text:
\section{Introduction}

Millimeter wave (mmWave) frequencies are an essential component of next-generation cellular systems, in order to meet the exponential increase of data demand and support a growing number of wireless devices \cite{saad2019vision}.
Due to a large available bandwidth, mmWave frequencies have a strong potential to provide high communication rates.
However,  the small wavelength of mmWave spectrum yields the high susceptibility to blockage caused by common objects, such as buildings and foliage, which seriously attenuate mmWave propagation \cite{semiari2017joint}.

In order to bypass obstacles and prolong the communication range, signal reflectors have been considered as an energy-efficient solution for mmWave communications.
Signal reflectors can  establish line-of-sight (LOS) links in face of blockage, by replacing a non-line-of-sight (NLOS) mmWave channel by multiple connected LOS links.
As a passive element, a signal reflector costs no energy and incurs no  additional receiving noise \cite{zhang2019reflections}.
A reflector-aided transmission enables the connected LOS links  to share the same frequency band, and, thus, yields a high spectrum efficiency.
Meanwhile, by aligning a large number of low-cost reflective components and jointly inducing phase shifts to incident signals,  an intelligent reflector (IR) can realize beamforming with very lower energy cost for mmWave communications \cite{soorki2019ultra}.
Moreover, to maintain LOS links in a mobile scenario, an IR can be equipped onto an unmanned aerial vehicle (UAV) platform \cite{zhang2019reflections}, so that the location of the IR can be adjusted intelligently, based on the real-time  communication environment, in order to improve the reliability of mmWave transmissions.
Compared with a UAV-aided relay station, a UAV-carried IR (UAV-IR) has a simpler antenna structure and smaller power cost.
Therefore, an IR facilitate multiple-input-multiple-output transmissions for the UAV platform, which has very limited onboard energy.

The use of IRs to improve the communication performance of mmWave has been studied in \cite{zhang2019reflections, soorki2019ultra,  wang2019intelligent, yue2020analysis, cao2019intelligent}.
In  \cite{zhang2019reflections}, we studied the problem of using a UAV-IR to maximize downlink transmissions towards a single mobile user.
The authors in \cite{soorki2019ultra} investigated the IR-aided  mmWave communications,  with a deep reinforcement learning (RL) framework, to improve the coverage and increase the data rate in an indoor network.
In \cite{wang2019intelligent} and \cite{yue2020analysis}, the authors proposed a hybrid precoding scheme to  jointly design the transmit precoding at the base station (BS) and the reflection parameters at the IR.
However, the prior works in \cite{ zhang2019reflections, soorki2019ultra, wang2019intelligent, yue2020analysis} focus on the downlink transmission to a single user, and they do not consider the more challenging problem of multi-user communications.
Meanwhile, the works in \cite{cao2019intelligent}  and \cite{guo2019weighted} developed a static IR-assisted mmWave communication framework for multiple downlink users, such that  the weighted sum-rate is maximized.
However, most of the previous works in \cite{soorki2019ultra,wang2019intelligent,cao2019intelligent, yue2020analysis,guo2019weighted} optimize the reflection transmission of the IR while assuming a fixed location.
Although a static IR establishes LOS links between transmitters and receivers in the face of blockage, maintaining LOS channels is  challenging, especially in a mobile communication scenario, where the movement of each user dynamically changes the channel state.
In particular, given the high susceptibility of mmWave signals to human body, a single body rotation can block the LOS link and render the reflection transmission inefficient, using a static IR.

Machine learning techniques were proposed in in \cite{soorki2019ultra} and  \cite{zhang2020millimeter,taha2019deep,huang2020reconfigurable} in order to address the  wireless channel dynamics and improve the performance of IR-aided communications.
For instance, in \cite{zhang2020millimeter}, we studied the problem of optimizing beamforming transmissions and reconfigurable reflection of an IR to serve multiple users, using a distributional RL method, so as to maximize the  downlink sum-rate.
The authors in \cite{taha2019deep} proposed a deep learning approach to optimize the IR phase shift, given a limited number of active reflective elements.
The work in \cite{huang2020reconfigurable} introduced an  RL-based scheme to jointly optimize the precoding transmission and signal reflection.
However, all the prior art in \cite{soorki2019ultra} and \cite{zhang2020millimeter,taha2019deep,huang2020reconfigurable} does not consider a mobile IR whose location can be dynamically optimized so as to enhance the mmWave reflection performance.

The main contribution of this paper is, thus, a novel  downlink framework using   a UAV-IR to assist a mmWave BS for multi-user  communications.
First, the  precoding matrix at the BS and reflection coefficient at the IR are jointly optimized to  maximize the downlink sum-rate towards multiple users.
Next,  to address the uncertainty of mmWave channels and maintain LOS links in a real-time manner, a distributional reinforcement learning approach \cite{dabney2018distributional}, based on quantile regression optimization, is introduced to learn the mmWave communication environment, such that the location of the UAV-IR is optimized  to maximize the communication sum-rate over a long-term horizon.
Simulation results show that the proposed learning-based deployment of the UAV-IR yields a significant advantage, compared to a non-learning UAV-IR, a static IR and a direct transmission schemes, in terms of the average data rate and the achievable downlink LOS probability.

The rest of this paper is organized as follows. Section \ref{sysModel_proFormulation} presents the system model and problem formulation. The optimal deployment of the UAV-IR for  multi-user downlink transmissions is proposed in Section \ref{solution}. Simulation results are shown in Section \ref{simulation}. Conclusions are drawn in Section \ref{conclusion}.

\section{System Model and Problem Formulation}\label{sysModel_proFormulation}

\begin{figure}[!t]
	\begin{center}
		\vspace{-0.2cm}
		\includegraphics[width=7cm]{systemModel}
		\vspace{-0.6cm}
		\caption{\label{systemmodel}\small A UAV-IR establishes LOS links between the BS and UEs for efficient downlink transmissions over mmWave frequencies. }
	\end{center}\vspace{-0.7cm}
\end{figure}

Consider a wireless BS serving a set $\mathcal{K}$ of $K$  cellular user equipment (UE) over the downlink via mmWave frequencies.
The BS has  $M$  transmit antennas, and each downlink UE has a single antenna.
As shown in Fig. \ref{systemmodel}, we assume that the direct transmission channel between the BS and each UE is blocked, and the received signal via the direct link is negligible.
In order to bypass the obstacle and improve the received power at each UE,  a UAV-IR with $N$ reflective elements is deployed to assist  downlink transmissions towards NLOS UEs.
By leveraging the mobility of the UAV, the UAV-IR can potentially replace each direct NLOS link with two connected LOS links, by adjusting its position and reflecting mmWave signals from the BS towards each UE.
Since an IR is a passive device, it cannot acquire the channel state information (CSI) or process received signals.
To enable information exchange, an active antenna is embedded onto the UAV to receive a control signal from the BS and feedback information from served UEs.

\subsection{Communications Capacity and Power Cost}

Consider a multi-user multiple-input-single-output downlink communications, in which the BS serves downlink UEs via a common mmWave band.
The BS-IR channel is denoted as $\boldsymbol{G} \in \mathbb{C}^{N\times M}$, and the IR-UE link for each UE $k$ is given as  $\boldsymbol{h}_k \in \mathbb{C}^{1\times N}$.
Let  $\mathcal{N}$ be the set of $N$ IR components.
For each component $n \in \mathcal{N}$,  the phase shift is denoted by $\phi_n \in [0,2\pi) $ and the amplitude attenuation is $\beta_n  \in [0,1]$.
Consequently, the IR's reflection coefficient is   $\Phi = \text{diag} (\beta_1  e^{j\phi_1},\cdots, \beta_N e^{j\phi_N} )$.
In order to provide downlink communications to multiple UEs, the BS precodes the transmit signal as an $M\times 1$ vector $\boldsymbol{a} = \sum_{k=1}^{K} \boldsymbol{w}_k s_k$, where  $\boldsymbol{w}_k \in \mathbb{C}^{M\times 1}$ is the precoding vector,  and $ s_k$ is the unit-power information symbol for UE $k$.
The  received signal at UE $k$ will thus be:
$	y_k =  \boldsymbol{h}_k \Phi \boldsymbol{G} \boldsymbol{a} + u_k$,
where  $u_k \sim \mathcal{CN}(0,\sigma^2)$ is the receiver noise at UE $k$.
In order to separate the mmWave propagation environment  with the IR's reflection, we rewrite the received signal at UE $k$ equivalently in the following form:\vspace{-0.2cm}
\begin{equation}\vspace{-0.2cm}
  	y_k =  \boldsymbol{\theta}\boldsymbol{D}_k \boldsymbol{a} + u_k,
\end{equation}
where  $\boldsymbol{\theta} = [\beta_1e^{j\phi_1},\cdots, \beta_N e^{j\phi_N}] \in \mathbb{C}^{1 \times N}$ is a vector of the UAV-IR reflection coefficients and $\boldsymbol{D}_k = \text{diag} ( \boldsymbol{h_k}) \boldsymbol{G} \in \mathbb{C}^{N \times M} $ is the CSI of the connected BS-IR-UE link towards UE $k$ without any phase shift.
The channel measurement approach for IR-aided cellular communications has been investigated in \cite{zhang2020millimeter}.
Here, we assume that the CSI $\boldsymbol{D}_k(\boldsymbol{x})$ of each BS-IR-UE link only depends on the location $\boldsymbol{x}$ of the UAV-IR, and the channel matrix $\boldsymbol{D}_k(\boldsymbol{x})$  is known to both BS and UAV-IR, as long as  $\boldsymbol{x}$  is given.
Therefore, the signal-to-interference-and-noise-ratio (SINR) of downlink communications from the BS, reflected by the IR, to each UE $k$ is
\begin{equation}\label{sinr}
\begin{aligned}
\eta_k ( \boldsymbol{W}, \boldsymbol{\theta}, \boldsymbol{x})
&=
\frac{  |\boldsymbol{\theta} \boldsymbol{D}_k(\boldsymbol{x}) \boldsymbol{w}_k |^2 }{  \sum_{i\ne k, i\in \mathcal{K}} |\boldsymbol{\theta} \boldsymbol{D}_k(\boldsymbol{x}) \boldsymbol{w}_i  |^2  + \sigma^2},
\end{aligned}
\end{equation}
where
$\boldsymbol{W} = [\boldsymbol{w}_1,\cdots,\boldsymbol{w}_K] \in \mathbb{C}^{M \times K} $ is a  precoding matrix at the BS.
Consequently, the total achievable rate that the IR-assisted communication can provide to all UEs is
\begin{align}
C (\boldsymbol{W}, \boldsymbol{\theta}, \boldsymbol{x}) = \sum_{k=1}^{K} b\log_2 ( 1+  \eta_k( \boldsymbol{W},\boldsymbol{\theta}, \boldsymbol{x})),
\end{align}
where $b$ is the downlink bandwidth.

