{t}^{(i)} \bigg)^{2} },
\end{equation}
where $T$ is the total number of predictions 

\section{Simulation Results}
In this section, we evaluate the performance of the proposed method to jointly detect the jammer and the spoofer using extensive simulations  We consider $\mathrm{N}=2$ vehicles interacting inside the environment and exchanging their states (i e , position and velocity) with the RSU  The vehicles move along predefined trajectories performing various maneuvers which are picked from the \textit{Lankershim} dataset proposed by \cite{5206559}  The dataset depicts a four way intersection and includes about $19$ intersection maneuvers  RSU assigns one subchannel realizing the V2I link for each vehicle over which the vehicles' states are transmitted  The transmitted signal carrying the vehicle's state and the jamming signal are both QPSK modulated  
The simulation settings are: carrier frequency of $2$GHz, BW${=}1 4$MHz, cell radius of $500$m, RSU antenna height and gain is $25$m and $8$ dBi, receiver noise figure of $5$dB, vehicle antenna height and gain is $1 5$m and $3$dBi, vehicle speed is $40$Km/h, V2I transmit power is $23$dBm, jammer transmit power ranging from $20$dBm to $40$dBm, SNR of $20$dB, path loss model ($128 1{+}37 6log d$), Log-normal shadowing with $8$dB standard deviation and a fast fading channel following the Rayleigh distribution 
\begin{figure}[ht!]
    \begin{center}
        \begin{minipage}[b]{ 55\linewidth}
        \centering
            \includegraphics[width=5 0cm]{Results/ObservedTrajectories_reference}
        \\[-1 5mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/ObservedRFsignal_Veh1_reference}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/ObservedRFsignal_Veh2_reference}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \caption{An example visualizing the received RF signals from the two vehicles and the corresponding trajectories: (a) Vehicles' trajectories, (b) received RF signal from vehicle 1, (c) received RF signal from vehicle 2 }
        \label{fig_receivedRFsignalandTrajectory}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/clusters_trajectory_veh1}
            \\[-1 5mm]
            {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/clusters_trajectory_veh2}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/clusters_RFsignal_veh1}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/clusters_RFsignal_veh2}
            \\[-1 5mm]
            {\scriptsize (d)}
        \end{minipage}
       
        \caption{GNG output after clustering the generalized errors obtained from different experiences: (a) clustered trajectory of vehicle 1, (b) clustered trajectory of vehicle 2, (c) clustered RF signal received from vehicle 1, (d) clustered RF signal received from vehicle 2 }
        \label{fig_GNG_of_receivedRFsignalandTrajectory}
    \end{center}
\end{figure}

The RSU aims to learn multiple interactive models (i e , C-GDBN models) encoding the cross relationship between the received RF signal from each vehicle and its corresponding trajectory  These models allow the RSU to predict the trajectory the vehicle will follow based on the received RF signal and evaluate whether the V2I is under jamming attacks or the satellite link is under spoofing  It is to note that the RSU is receiving only the RF signals from the two vehicles and obtaining their positions after decoding the RF signals  Thus, the RSU should be able to evaluate if the received RF signals are evolving according to the dynamic rules learned so far and if the vehicles are following the expected (right) trajectories to decide whether the V2I links are really under attack or whether the satellite link is under spoofing 

Fig ~\ref{fig_receivedRFsignalandTrajectory}-(a) illustrates an example of the interaction between the two vehicles performing a particular manoeuvre, and Fig ~\ref{fig_receivedRFsignalandTrajectory}-(b) shows the received RF signals by the RSU from the two vehicles  At the beginning of the learning process, RSU performs predictions according to the simplified model defined in \eqref{eq_continuousLevel} where $\mathrm{U}_{\mathrm{\Tilde{S}_{t}}^{(i)}} {=} 0$ 
After obtaining the generalized errors as pointed out in \eqref{GE_continuousLevel_initialModel}, RUS clusters those errors using GNG to learn two GDBN models encoding the dynamic rules of how the RF signal and the GPS signal evolve with time, respectively, as showed in Fig ~\ref{fig_GNG_of_receivedRFsignalandTrajectory} and Fig ~\ref{fig_graphicalRep_transitionMatrices}  RSU can couple the two GDBNs by learning the interactive transition matrix that is encoded in a C-GDBN as shown in Fig ~\ref{fig_interactiveMatrices} 
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/graphTransition_Trajectory_veh1}
            \\[-1 5mm]
            {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=4 5cm]{Results/graphTransition_Trajectory_veh2}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/graphTransition_RFsignal_veh1}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 5cm]{Results/graphTransition_RFsignal_veh2}
            \\[-1 5mm]
            {\scriptsize (d)}
        \end{minipage}
        \caption{Graphical representation of the transition matrices (TM): (a) TM related to the trajectory of vehicle 1, (b) TM related to the trajectory of vehicle 2, (c) TM related to the RF signal received from vehicle 1, (d) TM related to the RF signal received from vehicle 2 }
        \label{fig_graphicalRep_transitionMatrices}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
            \centering
                \includegraphics[width=3 8cm]{Results/interactiveMatrix_RFtoGPS_Neu5_veh1}
            \\[-1 0mm]
            {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=3 8cm]{Results/interactiveMatrix_RFtoGPS_Neu25_veh1}
            \\[-1 0mm]
            {\scriptsize (d)}
        \end{minipage}
       
        \caption{Interactive transition matrix defined in \eqref{interactiveTM_fromRFtoGPS} using different configurations: (a) $\mathrm{M_{1}}=5$, $\mathrm{M_{2}}=5$, (b) $\mathrm{M_{1}}=25$, $\mathrm{M_{2}}=25$ }
        \label{fig_interactiveMatrices}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
        \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_best_veh1}
        \\[-1 5mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_worst_veh1}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_best_veh2}
            \\[-1 5mm]
            {\scriptsize (c)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 9cm]{Results/RF_situation1_worst_veh2}
            \\[-1 5mm]
            {\scriptsize (d)}
        \end{minipage}
        \caption{An example visualizing the predicted and observed RF signals transmitted by the 2 vehicles using different configurations  Predicted RF signal from: (a) vehicle 1 using $\mathrm{M_{1}}{=}5$, $\mathrm{M_{2}}{=}5$, (b) vehicle 1 using $\mathrm{M_{1}}{=}25$, $\mathrm{M_{2}}{=}25$, (c) vehicle 2 using $\mathrm{M_{1}}{=}5$, $\mathrm{M_{2}}{=}5$, (d) vehicle 2 using $\mathrm{M_{1}}{=}25$, $\mathrm{M_{2}}{=}25$ }
            \label{fig_situation1_PredictedRF}
    \end{center}
\end{figure}

\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
        \centering
            \includegraphics[width=4 8cm]{Results/GPSfromRF_situation1_best}
        \\[-1 0mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 8cm]{Results/GPSfromRF_situation1_worst}
            \\[-1 0mm]
            {\scriptsize (b)}
        \end{minipage}
        %
        \caption{An example visualizing the predicted and observed trajectories of two vehicles interacting in the environment  (a) $\mathrm{M_{1}}{=}5$, $\mathrm{M_{2}}{=}5$, (b) $\mathrm{M_{1}}{=}25$, $\mathrm{M_{2}}{=}25$ }
            \label{fig_situation1_VehiclesTrajectories}
    \end{center}
\end{figure}

\begin{figure}[ht!]
    \begin{center}
        \begin{minipage}[b]{ 49\linewidth}
        \centering
            \includegraphics[width=4 8cm]{Results/rmse_on_trajectory}
        \\[-1 0mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{0 49\linewidth}
            \centering
            \includegraphics[width=4 8cm]{Results/rmse_on_RFSignal}
            \\[-1 0mm]
            {\scriptsize (b)}
        \end{minipage}
        \caption{The average RMSE after testing different experiences and examples of: (a) trajectories and (b) RF signals }
            \label{fig_rmse_onTraj_onSig}
    \end{center}
\end{figure}

Fig ~\ref{fig_situation1_PredictedRF} illustrates an example comparing between predicted RF signals and observed ones based on two different configurations in learning the interactive matrix (as shown in Fig ~\ref{fig_interactiveMatrices})  Also, Fig ~\ref{fig_situation1_VehiclesTrajectories} illustrates an example comparing between the predicted and observed trajectories of the two vehicles using the two interactive matrices depicted in Fig ~\ref{fig_interactiveMatrices}  From Fig ~\ref{fig_situation1_PredictedRF} and Fig ~\ref{fig_situation1_VehiclesTrajectories} we can see that using an interactive matrix with less clusters allows to perform better predictions compared to that with more clusters  This can be validated by observing Fig ~\ref{fig_rmse_onTraj_onSig} that illustrates the RMSE values versus different number of clusters related to the two models representing the dynamics of the received RF signals and the vehicles' trajectories  It can be seen that as the number of clusters increases the RMSE error increases, since adding more clusters decreases the firing probability that explains the possibility to be in one of the $M_{2}$ clusters of the second model conditioned in being in a certain cluster of the first model 

Fig ~\ref{fig_exNormal_Spoofed_JammedTrajectories} illustrates an example of vehicle's trajectory under normal situation (i e , jammer and spoofer are absent), under jamming attacks and under spoofing attacks  Also the figure shows the predicted trajectory which should follow the same dynamic rules learned during a normal situation  After that, we implemented the IM-MJPF on the learned C-GDBN to perform multiple predictions, i e , to predict the RF signal that the RSU is expecting to receive from a certain vehicle and the corresponding trajectory that the vehicle is supposed to follow  IM-MJPF through the comparison between multiple predictions and observations, produces multiple abnormality signals as defined in \eqref{eq_CLA1} and \eqref{eq_CLA2} which are used to detect the jammer and the spoofer 

