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Franklin Global Listed Infrastructure Fund - Advisor
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text:
\section{Conclusion}
\label{sec:conclu}

We have presented an end-to-end learning method for learning waveforms through joint optimization of constellation and pulse shaping to maximize an achievable information rate, with constraints on the \gls{ACLR} and power envelope.
Our simulations results show that the proposed approach enables lower \gls{ACLR} and less dispersive power envelopes while maintaining competitive rates.
Moreover, the end-to-end leaning method does not incur any additional complexity on the transmitter side, as it relies on conventional architectures, and can be applied to any channel model.
The presented results are therefore promising for evaluation on other channel models and to design waveforms for emerging beyond 5G services.
\section{End-to-end waveform learning}
\label{sec:e2e}

The key idea of end-to-end learning of communication systems~\cite{8054694} is to implement a transmitter, channel, and receiver as a single \gls{NN}, and to jointly optimize the trainable parameters of the transmitter and receiver for a specific channel model.

\subsection{Trainable transmit and receive filters}

Solving~\eqref{eq:prob} requires being able to evaluate with low-complexity and for any values of $\vecs{\theta}$ and $\vecs{\psi}$ the function $\alpha(t)$~\eqref{eq:alpha} and the noise covariance~\eqref{eq:noise_cov} to implement the channel transfer function~\eqref{eq:ch}.
It also requires having low-complexity implementations of the in-band energy function~\eqref{eq:inb}, the variance of the \gls{PED}~\eqref{eq:var}, and to ensure the transmit filter and constellation have unit energy~\eqref{eq:pc1}-\eqref{eq:pc2}.

As computing some of these quantities requires integration, using \glspl{NN} to implement the transmit and receive filters leads to intractable calculations.
One option would be to approximate these integrals using, e.g., Monte Carlo estimation or Riemann sums, but these approaches are computationally demanding and only result in approximations.

To accurately and efficiently implement trainable transmit and receive filters, we use the functions $\left\{ \text{sinc} \left( Df - s \right) \right\}_{s \in \mathbb{Z}}$, which form a basis in the frequency domain for functions time-limited to $\left( -\frac{D}{2}, \frac{D}{2} \right)$.
Therefore, the trainable transmit and receive filters are defined in the frequency domain as
\begin{align}
	\hat{g}_{tx,\vecs{\theta}}(f) &\coloneqq \sqrt{C(\vecs{\theta})} \sum_{s=-S}^{S} \theta_s \text{sinc} \left( Df - s \right) \label{eq:ftx}\\
	\hat{g}_{rx,\vecs{\psi}}(f) &\coloneqq \sum_{s=-S}^{S} \psi_s \text{sinc} \left( Df - s \right) \label{eq:frx}
\end{align}
where $S$ controls the number of trainable parameters of the transmit and receive filters.
Note that higher values for $S$ lead to more degrees of freedom for the trainable filters, at the cost of a higher complexity at training.
Moreover, the transmit and receive filters are not required to have the same number of parameters $2S+1$ or the same duration $D$, as it was done in this work for convenience.
In~\eqref{eq:ftx}, $C(\vecs{\theta})$ is a normalization constant that ensures the transmit filter has unit energy~\eqref{eq:pc1}, for which an expression is given later in this section.
Taking the inverse Fourier transform of~\eqref{eq:ftx} and~\eqref{eq:frx} leads to the time-domain expressions of the trainable filters
\begin{align}
	g_{tx,\vecs{\theta}}(t) &= \frac{\sqrt{C(\vecs{\theta})}}{D} \text{rect}\left( \frac{t}{D} \right) \sum_{s=-S}^{S} \theta_s e^{j2\pi\frac{s}{D}t} \label{eq:tx}\\
	g_{rx,\vecs{\psi}}(t) &= \frac{1}{D}\text{rect}\left( \frac{t}{D} \right) \sum_{s=-S}^{S} \psi_s e^{j2\pi\frac{s}{D}t}. \label{eq:rx}
\end{align}