In order to maintain LOS links with both the BS and UEs, the UAV-IR needs to frequently adjust its location, based on the real-time CSI.
Thus, the power cost of a UAV-IR includes the UAV's hovering power $p_h$, mobility power $p_m$, and the adjustment power $p_r$ for the IR's reflection coefficients.
In order to facilitate beamforming transmissions at the BS and ensure a reliable reflection at the IR,  we assume that downlink communication only happens when the UAV-IR has a fixed location.
Let  $v$ be the speed of the UAV-IR, and $\mathbbm{1}_{v =0}$ is an indicator function which equals to one when the UAV is in the hovering state with a zero speed.
Therefore, the  power cost of the UAV-IR for providing downlink reflection service is
$	p(v ) = \mathbbm{1}_{v =0} \cdot ( p_h + p_r ) + (1-\mathbbm{1}_{v =0}) \cdot  p_m$.

\subsection{Problem Formulation} \label{problemFormulation}

\begin{figure}[!t]
	\begin{center}
		\vspace{-0.8cm}
		\includegraphics[width=7.8cm]{process}
		\vspace{-0.8cm}
		\caption{\label{process}\small The two-stage deployment process of the UAV-IR. }
	\end{center}\vspace{-0.7cm}
\end{figure}

As shown in Fig. \ref{process}, in order to provide efficient and reliable  mmWave communications to downlink UEs, a dynamic deployment for the UAV-IR is considered, where the deployment process is divided into  two sequential and alternating stages: communication  and movement.
In the communication stage, the UAV-IR stays at a fixed location while reflecting mmWave signals towards downlink UEs.
However, once the average downlink rate is lower than a threshold $\rho$, blockage occurs in the downlink channels for most UEs.
In this case, the current communication stage ends, and the UAV-IR moves to a new position, so as to establish LOS links for efficient downlink communications.
Here, we assume that the CSI $\boldsymbol{D}_k$ is constant within each coherence time slot $\Delta T$.
Given that the duration of a communication stage depends on the real-time CSI  and the length of a movement stage is determined by the movement distance and the UAV's speed,  both stages can last for several coherence time slots.

Our goal is to jointly optimize the precoding matrix at the BS,  the reflection coefficient of the IR, and the location of the UAV, such that, before the UAV's onboard energy is exhausted, the total achievable data transmissions that the UAV-IR  provides to downlink UEs can be maximized, i.e.:
\begin{subequations}\label{equsOpt} \vspace{-0.24cm}
\begin{align}
	\max_{\{ \boldsymbol{W}(t),\boldsymbol{\theta}(t),\boldsymbol{x}(t)\}_{\forall t}} \quad &  \sum_{t=1}^{T}   \mathbbm{1}_{v(t)=0} \cdot C \left(\boldsymbol{W}(t),\boldsymbol{\theta}(t),\boldsymbol{x}(t)\right) \cdot \Delta T  \label{equOpt}\\
	\textrm{s. t.} \quad
	& \sum_{k=1}^{K}\|\boldsymbol{w}_k(t)\|^2 \le P_\textrm{max},  \label{consBSPower}\\
	&|\theta_n(t)| \le 1,  \quad \forall n \in \mathcal{N},  \label{consIR} \\
	& \sum_{t=1}^{T} p(v(t)) \cdot \Delta T \le E ,  \label{consUAVenergy}
\end{align}
\end{subequations}
where the random integer $T \in \mathbb{N}^{+}$ denotes the final time slot of the UAV's service, $v(t) = \frac{\|\boldsymbol{x}(t-1)-\boldsymbol{x}(t)\|}{\Delta T}$ is the average speed of the UAV during the coherence time $t$,
$ P_\textrm{max}$ is the maximal transmit power at the BS,
and $E$ is the initial onboard energy of the UAV.
Therefore, the objective function (\ref{equOpt}) is the summation of downlink data transmissions that the UAV-IR provides to all UEs before the end of its service, (\ref{consBSPower}) is the power limitation at the BS, (\ref{consIR}) is the reflection constraints at the IR, and (\ref{consUAVenergy}) is the energy constraint of the UAV.

The optimization problem in (\ref{equsOpt}) is  challenging to solve for two reasons.
First, during each coherence time, the objective function (\ref{equOpt}) is non-convex with respect to the optimal variables $\boldsymbol{W}$, $\boldsymbol{\theta}$ and $\boldsymbol{x}$.
Second, the relationship between the location $\boldsymbol{x}$ of the UAV-IR with the CSI $\boldsymbol{D}_k(\boldsymbol{x})$ is not explicitly known.
Meanwhile, it is impractical to apply a sweeping search by moving the UAV-IR to all possible locations and measuring the real-time CSI $\boldsymbol{D}_k$ for each UE $k$.
In order to address these challenges, in Section \ref{solution1}, the beamforming matrix $\boldsymbol{W}$ and reflection coefficient $\boldsymbol{\theta}$ will be optimized, given a fixed location and known CSI.
Next, the location optimization of the UAV-IR will be addressed using a learning-based approach to model the mmWave communication environment.

\section{Optimal Deployment of UAV-IR} \label{solution}

In this section, the precoding matrix at the BS, the reflection coefficients at the IR, and the location of the UAV-IR will be jointly optimized in a real-time manner to maximize the downlink transmission capacity.
In particular, a  distributional reinforcement learning (DRL) framework is proposed  to model the downlink CSI during each communication stage,  based on the UEs' feedback.

\subsection{Optimal precoding and reflection coefficients}  \label{solution1}

First, we focus on the communication stage, where the UAV-IR has a fixed location $\boldsymbol{x}$ and the downlink CSI $\boldsymbol{D}_k$ for each UE $k$ is known.
Then,  for each coherence time,  (\ref{equsOpt}) is reduced to optimize the precoding matrix and the reflection coefficients, so as to maximize the downlink sum-rate, i.e.:
\begin{subequations}\label{equsOptsub}
	\begin{align}
	\max_{  \boldsymbol{W} ,\boldsymbol{\theta}  } \quad &   C \left(\boldsymbol{W} ,\boldsymbol{\theta}  \right)  \label{equOptsub}\\
	\textrm{s. t.} \quad
	& \sum_{k=1}^{K}\|\boldsymbol{w}_k \|^2 \le P_\textrm{max},  \label{consBSPowersub}\\
	& |\theta_n | \le 1,  \quad \forall n \in \mathcal{N}.  \label{consIRsub}
	\end{align}
\end{subequations}
To solve this non-convex problem, we apply the Lagrangian dual transform method \cite{shen2018fractional}, introduce an auxiliary variable $\boldsymbol{\alpha} \in \mathbb{R}^{K\times 1}$, and equivalently rewrite the objective function (\ref{equOptsub}) into the following form:
\begin{equation}\label{sumrateAlpha}
	C_{\alpha} (\boldsymbol{W} ,\boldsymbol{\theta}, \boldsymbol{\alpha}) = b\sum_{k=1}^K \left(\log_2 (1 + \alpha_k)   -\alpha_k + \frac{(1+\alpha_k) \eta_k}{1+\eta_k}  \right),
\end{equation}
By holding $\boldsymbol{W}$ and $\boldsymbol{\theta}$  fixed and setting $\frac{\partial  C_{\alpha} }{\partial  \alpha_k} = 0$, we have the optimal value of $\alpha_k$ as $\alpha^o_k = \eta_k$. Then, for  a fixed $\boldsymbol{\alpha}$, the optimization problem of $\boldsymbol{W}$ and $\boldsymbol{\theta}$ is reduced to
\begin{subequations}\label{equsOptsub2}\vspace{-0.2cm}
	\begin{align}
	\max_{  \boldsymbol{W} ,\boldsymbol{\theta} } \quad &   \sum_{k=1}^K  \frac{\hat{\alpha}_k \eta_k}{1+\eta_k}   \label{equOptsub2}\\
	\textrm{s. t.} \quad  & (\text{\ref{consBSPowersub}}), (\text{\ref{consIRsub}}),
	\end{align}
\end{subequations}
where $\hat{\alpha}_k = b (1+\alpha_k)$.
Given that (\ref{equsOptsub2}) is a multiple-ratio fractional programming problem, we can fix the value of $\boldsymbol{W}$ and $\boldsymbol{\theta}$ alternatively, and solve the optimization problem via an iterative approach, detailed as follows.