Fig ~\ref{fig_abnormalitySignals_JammerSpoofer} illustrates the multiple abnormality signals related to the example shown in Fig ~\ref{fig_exNormal_Spoofed_JammedTrajectories}  We can observe that the abnormal signals related to both RF signal (Fig ~\ref{fig_abnormalitySignals_JammerSpoofer}-(a)) and trajectory (Fig ~\ref{fig_abnormalitySignals_JammerSpoofer}-(b)) are below the threshold under normal situations  This proves that RSU learned the correct dynamic rules of how RF signals and trajectories evolve when the jammer and spoofer are absent (i e , under normal situations)  Also, we can see that the RSU can notice a high deviation on both the RF signal and the corresponding trajectory due to a jamming interference from what it has learned so far by relying on the abnormality signals  In contrast, we can see that under spoofing attacks, RSU notice a deviation only on the trajectory and not on the RF signal since the spoofer has affected only the positions without manipulating the RF signal  In addition, it is obvious how the proposed method allows the RSU to identify the type of abnormality occurring and to explain the cause of the detected abnormality (i e , understanding if it was because of a jammer attacking the V2I link or a spoofer attacking the satellite link) 
\begin{figure}[t!]
    \centering
    \includegraphics[width=6 5cm]{Results/trajectories_underJamming_andSpoofing}
   
    \caption{Vehicle's trajectory under: normal situation, jamming and spoofing }
    \label{fig_exNormal_Spoofed_JammedTrajectories}
\end{figure}
\begin{figure}[t!]
    \begin{center}
        \begin{minipage}[b]{ 92\linewidth}
        \centering
            \includegraphics[height=2 6cm]{Results/abnSignal_onRF}
        \\[-1 5mm]
        {\scriptsize (a)}
        \end{minipage}
        \begin{minipage}[b]{ 92\linewidth}
            \centering
            \includegraphics[height=2 6cm]{Results/abnSignal_onGPS}
            \\[-1 5mm]
            {\scriptsize (b)}
        \end{minipage}
        %
        \caption{Abnormality Signals related to the example shown in Fig \ref{fig_exNormal_Spoofed_JammedTrajectories}: (a) abnormality indicators related to the RF signal, (b) abnormality indicators related to the trajectory }
            \label{fig_abnormalitySignals_JammerSpoofer}
    \end{center}
\end{figure}
\begin{figure}[t!]
    \centering
    \includegraphics[height=3 2cm]{Results/Detection_Probability_RFfromGPS_versusPj}
    \caption{Detection probability ($\mathrm{P_{d}}$) versus jammer's power ($\mathrm{P_{J}}$) using different number of clusters $\mathrm{M}_{2}$ }
    \label{fig_jammerDetectionProb}
\end{figure}
\begin{figure}[t!]
    \centering
    \includegraphics[height=3 2cm]{Results/spoofingDetectionProbability_falseAlarm_versusM2}
    \caption{Spoofing detection probability ($\mathrm{P}_{d}^{s}$) and spoofing false alarm ($\mathrm{P}_{f}^{s}$) versus the number of clusters $\mathrm{M}_{2}$ }
    \label{fig_spooferDetectionProb}
\end{figure}

Fig ~\ref{fig_jammerDetectionProb} shows the overall performance of the proposed method in detecting the jammer by testing many situations and examples and by considering different jamming powers which ranges from $20$dBm to $40$dBm  It can be seen that the proposed method is able to detect the jammer with high probabilities (near $1$) and by considering low and high jamming powers  Also, the figure compares the performance in detecting the jammer by varying the number of clusters ($M_{2}$) 
Fig ~\ref{fig_spooferDetectionProb} shows the overall performance of the proposed method in detecting the spoofer by testing different different examples of driving maneuvers  It can be seen that the RSU is able to detect the spoofer with high detection probability and null false alarm versus different number of clusters 

\section{Conclusion}
A joint detection method of GPS spoofing and jamming attacks is proposed  The method is based on learning a dynamic interactive model encoding the cross-correlation between the received RF signals from multiple vehicles and their corresponding trajectories  Simulation results show the high effectiveness of the proposed approach in jointly detecting the GPS spoofer and jammer attacks  
Subsequent work will extend the system model to consider more than two vehicles with different channel conditions and various modulation schemes to evaluate the effectiveness of the proposed method 