A benefit of using this approach to implement the transmit filter is that no additional complexity is required on the transmitter side.
Moreover, all the quantities required for training can be exactly obtained through direct calculations:
\begin{align}
	&C(\vecs{\theta}) = \frac{D}{\vecs{\theta}^{\mathsf{H}}\vecs{\theta}} \label{eq:c_norm}\\
	&\alpha(t) = \begin{cases}
	\frac{\sqrt{C(\vecs{\theta})}}{D} \vecs{\theta}^{\mathsf{T}}\vec{A}(t)\vecs{\psi} & \text{ if } t \in \left( -D, D \right)\\
	0 & \text{ otherwise}\\
	\end{cases}\\
	&{\small{\mathbb{E}} \left[ n_m n_{m+l}^* \right] = \begin{cases}
	\frac{N_0}{D} \vecs{\psi}^{\mathsf{T}} \vec{A}'\left( lT \right) \vecs{\psi}^* & \text{ if } lT \in \left( -D, D \right)\\
	0 & \text{ otherwise}\\
	\end{cases}}\\
	&E_I(\vecs{\theta}) = C(\vecs{\theta}) \vecs{\theta}^{\mathsf{H}} \vec{E} \vecs{\theta}
\end{align}
where $\vec{A}(t)$ is a $(2S+1) \times (2S+1)$ complex-valued matrix whose coefficients are given by
\begin{multline}
	A(t)_{s_1,s_2} = \\
	\begin{cases}
	e^{j2\pi\frac{s_1}{D}t}\Delta(t) \text{ if } s_1 = s_2\\
	e^{j\pi\left( 2\frac{s_1}{D}t + (s_2-s_1){\cal S}(t)\right)}\frac{\sin \left( \pi(s_2-s_1)\Delta(t) \right)}{\pi(s_2 - s_1)} \text{ otherwise}
	\end{cases}
\end{multline}
where $-S \leq s_1,s_2 \leq S$, $\Delta(t) = L_{max}(t) - L_{min}(t)$, and ${\cal S}(t) = L_{max}(t) + L_{min}(t)$, with $L_{max}(t) = \min\left\{ \frac{1}{2} ; \frac{t}{D} + \frac{1}{2} \right\}$, and $L_{min}(t) = \max\left\{ -\frac{1}{2} ; \frac{t}{D} - \frac{1}{2} \right\}$.
Similarly, $\vec{A}'(t)$ is a $(2S+1) \times (2S+1)$ complex-valued matrix whose coefficients are given by
\begin{multline}
	A'(t)_{s_1,s_2} = \\
	\begin{cases}
	e^{j2\pi\frac{s_1}{D}t}\Delta'(t) \text{ if } s_1 = s_2\\
	e^{j\pi\left( 2\frac{s_1}{D}t + (s_1-s_2){\cal S}'(t)\right)}\frac{\sin \left( \pi(s_1-s_2)\Delta'(t) \right)}{\pi(s_1 - s_2)} \text{ otherwise}
	\end{cases}
\end{multline}
where $-S \leq s_1,s_2 \leq S$, $\Delta'(t) = L_{max}'(t) - L_{min}'(t)$, and ${\cal S}'(t) = L_{max}'(t) + L_{min}'(t)$, with $L_{max}'(t) = \min\left\{ \frac{1}{2} ; -\frac{t}{D} + \frac{1}{2} \right\}$, and $L_{min}'(t) = \max\left\{ -\frac{1}{2} ; -\frac{t}{D} - \frac{1}{2} \right\}$.
Finally, $\vec{E}$ is a $(2S+1) \times (2S+1)$ real-valued matrix whose coefficients are given by
\begin{equation}
	E_{s_1,s_2} = \int_{-\frac{W}{2}}^{\frac{W}{2}} \text{sinc}\left( Df - s_1 \right) \text{sinc}\left( Df - s_2 \right)
\end{equation}
and which can be pre-computed prior to training.

\subsection{Trainable constellation}

The trainable constellation consists of a set of $2^K$ complex numbers denoted by $\tilde{{\cal C}}$, and corresponding to the constellation points.
To transmit the data, $\tilde{{\cal C}}$ is normalized to ensure that the constraint~\eqref{eq:pc2} is satisfied, i.e.,
\begin{equation}
	\label{eq:const_norm}
	{\cal C} = \frac{\tilde{{\cal C}}}{\sqrt{2^{-K}\sum_{c\in\tilde{{\cal C}}}\abs{c}^2}}.
\end{equation}

\subsection{Neural network receiver}

\begin{figure}
     \begin{subfigure}[b]{\columnwidth}
         \centering
		\includegraphics[width=1.0\textwidth]{figs/nnrx.png}
         \caption{Architecture of the \gls{NN}-based detector. Below each layer name figures the (number of kernels, kernel size, dilatation rate).}
     \end{subfigure}

     \begin{subfigure}[b]{\columnwidth}
         \centering
         \includegraphics[width=0.75\textwidth]{figs/resnetblock.png}
         \caption{Architecture of a ResNet block.}
     \end{subfigure}
        \caption{The receiver is implemented by a convolutional \gls{NN}.}
        \label{fig:nnrx}
\end{figure}

Fig.~\ref{fig:nnrx} shows the architecture of the \gls{NN} that implements the detector in the trainable end-to-end system.
It is a residual 1-dimensional convolutional \gls{NN}~\cite{He_2016_CVPR}, that takes $\vec{r} \in \mathbb{C}^{N}$ as input, and outputs a 2-dimensional tensor of \glspl{LLR} with shape $N \times K$.
The first layer converts the complex-valued input of length $N$ to a real-valued tensor with shape $N \times 2$, by stacking the real and imaginary parts.
Separable convolutional layers are leveraged to reduce the complexity of the \gls{NN}, while maintaining its performance.
Zero-padding is used to ensure the output has the same length as the input, and dilatation to increase the receptive field of the convolutional layers.