\subsubsection{Optimal precoding matrix}\label{optPrecoding}
For a fixed $\boldsymbol{\theta}$, the optimal precoding problem becomes
\begin{subequations}\label{equsOptsub3}
	\begin{align}
	\max_{  \boldsymbol{W}   } \quad &  f(\boldsymbol{W}) = \sum_{k=1}^K \hat{\alpha}_k  \frac{  |\boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_k |^2 }{  \sum_{i=1 }^{K} |\boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_i  |^2  + \sigma^2}  \label{equOptsub3}\\
	\textrm{s. t.} \quad  & \sum_{k=1}^{K}\|\boldsymbol{w}_k \|^2 \le P_\textrm{max}.
	\end{align}
\end{subequations}
The multiple-ratio fractional programming function in (\ref{equOptsub3}) is equivalent to $f_{\lambda}(\boldsymbol{W},\boldsymbol{\lambda}) = $
$- \sum_{k=1}^K |\lambda_k|^2  (\sum_{i=1}^K | \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_i |^2 + \sigma^2) $ $+$ $ \sum_{k=1}^K   2 \sqrt{\hat{\alpha}_k} \text{Re} \{ \lambda_k  \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_k  \}$,
where  $\boldsymbol{\lambda} \in \mathbb{R}^{K \times 1}$ is an auxiliary vector \cite[Theorem 2]{shen2018fractional}.
Since $f_{\lambda}$ is a convex function with respect to both $\boldsymbol{w}_k$ and ${\lambda}_k$, $\forall k$, an iterative approach can be applied to optimize  $\boldsymbol{W}$ and $\boldsymbol{\lambda}$ alternatively.
First, we fix $\boldsymbol{W}$ and set $\frac{\partial f_{\lambda} }{\partial \lambda_k}=0$. Then, the optimal value of $\lambda_k$ is
\begin{equation}\label{zerolambda}
	\lambda^o_k = \frac{\sqrt{\hat{\alpha}_k}  \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_k}{\sum_{i=1}^K | \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_i |^2 + \sigma^2 }.
\end{equation}
Then, by fixing $\boldsymbol{\lambda}$, the optimal $\boldsymbol{w}_k$ can be given by
\begin{equation} \label{zerow} \vspace{-0.1cm}
	\boldsymbol{w}_k^o = \sqrt{\hat{\alpha}_k} \lambda_k \boldsymbol{\theta} \boldsymbol{D}_k \left( \kappa_o \boldsymbol{I}_M + \sum_{i=1}^K |\lambda_i|^2 (\boldsymbol{\theta} \boldsymbol{D}_i )(\boldsymbol{\theta} \boldsymbol{D}_i )^H    \right)^{-1}   ,
\end{equation}
where $\kappa_o \ge 0$ is the minimum value such that $\sum_{k=1}^K\| \boldsymbol{w}_k^o \|^2 \le P_{\text{max}}$ holds.
By alternating between (\ref{zerolambda}) and (\ref{zerow}),  the precoding matrix will eventually converge to the unique and optimal value $\boldsymbol{W}^{*}$,  with a computational complexity of $\mathcal{O}(M^4)$.

\subsubsection{Optimal reflection coefficients}
Next, we fix the value of $\boldsymbol{W}$ and optimize the reflection coefficient $\boldsymbol{\theta}$ in (\ref{equsOptsub2}), i.e.:
\begin{subequations}\label{equsOptsub4} \vspace{-0.1cm}
	\begin{align}
	\max_{  \boldsymbol{\theta}   } \quad &  f(\boldsymbol{\theta}) = \sum_{k=1}^K \hat{\alpha}_k  \frac{  |\boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_k |^2 }{  \sum_{i=1 }^{K} |\boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_i  |^2  + \sigma^2}  \label{equOptsub4}\\
	\textrm{s. t.} \quad  &  |\theta_n | \le 1,  \quad \forall n \in \mathcal{N}.
	\end{align}
\end{subequations}
Similarly, an auxiliary vector $\boldsymbol{\delta}$ is introduced, so that (\ref{equOptsub4}) equivalently becomes
$f_{\delta} (\boldsymbol{\theta},\boldsymbol{\delta}) =  \sum_{k=1}^K   2 \sqrt{\hat{\alpha}_k} \text{Re} \{ \delta_k  \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_k  \} $ $ - \sum_{k=1}^K |\delta_k|^2  (\sum_{i=1}^K | \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_i |^2 + \sigma^2)$, which is convex with respect to both $\boldsymbol{\theta}$ and $\boldsymbol{\delta}$.
Therefore, the unique and optimal value of the reflection coefficients $\boldsymbol{\theta}^*$ can be obtained via a similar alternative approach as the precoding  optimization.
First, the optimal $\delta_k$ for a given $\boldsymbol{\theta}$ is
\begin{equation}\label{zerodelta}
	\delta_k^o = \frac{\sqrt{\hat{\alpha}_k}  \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_k}{\sum_{i=1}^K | \boldsymbol{\theta} \boldsymbol{D}_k  \boldsymbol{w}_i |^2 + \sigma^2 }.
\end{equation}
Then, the optimization of the reflection coefficient for a fixed $\delta_k$ becomes
\begin{subequations}\label{equsOptsub5}\vspace{-0.2cm}
	\begin{align}
	\max_{  \boldsymbol{\theta}   } \quad &  f(\boldsymbol{\theta}) =  -\boldsymbol{\theta} \boldsymbol{U} \boldsymbol{\theta}^H + 2\text{Re}\{ \boldsymbol{\theta} \boldsymbol{v} \} -C  \label{equOptsub5}\\
	\textrm{s. t.} \quad  &  |\theta_n | \le 1,  \quad \forall n \in \mathcal{N},   \label{cons}
	\end{align}
\end{subequations}
where  $C = \sum_{k=1}^K |\delta_k|^2\sigma^2$,  $\boldsymbol{v} = \sum_{k=1}^K {\delta_k}^H \boldsymbol{D}_k \boldsymbol{w}_k$, and $\boldsymbol{U} = \sum_{k=1}^K |\delta_k|^2 \sum_{i\ne k}  \boldsymbol{D}_k  \boldsymbol{w}_i ( \boldsymbol{D}_k  \boldsymbol{w}_i)^H $.
Given that $\boldsymbol{U}$ is a positive-definite matrix,   $ f(\boldsymbol{\theta})$ is quadratic concave with respect to $\boldsymbol{\theta}$.
Meanwhile, the constraint (\ref{cons}) is a convex set.
Thus, (\ref{equsOptsub5}) is solvable using a Lagrange dual decomposition \cite{guo2019weighted} with a computational complexity of $\mathcal{O}(N^6)$.

Therefore, given the CSI $\boldsymbol{D}_k$ of each BS-IR-UE link,  the precoding matrix $\boldsymbol{W}^*$ and reflection coefficient $\boldsymbol{\theta}^{*}$ can be optimally  and uniquely  determined.
Next,  the optimal location  of the UAV-IR will be studied to guarantee a LOS channel for each BS-IR-UE link.

\subsection{Optimal location of the UAV-IR}\label{solution2}
During the communication stage, at the end of each coherence time $t$, the UAV-IR can get feedback from each UE about the downlink transmission performance.
Whenever the average rate per UE is smaller than $\rho$, i,e, $C(t) < K\rho$,  blockage occurs in the downlink channels for most UEs.
In this case, the UAV-IR needs to move and rebuild LOS links.
The optimization problem of the UAV-IR's location is given as
\begin{subequations}\label{equsOptloc} \vspace{-0.1cm}
	\begin{align}
	\max_{\{ \boldsymbol{x}(t)\}_{\forall t}} \quad &  \sum_{t=1}^{T}   \mathbbm{1}_{v(t)=0} \cdot C \left(\boldsymbol{x}(t)\right) \cdot \Delta T  \label{equOptloc}\\
	\textrm{s. t.} \quad
	& \sum_{t=1}^{T} p(v(t)) \cdot \Delta T \le E .  \label{consUAVenergyloc}
	\end{align}
\end{subequations}

To determine the optimal location for each communication stage,  a DRL framework is designed to learn the dynamic communication environment and model the relationship between the UAV's location and  downlink CSI.
In our DRL framework, the downlink CSI $\{ \boldsymbol{D}_k\}_{\forall k}$ is the communication \emph{environment},
the UAV-IR is the \emph{agent} that takes \emph{action} $\Delta \boldsymbol{x}$ to change its location from $\boldsymbol{x}$ to  $\boldsymbol{x} +\Delta \boldsymbol{x}$,
and the communication \emph{state} $\boldsymbol{e}$ is a vector of the received signal power at each UE, where $\boldsymbol{e} = [|y_1|^2, \cdots, |y_K|^2]$.
At the end of each coherence time, the UAV-IR receives \emph{reward}  $r(\boldsymbol{x}) = \mathbbm{1}_{v=0} C(\boldsymbol{x}) \Delta T$, which is the total received data in the downlink transmission.
Due to the small‐scale fading of mmWave channels, the downlink CSI $\boldsymbol{D}_k(\boldsymbol{x})$ may vary between different time slots, even for a fixed location $\boldsymbol{x}$ of the UAV-IR.
Thus, it is more suitable to consider the  reward $r$ as a random variable  with respect to $\boldsymbol{x}$, rather than a determined value.
Meanwhile,  $P(\boldsymbol{e}^{'}|\boldsymbol{e},\Delta \boldsymbol{x})$ is the state transition probability  from $\boldsymbol{e}$  to $\boldsymbol{e}^{'}$ after taking action $\Delta \boldsymbol{x}$.