\bibliographystyle{IEEEtran}

Context 2: '无锡速芯微电子有限公司是一家集芯片 研发，销售和服务于一体的国家高新技 术企业，为客户提供高性能，高集成 度，极致体验的全协议快充芯片。 无锡速芯微电子有限公司 FastSOC Microelectronics Co ,Ltd  销售联系方式： 联系人：顾先生 手机：1800 185 3071 邮箱：gpp@fastsoc com 网址：www fastsoc com 地址：无锡市新吴区菱湖大道200号中国物联网国际创新园E-503室 顾工微信号 速芯微公众号 免责声明：本文所述方法、方案均供客户参考，用于提示或者展示芯片应用的一种或者多种方式，不作为最终产品的实际方案。文中所描述的功能和性能指标在实 验室环境下测试得到，部分可以提供第三方测试报告，但是不保证客户产品上能获得相同的数据。本文信息只作为芯片使用的指导，不授权用户使用本公司或者其 他公司的知识产权。本文信息只作为芯片使用的指导，不承担因为客户自身应用不当而造成的任何损失。 **文中信息仅供参考，详情请联系我司获取最新资料” 无锡速芯微电子有限公司 FastSOC Microelectronics Co ,Ltd  产品手册 2023年 
新品快览 FS312A：PD3 0 诱骗- FS312A支持PD2 0/PD3 0最高诱骗电压：20V - FS312AE支持PD2 0/PD3 0 最高诱骗电压：20V支持Emarker模拟功能 - 封装：SOT23-5 VBUS CC1 CC2 DM DP 用电电路 4 7K 0 47uF R C C 1 V D D F U N C C C 2F S 3 1 2 B D M D P EP GND 应用图 FS8628：A+C快充协议CC2 CC1 VBUS CC2 CC1 FS312A FUNC GND VDD 4 7K GND R 用电电路 1uF GND 应用图 多口极简方案 FS8611SP*2+CCM-8611SP-A+7533B-T 双C智能降功率方案 FS8611S USB-C AC-DC 双变压器 7533B-T CCM-8611SP-A FS8611S USB-C 采用2颗FS8611SP搭配CCM-8611SP-A （MCU），7533B-T配合工作 - 支持多种协议 - 支持I2C控制 - 任意单 C 的为 35W - 双 插 降 功 率 ， 三 档 功 率 智 能 配 置：27 4W+7 4W；17 4W+17 4W； 27 4W - BOM极简，成本低 FS312B：PD3 1 诱骗FS8611K*2+CCM-8611K-A+7550B-T 双C方案 - FS312BL支持PD2 0/PD3 0/PD3 1/第三方协议最高诱骗电压：20V - FS312BLE支持PD2 0/PD3 0/PD3 1/第三方协议最高诱骗电压：20V支持Emarker模拟功能 - FS312BH支持PD2 0/PD3 0/PD3 1/第三方协议最高诱骗电压：48V - FS312BHE支持PD2 0/PD3 0/PD3 1/第三方协议最高诱骗电压：48V 支持Emarker模拟功能 - 封装：DFN2x2-6L - 兼容兼容BC1 2、Apple2 4A、 QC2 0 Class A、QC3 0 Class A/B、 FCP、SCP、AFC、低压直充等 - 兼容Type-C PD2 0、Type-C PD3 0、 Type-C PD3
Context 3: Current address: Division of Brain Sciences, Department of Medicine, Imperial College London, London, United Kingdom 
In a variety of species, reduced food intake, and in particular protein or amino acid (AA) restriction, extends lifespan and healthspan  However, the underlying epigenetic and/or transcriptional mechanisms are largely unknown, and dissection of specific pathways in cultured cells may contribute to filling this gap  We have previously shown that, in mammalian cells, deprivation of essential AAs (methionine/cysteine or tyrosine) leads to the transcriptional reactivation of integrated silenced transgenes, including plasmid and retroviral vectors and latent HIV-1 provirus, by a process involving epigenetic chromatic remodeling and histone acetylation  Here we show that the deprivation of methionine/cysteine also leads to the transcriptional upregulation of endogenous retroviruses, suggesting that essential AA starvation affects the expression not only of exogenous non-native DNA sequences, but also of endogenous anciently-integrated and silenced parasitic elements of the genome  Moreover, we show that the transgene reactivation response is highly conserved in different mammalian cell types, and it is reproducible with deprivation of most essential AAs  The General Control Non-derepressible 2 (GCN2) kinase and the downstream integrated stress response represent the best candidates mediating this process; however, by pharmacological approaches, RNA interference and genomic editing, we demonstrate that they are not implicated  Instead, the response requires MEK/ERK and/or JNK activity and is reproduced by ribosomal inhibitors, suggesting that it is triggered by a novel nutrient-sensing and signaling pathway, initiated by translational block at the ribosome, and independent of mTOR and GCN2  Overall, these findings point to a general transcriptional response to essential AA deprivation, which affects the expression of non-native genomic sequences, with relevant implications for the epigenetic/transcriptional effects of AA restriction in health and disease 
Copyright: © 2018 De Vito et al  This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited 
Data Availability: All relevant data are within the paper and its Supporting Information files  RNAseq data are available in the ArrayExpress database under the accession number E-MTAB-6452 
Funding: This study was funded by the Ajinomoto Innovation Alliance Program, (AIAP; https://www ajinomoto com/en/rd/AIAP/index html#aiap) (to M V S and D G), which is a joint research initiative of Ajinomoto Co , Inc , Japan  One of the authors [M B ] is an employee of Ajinomoto Co , and his specific roles are articulated in the ‘author contributions’ section  The commercial funder provided support in the form of salary for author [M B ] and some of the necessary research materials (medium for cell culture), but did not have any additional role in the study design, data collection and analysis, or preparation of the manuscript, and the authors had unrestricted access to the data  Due to a confidentiality agreement, the commercial funder participated only in the decision to publish the data obtained during the study, without any restriction 
Competing interests: This study was funded by Ajinomoto Co , Inc , Japan and one of the authors [M B ] is an employee of this commercial funder  No other employment or consultancy relationships exist with the commercial funder, and no patents, products in development, or marketed products result from this study  The authors declare that no competing interests exist and that the commercial affiliation of one of the authors does not alter the adherence of authors to all PLOS ONE policies on sharing data and materials 
In animals, excessive, insufficient, or imbalanced nutrient availability is known to strongly impact on phenotype and health, both short and long-term, and across generations [1, 2]  In particular, studies in yeast, animal models and humans have shown that reduced food intake, reducing either overall calories, or only sugars, proteins, or even single amino acids (AA), such as Methionine (Met), may extend lifespan and healthspan, and reduce the risk of cancer and other age-related diseases [3–9]  In addition, fasting or specific AA deprivation have shown potential therapeutic applications, owing to their ability to directly reduce the growth of some tumor types [10, 11], sensitize cancer cells to chemo- or immunotherapy [12, 13], and allow efficient hematopoietic stem cell engraftment   However, little is known about the specific processes and molecular mechanisms mediating the roles of nutrient restriction in human health and longevity 
A properly balanced diet in metazoans contains optimal amounts of a subset of AA, which cannot be synthetized de novo and are therefore named essential amino acids (EAAs)  In humans these include Met, Histidine (His), Isoleucine (Ile), Leucine (Leu), Lysine (Lys), Phenylalanine (Phe), Threonine (Thr), Tryptophan (Trp), and Valine (Val), while a few others are considered as semi-essential, such as Glutamine (Gln) and Tyrosine (Tyr) [15, 16]  Consistently, EAA deprivation triggers a cell-autonomous adaptive response, characterized by extensive metabolic and gene expression modifications, implementing biosynthetic, catabolic, and plasma membrane transport processes, aimed at reconstituting the full AA complement [17, 18]  The best known and conserved pathways responding to AA deprivation are triggered by mechanistic Target of Rapamycin Complex 1 (mTORC1) and General amino acid Control Non-derepressible 2 (GCN2) protein kinases [15, 19, 20]  Activation of mTORC1 requires in particular the presence of Gln, Arg and Leu, but also Met , which activate the kinase through sensors mainly acting upstream of Rag GTPases at lysosomal membranes   In turn, mTORC1 promotes cell growth, proliferation and anabolism upon activation, and translational attenuation and autophagy upon inhibition [19, 20] 
By contrast, GCN2 is activated by deprivation of any individual EAA, by means of its histidyl-tRNA synthetase-related domain, which binds uncharged tRNAs accumulating during AA limitation [23, 24]  Upon activation, GCN2 phosphorylates and inhibits its only known downstream target, namely the eukaryotic Initiation Factor 2 α (eIF2α), thereby initiating the Integrated Stress Response (ISR)  This leads to attenuation of general translation, and induction of a transcriptional/translational program, aimed at increasing stress resistance and restoring cell homeostasis, by upregulating a specific subset of genes, including Activating Transcription Factor 4 (ATF4) and C/EBP-Homologous Protein (CHOP) [25–27]  Thus, inhibition of mTORC1 and activation of GCN2 by AA restriction cooperate to attenuate general translation at the initiation step, increase catabolism and turnover, and enhance stress resistance to promote adaptation   However, how these processes eventually induce protective mechanisms against the alterations associated with aging, which include pervasive epigenetic and transcriptional changes [28, 29], remains largely unknown 
We previously reported the unexpected observation that prolonged deprivation of either Tyr, or of both Methionine and Cysteine (Met/Cys), triggers the selective and reversible reactivation of exogenous transcriptional units, including plasmids, retroviral vectors and proviruses, integrated into the genome and transcriptionally repressed by defensive mechanisms against non-native DNA sequences [30, 31]  This phenomenon was observed both in HeLa epithelial and ACH-2 lymphocytic human cells, and was independent of the transgene or provirus (Ocular Albinism type 1, OA1; Green Fluorescent Protein, GFP; Lysosomal-Associated Membrane Protein 1, LAMP1; Human Immunodeficiency Virus-1, HIV-1), or of the exogenous promoter driving their transcription, either viral (cytomegalovirus, CMV; Long Terminal Repeat, LTR) or human (Phospho-Glycerate Kinase 1, PGK1; Elongation Factor-1α, EF-1α)   Furthermore, this transgene reactivation response was not reproduced by serum starvation, activation of p38, or pharmacological inhibitors of mTOR (PP242 or rapamycin), sirtuins and DNA methylation  By contrast, it was induced by pan histone deacetylase (HDAC) inhibitors, and by selective inhibitors of class II HDACs   Consistently, we found that the mechanism responsible involves epigenetic modifications at the transgene promoter, including reduced nucleosome occupancy and increased histone acetylation, and is mediated in part by reduced expression of a class II HDAC, namely HDAC4  
These findings indicate that AA deprivation induces a specific epigenetic and transcriptional response, affecting the expression of newly-integrated exogenous transgenes and proviruses, and suggesting that endogenous sequences sharing similar structural and functional features may represent a transcriptional target as well [30, 31]  In particular, transposable elements, such as LTR-retrotransposons (or endogenous retroviruses, ERVs), are genomic “parasites” anciently-integrated into the genome, and silenced by epigenetic mechanisms of mammalian cells against the spreading of mobile elements, eventually becoming "endogenized" during evolution [32, 33]  This raises the question of whether their expression is also sensitive to AA restriction  In addition, it remains unclear whether or not the transgene reactivation response is related to specific AA deprivations, and most importantly which is the AA sensing/signaling pathway involved, in particular whether the GCN2 kinase is implicated  Thus, here we used the reactivation of silenced transgenes in cultured cells, as a model to investigate a novel molecular pathway induced by imbalanced EAA starvation, implicated in the epigenetic/transcriptional regulation of exogenous non-native DNA sequences and possibly of other endogenous anciently-integrated genomic elements 
HeLa human epithelial carcinoma, HepG2 human hepatocellular carcinoma and C2C12 mouse skeletal muscle cells were maintained in DMEM containing glutaMAX (Invitrogen) and supplemented with 10% FBS (Sigma), 100 U/ml penicillin G (Invitrogen), 100 mg/ml streptomycin (Invitrogen), at 37°C in a 5% CO2 humidified atmosphere  Cell lines carrying integrated and partially silenced transgenes were also maintained in 600–1000 μg/ml G418 