\subsection{Training algorithm}

Training of the end-to-end system requires evaluation of the achievable rate $R$~\eqref{eq:R}.
As usually done in end-to-end learning (e.g.,~\cite{aoudia2021trimming}), maximization of $R$ is achieved through the minimization of the total binary-cross-entropy
\begin{multline}
	\label{eq:loss}
	{\cal L}({\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma})\\
	\coloneqq -\frac{1}{N} \sum_{m=0}^{N-1} \sum_{k=0}^{K-1} {\mathbb{E}} \left[ \log{Q_{\vecs{\gamma}}\left( B_{m,k} | \vec{r} \right)} | {\cal C},\vecs{\theta},\vecs{\psi} \right]
\end{multline}
which is related to $R$ by
\begin{equation}
	{\cal L}({\cal C}, \vecs{\theta},\vecs{\psi},\vecs{\gamma}) = K - R({\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma}).
\end{equation}
Since~\eqref{eq:loss} is numerically difficult to compute, it is estimated through Monte Carlo sampling by
\begin{multline}
	{\cal L}({\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma})\\
	\approx -\frac{1}{MN} \sum_{i=0}^{M-1} \sum_{m=0}^{N-1} \sum_{k=0}^{K-1} \log{Q_{\vecs{\gamma}}\left( B_{m,k}^{[i]} \lvert \vec{r}^{[i]} \right)}
\end{multline}
where $M$ is the batch size, i.e., the number of samples used to compute the estimate of ${\cal L}$, and the superscript $[i]$ is used to refer to the $i^{th}$ example within a batch.

\begin{algorithm}
\caption{Training algorithm}
\label{alg:alt}
\begin{algorithmic}[1]
\State Initialize $\tilde{{\cal C}}$, $\vecs{\theta}$, $\vecs{\psi}$, $\vecs{\gamma}$, $\eta^{[0]}$, $\lambda_A^{[0]}$, and $\lambda_V^{[0]}$.
  \For{$u=0,\cdots$}
    \State Perform SGD on ${\cal L}_A\left( {\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma};\lambda_A^{[u]},\lambda_V^{[u]}, \eta^{[u]} \right)$\label{lst:sgd}
    \State \LineComment{Update Lagrange multipliers:}
    \State $\lambda_A^{[u+1]} \gets \lambda_A^{[u]} - \eta^{[u]} \left( \text{ACLR}(\vecs{\theta}) - \epsilon_A \right)$
    \State $\lambda_V^{[u+1]} \gets \lambda_V^{[u]} - \eta^{[u]} \left( V(\vecs{\theta},{\cal C}) - \epsilon_V \right)$
    \State \LineComment{Update penalty parameter:}
    \State Set $\eta^{[u+1]}$ such that $\eta^{[u+1]} > \eta^{[u]}$ \label{lst:eta}
  \EndFor
\end{algorithmic}
\end{algorithm}

\begin{figure*}
	\centering
     \begin{subfigure}[b]{0.47\linewidth}
         \centering
	\includegraphics[width=1.0\textwidth]{figs/results.png}
	\caption{\glspl{ACLR} and rates achieved by the compared schemes.The roll-off factor value is indicated near each point for the baseline.\label{fig:results_r_aclr}}
     \end{subfigure}
     \quad\quad
     \begin{subfigure}[b]{0.48\linewidth}
         \centering
         \includegraphics[width=1.0\textwidth]{figs/results_pow.png}
         \caption{CCDF of the NPD of the baseline and ML schemes for $\epsilon_A = -30\:$dB.\label{fig:results_pow}}
     \end{subfigure}
     \caption{Rate, ACLR, and NPD achieved by the baseline and ML schemes.\label{fig:res}}
\end{figure*}

Finding a local optimum of~\eqref{eq:prob} is made challenging by the constraints~\eqref{eq:pc1}--\eqref{eq:pc4}.
The constraint~\eqref{eq:pc1} is enforced through the normalization constant $C(\vecs{\theta})$~\eqref{eq:c_norm} in~\eqref{eq:tx}, and the constraint~\eqref{eq:pc2} is enforced through the normalization of the constellation~\eqref{eq:const_norm}.
To handle the constraints on the \gls{ACLR}~\eqref{eq:pc3} and \gls{PED}~\eqref{eq:pc4}, the augmented Lagrangian method~\cite[Chapter~17]{nocedal2006numerical} is used, which, when applied to our setup, is shown in Algorithm~\ref{alg:alt}.
The augmented Lagrangian method consists in solving a sequence of unconstrained optimization problems (line~\ref{lst:sgd}), each aiming at minimizing the augmented Lagrangian
\begin{multline}
	{\cal L}_A \left( {\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma};\lambda_A^{[u]},\lambda_V^{[u]}, \eta^{[u]} \right) \coloneqq {\cal L}({\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma})
	\\- \lambda_V^{[u]}\left( V(\vecs{\theta},{\cal C}) - \epsilon_V \right) - \lambda_A^{[u]}\left( \text{ACLR}(\vecs{\theta}) - \epsilon_A \right)\\
	+ \frac{\eta}{2}\left( \left( V(\vecs{\theta},{\cal C}) - \epsilon_V \right)^2 + \left( \text{ACLR}(\vecs{\theta}) - \epsilon_A \right)^2 \right)
\end{multline}
where the superscript $[u]$ refers to the $u^{th}$ iteration, $\lambda_A$ and $\lambda_V$ are the Lagrange multipliers, and $\eta$ a positive penalty parameter that is progressively increased (line~\ref{lst:eta}).
At each iteration, minimizing the augmented Lagrangian is approximately achieved through \gls{SGD}.

\section{Introduction}

While 5G communication infrastructures are actively deployed, academic and industrial research has shifted focus towards the next generation of cellular communication systems~\cite{9040431}.
To support the numerous services envisioned for future systems, such as sub-THz communication or joint communication and sensing/power transfer, the design of new waveforms is required.
As an example, communication in the sub-THz bands involves lower power amplifier efficiency, higher phase noise, and meeting strict regulation on out-of-band emission.
While most of current communication systems rely on \gls{OFDM} due to its very efficient implementation, its high \gls{PAPR} and \gls{ACLR} make it unsuitable for many emerging services.