To properly capture the relationship between the UAV's movement and downlink transmission performance, first, a \emph{policy} $\pi(\Delta \boldsymbol{x} | \boldsymbol{e})$ is introduced to define the probability that the UAV-IR will move by $ \Delta \boldsymbol{x}$,  under a current state $\boldsymbol{e}$.
Meanwhile, to quantify the potential of each action $\Delta \boldsymbol{x}$ for improving the downlink rate under a state $\boldsymbol{e}$, we define the return function of each state-action pair for any time slot $t$ as
\begin{equation}\label{Qfunction}
\begin{aligned}
Z^{\pi}(\boldsymbol{e}_t,\Delta\boldsymbol{x}_t) =      \sum_{i=t}^{T} \gamma^{i-t} r(\boldsymbol{e}_i,\Delta\boldsymbol{x}_i) ,
\end{aligned}
\end{equation}
where $\Delta \boldsymbol{x}_i \sim \pi(\cdot|\boldsymbol{e}_i)$, $\boldsymbol{e}_{i+1} \sim P(\cdot|\boldsymbol{e}_i,\Delta \boldsymbol{x}_i)$ and $\boldsymbol{x}_{i+1} = \boldsymbol{x}_i + \Delta \boldsymbol{x}_i$.
Here, $\gamma \in (0,1)$  discounts the future rewards in the current estimation for each state-action pair.
If $\gamma \rightarrow 1$, the return function $Z^{\pi}$ will approximate  (\ref{equOptloc}).
Thus, the return function (\ref{Qfunction}) defines a cumulative discounted reward that the UAV-IR can achieve by reflecting mmWave signals at location $\boldsymbol{x}_t + \Delta\boldsymbol{x}_t$ for the next communication stage.
Meanwhile, given that $r$ is a random variable, it is necessary to model a distribution function of (\ref{Qfunction}) to identify the return value for each state-action pair.
Once the return distribution  is known, the optimal policy $\pi$ that maximizes the expectation of the cumulative rewards can be defined by
$\Delta \boldsymbol{x}^{*} = \arg \max_{\Delta \boldsymbol{x}}  \mathbb{E}(Z^{\pi}(\boldsymbol{e}_t,\Delta\boldsymbol{x}_t ))$.
Thus, the optimal location of the UAV-IR for the next time slot will be $\boldsymbol{x}_{t+1} =\boldsymbol{x}_{t} + \Delta \boldsymbol{x}^{*} $.

In order to model the return distribution for each state-action pair, a quantile regression (QR) method \cite{dabney2018distributional} is applied.
A $Q$-quantile model $Z_Q$ approximates the target distribution $Z^{\pi}$, using a discrete function with variable locations of $Q$ supports and fixed quantile  of  $\frac{1}{Q}$ probabilities \cite{zhang2020millimeter}, for a fixed integer $Q \in \mathbb{N}^{+}$.
Mathematically, a $Q$-quantile model is denoted by $Z_Q(\boldsymbol{e},\Delta\boldsymbol{x} ) = [z_1(\boldsymbol{e},\Delta\boldsymbol{x} ), \cdots , z_Q(\boldsymbol{e},\Delta\boldsymbol{x} )] $, with a cumulative probability $F_{Z_Q}(z_q) = \frac{q}{Q}$ for $q = 1,\cdots, Q$.
The objective is to find the optimal location for each support, such that the ``distance'' between  the target distribution $Z^{\pi}$ and the $Q$-quantile model $Z_Q$ can be minimized.
However, given that the actual return distribution $Z^{\pi}$  is not explicitly known, an empirical distribution $Z$ will be formed, based on the UEs' feedback during each time slot, and $Z$ is used as the target distribution to model the return approximation  $Z_Q$.
To quantify the ``distance'' between two distribution functions, the quantile regression loss is defined as \cite{dabney2018distributional},
\begin{equation}
	\mathcal{L}_Z(Z_Q) = \sum_{q=1}^Q \mathbb{E}_Z \left[|\omega_q - \mathbbm{1}_{z<z_q}| \cdot (z - z_q)^2 \right],
\end{equation}
where $\omega_q = \frac{2q-1}{2Q}$, $|\omega_q - \mathbbm{1}_{z<z_q}| $ is the weight of regression loss penalty, and $(z - z_q)^2$ is the square of approximation error.
Thus, the  problem of the return distribution modeling becomes to minimize the quantile regression loss, i.e.,
\begin{equation}\label{1WminProj}
\min_{ z_1, \cdots, z_Q } 	\mathcal{L}_Z(Z_Q).
\end{equation}
Since the objective function in (\ref{1WminProj}) is convex with respect to $Z_Q$, the minimizer $\{ z^{*}_q \}_{q=1,\cdots,Q}$ can be found by conventional  gradient-descent approaches  with a computational complexity of $\mathcal{O}(Q^2)$.
As a result, for each state-action pair, its return distribution $Z_Q(\boldsymbol{e},\Delta \boldsymbol{x}) $ can be approximated by a  Q-quantile $\{ z^{*}_1(\boldsymbol{e},\Delta \boldsymbol{x}) , \cdots, z^{*}_Q(\boldsymbol{e},\Delta \boldsymbol{x})  \}$ via (\ref{1WminProj}).

Consequently, in the location optimization problem of the UAV-IR, after observing a communication state $\boldsymbol{e}_t$, the UAV-IR can estimate the expected return value for each action $\Delta \boldsymbol{x}$, by computing the marginal distribution of  $Z_Q(\boldsymbol{e},\Delta \boldsymbol{x}) $, and choose the optimal location $\boldsymbol{x}_{t+1} = \boldsymbol{x}_t + \Delta \boldsymbol{x}^{*} $ that maximize the summation of future downlink  transmissions via
\begin{equation}
\begin{aligned}
\Delta \boldsymbol{x}^{*} = \arg \max_{\Delta \boldsymbol{x}}\mathbb{E} \left[  Z_Q(\boldsymbol{e}_t,\Delta \boldsymbol{x})  \right]
=   \arg \max_{\Delta \boldsymbol{x}} \frac{1}{Q} \sum_{q=1}^Q z_q(\boldsymbol{e}_t,\Delta \boldsymbol{x}).
\end{aligned}
\end{equation}

After the UAV-IR arrives at the new location $\boldsymbol{x}_{t+1}$ and provides downlink service to UEs, a new state $\boldsymbol{e}_{t+1}$ and reward $r_{t+1}$ will be updated  at the end of the $l+1$ time slot.
Given the downlink transmission,  the empirical distribution can be updated via a Q-learning approach, where
$z_i(\boldsymbol{e}_t,\Delta \boldsymbol{x}_t) \leftarrow r_{t+1} + \gamma z_i^t(\boldsymbol{e}_{t+1},\Delta \boldsymbol{x}_{t+1}), \forall i = 1,\cdots,Q$.
As a result, the return distribution $Z^t_Q$ is updated by minimize the distance from the target distribution $Z$, based on (\ref{1WminProj}).
The training and update algorithm of the DRL model for the real-time optimal deployment of the UAV-IR  is summarized in Algorithm \ref{algo}.
The convergence property of this iterative algorithm has been proved  in \cite[Theorem 1]{zhang2020millimeter}.

\begin{algorithm}[h] \small
\caption{DRL-optimized deployment for the UAV-IR } \label{algo}
\begin{algorithmic}
	\State \textbf{Initialize} the precoding matrix $\boldsymbol{W}_0$, the reflection coefficient $\boldsymbol{\theta}_0$, the location $\boldsymbol{x}_0$, the onboard energy $E_0$, and the DRL model  function $Z^0_{Q}(\boldsymbol{e}, \Delta \boldsymbol{x})$ for each state-action pair. \\
	\textbf{For} $t = 1, \cdots, T$:\\
	\quad A. If $v_t>0$, the UAV-IR continues its movement; \\
	\quad B .If $v_t=0$, the UAV-IR is in the communication stage;\\
	\quad \textbf{Repeat}:\\
	\quad \quad B1. Update the auxiliary variable $\alpha_k = \eta_k$; \\
	\quad \quad B2. Optimize $\boldsymbol{W}_t^{*}$ by alternating between (\ref{zerolambda}) and (\ref{zerow}); \\
	\quad \quad B3. Optimize $\boldsymbol{\theta}_t^{*}$ , by alternating between (\ref{zerodelta}) and (\ref{equsOptsub5}); \\
	\quad \textbf{Until} the value of $C_{\alpha}$ in (\ref{sumrateAlpha}) converges;  \\
	\quad \quad B4. Receive the reward $r_t$ and the  state $\boldsymbol{e}_t$.  If $r_t \ge K\rho \Delta T$,  \\
	\quad  \quad \quad  $\boldsymbol{x}_{t+1} = \boldsymbol{x}_t$;   Otherwise, the UAV-IR moves by \\
	\quad \quad \quad \quad $\Delta \boldsymbol{x}^{*} = \arg \max_{ \Delta \boldsymbol{x}} \frac{1}{Q} \sum_{q=1}^Q z^{t-1}_q (\boldsymbol{e}_t,\Delta \boldsymbol{x}) $.   \\
	\quad \quad B5. Update the empirical distribution $Z$ via \\
	\quad \quad \quad  $z_i(\boldsymbol{e}_{t-1},\Delta \boldsymbol{x}_{t-1})  \leftarrow r_t + \gamma z_i^{t-1}(\boldsymbol{e}_t,\Delta \boldsymbol{x}_t)$, $\forall i=1,\cdots,Q$. \\
	\quad \quad B6. Update the DRL model  $Z^t_Q$  via,   \\
	\quad \quad \quad $ \arg \min_{ \{z_q\}_{\forall q} }  \sum_{q=1}^Q \sum_{i=1 }^Q |\frac{2q-1}{Q} - \mathbbm{1}_{z_i<z_q}|\cdot (z_i-z_q)^2$. \\
	\quad C. Update onboard energy via
	$E_{t+1} = E_t -p(v_t)\Delta T$. \\
	\textbf{Until} $E_t =0$.
\end{algorithmic}
\end{algorithm}