The C2C12 cell line was provided by ATCC  HeLa and HepG2 cells were obtained by Drs  F  Blasi and G  Tonon at San Raffaele Scientific Institute, Milan, Italy, respectively, and were authenticated by Short Tandem Repeat (STR) profiling, using the Cell ID System kit (Promega), according to the manufacturer’s instructions  Briefly, STR-based multiplex PCR was carried out in a final volume of 25 μL/reaction, including 5 μL Cell ID Enzyme Mix 5X, 2 5 μL Cell ID Primer Mix 10X and 3 ng of template DNA  The thermal cycling conditions were: 1 cycle at 96°C for 2 min, followed by 32 cycles at 94°C for 30 sec, 62°C for 90 sec, and 72°C for 90 sec, and 1 cycle at 60°C for 45 sec  The following STR loci were amplified: AMEL, CSF1PO, D13S317, D16S539, D21S11, D5S818, D7S820, TH01, TPOX, vWA  Fragment length analysis of STR-PCR products was performed by Eurofins Genomics, using standard procedures of capillary electrophoresis on the Applied Biosystems 3130 XL sequencing machine, and assessment of the STR profile was performed at the online STR matching analysis service provided at http://www dsmz de/fp/cgi-bin/str html 
Stable cell clones, expressing myc-tagged human OA1 (GPR143) or GFP transcripts, were generated using pcDNA3 1/OA1myc-His or pcDNA3 1/EGFP vectors   Briefly, HeLa, HepG2 and C2C12 cells were transfected using FuGENE 6 (Roche) and selected with 800, 1000, and 650 μg/ml of G418 (Sigma), respectively, which was maintained thereafter to avoid loss of plasmid integration  G418-resistant clones were isolated and analyzed for protein expression by epifluorescence and/or immunoblotting 
Full DMEM-based medium, carrying the entire AA complement, and media deprived of Met/Cys (both AAs), Met (only), Cys (only), Alanine (Ala), Thr, Gln, Val, Leu, Tyr, Trp, Lys and His were prepared using the Nutrition free DMEM (cat #09077–05, from Nacalai Tesque, Inc , Kyoto, Japan), by adding Glucose, NaHCO3, and either all 20 AAs (for full medium) or 18–19 AAs only (for deprivations of two-one AAs)  Single AAs, Glucose, and NaHCO3 were from Sigma  Further details and amounts utilized are indicated in S1 Table  All media were supplemented with 10% dialyzed FBS (Invitrogen), 100 U/ml penicillin G (Invitrogen), 100 mg/ml streptomycin (Invitrogen), and G418 as required  HBSS was from Invitrogen  Cells were seeded at 10–30% of confluency; cells to be starved for 48 h were plated 2–3 times more confluent compared to the control  The following day, cells were washed and cultured in the appropriate medium, with or without EAA, for 24–48 h 
L-Histidinol (HisOH), PP242, Integrated Stress Response Inhibitor (ISRIB), SP600125, Cycloheximide (CHX) were from Sigma; Salubrinal was from Tocris Bioscience; U0126 was from Promega  Drugs were used at the following final concentrations: HisOH at 4–16 mM; PP242 at 1–3 μM; ISRIB at 100 nM; SP600125 at 20 μM in HepG2 cells and 50 μM in HeLa cells; Cycloheximide (CHX) at 50 ug/ml in HepG2 cells and 100 ug/ml in HeLa cells; Salubrinal at 75 μM; U0126 at 50 μM  Vehicle was used as mock control  Treatments with drugs to be tested for their ability to inhibit transgene reactivation (ISRIB, SP600125 and U0126) were initiated 1h before the subsequent addition of L-Histidinol (ISRIB) or the subsequent depletion of Met/Cys (SP600125 and U0126) 
Total RNA was purified using the RNeasy Mini kit (Qiagen), according to manufacturer’s instructions  RNA concentration was determined by Nanodrop 8000 Spectrophotometer (Thermo Scientific)  Equal amount (1 μg) of RNA from HeLa, HepG2 and C2C12 cells was reverse transcribed using the SuperScript First-Strand Synthesis System for RT-PCR (Invitrogen) using oligo-dT as primers, and diluted to 5 ng/μl  The cDNA (2 μl) was amplified by real-time PCR using SYBR green Master Mix on a Light Cycler 480 (Roche), according to manufacturer’s instructions  The thermal cycling conditions were: 1 cycle at 95°C for 5 min, followed by 40–45 cycles at 95° for 20 sec, 56° for 20 sec and 72° for 20 sec  The sequences, efficiencies and annealing temperatures of the primers are provided in S2 Table  Data were analyzed with Microsoft Excel using the formula EtargetΔct target (control-sample) /EreferenceΔct reference (control-sample)   Reference genes for normalizations were ARPC2 (actin-related protein 2/3 complex, subunit 2) for HeLa and HepG2 cells; and Actb (actin beta) for C2C12 cells, unless otherwise indicated 
siRNA (Mission esiRNA, 200 ng/μL; Sigma) against ATF4 and GCN2 were designed against the targeted sequences NM_001675 and NM_001013703, respectively  Cells seeded in 6-well plates were transfected with 1 μg of siRNAs and 5 μL of Lipofectamine 2000 (Invitrogen), following manufacturer’s instructions, at day 1 post-plating for ATF4 and at day 1 and 2 post-plating for GCN2  At day 2 (ATF4) or 3 (GCN2) post-plating, cells were washed and cultured in medium in the absence or presence of HisOH 4 mM for 6 h  siRNAs against RLuc (Sigma), targeting Renilla Luciferase, were used as negative control  For CRISPR/Cas9 experiments, we used the “all-in-one Cas9-reporter” vector, expressing GFP (Sigma), which is characterized by a single vector format including the Cas9 protein expression cassette and gRNA (guide RNA)  GFP is co-expressed from the same mRNA as the Cas9 protein, enabling tracking of transfection efficiency and enrichment of transfected cells by fluorescence activated cell sorting (FACS)  The human U6 promoter drives gRNA expression, and the CMV promoter drives Cas9 and GFP expression  The oligonucleotide sequences for the three gRNAs targeting GCN2 exon 1 or 6 are listed in S2 Table  We transfected HeLa and HepG2 cells with these plasmids individually (one plasmid one guide) and sorted the GFP-positive, transfected cells by FACS  Screening GCN2-KO clones was performed by western blotting  In the case of HepG2-OA1 cells, two rounds of selection were necessary to obtain three GCN2-KO clones by using a guide RNA against exon 1  Compared to the original HepG2-OA1 cell line and to the clone resulting from the first round of selection (185#27), the selected clones E23, F22 and F27 showed a very low amount—if any—of residual GCN2 protein (see results) 
Genomic DNA of HeLa and HepG2 cells was purified using DNeasy Blood and Tissue kit (Qiagen), according to the manufacturer’s instructions  DNA concentration was determined by Nanodrop 8000 Spectrophotometer (Thermo Scientific)  PCR conditions for amplification of GCN2 exon 1 and 6 were as follows: 1 cycle at 94°C for 5 min, followed by 35 cycles at 94°C for 40 sec, 56°C for 40 sec, and 72°C for 40 sec; and a final extension step of 5 min at 72°C  The primer sequences are provided in S2 Table 
For OA1, western immunoblotting was carried out as described   For GCN2, cells were lysed in RIPA buffer, boiled at 95°C for 5 min and resolved on a 7 5% polyacrylamide gel; immunoblotting was then performed following standard procedures  Primary Abs were as follows: anti-human OA1, previously developed by our group in rabbits ; anti-GCN2 (Cell Signaling, Cat  #3302) 
Statistical analyses were performed using Microsoft Excel for Mac (version 15 32, Microsoft) for Student’s t-test; or GraphPad Prism (version 5 0d for Mac, GraphPad Software, Inc ) for one-way analysis of variance (ANOVA), followed by Dunnett’s or Tukey’s multiple comparisons post-tests  T-test was used when only two means, typically sample versus control, were compared, as specified in the figure legends  One way ANOVA was used for multiple comparisons, followed by either a Dunnett’s (to compare every mean to a control mean), or a Tukey’s (to compare every mean with every other mean) post-test, by setting the significance level at 0 05 (95% confidence intervals)  Both tests compare the difference between means to the amount of scatter, quantified using information from all the groups  Specifically, Prism computes the Tukey-Kramer test, allowing unequal sample sizes  P values in Figures are generally referred to comparison between a sample and the control (full medium/mock), and are indicated as follows: *P<0 05, **P<0 01, ***P<0 001  Comparisons not involving the control are similarly indicated, by a horizontal line at the top of the graphs, encompassing the two samples under analysis  Additional details regarding the specific experiments are reported in the Figure Legends 
To examine the expression behavior of genomic repeats upon AA starvation, we performed a transcriptomic analysis taking advantage of an intramural sequencing facility  HeLa-OA1 cells were cultured in normal medium (for 6-30-120 hours) or in absence of Met/Cys (for 6-15-30-72-120 hours)  Total RNA was prepared using Trizol (Sigma) to preserve transcripts of both small and long sizes (from Alu, of about 0 3 kb, to Long Interspersed Nuclear Elements, LINEs, and ERVs, up to 6–8 kb long), DNase treated to avoid contamination of genomic DNA, and processed for NGS sequencing by Ovation RNA-Seq System V2 protocol and HiSeq 2000 apparatus  Raw sequence data (10–20 M reads/sample) were aligned to the human genome (build hg19) with SOAPSplice   Read counts over repeated regions, defined by RepeatMasker track from UCSC genome browser , were obtained using bedtools suite   Normalization factors and read dispersion (d) were estimated with edgeR , variation of abundance during time was analyzed using maSigPro package , fitting with a negative binomial distribution (Θ = 1/d, Q = 0 01), with a cutoff on stepwise regression fit r2 = 0 7  Read counts were transformed to RPKM for visualization purposes  The expression of the OA1 transgene and HDAC4, which are progressively up- and down-regulated during starvation, respectively , were used as internal controls 
For genomic repeat analysis, reads belonging to repetitive elements were classified according to RepeatMasker and assigned to repeat classes (total number in the genome = 21), families (total number in the genome = 56) and finally subfamilies (total number in the genome = 1396), each including a variable number of genomic loci (from a few hundred for endogenous retroviruses, up to several thousand for Alu)  Repeat subfamilies were then clustered according to their expression pattern in starved vs control cells, by maSigPro using default parameters, and repeats classes or families that are significantly enriched in each cluster, compared to all genomic repeats, were identified by applying a Fisher Exact test (using scipy stats, a statistical module of Python)  Alternatively, differentially expressed repeat subfamilies were identified by averaging three time points of starvation (15-30-72 h) and controls  Repeats significantly up- or downregulated (104 and 77, respectively) were selected based on a P value <0 05 (unpaired two-tailed Student’s t-test, assuming equal variance), and analyzed for their class enrichment by a Fisher Exact test as described above 
For gene set enrichment analysis of Met/Cys deprived vs control HeLa cells, differentially expressed genes were selected considering three time points of starvation (15-30-72 h) and controls, based on a P value <0 05 (unpaired two-tailed Student’s t-test, assuming equal variance) and a fold change >2  This led to a total of 2033 differentially expressed genes, 996 upregulated and 1037 downregulated  The enrichment analysis was performed separately for up and down regulated genes, or with all differentially expressed genes together (both), using the KEGG database  The analysis was performed with correction for the background of all expressed genes (about 13600 genes showing an average expression over 3 starvation and 3 control samples of at least 5 counts) and by using default parameters (adjusted P value and q-value cut-off of <0 05 and 0 2, respectively)  Differentially expressed genes were also selected considering all starvation time points, as with genomic repeats, by maSigPro using default parameters, and a fold change of at least 1 5, leading to similar enrichment results (not shown)  RNAseq gene expression data are available in the ArrayExpress database under the accession number E-MTAB-6452 