We propose in this work to use end-to-end learning to design new waveforms that maximize an achievable information rate, while strictly satisfying constraints on the \gls{ACLR} and \gls{PED}.
End-to-end learning consists in implementing the transmitter, channel, and receiver as a \gls{NN}, that is trained to achieve the highest possible information rate~\cite{9118963}.
This idea has been successfully applied to many fields, including optical fiber~\cite{Karanov:18}, coding~\cite{9252949}, and more recently to achieve pilot- and \gls{CP}-less communication in \gls{OFDM} systems~\cite{aoudia2021trimming}.
In this work, a waveform is learned on the transmitter side through optimization of the constellation geometry and transmit filter, that replace, e.g., conventional \gls{QAM} and \gls{RRC} filtering.
On the receiver side, a receive filter and \gls{NN}-based detector are jointly optimized for the constellation and transmit filter.
The \gls{NN}-based detector computes \glspl{LLR} on the transmitted bits directly from the received samples.
Optimization of the constellation geometry and transmit filter are performed with constraints on the \gls{ACLR} and \gls{PED}.
To the best of our knowledge, this is the first work that demonstrates how the transmit and receive filters of a communication system can be jointly optimized through end-to-end learning to design waveforms.

We have considered an \gls{AWGN} channel and conventional \gls{RRC} filtering with Blackman windowing for benchmarking.
However, applying the proposed method to other channel models is straightforward.
The \gls{RRC} filter allows control of the tradeoff between the excess bandwidth and the magnitude of the ripples through the roll-off factor parameter, which also impacts the \gls{PED}.
Our results show that the proposed approach allows fine-grained control of the \gls{ACLR} and \gls{PED} variance, while maximizing the information rate.
Compared to the baseline, the learned waveforms enable up to three orders of magnitude lower \glspl{ACLR}, with similar \glspl{PED} and competitive information rate.

\paragraph*{Notations}
$()^*$ is the complex conjugate operator.
$\ln{\cdot}$ denotes the natural logarithm and $\log{\cdot}$ the binary logarithm.
The $(i,k)$ element of a matrix $\vec{X}$ is denoted by $X_{i,k}$. The $k^{th}$ element of a vector $\vec{x}$ is $x_k$
The operators $()^{\mathsf{H}}$ and $()^{\mathsf{T}}$ denote the Hermitian transpose and transpose, respectively.
Finally, $j$ denotes the imaginary unit, i.e., $j^2 = -1$.
\section{Problem formulation}

In our setting, the transmitter includes a trainable transmit filter $g_{tx,\vecs{\theta}}(t)$ with trainable parameters $\vecs{\theta}$, and a trainable constellation ${\cal C}$.
The receiver includes a trainable receive filter $g_{rx,\vecs{\psi}}(t)$ with trainable parameters $\vecs{\psi}$, and an \gls{NN}-based detector with trainable parameters $\vecs{\gamma}$, which generates posterior probabilities on the transmitted bits $B_{m,k}$ denoted by $Q_{\vecs{\gamma}}(B_{m,k} | \vec{r})$, $0 \leq m \leq N-1$, $0 \leq k \leq K-1$.
The transmit and receive filters are both time-limited to the interval $\left( -\frac{D}{2}, \frac{D}{2} \right)$, i.e., for $t \notin \left( -\frac{D}{2}, \frac{D}{2} \right)$, $g_{tx,\vecs{\theta}}(t) = g_{rx,\vecs{\psi}}(t) = 0$.

The end-to-end system is trained to maximize the rate
\begin{multline}
	\label{eq:R}
	R({\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma}) \coloneqq \frac{1}{N} \sum_{m=0}^{N-1} \sum_{k=0}^{K-1} I(B_{m,k};\vec{r} | {\cal C},\vecs{\theta},\vecs{\psi})\\
	- \frac{1}{N} \sum_{m=0}^{N-1} \sum_{k=0}^{K-1}{\mathbb{E}}_{\vec{r}} \left[ \text{D}_{\text{KL}} \left( \Pr\left( B_{m,k} | \vec{r} \right) || Q_{\vecs{\gamma}}\left( B_{m,k} | \vec{r} \right) \right) \right]
\end{multline}
which is an achievable rate for practical \gls{BICM} systems~\cite{bmi}.
In~\eqref{eq:R}, $I(B_{m,k};\vec{r} | {\cal C},\vecs{\theta},\vecs{\psi})$ is the mutual information between $B_{m,k}$ and $\vec{r}$ conditioned on the constellation ${\cal C}$ and filters parameters $\vecs{\theta}$ and $\vecs{\psi}$, $\text{D}_{\text{KL}}(\cdot||\cdot)$ is the \gls{KL} divergence, $\Pr\left( B_{m,k} | \vec{r} \right)$ is the \emph{true} posterior distribution on $B_{m,k}$ given $\vec{r}$, and $Q_{\vecs{\gamma}}\left( B_{m,k} | \vec{r} \right)$ is the posterior distribution on $B_{m,k}$ given $\vec{r}$ \emph{approximated} by the \gls{NN}-based detector.
Intuitively, the first term in the right-hand side of~\eqref{eq:R} corresponds to an achievable rate assuming an optimal receiver, i.e., one that implements $\Pr\left( B_{m,k} | \vec{r} \right)$.
The second term is the rate loss due to the use of a mismatched receiver $Q_{\vecs{\gamma}}\left( B_{m,k} | \vec{r} \right) \neq \Pr\left( B_{m,k} | \vec{r} \right)$.