\begin{figure*}[!t]
	\begin{center}\vspace{-0.15cm}
		\begin{subfigure}{.325\textwidth}
			\centering
			\includegraphics[width=6.4cm]{probability
			\caption{\label{probability} }
		\end{subfigure}
		\begin{subfigure}{.325\textwidth}
			\centering
			\includegraphics[width=6.4cm]{power
			\caption{\label{power}  }
		\end{subfigure}
		\begin{subfigure}{.33\textwidth}
			\centering
			\includegraphics[width=6.5cm]{distribution
			\caption{\label{distributions} }
		\end{subfigure}
		\vspace{-0.15cm}
		\caption{\small{\label{fig:both} (a) The achievable LOS probability of downlink mmWave channels. (b) The downlink rate increases, as the transmit power at the BS  increases. (c) The return distribution of each action under the worst-case communication state $\boldsymbol{e} = \boldsymbol{0}_K$. }
		}
	\end{center}
	\vspace{-0.4cm}
\end{figure*}

\section{Simulation Results and Analysis}\label{simulation}

For our simulations, we consider a uniform square array of antennas at both the BS and the UAV-IR with $M = 16$  and  $N = 16$, and the number of downlink UEs is $K =4$.
The BS is located at $(0,0,20)$, each UE's location follows an i.i.d. two-dimensional Gaussian $\mathcal{N}((20,0),8\boldsymbol{I}_2)$ with zero height, and the mobility pattern of each UE follows a Markov decision process in \cite{zhang2019reflections}.
A building located  at $(10,0,0)$ with a height of $18$ meters permanently blocks direct BS-UE links.
The path loss and mmWave channel model  are based on  \cite{zhang2020millimeter}.
For communication parameters, we set   $f = 30$ GHz,  $b=2$ MHz,  $P_{\text{max}}=40$ dBm, and  $\Delta T = 0.1$ second.
The average speed of the UAV during the mobility stage is $v = 10$ m/s, the maximal onboard energy is $E_{\text{max}} = 20$ Wh, and the power cost are $p_m = 20$ W, $p_h = 16$ W, and $p_r = 0.16$ W.
In the DRL model, we set $Q = 40$, and $\gamma = 0.9$.
In order to have a finite state-action  space, we  discretize the communication state $\boldsymbol{e}$ to be a binary vector, where  if the received power of UE $k$ is smaller than a threshold $\tau$, $e_k = 0$; otherwise $e_k = 1$.
The discrete action space is defined as:  $\Delta \boldsymbol{x}_1$ is ``ascend by one meter'', $\Delta \boldsymbol{x}_2$ is ``descend by one meter'', and $\Delta \boldsymbol{x}_3$ to $\Delta \boldsymbol{x}_{2+K}$ are ``move towards UE $k$ by one meter'' for each $k \in \mathcal{K}$.

In Fig. \ref{probability}, we first show the empirical probability of having a LOS downlink channel towards each UE.
To evaluate the performance of the proposed DRL approach for the UAV-IR deployment, a direct transmission, a static IR, and a UAV-IR without learning are introduced as baselines.
The static IR is placed at $(20,10,20)$ to bypass the building and establish LOS BS-IR-UE links. However, the bodies of human users may block mmWave channels.
For the non-learning scheme, the UAV-IR moves towards a UE by one meter, every time downlink blockage occurs.
As shown in Fig. \ref{probability}, the static IR scheme yields a LOS probability of around $50\%$.
Due to the mobility of the UAV, the proposed UAV-IR scheme can maintain a LOS probability of over $90\%$, and the non-learning UAV-IR  results in a probability of over $60\%$.
Moreover, as the altitude of the UAV-IR increases, the LOS downlink probability will naturally increase for both UAV-IR schemes.
However, since the DRL-based deployment can estimate the potential of each action in improving the mmWave communication over a long term, the proposed  method always yields a higher LOS probability than the non-learning  scheme.

Fig. \ref{power} shows the time-average  data rate of mmWave  downlink communications, as the transmit power of the BS increases.
When the transmit power increases from $20$ to $40$ dBm,
the downlink data rates of all schemes become higher.
First,  compared with the direct transmission scheme,  the proposed UAV-IR approach yields a performance gain of over two-folds in the downlink data rate, due to a higher LOS probability.
Meanwhile, the DRL-enabled deployment of the UAV-IR improves the communication performance by over $25\%$ and $50\%$, compared to the non-learning UAV-IR and the static IR, respectively.
For the non-learning scheme, its short-sighted  strategy causes a frequent movement of the UAV-IR,  thus yielding a lower downlink rate.

Fig. \ref{distributions} shows how to choose the optimal action under a worst-case  state $\boldsymbol{e} = \boldsymbol{0}_K$, where the received power at each UE is lower than the threshold.
In this case, Fig. \ref{distributions} shows the  return distribution and the expected return value of each action.
Since $\Delta \boldsymbol{x}_1$ yields the highest expected reward, the optimal action under the worst-case communication state $\boldsymbol{e} = \boldsymbol{0}_K$ is to increase the altitude of the UAV-IR by one meter.

\section{Conclusion}\label{conclusion}

In this paper, we have proposed  a novel DRL-enabled approach to the deploy a UAV-IR for efficient downlink transmissions over mmWave frequencies towards multiple UEs.
To maximize the downlink sum-rate, the optimal precoding matrix at the BS and reflection coefficient of the IR have been derived.
In order to model the propagation environment of mmWave communications, the DRL method has been proposed  to optimize the location of the UAV-IR, so as to maximize the downlink communication capacity.
Simulation results show that the proposed DRL-based deployment of the UAV-IR yields a significant advantage, compared to a non-learning UAV-IR, a static IR, and a direct transmission schemes, in terms of the average data rate and the achievable downlink LOS probability.
Future research will focus on  multiple UAV-IRs in outdoor communication scenarios with mobile  users.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


text:
'Fiction is a solution, the best solution, to the problem of existential solitude'
Maria Callas: Sacred Monster
Stelios Galatopoulos
The definitive biography of one of the greatest performers of the century by one of her closest friends. Highly illustrated with many previously unseen photographs.
Maria Callas (1923-1977) possessed the voice that characterised the age; even that golden age of singers which she all too briefly spanned. Stelios Galatopoulos first met Callas as a fan, at a performance of La Gioconda in 1947. Aged 24, she was still a large woman, hiding the gaunt dramatic figure she was to become. Galatopoulos was there at her debut at Covent Garden in 1952 and by 1957 had become a friend.
By 1959, her first marriage had broken down and her affair with Onassis began. Until her retirement in 1965 the performances were few. Her friendship with Galatopoulos grew during this period and they had become very close by1977, the year of her shockingly early death. Early that year Galatopoulos had asked her if she planned to write an autobiography. She replied 'My memoirs are in the music I interpret… don't you think I am too young to write my memoirs. I am not eighty yet, you know.' In 1998 she would have been 75. Maria Callas: Sacred Monster is the closest we shall get to an autobiography. In that last year she opened her heart to Galatopoulos. Since her death too many biographies have distorted her image beyond recognition and too many untruths have lain unchallenged for Galatopoulos to remain silent any longer. Incorporating much material from conversations between Callas and the author – never previously published – this is the definitive portrait of one of the greatest performers of the century.
Reviews of Maria Callas: Sacred Monster
More from Stelios Galatopoulos