To provide proof-of-principle that AA starvation may affect the expression of transposable elements, we performed an RNAseq analysis of the previously described HeLa-OA1 cells, carrying an integrated and partially silenced OA1 transgene   Since the reactivation of the transgene by starvation is a progressive phenomenon , we performed a time-course experiment, where each time point represents one biological sample, rather than a biological triplicate of a single time point  To this aim, cells were cultured either in normal medium, or in absence of Met/Cys for different time points (6-15-30-72-120 hours), resulting in the progressive upregulation of the OA1 transgene during starvation (Fig 1A and 1B), consistent with previously published results   The expression of genomic repeats was determined according to RepeatMasker annotation and classification into classes, families, and subfamilies  Repeat species were then subjected to differential expression and enrichment analyses in starved vs control conditions  Out of 1396 annotated repeat subfamilies, 172 species displayed a differential expression profile during starvation 
Fig 1  Exogenous transgene and endogenous retroviruses are upregulated in Met/Cys-deprived HeLa cells 
(A,B) Exogenous integrated transgene (OA1) mRNA abundance in HeLa-OA1 cells, cultured in Met/Cys-deprived medium for the indicated time points, and analyzed by RNAseq (A), or RT-qPCR (B), compared to full medium  Data represent RPKM (A), or mean ± SD of 2 technical replicates, expressed as fold change vs  control (full medium at 6 h = 1) (B)  (C) Clustering of 172 genomic repeat subfamilies, differentially expressed upon starvation, according to their expression profile  (D) Class distribution of repeat subfamilies belonging to differential expression clusters, compared to all genomic repeat subfamilies (first column)  Class DNA includes DNA transposons; SINE includes Alu; LINE includes L1 an L2; LTR includes endogenous retroviruses and solitary LTRs; Satellite includes centromeric acrosomal and telomeric satellites; Others includes SVA, simple repeats, snRNA, and tRNAs  LTR-retroelements are significantly enriched among repeats that are upregulated upon starvation, while LINEs are significantly enriched among repeats that are downregulated  *P<0 05, ***P<0 001 (Fisher exact test) 
As shown in Fig 1C, the clustering of differentially expressed repeats, according to their expression pattern, reveals profiles comparable to the behavior of the transgene in the same conditions, i e  upregulation upon starvation and no change in regular medium (Cluster 1 and 2)  In particular, Cluster 1 contains sequences that, similarly to the OA1 transgene, are progressively upregulated upon starvation (Fig 1A and 1C) , while Cluster 2 contains sequences that are upregulated at early time points  Interestingly, repeat families that are significantly enriched in these two clusters belong mostly to the group of LTR-retrotransposons, including ERV1, ERVK, ERVL, ERVL-MaLR and other LTR sequences (Fig 1D; S1A and S2A Figs)  By contrast, DNA transposons (such as TcMar-Tigger) and L1 non-LTR retrotransposons are enriched among repeats that are downregulated during starvation, particularly at late time points (Clusters 3 and 4) (Fig 1D; S1A and S2A Figs)  Consistent results were obtained by selecting significantly up- or downregulated genomic repeats (overall 181 species), based on their average expression out of three time points of starvation (15-30-72 h, when the transgene upregulation is more homogeneous) and controls, and on a P value <0 05 (S1B and S2B Figs)  These findings suggest that EAA starvation induces genome-wide effects involving repetitive elements, and that—among major repeat classes—it upregulates in particular the expression of ERVs 
In addition, to obtain a general overview of main gene pathways changing their expression together with the transgene during AA starvation, we performed gene expression and enrichment analyses of regular genes, by considering three time points of starvation (15-30-72 h) and controls  Differentially expressed genes were selected based on a P value <0 05 and a fold change between means of at least 2, and analyzed with the EnrichR tool   As shown in Fig 2 and S1 File, enrichment analyses against the KEGG and Reactome databases reveals a predominance of downregulated pathways, namely ribosome and translation, proteasome, AA metabolism, oxidative phosphorylation and other pathways related to mitochondrial functions, which are affected in Huntington, Alzheimer and Parkinson diseases (http://www genome jp/kegg/pathway html)  In particular, a large fraction of ribosomal protein mRNAs is downregulated upon Met/Cys starvation (Fig 2A and 2C; S1 File), consistent with the notion that their genes–despite being scattered throughout the genome—are coordinately expressed in a variety of conditions   This reduced expression may depend on multiple pathways that control ribosome biogenesis in response to external stimuli, including the downregulation of Myc activity , the downregulation of mTORC1 [42, 44], or possibly the activation of the ISR, as described in yeast   By contrast, upregulated genes show a significant enrichment for transcription and gene expression (Fig 2B)  Similar results were obtained by the Gene Ontology Biological Process (GO-BP) database (S1 File), overall indicating a general downregulation of translation and metabolism, and upregulation of transcription, during the time interval of Met/Cys starvation corresponding to the transgene upregulation 
Fig 2  Gene set enrichment analysis of Met/Cys-deprived HeLa cells 
Differentially expressed genes between three time points of starvation (15-30-72 h) and controls were selected based on a P value <0 05 and a fold change of at least 2, leading to a total of 996 upregulated, and 1037 downregulated genes  The enrichment analysis was performed separately for up and down regulated genes, using the EnrichR tool and the KEGG (A) and REACTOME (B, C) databases  Ranking is based on the combined score provided by EnrichR, and categories are displayed up to 20 items with an Adjusted P value <0 05  No significant categories were found with upregulated genes against the KEGG database  All data are shown in S1 File  The enrichment analysis using all differentially expressed genes together did not reveal any additional enriched process 
To characterize the pathway leading to the reactivation of silenced transgenes, we used HeLa-OA1 and HeLa-GFP cells, as described   In addition, to test cell types relevant for AA metabolism, such as liver and muscle, we generated clones of HepG2 human hepatoma and C2C12 mouse skeletal muscle cells, stably transfected with plasmids for OA1 and GFP transgenes, respectively (HepG2-OA1 and C2C12-GFP cells; endogenous OA1 is not expressed in any of these cell types)  In all cases, the integrated transgenes are under the control of the CMV promoter in the context of a pcDNA3 1 plasmid, are partially silenced, and can be efficiently upregulated by HDAC inhibitors (trichostatin A, TSA; ref   and S3A, S3B and S4A Figs), indicating that their expression is controlled at least in part by epigenetic mechanisms, as previously described  
To establish whether the reactivation response results from the shortage of specific AAs only, such as Met/Cys, or it is triggered by any AA deprivations, we cultured HeLa-OA1, HeLa-GFP, HepG2-OA1 and C2C12-GFP cells for 24–48 hours with a battery of media deprived of EAAs or semi-EAAs, including Met/Cys, Thr, Gln, Val, Leu, Tyr, Trp, Lys, and His  As negative controls, cells were cultured in full medium, carrying the entire AA complement, and in a medium deprived of Ala, a non-essential AA  The expression of the transgene transcript was then evaluated by RT-qPCR  As shown in Fig 3, and in S3C and S4B Figs, most EAA-deficiencies induced reactivation of the OA1 or GFP transgenes in all four cell lines, with the notable exception of Trp deprivation, which consistently resulted in no or minimal reactivation of the transgenes  Indeed, despite some variability, Met/Cys deficiency, but also Thr, Val, Tyr, and His deprivation always gave an efficient response, while Leu, Gln and Lys elicited evident responses in some cases, but not in others  Depletion of Phe gave results comparable to Tyr deprivation, however it significantly altered multiple reference genes used for normalization and therefore was eventually omitted from the analysis (not shown)  Finally, in the above experiments we used a combined Met/Cys deficiency, to avoid the potential sparing of Met by Cys  and for consistency with our previous studies   Nevertheless, the analysis of single Met or Cys starvation, both at the protein and transcript levels, revealed an exclusive role of Met deprivation in transgene reactivation, consistent with the notion that Cys is not an EAA (S3D and S3E Fig) 
Fig 3  EAA deprivation induces reactivation of silent transgenes in HeLa and HepG2 cells 
Relative transgene (OA1) and CHOP mRNA abundance in HeLa-OA1 (A) and HepG2-OA1 (B) cells, cultured in various AA-deprived media for 48 h and 24 h, respectively, compared to full medium  Mean ± SEM of 3 independent experiments  Data are expressed as fold change vs  control (full medium = 1)  *P<0 05, **P<0 01, ***P<0 001 (one way ANOVA, followed by Dunnett’s post-test vs  full medium) 
Collectively, these results indicate that transgene reactivation by EAA starvation is reproducible with most EAAs, shared by different cell types (epithelium, liver, and skeletal muscle), and conserved in different mammalian species (human, mouse) 
mTORC1 inhibition and GCN2 activation trigger the best-known signaling pathways responding to AA starvation   We previously showed that inhibition of mTORC1 is not sufficient to reproduce transgene reactivation in HeLa cells   By contrast, the involvement of GCN2 and the ISR, including the downstream effectors ATF4 and CHOP, has never been tested  In addition, this pathway has been typically assessed in transient assays, lasting for a few hours, which may not be comparable with the prolonged starvation conditions necessary to reactivate the transgene expression (at least 15–24 h)  Thus, we tested whether CHOP expression was upregulated upon incubation of HeLa-OA1, HepG2-OA1 and C2C12-GFP cells in media deprived of different EAAs for 24–48 h 
As shown in Fig 3 and S4B Fig, we found that CHOP expression is increased in all EAA-starvation conditions, but not in the absence of Ala, in all tested cell lines  Similar, yet less pronounced, results were obtained with ATF4, consistent with the notion that activation of this transcription factor is mainly mediated by translational upregulation (not shown) [15, 26]  However, the upregulation of CHOP does not parallel quantitatively that of the transgene, neither appears sufficient to induce it  In fact, CHOP is highly upregulated even upon Trp starvation, which consistently results in no or minimal reactivation of the transgenes (compare CHOP with OA1 or GFP expression; Fig 3 and S4B Fig)  Thus, while the ISR appears widely activated upon EAA starvation, the upregulation of its downstream effector CHOP only partly correlates with transgene reactivation and may not be sufficient to induce it 