The waveform of the transmitted signal $x(t)$~\eqref{eq:x} (where $g_{tx,\vecs{\theta}}(t)$ is used for filtering) is enforced to meet practical constraints.
To begin with, the transmit filter and constellation are required to have unit energy, i.e.,
\begin{align}
	&\int_{-\frac{D}{2}}^{\frac{D}{2}} \abs{g_{tx,\vecs{\theta}}(t)}^2 dt = 1 \label{eq:cst_en}\\
	&{\mathbb{E}}_{c \sim {\cal U}\left({\cal C}\right)} \left[ \abs{c}^2 \right] = 1
\end{align}
where ${\cal U}\left({\cal C}\right)$ is the uniform distribution on ${\cal C}$.
Focusing on the \gls{ACLR}, it is defined by
\begin{equation}
	\text{ACLR}(\vecs{\theta}) \coloneqq \frac{E_O(\vecs{\theta})}{E_I(\vecs{\theta})} = \frac{1}{E_I(\vecs{\theta})}-1
\end{equation}
where $E_I(\vecs{\theta})$ is the in-band energy, $E_O(\vecs{\theta})$ the out-of-band energy, and the second equality comes from~\eqref{eq:cst_en} as it leads to $E_I(\vecs{\theta}) + E_O(\vecs{\theta}) = 1$.
As the sequence of modulated symbols $\vec{s}$ is assumed to be \gls{iid}, the in-band energy is
\begin{equation}
	\label{eq:inb}
	E_I(\vecs{\theta}) = \int_{-\frac{W}{2}}^{\frac{W}{2}} \abs{\hat{g}_{tx,\vecs{\theta}}(f)}^2 df
\end{equation}
where $W \coloneqq \frac{1}{T}$ is the bandwidth of the radio system, and $\hat{g}_{tx,\vecs{\theta}}(f)$ the Fourier transform of $g_{tx,\vecs{\theta}}(t)$.

Concerning the \gls{PED}, we denote by $p(t) \coloneqq \abs{x(t)}^2$ the signal power at time $t$.
Motivated by Chebyshev's inequality
\begin{equation}
	\Pr\left( \abs{p(t) - {\mathbb{E}} \left[ p(t) \right]} > a \right) \leq \frac{\text{Var}\left( p(t) \right)}{a^2}
\end{equation}
we choose to constrain the variance of the power $\text{Var}\left( p(t)\right)$ to enforce the \gls{PED} to have limited dispersion, and as a consequence to increase the power amplifier efficiency.
As the sequence of modulated symbols $\vec{s}$ is \gls{iid}, one has
\begin{multline}
	\label{eq:var}
	\text{Var}\left( p(t) \right) = \left( \mu_4 - \mu_2^2 \right) \sum_l \abs{g_{tx,\vecs{\theta}}(t - lT)}^4
	\\+ \mu_2^2 \sum_l \sum_{i \neq l} \abs{g_{tx,\vecs{\theta}}(t - lT)}^2 \abs{g_{tx,\vecs{\theta}}(t - iT)}^2
	\\+ \tilde{\mu}_2 \sum_l \sum_{i \neq l} \left( g_{tx,\vecs{\theta}}(t - lT) \right)^2 \left( g_{tx,\vecs{\theta}}^*(t - iT) \right)^2
\end{multline}
where
\begin{align}
	\mu_4 &= {\mathbb{E}}_{c \sim {\cal U}\left({\cal C}\right)}\left[ \abs{c}^4 \right]\\
	\mu_2 &= {\mathbb{E}}_{c \sim {\cal U}\left({\cal C}\right)}\left[ \abs{c}^2 \right]\\
	\tilde{\mu}_2 &= {\mathbb{E}}_{c \sim {\cal U}\left({\cal C}\right)}\left[ c^2 \right] {\mathbb{E}}_{c \sim {\cal U}\left({\cal C}\right)}\left[ \left( c^* \right)^2 \right].
\end{align}
The variance of the \gls{PED} therefore depends on the constellation ${\cal C}$ and transmit filter $g_{tx,\vecs{\theta}}(t)$.
Moreover, as a consequence of $\vec{s}$ being \gls{iid}, $p(t)$ and $p(t + lT)$, $l \in \mathbb{Z}$, share the same probability distribution for any $t$ and $t + lT$ distant by at least $\frac{D}{2}$ from the signal temporal edges.
Hence, it is enough to focus on a single period $\left( -\frac{T}{2}, \frac{T}{2} \right)$.