redpajama_set_name: RedPajamaCommonCrawl


text:
Honda CR-Z Specification Suspension Rebates Price Color Safety Features and Review
The Honda CR-Z, also known as the first hybrid sports car, is a compact hybrid electric automobile manufactured by Honda. The CR-Z is regarded as the spiritual successor to the second generation Honda CR-X in both name and exterior design.
It is rated one of Europe's safest cars after independent crash test results from Euro NCAP, and in the U.S., is rated as an Advanced Technology Partial Zero Emissions Vehicle (AT-PZEV).
Currently, CR-Z is the only gasoline-electric hybrid model comes with a manual transmission.
Exterior style:
When look at the CR-Z, you get the distinct notion that: this car simply looks like nothing else on the road. From the raked rear window inspired by the CR-X, to the pointy rear lights and bulges distributed in key areas - it's absolutely unique and cannot be mistaken from other cars.
The exterior of CR-Z shares its basic structure and suspension design with the Honda's current Insight hybrid. However, Honda has made the CR-Z shorter by about a foot, widened the track slightly and reduced overall height by a couple inches. You may at first think that the trimming reduces a lot curb weight, but in fact the CR-Z only weighs about 80 pounds fewer than the Insight, however, the end result of all this is that Honda has indeed created a sporty hybrid.
The CR-Z looks sharp and is fun to drive around town thanks to its small size and quick steering. In general, the CR-Z is still one of the most nimble cars you can buy today.
The Honda CR-Z comes with three versions: base, EX and EX with navigation. The base version equipped standard with 16-inch alloy wheels, automatic headlights, hill-start assist (manual transmission), automatic climate control, full power accessories, manual seats with driver-side height adjustment, a tilt-and-telescoping steering wheel, cruise control and a six-speaker CD audio system (with steering-wheel controls and USB/auxiliary audio jacks).
For the EX versions, Honda has added xenon headlights, fog-lights, heated side mirrors, metallic interior trim, a leather-wrapped steering wheel, Bluetooth and a seven-speaker premium audio system. With extra bucks, you can get a voice-activated navigation system, 17-inch wheels, performance tires and satellite radio.
Power & Performance:
Under the hood, the CR-Z comes with Honda's Integrated Motor Assist (IMA) hybrid-electric system, which means that the engine acts like a turbo with the electric motor boosting the 1.5 L gasoline engine, resulting in a combined output of 122bhp at 6000 rpm (The gasoline motor itself outputs only 111 bhp at 6000 rpm)
A six-speed manual transmission is standard equipment, and a continuously variable transmission (CVT) with paddle shifters is optional. There are also three different driving modes: Sport, Normal and Econ. With the Sport you can increase steering weight, the Econ has a softer acceleration and steering and with Normal you are somewhere between the other two.
According to 2011 EPA rating, the CR-Z can get 31 mpg on city road and 37 mpg on the highway with manual transmission. The model equipped with CVT transmission has a rating of 35 miles per gallon for city driving and 39 miles per gallon for highway. It is ranked number four on 2011 EPA top ten list of fuel efficient vehicles for CVT equipped model and number ten for manual transmission equipped mode.
The driving experience:
Driving the CR-Z is comfortable, confident and agile for a hybrid. Its well-balanced chassis and light 2,600 lb curb weight make it agile and it absolutely sticks to the ground in the corners.
But if you're expecting sharp handling like a Civic Si, you're going to be disappointed.
However, if you lower your expectations a little, you'll find the CR-Z reasonably fun to drive. The steering, though not hugely informative, is precise and is undeniably some of the most heavily weighted this side of a Lamborghini Murcielag. The brake system is controlled by software modulating regeneration and friction braking, means it is a better braking system than in other hybrids. The power from the hybrid powertrain is certainly sufficient, and you will feel a little more energetic than driving the other cars due to the burst of extra torque from the electric motor at low speed.
Base model start at $19,200, while a nicely equipped EX with the CVT goes for $21,410.
My opinion: It's perfectly targeted at younger urban buyers and its priced right too, so get one and you will have extremely fun with it.
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I'm reading: Honda CR-Z Specification Suspension Rebates Price Color Safety Features and Review ~


Former FBI Director James Comey is accusing current FBI leadership of bowing to political pressure by reassigning the FBI's top lawyer.
"Sadly, we are now at a point in our political life when anyone can be attacked for partisan gain," Comey tweeted Friday night, in a rare public statement.
"James Baker, who is stepping down as FBI General Counsel, served our country incredibly well for 25 years & deserves better," he continued. "He is what we should all want our public servants to be."Baker worked closely with Comey during the latter's time at the FBI and served as the head of the FBI's Office of General Counsel during Comey's time as director.
Baker's reassignment duties are not clear.
The new FBI director, Christopher Wray, is reorganizing some of the top leaders at the agency as he forms his own team of senior advisers,The Washington Post reported. It is common for a new director to reorganize when taking charge of an agency.
But according to the New York Times,Wray is also under pressure from President Trump to reassign Comey loyalists within the agency.
The FBI faces heavy criticism from the president — who has said the agency's reputation is in "tatters" in part because of Comey, whom he fired in May — and Republican scrutiny amid accusations of anti-Trump bias.
Baker was one of the senior officials under fire for an alleged connection to the leak of a dossier last year containing unverified and salacious claims about the president, including reports of collusion between Trump and Russia.
That issue was not cited as a reason for Baker's reassignment, according to the Post. An internal investigation into Baker's role in the leak ended with no charges.


text:
Quick links... Taste and See Tampa Bay
LifestyleTaste and See Tampa Bay
4 Hidden Gem Museums in Tampa Bay
From World War II ships to the experience of motherhood, and from the Beatles to the history of pinball, there are some amazing museums that are hidden right in our own backyard!
By: Teyonna Edwards
Posted at 12:46 PM, May 07, 2021
From a World War II ship to the experience of motherhood, and from the Beatles to the history of pinball, there are some amazing museums that are hidden right in our own backyard!
Location: 705 Channelside Drive, Tampa
Cost: Adults $10 | Kids $5 (plus discounts for seniors, veterans and students with ID)
The American Victory was a cargo ship that was built for WWII and also served in the Vietnam and Korean wars. It's one of four fully-operational WWII ships left in the country. It was built in 1945 then brought to Tampa in 1999 to be converted into a memorial and mariners museum.
"We really let folks explore the ship," said Bill Kuzmick, president of Victory Ship Inc. "You can go into almost any kind of space and just explore everything...and they love that."
Guests can take a step back into the 1940s as they look through artifacts, see the soldiers sleeping quarters and even play at the ship's wheel. Choose to do a self-guided tour or set up a docent tour, usually led by one of the museum's knowledgeable volunteers. But make sure to wear comfortable shoes—there are a lot of steep steps to climb!
"I like to say (the ship) still serves today," said Kuzmick. "We do a lot of training with FBI, law enforcement, firefighters."
American Victory also offers events throughout the year, like private rentals during the 4th of July and Undead in the Water, a haunted ship experience for Halloween. The ship hopes to go into dry dock by early next year so that it can be ready to go for its Relive History cruises, where guests can experience the American Victory out on the waters of Tampa Bay.
The museum is open from 12 p.m. - 5 p.m. on Monday and 10 a.m. - 5 p.m. Tuesday through Sunday.
"It's a phenomenal step back in time and...we have to embrace what we have," said Kuzmick. "We lose elements like this of our nation, and I think that's something that we need to keep...close to our heart."
Museum of Motherhood
Location: 538 28th St N, St. Petersburg
Cost: Suggested donation
Museum of Motherhood explores the art, history, science and experience of motherhood.
In the 1990s, museum director and founder Martha Joy Rose became interested in the topic of motherhood. "As an artist in New York City who was a musician and singer, I noticed there was no artistic venue, or no artistic expression for mothers at the time."
From there, she aimed to create a genre of art and music about motherhood with her big music festival called Mamapalooza and opened her first motherhood exhibit in her store in New York. She now runs the museum out of her home in Historic Kenwood.
The Museum of Motherhood is all about education. Guests can sit in the library and choose from almost 800 books to read, play an educational board game about what to expect during birth, try on a weighted pregnancy belly and browse art showcasing the highs and lows of motherhood. There is also additional literature on studies of the motherhood experience and mother activists.
"We're small and mighty, people always love it," said Rose. "Half of the exhibits here are over at USF Women and Gender Studies Department right now in a pop up over there, so we get around."
The museum is open for appointment only—call 877-711-6667 or email Info@MOMmuseum.org to schedule a visit. Rose is usually on site to answer any questions and to provide some unique insight into the history of mothers.
"Women have not seen their day, and...I want them to," said Rose. "I want everyone to. I celebrate the women and mothers everywhere."
Penny Lane, Beatles Museum
Location: 730 Broadway, Dunedin
One of the largest Beatles collections in the United States is right here in Downtown Dunedin! Explore an array of memorabilia—posters, signed guitars, Ringo's drumsticks, John Lennon's glasses, pieces of hair, swatches of hotel sheets the Beatles slept on—all while listening to classic Beatles hits.
"The Penny Lane Beatles Museum is a collection of...Beatles memorabilia for the last 60 years," said Colin Bissett, curator and CEO of the museum. "It's a collection of a private individual in town...that has been collecting for over 40 years."
The collection consists of almost a thousand pieces (only about 2/3 of it are currently on display), dating back to posters of the Quarrymen, which was the Beatles' name when they first got started in Liverpool with Pete Best as the original drummer.
"They always remember the first time they saw the Beatles," said Bissett regarding the guests who come the museum. "Everyone's got a personal take, which is wonderful to hear. And they come from all over the world."
The museum is open 11 a.m. - 3 p.m. Thursday through Sunday. Though the museum is free, they do accept donations, and they also sell Penny Lane shirts, mugs, signs and other souvenirs. The museum is perfect for Beatles fanatics and those who are just discovering their music.
"The pieces are quite historic," said Bissett. "So this is a wonderful piece of memorabilia, and it's a great experience for people."
Replay Amusement Museum
Location: 119 E Tarpon Ave, Tarpon Springs
Cost: Adults $14 | Kids $8
Replay is a hands-on museum where you can see the evolution of pinball and arcade games. Try out 120 games including pinball machines up to 50 years old.
"At Replay, it does kind of just look like an arcade, but it's generation over decades of games," said Bobbi Douthitt, special events coordinator for the museum. "You get to see the evolution of gaming, changes in graphics, and how everything is affected by technology."
RELATED| Play vintage pinball and arcade games at Replay Amusement Museum
Between playing games, guests can read the info toppers on each of the pinball machines to learn about when it was built and who it was made by, as well as read reference books all about pinball and arcade games. Replay is also home to the world's largest pinball machine—Hercules made by Atari in 1979. Less than 400 were ever created, and the pinball machine is so large it uses a cue ball from a pool table.
The museum provides an interactive and family-friendly way to experience the evolution of pinball. "I see ages 5 to 85 come through my door," said Douthitt.
Replay Amusement Museum is open 11 a.m. - 7 p.m. Wednesday through Sunday, and open 7 days a week during summer break. Tickets are good to play all day, meaning you can leave and come back as you please. There are a variety of games to choose from, all set to "free play" so no quarters are required.
"Really, if you don't like a game that's in here, you don't like games," said Douthitt.