The activation of the ISR upon AA starvation suggests that GCN2 may be involved in the transgene reactivation response  Therefore, we tested whether direct pharmacological activation of this kinase is sufficient to trigger the transgene reactivation similarly to starvation  In addition, we used pharmacological inhibitors of mTOR to corroborate previous negative results in HeLa cells  in the other cell lines under study  To this aim, HeLa-OA1 or GFP, HepG2-OA1 and C2C12-GFP cells were cultured in the presence of different concentrations of PP242 (mTOR inhibitor) or L-Histidinol (GCN2 activator, inhibiting tRNAHis charging by histidyl-tRNA synthetase), either alone or in combination for 24 h, compared to Met/Cys-deprived and full medium  As shown in Fig 4 and S5 Fig, while inhibition of mTORC1 consistently leads to minor or no effects, in agreement with previous findings , treatment with L-Histidinol results in efficient reactivation of the transgene in HepG2-OA1 and C2C12-GFP cells, but not in HeLa cells 
Fig 4  mTOR inhibition and GCN2 activation differently affect transgene expression in HeLa and HepG2 cells 
Relative transgene (OA1) and CHOP mRNA abundance in HeLa-OA1 (A) and HepG2-OA1 (B) cells, cultured in Met/Cys-deprived medium, or in the presence of PP242 (mTOR inhibitor; 1–3 μM) or L-Histidinol (HisOH, GCN2 activator; 4–16 mM), either alone or in combination for 24–48 h, compared to full medium  Mean ± SEM of 4 (A) or 3 (B) independent experiments  Data are expressed as fold change vs  control (full medium = 1)  *P<0 05, **P<0 01, ***P<0 001 (one way ANOVA, followed by Dunnett’s post-test vs  full medium)  PP-1 and PP-3, PP242 at 1 and 3 μM, respectively; HisOH-4 and HisOH-16, L-Histidinol at 4 and 16 mM, respectively 
Specifically, L-Histidinol is not effective in HeLa-OA1 and HeLa-GFP cells, either alone or in combination with PP242 (Fig 4A and S5A Fig), or by using different concentrations of the drug, with or without serum (not shown)  In these cells, L-Histidinol appears also unable to trigger the ISR, as indicated by lack of CHOP upregulation, possibly due to their different sensitivity to the drug  These findings are consistent with previous reports, describing the use of L-Histidinol in HeLa cells in conditions of low His concentration in the culture medium , which would resemble AA starvation in our system and therefore may not be applicable  Thus, even though the amount of the amino alcohol was adapted to exceed 20 to 80 times that of the amino acid, as described , HeLa cells may be resistant or able to compensate 
In contrast, in other cell types, L-Histidinol has been utilized in regular DMEM, to mimic the AA response triggered by DMEM lacking His [48, 49]  Consistently, in HepG2-OA1 cells, L-Histidinol is sufficient to elicit extremely high levels of transgene reactivation, and its combination with PP242 results in additive or even synergistic effects, possibly due to an indirect effect of mTOR inhibition on GCN2 activity (Fig 4B) [50, 51]  Similarly, C2C12-GFP cells efficiently reactivate the transgene upon treatment with L-Histidinol, but not PP242 (S5B Fig)  However, differently from HepG2-OA1 cells, simultaneous treatment of C2C12-GFP cells with L-Histidinol and PP242 does not lead to synergistic effects  Consistent with stimulation of the ISR, CHOP and to a minor extent ATF4 are upregulated by L-Histidinol in both cell lines, yet their expression levels show only an incomplete correlation with those of the transgene (Fig 4B, S5B Fig, and not shown) 
The finding that GCN2 activation by L-Histidinol is sufficient to reactivate the transgenes in both HepG2-OA1 and C2C12-GFP cells pointed to this kinase, and to the downstream ISR, as the pathway possibly involved in the EAA starvation response  Thus, we investigated whether the ISR is sufficient to trigger upregulation of the OA1 transgene in HepG2-OA1 cells by pharmacological means  As CHOP expression does not correspond quantitatively and is not sufficient to induce transgene reactivation, we tested the role of the core upstream event of the ISR, namely the phosphorylation of eIF2α , which can be induced by pharmacological treatments, independent of GCN2 (Fig 5A)  To this aim, we used Salubrinal, a specific phosphatase inhibitor that blocks both constitutive and ER stress-induced phosphatase complexes against eIF2α, thereby increasing its phosphorylation   We found that, while the ISR is activated upon Salubrinal treatment, as shown by increased CHOP expression, it does not induce OA1 transgene reactivation (Fig 5B) 
Fig 5  The ISR is neither sufficient nor necessary to induce transgene reactivation in HepG2 cells 
(A) Schematic representation of GCN2 activation by AA starvation, resulting in phosphorylation of eIF2a and initiation of the downstream ISR  In addition to GCN2, the ISR may be activated by other eIF2a kinases (PKR, HRI and PERK; not shown in the picture)  (B) Relative transgene (OA1) and CHOP mRNA abundance in HepG2-OA1 cells treated for 24 h with Salubrinal (a drug that induces the ISR by inhibiting the dephosphorylation of eIF2α; 75 μM), compared to full medium  Mean ± range of two experiments  Data are expressed as fold change vs  control (DMEM = 1)  *P<0 05 (paired two-tailed Student’s t-test vs  control)  (C) Relative transgene (OA1) and CHOP mRNA abundance in HepG2-OA1 cells treated for 6 h with L-Histidinol (HisOH, GCN2 activator; 4 mM), in the absence or presence of ISRIB (a drug that bypasses the phosphorylation of eIF2α, inhibiting triggering of the ISR; 100 nM)  Mean ± range of two experiments  Data are expressed as fold change vs  control (DMEM = 1)  **P<0 01, ***P<0 001 (one way ANOVA, followed by Tukey’s post-test; P values refer to comparisons vs  control, unless otherwise indicated)  (D) Relative transgene (OA1) and ATF4 mRNA abundance in HepG2-OA1 cells transfected with control (CTRL) or anti-ATF4 siRNAs, and incubated in the presence or absence of L-Histidinol (HisOH, GCN2 activator; 4 mM) for 6 h  Mean ± range of two experiments  Data are expressed as fold change vs  control (w/o HisOH = 1, top; control siRNA = 1, bottom)  *P<0 05 (one way ANOVA, followed by Tukey’s post-test; P values refer to comparisons vs  control, unless otherwise indicated) 
To test whether the ISR is necessary to trigger the transgene response to L-Histidinol, we used the chemical compound ISRIB, which inhibits the activation of the ISR, even in the presence of phosphorylated eIF2α, likely by boosting the activity of the guanine-nucleotide exchange factor (GEF) for eIF2α, namely eIF2B [53, 54]  HepG2-OA1 cells were stimulated with L-Histidinol, either in the presence or absence of ISRIB  As shown in Fig 5C, while the expression of CHOP is inhibited by ISRIB, as expected, the reactivation of the OA1 transgene is not affected  In addition, knockdown of the closest eIF2α downstream effector ATF4 by siRNAs does not interfere with the reactivation of the OA1 transgene by L-Histidinol (Fig 5D)  Together, these data suggest that eIF2α phosphorylation and the downstream ISR pathway are neither sufficient nor necessary to induce transgene reactivation 
To definitively establish if GCN2 is necessary to trigger the transgene reactivation response to EAA starvation, we directly suppressed its expression by CRISPR/Cas9-mediated knock-out (KO)  We generated three independent GCN2-KO clones from the parental HeLa-OA1 cell line, by using three different guide RNAs, two against exon 1 (clones 183#11 and 185#5), and one against exon 6 (clone 239#1) of the GCN2 gene  Genomic characterization confirmed the presence of mutations on both alleles of exon 1 of the GCN2 gene in clone 183#11, and on both alleles of exon 6 in clone 239#1; by contrast, clone 185#5 showed multiple alleles in exon 1, consistent with the presence of two cell populations, and was not characterized further at the genomic level (S6 Fig)  None of these clones express GCN2 at the protein level, as shown by immunoblotting (Fig 6A)  To test the GCN2-KO cells for their ability to respond to EAA starvation, parental HeLa-OA1 cells and the three GCN2-KO clones were cultured in media deprived of Met/Cys or Thr (corresponding to the most effective treatments in this cell line; see Fig 3A) for 24–48 h and transgene expression was assessed by RT-qPCR  We found that the reactivation of the OA1 transgene is neither abolished, nor reduced by KO of GCN2, thus excluding that this kinase is necessary for the response to EAA starvation in HeLa-OA1 cells (Fig 6B and 6C) 
Fig 6  GCN2 knockout does not interfere with transgene reactivation in HeLa cells 
(A) Immunoblotting of protein extracts from the HeLa-OA1 parental cell line and GCN2-KO clones 183#11, 185#5 and 239#1, immunodecorated with anti-GCN2 antibody  Arrow, GCN2 specific band  Ponceau staining was used as loading control  (B, C) Relative transgene (OA1) mRNA abundance in HeLa-OA1 cells and GCN2-KO clones, cultured in Met/Cys (B) or Thr (C) deprived medium for 24 h or 48 h, respectively, compared to full medium  Mean ± SD of 3 technical replicates from 1 experiment  Data are expressed as fold change vs  control (full medium = 1)  Since independent clones may display variable reactivation responses (e g  due to different levels of transgene expression in basal conditions), the results are not shown as means of the three clones, but as separate replicates 
Similarly, we generated GCN2-KO clones from the parental HepG2-OA1 cell line by the same strategy  By using a guide RNA against exon 1 of the GCN2 gene, we obtained three independent GCN2-KO clones, namely E23, F22 and F27  Genomic characterization confirmed the presence of mutations on both alleles of exon 1 of the GCN2 gene in clone F27 (S7 Fig) and all three clones showed a very low amount—if any—of residual GCN2 protein, compared to the original HepG2-OA1 cell line (Fig 7A)  To assess the ability of GCN2-KO cells to reactivate the transgene upon starvation, we cultured parental HepG2-OA1 cells and the three GCN2-KO clones in media deprived of Met/Cys or His (corresponding to the most effective treatments in this cell line; see Fig 3B) for 24 h, and evaluated the transgene expression by RT-qPCR  As shown in Fig 7B and 7C, we found that the reactivation of the OA1 transgene is neither abolished, nor reduced by KO of GCN2, as in HeLa cells  To further confirm this result, we knocked-down GCN2 by RNA interference (RNAi), and incubated the cells with or without L-Histidinol for 6 h  As shown in Fig 8, treatment of HepG2-OA1 cells with L-Histidinol results in efficient transgene reactivation, even upon significant GCN2 downregulation, both at the mRNA and protein levels  Taken together, these data strongly support the conclusion that GCN2 is not necessary for transgene reactivation in response to EAA starvation, either in HeLa or in HepG2 cells 
Fig 7  GCN2 knockout does not interfere with transgene reactivation in HepG2 cells 
(A) Immunoblotting of protein extracts from the HepG2-OA1 parental cell line and GCN2-KO clones 185#27, E23, F22, F27, immunodecorated with anti-GCN2 antibody  Clone 185#27 results from the first round of selection, and was used to generate clones E23, F22, F27  Arrow, GCN2 specific band  For GCN2 protein quantification, Ponceau staining was used as loading control and data are expressed as fold change vs  parental cell line (= 1)  (B, C) Relative transgene (OA1) mRNA abundance in HepG2-OA1 cells and GCN2-KO clones, cultured in Met/Cys (B) or His (C) deprived medium for 24 h, compared to full medium  Mean ± SD of 3 technical replicates from 1 experiment 