Maximizing $R$ with constraints on the \gls{ACLR} and \gls{PED} leads to the optimization problem that we aim to solve, and which can be formally expressed as follows
\begin{subequations}
\begin{align}
& \underset{{\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma}}{\text{maximize}}
& & R({\cal C},\vecs{\theta},\vecs{\psi},\vecs{\gamma}) \label{eq:prob} \tag{P}\\
& \text{subject to}
& &\int_{-\frac{D}{2}}^{\frac{D}{2}} \abs{g_{tx,\vecs{\theta}}(t)}^2 dt = 1 \label{eq:pc1} \tag{Pa}\\
& & & {\mathbb{E}}_{c \sim {\cal U}\left({\cal C}\right)} \left[ \abs{c}^2 \right] = 1 \label{eq:pc2} \tag{Pb}\\
& & & \text{ACLR}(\vecs{\theta}) = \epsilon_A \label{eq:pc3} \tag{Pc}\\
& & & V(\vecs{\theta}, {\cal C}) = \epsilon_V \label{eq:pc4} \tag{Pd}
\end{align}
\end{subequations}
where~\eqref{eq:pc1} and~\eqref{eq:pc2} constrain the energy of the waveform,~\eqref{eq:pc3} enforces the \gls{ACLR} to equal a predefined value $\epsilon_A$, and~\eqref{eq:pc4} enforces the average \gls{PED} variance
\begin{equation}
	V(\vecs{\theta}, {\cal C}) \coloneqq {\mathbb{E}}_{t\sim{\cal U}\left(-\frac{T}{2},\frac{T}{2}\right)} \left[ \text{Var}\left( p(t) \right) \right]
\end{equation}
to equal a predefined value $\epsilon_V$.
\section{Evaluation of end-to-end learning}
\label{sec:results}

\begin{figure*}
	\centering
     \begin{subfigure}[b]{0.56\linewidth}
         \centering
	\includegraphics[width=1.0\textwidth]{figs/spectrums.png}
	\caption{PSD of the baseline and learned filters ($\epsilon_V = 0.5$).\label{fig:spec}}
     \end{subfigure}
     \quad\quad
     \begin{subfigure}[b]{0.39\linewidth}
         \centering
         \includegraphics[width=1.0\textwidth]{figs/const.png}
         \caption{Transmitted signal $x(t)$ ($\epsilon_A = -30\:$dB).\label{fig:const}}
     \end{subfigure}
     \caption{Visualization of the transmitted signal with the learned waveform.\label{fig:viz}}
\end{figure*}

We will now present the results of the simulations we have conducted to evaluate the end-to-end learning scheme introduced in the previous section, referred to as the \gls{ML} scheme.
This section first provides details on the training and evaluation setup.
The ML scheme is then compared to the baseline.

\subsection{Evaluation setup}

An \gls{AWGN} channel implemented as described in Section~\ref{sec:sys_mod} was considered to train and to benchmark the ML scheme against the baseline presented in Section~\ref{sec:bsl}.
Note that the approach proposed in Section~\ref{sec:e2e} can be applied to any channel model whose output is differentiable with respect to its input, such as multi-paths channels.
However, evaluation on such channel models is left for future investigation.
The carrier frequency was set to $3.5\:$GHz, and the bandwidth to $W = 5\:$MHz.
The duration of the transmit and receive filters were set to $D = 32T$, and the number of parameters was set to $S = 100$ for the trainable filters.
The block length was set to $N = 990$ symbols, and the modulation order to $16$ ($K = 4$).
A Gray-labeled 16\gls{QAM} was used for the baseline.
The \gls{NN}-based receiver operates on the entire block of $N$ symbols.
The \gls{SNR} is defined by $\text{SNR} \coloneqq \frac{1}{N_0}$, and was set to $10\:$dB.
Training of the ML system was carried out using the Adam~\cite{adam} optimizer to perform \gls{SGD}, and with batches of size $M = 10$ and a learning rate set to $10^{-3}$.
The penalty parameter was initialized to $\eta^{[0]} = 10^{-2}$, and increased following a multiplicative schedule $\eta^{[u+1]} = 1.2\eta^{[u]}$.
The Lagrange multipliers were both initialized to $0$.

\subsection{Evaluation results}

Fig.~\ref{fig:results_r_aclr} shows the rates $R$ and \glspl{ACLR} achieved by the baseline and the ML schemes, for different values of $\epsilon_A$ and $\epsilon_V$.
Concerning the baseline, setting the roll-off factor $\beta$ to 0 gives the lowest \gls{ACLR}, at the cost of a rate loss due to the \gls{ISI} introduced by the windowing.
Higher values of $\beta$ lead to lower ripples making the filter more robust to windowing, at the cost of higher \glspl{ACLR}.
The \gls{ML} approach, on the other hand, allows accurate control of the \gls{ACLR} through the parameter $\epsilon_A$.
Moreover, it enables \glspl{ACLR} up to $30\:$dB lower than the ones of the baseline, without significant loss of rate assuming high enough values of $\epsilon_V$.

The constraint on the \gls{PED}~\eqref{eq:pc4} has the strongest impact of the rate $R$.
To quantify the impact of this constraint, Fig.~\ref{fig:results_pow} shows the \gls{CCDF} of the \gls{NPD},
\begin{equation}
	\text{NPD} \coloneqq \frac{\abs{p(t) - {\mathbb{E}}\left[ p(t) \right]}}{{\mathbb{E}}\left[ p(t) \right]}.
\end{equation}
As one can see, for the lowest values of $\epsilon_V$, the ML scheme achieves the lowest \gls{NPD}, at the cost of a rate loss (Fig.~\ref{fig:results_r_aclr}).
This leads to a \gls{PAPR} of $7.53\:$dB for the baseline when $\beta = 0$, whereas for $\epsilon_V = 0.4$ and $\epsilon_A = -30\:$dB, the \gls{ML} approach achieves a \gls{PAPR} of $6.45\:$dB, while enabling a significantly smaller \gls{ACLR} and a higher rate.