text:
package org.apache.nifi.flow;

import io.swagger.annotations.ApiModelProperty;

public class VersionedPropertyDescriptor {
    private String name;
    private String displayName;
    private boolean identifiesControllerService;
    private boolean sensitive;
    private VersionedResourceDefinition resourceDefinition;

    @ApiModelProperty("The name of the property")
    public String getName() {
        return name;
    }

    public void setName(String name) {
        this.name = name;
    }

    @ApiModelProperty("The display name of the property")
    public String getDisplayName() {
        return displayName;
    }

    public void setDisplayName(String displayName) {
        this.displayName = displayName;
    }

    @ApiModelProperty("Whether or not the property provides the identifier of a Controller Service")
    public boolean getIdentifiesControllerService() {
        return identifiesControllerService;
    }

    public void setIdentifiesControllerService(boolean identifiesControllerService) {
        this.identifiesControllerService = identifiesControllerService;
    }

    @ApiModelProperty("Whether or not the property is considered sensitive")
    public boolean isSensitive() {
        return sensitive;
    }

    public void setSensitive(boolean sensitive) {
        this.sensitive = sensitive;
    }

    @ApiModelProperty("Returns the Resource Definition that defines which type(s) of resource(s) this property references, if any")
    public VersionedResourceDefinition getResourceDefinition() {
        return resourceDefinition;
    }

    public void setResourceDefinition(final VersionedResourceDefinition resourceDefinition) {
        this.resourceDefinition = resourceDefinition;
    }
}

redpajama_set_name: RedPajamaGithub


The Hurricanes scored a bonus point try to win 30-23 against the Blues in a Palmerston North thriller in Friday's early Vodacom Super Rugby action. The Canes got off to a positive start as they dominated possession from the onset. Beauden Barrett slotted over a penalty in the fifth minute to put the home side 3-0 ahead.
A brilliant break by Julian Savea saw TJ Perenara go over to score the first try of the match. Barrett was unable to add the extras. The Welington franchise looked damaging on attack, but a miraculous intercept by Lolagi Visinia saw him score a 95 metre try.
Ihaia West converted to put them within 4 points. Winger Frank Halai powered over as he put the men from Auckland in the lead in the 29th minute with West adding the sundries. With half time emerging, Matt Proctor scored off a spectacular chip kick from Barrett.
The flyhalf converted to give the Canes the edge at the break. A scrappy start to the second half saw both sides turning over the ball easily. West got his side back in front with a difficult penalty kick in the 47th minute.
Jamie Joseph's men struck back through a try by Savea and Barret converted to give his side a five point buffer. West, being brilliant with the boot, continued kicking them over as the match remained on a knife's edge. Some good phases and patience by the Canes saw Savea go over for the bonus point try as the Canes win by seven points.


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Home › . › Linda Macdonald › Sea Witches
Sea Witches
Whilst the poets Ted Hughes and Sylvia Plath were married Ted began an affair with a woman called Assia Wevell. Devastated by the discovery of the affair the couple separated and a few months later Plath committed suicide by putting her head in the gas oven. Before doing this she sealed up the bedroom door of her two children to make sure they were not affected by the fumes.
As Sylvia Plath`s reputation grew after her death, it was said that Assia seemed to be haunted by the specter of Plath. Although Assia and Hughes had a daughter together called Shura, their relationship began to deteriorate and he began to see other women. Assia re-enacted Plath`s suicide by gassing herself and Shura.
The starting point for my work was Shura and the reasons for her death. The baby dress in the prints was once worn by me. as Shura and I would have been contemporaries, it seemed right to use it to represent her, My mother who had died when I was a child, kept my dress, then I kept it for another 30 years with out really knowing why. Making these prints ruined the dress but it felt like a cathartic thing to do.
The commercial sea witches was directed and devised by Assia and is a parody of the Greek myth of the sirens. In the commercial the sirens destroy men with their dyed hair. the largest piece of work is a screen print of my hair. I feel the 1966 advert and the use of Greek tragedy seems to tie in with the tragedy of Shura, Plath, Assia and Hughes as a kind of foreshadowing.
More Portfiolios From Linda MacDonald
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Q: Troubleshooting AttributeError: 'NoneType' object has no attribute 'send' At the moment this snippet is from a command that logically works, except for sending the embed to the respective channel.
@bot.command(name="share")
@commands.dm_only()
async def on_message(ctx):
#other logic that I used such as a cooldown and so on
#function primarily takes a user's DM and shares to a channel inside a server
.....

if message.guild is None and not message.author.bot:
        now = datetime.datetime.now()
        t = now.strftime('%A %Y/%m/%d  %I:%M %p')
        print("A User Has Shared A Link. \nUserID: {}\nTime is: {}".format(
            message.author.id, t))
        print(message.content + "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n")

        embed = discord.Embed(title="Shared Message: ",
                              description=message.content, color=(0x92f852))
        embed.timestamp = datetime.datetime.utcnow()
        embed.set_footer(text="Stay Frostyyy",icon_url="") #redacted image url
        channel = bot.get_channel(863712965525766144)
        await channel.send(embed=embed)
    await bot.process_commands(message)

All the logic prior to the chanel=bot.get_channel line works just the few lines after is causing the issue. The issue I am running into is the channel.send(embed=embed) line because of an error:
AttributeError: 'NoneType' object has no attribute 'send'
Would appreciate any help!

redpajama_set_name: RedPajamaStackExchange


An Egyptian atheist who was invited on privately owned TV network "Alhadath Alyoum" to present his ideas was summarily kicked off the show by its host earlier this month, with both the anchor and a second guest — a cleric — suggesting that the young man should see a psychiatrist.
In the February 11 segment, translated by the Middle East Media Research Institute, atheist Mohammad Hashem was barely allowed to explain his positions. He managed to say that "there is no scientific evidence for the existence of God" and that he did not "need religion to have moral values or to be a productive member of society," before he was assailed by host Mahmoud Abd Al-Halim.
"How can you say that? Who created you? Who made you exist as a human being? …How come you exist in this universe?" Abd Al-Halim asked.
Egypt court sentences 8 to death for violence..


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And there is more... If your video gets the most views on Facebook by July 13, you will be awarded a tour around the NOS studios!
Download the NOS Reporter-app via the App Store.


Basketball fans all know LeBron James because he is already making it possible to form part of the history of this wonderful game. Talk of people like Michael Jordan and Kobe Bryant, you cannot help it but include LeBron because he belongs to that caliber. This superstar started making name for himself from the days of high school. He reached his epitome when he helped Miami Heat to reach finals and finally winning tournaments and trophies back-to-back for years. No other basketball player in the NBA has managed this winning streak before.
This is not the only thing that catapulted the superstar to fame. He also has also become the center of focus after receiving numerous endorsement deals. These deals includes the one with Nike, one of the largest sports accessory makers in the planet. Inasmuch as LeBron is a public figure, there are many things many of his so-called fans have no idea of. In this post, we will discuss LeBron James' age, shoe size and facts.
What Really Is LeBron James Age?
It is uncommon to hear people talk about the age of celebrities especially those in the sports industry. This is because age will give you an idea of how long that athlete will be active as many athletes tend to perform better when they are still young. According the available information, LeBron James was born on December 30, 1984. This makes him just about 30 years at the time of writing this post.
The Cleveland Cavalier forward has been active for approximately 12 years. During this period he has managed to display some of the best performances in the game earning him several endorsement deals. He is now considered one of the best basketball players due to his enormous size, athleticism and court vision. The average career length of basketball players is hard to determine but LeBron is expected to play for a few more years before retiring.
LeBron's shoe size could even explain why he plays so well on the court. The first thing you need to know is that King James (as he is commonly referred to by his ardent fans), wears signature Nike brand of shoes which bear his name. According to Forbes magazine, LeBron's shoes outsold any other NBA player's signature shoes in 2014 by what they call a landslide.
His actual shoe size is rather unusual for standard people to understand. He wears size 15-shoes, which is rather larger, compared to what others of his height wear. That notwithstanding, it is important to point out that height has very little (if any) to do with the size of shoes a person actually wears. He has stopped growing and therefore his shoe size is unlikely to change any further. He will always wear shoe size 15 while playing.
Bryce Maximus James, LeBron's second born son, was born during the superstar's first trip to the finals in 2007.
He first met his friend-turned-agent, Rich Paul (former seller of sports jerseys) at the Akron-Canton airport when James was still in high school.
LeBron had dreamt of being in the cover of Sports Illustrated (SI). He first had a fake SI cover displayed above the Television set in his family's living room, entitled, "Is he the next Michael Jordan?" His wish came true when he graced the cover of SI at the age of 17 years.
He is actually married to his high school sweetheart, Brinson Savanna, with whom he has had three children – two sons and a daughter.
LeBron's first son (his namesake) is just 10 years old, loves basketball and has already been recruited by the NCAA. He will surely take after his father.
Tom and Jerry' is the favorite cartoon of the James' family but he also watches "SpongeBob SquarePants" at times. He confesses his love for cartoons.
Of the many stats that players usually register, James claims that his favorite stats are assists (because he loves the success of his team mates that his own').