ground_truth: The generative interactive model used in the method is called the Coupled Generalized Dynamic Bayesian Network (C-GDBN).

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: 对于PD3.0协议，FS312BH支持的最高诱骗电压是多少？

Read the following text and answer briefly.

Context 2: 0 PPS、QC4 0协议 - 支持两路DP/DM - 支持CV/CC（分段CC）功能 - 支持定制PDO - 支持A+C双口工作，电压自动回5V - 支持FB/OPTO反馈 - 封装：QFN3x3-20L VPWR FB PowerSystem 100K GND R1 GND 19 VIN 17 FB FUNC1 FUNC2 20 15 18 13 PLUGIND VFB FS8628 QFN3x3-20L AGATE 47K 7 5K 47K 7 5K 1 16 8 7 3 4 5 6 10 9 11 CGATE CVBUS CC2 CC1 CDP CDM AVBUS DM DP ISP ISN 12 应用图 2 V3P3 100Ω 1u EP GND GND CVBUS TYPE- C CC2 CC1 CDP CDM CGND TYPE-A AVBUS DM DP 10n 200 AGND 5mΩ GND FS8611K USB-C AC-DC DC-DC 7550B-T CCM-8611K-A FS8611K USB-C 采用2颗FS8611K搭配CCM-8611K-A （MCU）工作，7550B-T配合工作 - 支持PD2 0/PD3 0/QC2 0/AFC/FCP - 支持PDO定制 - 任意单 C 的为 35W(可定制) - 双插18W（可定制15W/20W） - BOM极简，成本低 FS212C+ACM-212C-A+7550B-T 双C方案 FS212C USB-C AC-DC DC-DC 7550B-T ACM-212C-A FS8623B-A+C方案 AC-DC DC-DC FS8623B USB-A USB-C USB-A 采 用 1 颗 F S 2 1 2 C 搭 配 ACM-212C-A 工 作，7550B-T配合工作 - 支持PD2 0/PD3 0 - 支持PDO定制 - 任意单 C 的为20W - 双插7 5W回5V - BOM极简，成本低 采用一颗FS8623B实现A+C方案 - 兼容兼容Apple2 4A/低压直充 QC2 0 Class A/QC3 0 Class A/B/ FCP/SCP等 - 兼 容Type -C PD2 0 / PD3 0 / PD3 0PPS/QC4 0协议 - 支持PDO定制 - 双插回5V 
多口方案选型 产品选型 受电端芯片选型 速芯微现有多种多口的方案选择：A+C，C+C，C+C+A，C+C+C，C+C+A+A等方案。对于 A+C的方案，可使用1颗芯片实现，也可用多颗芯片来实现。 速芯微现有多种受电端诱骗芯片，客户可根据应用需求进行选择。 受电端诱骗芯片应用领域 筋膜枪 无线充 线材 无人机 产品型号 PD2 0 PD3 0 PD3 1 第三方协议 诱骗电压(V) 控制方式 内置Emarker 定制 封装 FS312A √ √ 5/9/12/15/20 电阻阻值 可变电压策略 SOT23-5 FS312AE √ √ 5/9/12/15/20 电阻阻值 √ (公头专用) 可变电压策略 SOT23-5 FS312BL √ √ √ √ 5/9/12/15/20 电阻阻值 可变电压策略 DFN2x2-6 FS312BLE √ √ √ √ 5/9/12/15/20 电阻阻值 √ (公头专用) 可变电压策略 DFN2x2-6 FS312BH √ √ √ √ 5/20/28/36/48 电阻阻值 可变电压策略 DFN2x2-6 FS312BHE √ √ √ √ 5/20/28/36/48 电阻阻值 √ (公头专用) 可变电压策略 DFN2x2-6 FS312LC √ √ √ 5/9/12 电阻阻值 可变第三方 协议 SSOP10 FS312HC √ √ √ 5/9/12/15/20 电阻阻值 可变第三方 协议 SSOP10 FS2711Q √ √ √ 任意设置 I2C √ QFN3x3-16 FS2711P √ √ √ 任意设置 I2C √ QFN3x3-16 FS2711PA √ √ 全协议 任意设置 I2C √ SSOP10 FS2711SW √ √ 全协议 SSOP10 FS512 √ √ 全协议 任意设置 I2C √ SSOP10 方案 类型 产品型号 单C 单A 双插 A+C方案 FS8623 20W（PPS）（可定制） A口全协议18w 5V共享3A FS8623B 20W（PPS）(可定制) A口全协议18w 5V共享3A FS8628 20W（PPS）(可定制) A口全协议18w 5V共享3A FS8611RPC+FS116DB 65W（PPS）(可定制) A口全协议18w A口：5V/2 4A C口：45W FS8628RC+FS116DB 35W(可定制) A口全协议18w A口：5V（BC1 2，Apple 2 4） C口：20W 方案类型 产品型号 单C1 单C2 C1/C2 C+C方案 FS8611RPB*2 30W(可定制) 30W(可定制) C1/C2：5V/3A(或5V/2 4A) FS8611GH*2 35W（可定制） 35W（可定制） C1/C2:18W（可定制） FS8628P*2 35W（可定制） 35W（可定制） C1/C2：17 4W可定制） FS8611KL*2 20W（可定制） 20W（可定制） C1/C2：5V/1 5 A FS8611PC*2 35W 35W C1/C2：18W FS8611BH*2 65W（可定制） 65W（可定制） C1：45W（可定制）C2：20W（可定制） FS8628RPC+FS8611RB 45W（可定制）） 36W （可定制）） C1：30W（可定制）C2：5V/1 5A（可定制） 方案类型 产品型号 单C1 单C2 单A C1+C2 C1/C2+A C1+C2+A C+C+A FS8611S*2+FS116DB 65W（可定制） 65W（ 可定制）） A口全协议18w 智能分配功率 45W+18W C1/C2：智能分配功率 A：18W（或5V1 5A） FS8612C+FS8628P 100W（可定制） 35W （可定制）） 20W C1：65W C2：20W C1+A：65W+20W C2+A：7 5W+7 5W C1：65W C2：7 5W A：7 5W 其他 
Source-TYPE C协议芯片选型 Source-TYPE A协议芯片选型 速芯微现有多种TYPE-C的快充协议芯片，支持多种协议，支持客户定制，多样化，满 足客户对TYPE C的各种快充需求。 速芯微现有多种TYPE A快充协议芯片，支持全协议，支持定制，满足客户对A口协议的各种需 求。速芯微的TYPE-A快充协议芯片的协议丰富，FS112系列拥有多种的型号；FS116D 系列带插入指示，可搭配TYPE-C快充协议芯片，实现A+C，A+C+C，A+A+C+C等多口方 案，协议丰富，其中FS116A一般用于插入指示使用 Source-TYPE A协议芯片引脚封装图 D+ VSS FB 1 2 3 FS112 6 5 4 D- VDD FUNC GATE VIN FUNC FB LED/PLUG_IN 1 2 3 4 5 FS116D 10 DM 9 8 7 6 DP CSP CSN VSS速芯微的各TYPE-C快充协议芯片之间可搭配使用，实现多口方案，更多详情请咨 询我司工作人员。 多口降功率专用快充协议芯片：FS8611RB，FS8611RC，FS8611RPB，FS8611RPC， FS8612CP。 带I2C快充协议芯片：FS8611S，FS8611SP 产品型号 BC1 2 Apple 2 4 QC2 0 QC3 0 AFC FCP SCP HISCP 大电流直充 封装 FS112 √ √ √ √ √ √ √ SOT23-6 FS112H √ √ √ √ √ √ √ √ √ SOT23-6 FS113 √ v √ √ √ √ √ √ √ SOT23-6 FS116DP √ √ √ √ √ √ √ √ SSOP10 FS116DB √ √ √ √ √ √ √ √ SSOP10 FS116E √ √ √ √ √ √ √ √ √ SSOP10 FS116A √ √ SSOP10 其他 可定制 PD2 0 PD3 0 PD3 0 PPS 第三方协议 反馈方式 MOS CV/CC 定制 封装 FS212C √ √ FB √ SOT23-6 FS212CM √ √ FB PMOS(可省) √ SOT23-6 FS212D √ √ √ FB √ SOT23-6 FS212DH √ √ √ FB √ SOT23-6 FS212DP √ √ √ FB PMOS √ SOT23-6 FS212DG √ √ √ FB PMOS √ SOT23-6 FS8611G √ √ FB PMOS(可省) √ SOP-8 FS8611K √ √ QC2 0/AFC/FCP FB PMOS(可省) √ SOP8 FS8611J √ √ √ 全协议 FB PMOS(可省) √ SOP8 FS8611B √ √ √ 全协议 FB PMOS(可省) √ SSOP10 FS8611RB √ √ 全协议 FB PMOS √ SSOP10 FS8611RC √ √ 全协议 FB PMOS √ SSOP10 FS8611S √ √ √ 全协议 FB PMOS √ SSOP10 FS8611PP √ √ √ 全协议 FB PMOS √ SSOP10 FS8611BP √ √ √ 全协议 FB PMOS(可省) √ SSOP10 FS8611RPB √ √ √ 全协议 FB PMOS √ SSOP10 FS8611RPC √ √ √ 全协议 FB PMOS √ SSOP10 FS8611SP √ √ √ 全协议 FB PMOS(可省) SSOP10 FS8612 √ √ √ 全协议 OPTO PMOS √ √ SSOP16 FS8612B √ √ √ 全协议 FB PMOS √ √ SSOP16 FS8612BP √ √ √ 全协议 FB PMOS √ √ SSOP16 FS8612C √ √ √ 全协议 FB/OPTO PMOS √ √ QFN4x4-16 FS8612CP √ √ √ 全协议 FB/OPTO PMOS √ √ QFN4x4-16 
'



ground_truth: 48V.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Is the ISR necessary for transgene reactivation?

Read the following text and answer briefly.

Context 4:  In the model, k 1 y represents the linear restoring force of the fluid, and k 2 y 2 and k 3 y 3 are respectively the quadratic and cubic nonlinear restoring forces of the fluid 

Volterra kernel functions

Generally, the first several order responses dominate the total response of a system  Hence, the order of the Volterra series in Eq  22 is chosen to be 3, namely, N = 3  For computing the first three order responses from Eq  22, the first three order Volterra kernel functions need to be known  Since Volterra kernel functions and corresponding frequency response functions are related by a specific Fourier transform pair, we can first write the first three orders of frequency response functions directly from Eq  28 
Then, Volterra kernel functions are obtained by the inverse Fourier transform  Based on the harmonic probing algorithm , the linear frequency response function (LFRF) H 1 (ω), the quadratic frequency response function (QFRF) H 2 (ω 1 , ω 2 ) and the cubic frequency response function (CFRF) H 3 (ω 1 , ω 2 , ω 3 ) are analytically given by:
and Figures show H 1 (ω), H 2 (ω 1 , ω 2 ) and H 3 (ω 1 , ω 2 , ω 3 ), respectively, which agree well with those reported in Ref    As expected, the modulus of H 1 (ω) in Fig  peaks near the linear natural frequency ω 0 , and the phase angle decreases monotonically from 0 to -π with increasing frequency 
Figure shows the sum frequency QFRF, where the energy converges along the line of ω 1 +ω 2 ≈ ω 0   Therefore, when the sum frequency of a two-tone excitation equals the linear resonant frequency, the second-order response may reach its maximum  Additionally, those pairs of excitations in line ω 1 + ω 2 ≈ ω 0 may produce non-negligible vibration magnitudes due to second-order nonlinear effects 
For the difference frequency QFRF in Fig  (b), the energy converges along two main lines, i e , ω 1 ≈ ω 0 and ω 2 ≈ ω 0   Figures show moduli of H 3 (ω, ω, ω) and H 3 (ω, ω, −ω), which are diagonal terms of the sum frequency CFRF and the difference frequency CFRF, respectively  While the modulus of H 3 (ω, ω, ω) peaks near ω ≈ ω 0 /3 and ω 0 , that of H 3 (ω, ω, −ω) peaks near ω ≈ ω 0 with a small hump around ω ≈ ω 0 /2 
Values at ω ≈ ω 0 /3 and ω 0 /2 may be magnified by higher-order stiffness terms in Eq  28  By performing the inverse fast Fourier transform to Eqs  29-31, the corresponding linear impulse response function h 1 (t), quadratic impulse response function h 2 (t 1 , t 2 ) and cubic impulse response function h 3 (t 1 , t 2 , t 3 ) are obtained 
Here, h 1 (t) and h 2 (t 1 , t 2 ) are plotted in Figs  , respectively, and h 3 (t, t, t) is shown in Fig    In the numerical implementation, Eqs  29-31 have been utilized with the frequency interval ∆ω = 0 1, number of frequency components N n = 1025, and cut-off frequencies 102 4 and −102 4  For decoupling Volterra kernel functions by using Laguerre polynomials, the damping rate and number of Laguerre polynomials for each order Volterra kernel function need to be determined (see Eqs  4 and 6) 
In this example, we set a 1 = a 2 = a 3 = 2 and R 1 = R 2 = R 3 = 24 because coefficients c p 1    pn become very small when R n > 24, n = 1, 2, 3  According to Eq  7, the coefficients of the first three order Volterra kernel functions are calculated, which are shown in Figs  9 and 10  For convenience, Fig  plots only c p 1 p 2 p 3 for p 3 = 0 
With the increase of the order of Laguerre polynomials, coefficients in Figs  9 and 10 gradually decrease, which illustrates how the first several orders of Laguerre polynomials dominate all orders of the Volterra kernel function  With the known Laguerre polynomials and corresponding coefficients, Volterra kernel functions are reconstructed by Eq  6 
For comparison, reconstructed Volterra kernel functions are also plotted in Figs    The reconstructed results agree well with the analytical values, which verifies the accuracy of the decomposition 