Fig.~\ref{fig:spec} shows the \gls{PSD} of the learned filters ($\epsilon_V = 0.5$) and of the baseline ($\beta = 0$).
As expected, the learned filter emits less in the adjacent bands, especially for low values of $\epsilon_A$, which translates into lower \glspl{ACLR}.
Concerning the constraint on the \gls{PED}, Fig.~\ref{fig:const} shows samples from the transmitted signal $x(t)$ for two different values of $\epsilon_V$.
As one can see, with low values of $\epsilon_V$, the samples are concentrated in a ``doughnut-like'' shape, corresponding to a constant envelope signal, and which would lead to a higher power amplifier efficiency.
\section{System model and baseline}
\label{sec:sys}

\subsection{System model}
\label{sec:sys_mod}

A single-carrier system is considered, and the matrix of bits to be transmitted is denoted by $\vec{B} \in \{0,1\}^{N \times K}$, where $N$ is the number of baseband symbols forming a block, and $K$ the number of bits per channel use.
As illustrated in Fig.~\ref{fig:sys}, $\vec{B}$ is modulated onto a vector of baseband symbols $\vec{s} \in {\cal C}^N$ according to some constellation ${\cal C}$, e.g., a $2^K$-\gls{QAM} or a learned constellation.
The modulated symbols are then shaped using a transmit filter $g_{tx} : t \in \mathbb{R} \rightarrow \mathbb{C}$ to generate the time-continuous baseband signal
\begin{equation}
	\label{eq:x}
	x(t) = \sum_{m=0}^{N-1} s_m g_{tx}\left( t-mT \right)
\end{equation}
where $T$ is the symbol period.

\begin{figure}
 	\centering
	\includegraphics[scale=0.7]{figs/e2e.png}
	\caption{Single-carrier communication system, where ${\cal C}$ is the constellation used for modulation, $g_{tx}(t)$ the transmit filter, and $g_{rx}(t)$ the receive filter.\label{fig:sys}}
\end{figure}

The time-continuous channel output is denoted by $y(t)$.
On the receiver side, the received signal is first filtered using a receive filter $g_{rx} : t \in \mathbb{R} \rightarrow \mathbb{C}$ to generate the signal
\begin{equation}
	r(t) = \int_{-\infty}^{+\infty} y(z) g_{rx}\left( t-z \right) dz
\end{equation}
which is then sampled with a period $T$ to form the vector $\vec{r} \in \mathbb{C}^N$.
Assuming an \gls{AWGN} channel, one has
\begin{equation}
	\label{eq:ch}
	r_m = r(mT) = \sum_l s_{m-l} \alpha \left( lT \right) + n_m
\end{equation}
where $n_m$ is the additive Gaussian noise, and the function $\alpha(\cdot)$ is the convolution between the transmit and receive filter, i.e.,
\begin{equation}
	\label{eq:alpha}
	\alpha(t) = \int_{-\infty}^{+\infty} g_{tx}(z) g_{rx}(t-z) dz.
\end{equation}
Moreover, the correlation of the additive noise sequence $\left\{ n_m \right\}_{0\leq m \leq N-1}$ is controlled by the receive filter,
\begin{equation}
	\label{eq:noise_cov}
	{\mathbb{E}} \left[ n_m n_{m+l}^* \right] = N_0 \int_{-\infty}^{+\infty} g_{rx}(z) g_{rx}^*\left( z-lT \right) dz
\end{equation}
where $N_0$ is the noise power density.
As shown in Fig.~\ref{fig:sys}, $\vec{r}$ is processed by a detector which computes \glspl{LLR} on the transmitted bits.
The \glspl{LLR} could then be fed to a channel decoder to reconstruct the transmitted bits.

\subsection{QAM with RRC filtering}
\label{sec:bsl}

Conventional transmit and receive filters are designed to minimize the \gls{ACLR}, \gls{PAPR}, and to avoid \gls{ISI} by satisfying the Nyquist \gls{ISI} criterion~\cite[Chapter~9.2.1]{proakis1994communication}, i.e.,
\begin{equation}
	\label{eq:nyquist_isi}
	\alpha(lT) =
	\begin{cases}
		1 & \text{ if } l = 0\\
		0 & \text{ otherwise}
	\end{cases}
\end{equation}
where $l \in \mathbb{Z}$.
The \gls{RRC} filter, denoted by $\text{rrc}_{\beta}(t)$, where $\beta \in (0,1)$ is the roll-off factor, is widely used as transmit and receive filter, and is considered in this work as a baseline.
It is defined such that its autoconvolution is the raised-cosine function, which satisfies the Nyquist \gls{ISI} criterion~\eqref{eq:nyquist_isi}.
The roll-off factor $\beta$ controls a tradeoff between the excess bandwidth and the magnitude of the ripples.
As the \gls{RRC} filter is not time-limited, it is windowed by the well-known Blackman windowing function $w(t)$ for practical use, which results in the following transmit and receive filters:
\begin{equation}
	g_{tx}(t) = g_{rx}(t) = \text{rrc}_{\beta}(t) w\left(\frac{t}{D}\right)
\end{equation}
where $D > 0$ is the filter duration.