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Home » Movies » The Patriot
Zain Bhatti July 17, 2021 2159
Mel Gibson, is a highly controversial figure in Hollywood. Though, there is still one thing about him that will never be taken back. He is an exceptional filmmaker; some of his films have gone on to become record Breakers in the award department. From his work in George Miller's Mad Max series to his own films such as Braveheart and Hacksaw Ridge; he has proven himself as one of the best filmmakers in Hollywood. The Problem with Mel Gibson arises, in the fact that he literally does any film that is given to him. One of such films is The Patriot.
How to Stream or Download The Patriot
To stream or to download The Patriot, click on the Download button located below this review. You will be able to get it from a digital store of your choice.
One would think that Mel Gibson starring in an American historical epic would be a good sign for the film; however that is not the case. The Patriot is one of the most underwhelming war films that I have ever seen in my life, and it's not just about the film's film-making, it is also the fact that it feels like it is historically inaccurate.
The film uses dramatization in a very melodramatic way and creates a sense of unrealism to its overall aesthetic. This is sad because the film could have been so much better if it just took the more realistic route.
The film is set during the American Revolutionary War in 1776; it follows captain Benjamin Martin a veteran of the French and Indian wars who is a widower with seven children. The film follows as Benjamin tries to avoid fighting in the war, yet his violent capabilities are soon to be pulled out of him when the war comes to him.
For a historical epic, it does have a huge cost. Mel Gibson, Heath Ledger, Jason Isaacs, Chris Cooper, and Joely Richardson all take part in this phone. I should make it clear that the performances in this film are pretty darn good. The problem with this film is that the direction is very broken.
The film has a huge pacing problem, as it takes a huge time to build characters off. By the end, it doesn't really matter because the film ends on such a sharp note. It also feels quite an uninspired film; every single shot in the film feels very repetitive and unimaginative. If the film had better direction, and a bit more of a realistic one then it could have been a much better film overall.
It is said that the screenwriter for this film, Robert Rodat wrote around 18 different drafts for this film before the final one was accepted. That alone is a bad sign for the film being pushed full scale into production!
The problem with this film was best described by Harrison Ford, "It boiled the American Revolution down to one guy wanting revenge." You cannot describe the film better than that; it is a terrible retelling of the American Revolution from an independence war to a revengeful.
The best part about this film is the production design, the sets feel gigantic and the war sequences look realistic. It was shot entirely on location in South Carolina on Charleston and Rock Hill. Even the music of this film, was exceptionally good when it came to the overall aesthetic and theme of the film.
Everything about this film bit, the cinematography in the film is pretty good as well though the film lacks a lot of innovation in that department. The lighting is quite dull for the most part, with bloom being used a lot to showcase the goodness and the niceness in human beings which feels very lackluster and old.
In all honesty, I do not like this film. It is a boring, and quite a dull retelling of the American Revolution wars with a revenge film twist. It feels like something that could have been done back in the 1980s however it was executed the same way in the year 2000.
So, in conclusion, I would just like to say that this is a mediocre film starring Mel Gibson and Heath Ledger, which could have been done much better if things were different in the direction department.
The Patriot is a film with the setting in the times of the American War of Independence. Download it and watch Mel Gibson & Heath Ledger.
The Patriot Review Summary
User Rating: 4.33 (3 %s votes)
www.sonypictures.com
Tags: Epic MoviesHistorical Drama MoviesWar Movies
Ace Ventura: Pet Detective


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James Gunn to Direct 'Guardians of the Galaxy'
By: Julian Stark | Movie News | August 19, 2012
James Gunn has only helmed two feature films, the 2006 horror comedy Slither and the 2011 superhero comedy Super. Though neither film was a massive success, Gunn's work gained him a cult following. Now he might be breaking through to the big leagues.
The Hollywood Reporter relays that Marvel Studios wants Gunn to helm Guardians of the Galaxy. The studio reportedly admires his ability to combine comedy, action, and horror like Joss Whedon, who directed The Avengers. Though Gunn is in exclusive negotiations with Marvel, the studio has yet to rule out Bring It On's Peyton Reed or Half Nelson directors Anna Boden and Ryan Fleck.
Marvel is known for making unconventional choices in directors, such as Sir Kenneth Branagh for Thor and Jon Favreau for Iron Man. "Guardians" will be the first non-sequel in Marvel's "Phase 2" and is currently slated to hit theaters on August 1, 2014.
Julian Stark


It's a simple truism in cooking that chicken stock makes everything taste better, and that includes your red beans and rice.
Why settle for using just water in your beans when this stock can add hints of chicken along with the delicious essences of an array of aromatic vegetables, herbs, and spices?
Use as much chicken stock as you want in your beans. Even just a little should improve the overall taste of the final product. Or you can go all out and use stock entirely in the place of water.
Another great option: Use chicken stock, not water, as the liquid base for your rice.
And if it's a truism that chicken stock makes everything better, then, naturally, homemade chicken stock trumps chicken stock out of a can or carton, or in a bouillon cube or powdered form.
Whenever you have a whole chicken as a main meal, get into the habit of throwing the carcass — bones, skin, leftover meat, and all — into a stock pot or Dutch oven, then bring it to a boil along with some aromatic vegetables (such as onion, celery, carrots, garlic, leeks); herbs and spices (such as parsley, bay leaf, thyme, cloves, pepper, or anything that would go in a classic bouquet garni); along with, of course, water or even wine. The options are endless, and cookbooks are full of stock recipes. However, you probably don't want to add salt to your stock-in-process because your chicken carcass, presumably, already contains sodium.
Let the stock simmer for several hours and then strain it, removing the fat and other particles along with the carcass. Store the broth in containers in your refrigerator or freezer to be used when needed. Obviously, freezing stock will make it last longer.
Stocks also can be made in similar fashion out of leftover seafood, fish, beef, veal, duck, game, or other meats for use in gumbos and other dishes. And if you're a vegetarian, just leave out the meat and sauté your aromatic vegetables before starting the stock-making process.
If you don't have the time or the inclination to make your own stock, try the premade products. Using a commercial version is better than using no stock at all. And in recent years, high-quality organic versions have become available, some marketed by celebrity chefs.
Red beans and rice already is the quintessential meal of south Louisiana. Adding chicken stock will add even more flavor dimensions that can only improve your final dish.


Temazcal is a type of sweat lodge originally used by many of the pre-hispanic peoples of México to cleanse the body, heal the sick, and prepare women for giving birth. Many indigenous peoples in México still use the temazcal today. In recent years, the temazcal has been discovered by many non-indigenous Méxicans and foreigners because of its perceived health and spiritual benefits.
The contemporary temazcal is usually carried out in a one-room dome adobe building with a fire pit in the center or fireplace off to the side. To induce sweating, water containing medicinal herbs is sprinkled on volcanic rocks heated by the fire, filling the room with hot steam. A massage is usually part of the experience as well. Many believe the combination of the the heat, the steam, the herbs, and the massage heals the body by cleansing it of toxins. Most who try the temazcal, even skeptics of its healing or spiritual benefits, describe experiencing feelings of deep relaxation.
For more information, read the article "Temazcal" by Dr. Horacio Rojas Alba.
This page was last modified on 22 May 2013, at 19:56.


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Hey, all! I have some cool things coming your way in July as I end my quest of 365 blog posts in a row. I appreciate you for reading. After today, 1 post to go!
It's been a long journey, and I'm happy to say that I've blogged in Europe, Hawaii, all over the continental U.S., and many sleepy, countless nights at my kitchen table and in my basement, but here we are…the last two posts of this 365 journey.
I want to leave you with what I feel to be two helpful, honest days to end it. Today, I will be blogging about the top three things that I have learned from this journey that you can use on your own journey, and tomorrow, I will blog about the top 10 books of the entire 365.
1.) Try not to make promises. It's your quest. It's your goal. If you need to change plans, then do it, but it feels better when you stick to what you said you were going to do. At the start of the project, I was going to review 365 books. That did not happen. I did (if today and tomorrow pan out) get 365 blog posts in a row done; but they were not all reviews. And people loved a lot of my non-review posts. My suggestions of graphic novels for local and school libraries was one of my most popular posts of the year! But looking back, I should have just said 365 blog posts in 365 days. Not a big deal, but, you know…if you do it, try to be true to your word a bit more than I was when I started out. I had to switch it up, which brings me to #2.
2.) Switch it up. Don't paint yourself into a corner for an entire year. One of the best things I did over the year was find cool, interesting ways to bring quality content while still being true to my mission. Being able to explore avenues and pathways of your mission allows for the creation of interesting content for your readers and allows you to create in more meaningful ways. When inspiration hits, you'll be able to use it.
3.) Believe in yourself! A year ago, if I'm being honest, I never thought I could do this. 365 blog posts in 365 days was a dream. I was thinking I'd be lucky to get to 125, but here was are at 364, and I did not miss a day. I had help from friends with guest reviews, but I posted original content to this blog every day for the past 364 days. And most of the posts contain between 400-500 words, which means, I've put up the word-count equivalent of a 500-page novel. It became a habit quickly, and I don't know if there will be many days in my next adventure that I won't write. It's now part of who I am. Like someone that religiously works out, it's just what I do. It's not all great, but I've gotten better, and I've worked at it. I've most def become a better editor of my own work, and I have exemplified dedication to my students. I had homework every night of the school year, including weekends. A quest like this will make you a better student and teacher. I promise.
I look forward to bringing you my top ten books of the 365 tomorrow, and my next project looks to be coming together nicely!