Sinusoidal excitation

From Eq  28, we consider a sinusoidal excitation where A and Ω are the amplitude and the frequency, respectively  Five cases of A and Ω are shown in Table   Excitation frequencies in Cases 1 and 2 are larger than the linear natural frequency (ω 0 ≈ 3 16), those in Case 3 are very close to ω 0 , and those in Cases 4 and 5 are smaller than ω 0  
All cases have same amplitudes  The poles of a sinusoidal excitation are λ 1,2 = ±iΩ, and the residues are α 1,2 = ∓iA/2  Numerical values of excitation poles and residues for different cases are listed in Table   Table : Parameter values, poles and residues of the sinusoidal excitation Substituting poles and residues of the excitation, as well as those of the system into Eqs 
20 and 19, response coefficients β p i ,k corresponding to system poles −a i and response coefficients γ p i ,ℓ corresponding to excitation poles λ ℓ are calculated, respectively  According to Eq  22, the first three orders of responses for each case in Table are calculated  Figures )-15(a) show the comparison of responses obtained by the proposed method and the fourth-order Runge-Kutta method with ∆t = 10 −4  
For Cases 1 and 2, the first-order responses agree well with the total responses obtained by the Runge-Kutta method, and the higher-order responses only slightly improve the transient parts  For Cases 3-5, the sum of the first three orders of responses is in good agreement with the Runge-Kutta solution 
When the response nonlinearity increases, higher-order responses need to be considered  In other words, the proposed method can accurately compute the nonlinear responses by choosing a small number N of Volterra series terms  Figures )-15(b) show the contributions of the three response components for the five cases 
In each case, the first-order response is the most dominant component, and the contributions of secondand third-order responses are much less than those of the first-order response  Especially for Cases 1 and 2, whose excitation frequencies are far from the linear natural frequency, second-and thirdorder responses are close to zero 
This may be because the QFRF and CFRF approach zero when the frequency is larger than 4 rad/s (see Figs  )  Furthermore, the mean values of the first-order responses are approximately zero, and those of the second-order responses are always smaller than zero, which are the difference frequency components in Eq  27 
Moreover, it is clearly observed that second-order responses for Cases 3-5 exhibit a periodic oscillation with a period near half of that for the first-order response, which is excited by the sum frequency component of the excitation (see second part of Eq  27)  Compared with steady-state solutions of first-and second-order responses, those of third-order responses in Cases 3-5 are no longer single regular motions 
By performing the FFT, frequency spectra of these three third-order responses are shown in Fig    We find that these three third-order responses are all dominated by their own fundamental harmonic component and the third harmonic (triple frequency) component  Figure shows the computational time to calculate the response of the oscillator for Case 1 by the proposed method, the fourth-order Runge-Kutta method and the convolution method 
The proposed method, which has an explicit solution, is much more efficient in computational time than the latter two methods, which need small time steps to obtain high-precision solutions  In particular, the efficiency of the proposed method increases with the length of the response time  Computation time (sec )
t=0 02s Convolution, t=0 02s Convolution, t=0 001s Runge-Kutta, t=0 001s Fig  : Comparison of computation efficiency of the proposed method, the fourth-fifth order Runge-Kutta method and the convolution method regular loading in Case 1

Irregular excitation

In Eq  28, considering an irregular excitation consisting of several cosine functions where N f is the number of cosine components; A n , Ω n and θ n are the amplitude, frequency and phase angle of the n th component, respectively  Table lists three cases of these parameters  In each case, the amplitudes of all components are the same, and phase angles θ n uniformly distributed between 0 and 2π are randomly generated 
To decompose the excitation into a pole-residue form, the Prony-SS method is used, whose concept is similar to that of a principal component method  The readers are referred to Ref  for details  The chosen rank of each case is also shown in Table   Figure shows the comparison of original excitations and reconstructed results of these three cases, which all have excellent agreement 
show the results computed by the fourth-order Runge-Kutta method  In all cases, the sums of the first three orders of responses agree well with those obtained by the Runge-Kutta method  The contributions of the first three orders of responses for each case are plotted in Figs  )-21(b)  Similarly, the system vibration is dominated by the first-order response 
However, the contributions of second-and third-order significantly grow with increasing excitation magnitude and frequency number  Furthermore, when the magnitude of the nonlinear response becomes large, sharp troughs are present  This phenomenon may be induced by the nonlinear stiffness  While the first-order response fails to capture these troughs, the higher-order responses successfully capture these troughs 
Figure plots the computational time to calculate the response of the oscillator for the irregular loading in Case 1 by the proposed method and the fourth-fifth order Runge-Kutta method, respectively  While the fourth-fifth order Runge-Kutta method is more efficient under a small response length, the proposed method becomes much more efficient when the response length is larger than about 130 s 
In addition, the proposed method obtains the explicit response solution, so one can directly obtain the response value at a specific time t p instead of integrating from 0 to t p for traditional numerical methods  Computation time (sec ) Proposed, t=0 02s Runge-Kutta, t=0 001s Fig  : Comparison of computation efficiency of the method and the fourth-fifth order Runge-Kutta method for irregular loading in Case 1

An unknown nonlinear

To check the applicability of the proposed method to an unknown nonlinear system, a known input excitation and its corresponding response are used to identify its Volterra kernel functions  When the Volterra kernel functions are known, we can follow the procedure in Section 4 1 to predict system responses 
In this study, the input excitation is white noise with a constant power spectrum S 0 = 0 001, and the corresponding response is obtained by solving Eq  28 by the fourth-order Runge-Kutta method, which is shown in Fig    From Section 4 1, we determine that the sum of the first two orders of responses agrees well with the total response 
In this study, the order of Volterra series N is chosen to be 2, damping rates of Laguerre polynomials are a 1 = a 2 = 2, and numbers of Laguerre polynomials are R 1 = R 2 = 24  To estimate the first two orders of Volterra kernel functions, a matrix equation is constructed using excitation data and response data 
By using the least square method to solve this matrix equation, coefficients c p 1 and c p 1 p 2 in Eq  8 are identified  Figure plots c p 1 and c p 1 p 2 , respectively, which have good agreement with the exact results in Fig    Then, the first two order Volterra kernel functions are constructed by Eq  6 
Compared with the exact results in Figs  , the identified Volterra kernel functions in Fig  completely agree well with the exact solutions  Note that the white noise excitation, which can excite more frequency components of the response, is chosen to obtain good Volterra kernel functions  A regular excitation f (t) = sin(πt) and an irregular excitation f (t) = N f n=1 A n cos(Ω n t + θ n ) with A n = 0 3 and Ω n varying from 0 to 40 with equal interval 1 are chosen as input excitations 
The predicted responses, along with results obtained by the fourth-order Runge-Kutta method, are shown in Fig    In both cases, the proposed method accurately predicts system responses  As presented in Eq  23, a nonlinear response is the sum of three terms: natural response y s (t), forced response y f (t) and cross response y c (t) 
These individual terms, as well as their sum to two excitations, are shown in Figs  27 and 28, respectively  As shown in Figs  and 28, both first-and second-order responses include the natural response y s (t) and the forced response y f (t), but the cross response y c (t) only exists in second-order responses 
When t becomes larger, both y s (t) and y c (t) diminish due to the presence of system damping, and the total response is entirely governed by y f (t)  Moreover, we notice some features at t = 0 for these components, including y s (0) = −y f (0) for the first-order response and y s (0) + y f (0) = −y c (0) for the second-order response, which are due to imposed zero initial conditions 

Conclusions

Considering arbitrary irregular excitations, an efficient generalized pole-residue method to compute the nonlinear dynamic response modelled by the Volterra series was developed  A core of the proposed method was obtaining poles and corresponding coefficients of Volterra kernel functions, then those of each order response modelled by each order Volterra series 
Once the poles and corresponding coefficients of Volterra kernel functions and excitations were both available, the remaining derivation could follow a similar pole-residue method that had been developed for ordinary linear oscillators  To obtain the poles and corresponding coefficients of Volterra kernel functions, two steps were included: (1) using Laguerre polynomials to decouple higher-order Volterra kernel functions with respect to time and (2) obtaining poles and corresponding coefficients of Laguerre polynomials in the Laplace domain 
Because the proposed method gave an explicit, continuous response function of time, it was much more efficient than traditional numerical methods  Moreover, many meaningful physical and mathematical insights were gained because not only each order response but also the natural response, the forced response and the cross response of each order were obtained in the solution procedure 
To demonstrate that the proposed method was not only suitable for a system with a known equation of motion but also applicable to a system with an unknown equation of motion, two numerical studies were conducted  For each study, regular excitations and complex irregular excitations with different parameters were investigated 
The efficiency of the proposed method was verified by the fourth-order Runge-Kutta method  This paper only computes the response under zero initial conditions  The response under non-zero initial conditions will be investigated in our future work 



ground_truth: No, it is not necessary.