After sampling, detection is performed assuming no \gls{ISI}, and using the usual \gls{AWGN} detector to compute \glspl{LLR}, i.e.,
\begin{equation}
	\text{LLR}(m,k) = \ln{\frac{\sum_{c\in{\cal C}(k,0)} \exp{-\frac{\abs{r_m-c}^2}{N_0}} }{ \sum_{c\in{\cal C}(k,1)} \exp{-\frac{\abs{r_m-c}^2}{N_0}} } }
\end{equation}
where $\text{LLR}(m,k)$ is the \gls{LLR} for the $k^{th}$ bit ($0 \leq k \leq K-1$) of the $m^{th}$ symbol ($0 \leq m \leq N-1$), and ${\cal C}(k,0)$ (${\cal C}(k,1)$) is the subset of ${\cal C}$ which contains all constellation points with the $k^{th}$ bit label set to 0(1).

redpajama_set_name: RedPajamaArXiv


text:
Lights, camera, action! Edible insects in focus at IFT 2015
By Elaine Watson contact
22-Jul-2015 - Last updated on 28-Sep-2021 at 10:13 GMT
Related tags: Nutrition, Flour, Cooking
No self-respecting food conference would be complete these days without a session on edible insects. But are they a gimmick or a serious source of alternative protein? FoodNavigator-USA editor Elaine Watson headed to the 2015 IFT show in Chicago to find out...
We spoke to four experts to get a sense of what insects are like to cook with, getting past the yuck factor, allergen issues, and what needs to change for cricket powder to move from a novelty to a mass market food ingredient…
COOKING WITH BUGS: Chef Michael McGreal, dept chair of culinary arts, Joliet Junior College:
"They are kind of like a blank canvas, at least some of them. With cricket flour, it's a fairly neutral ingredient, so whatever you are cooking, it kind of absorbs the flavor of it, so it's really like adding nutrients without really adding flavor, texture or color, so it's a pretty neat component.
"Meal worms are a little different, they are more like ground chicken or turkey, they have a little bit more flavor, but if you cut them in equal parts with some other meats, that works well, and we've used them to make hamburger patties and sliders.
"When I first introduced [insect ingredients] into the classroom, the students looked at them with that look of 'I hope you don't expect us to try these', but then we talked about the fact that many foods we use come from a body part of an animal… and once they got past that, and understand that it's just another possible food source, we made foods, they tried it, and that they actually thought they tasted pretty good, and the fact that they were getting more nutrients, they thought that was a pretty neat thing too."
ALLERGIES: Dr Phil Johnson, assistant professor, University of Nebraska-Lincoln:
"The primary issue at the moment is that shellfish allergics appear to be also sensitive to insect protein, there seems to be a cross reaction, but we don't know enough about it to give solid advice to producers.
"So at the moment all we can suggest is that people that make foods containing insect protein should label them appropriately as being not suitable for shellfish allergics."
BUG-EATING TRADITIONS: Dr Julie Lesnik, assistant professor, anthropology, Wayne State University:
"Insects have been an important part of the human diet for millions of years... they would have been a very nutritional resource that our hominid ancestors would have utilized a lot…
"We think of insects here in the United States as an 'alternative' protein, when really they are a primary food source for billions of people around the world today."
MASS PRODUCTION: Dr Aaron Dossey, founder & CEO, All Things Bugs:
"As soon as production is mechanized they'll be very cheap … insects are a very secure source of food/protein, their growth rates are high, they are very prolific, they produce a lot of protein very quickly and efficiently, they are easy to process and they work well in pasta, baked goods, protein shakes and just about any kind of food product…"
Snacks, snack bars and protein powders are the top application areas of interest for edible insect right now. However, cricket powder also works well in burgers, sausages, fruit rollups, shakes and other products. Inclusion rates vary by product, and are in many cases limited by cost rather than functionality, said Laurie Keeler senior manager, product development, at the University of Nebraska, Lincoln.
However, cricket powder is more like a protein powder than wheat flour, said Dr Dossey from All Things Bugs, who is trying to wean people away from using the term 'cricket flour' (click HERE).
"You can't just do a 1:1 substitution for wheat flour and expect the recipe to turn out the same; you might replace maybe a quarter or a third of wheat flour, but more than that and you'll run into issues, as wheat flour is mostly starch and cricket powder is mostly protein [67%+] and oil."
While many firms roast and then grind crickets to make a dark, coarser powder, All Things Bugs grinds its insects before heat-treating them, creating a paler, finer powder with a more neutral flavor and smaller particle size (less than 100 microns) with a shelf-life of at least 12 months.
Having trouble watching the video? Try watching it on YouTube instead.
Edible insects will be on the menu at Food Vision USA in October, where delegates will hear from Tiny Farms co-founder Daniel Imrie-Situnayake. Click HERE for full details...
Related topics: Ingredients, Snacks
Exo launches new line of savory cricket bars
The cricket bar: A healthy alternative to steak?
Insect oil: Bugs aren't just about protein

redpajama_set_name: RedPajamaCommonCrawl


text:
function gen_output_copy()
    global mem
    mem.output = mem.activations{length(mem.activations)};
end

redpajama_set_name: RedPajamaGithub


Why Pork Belly Instead of Bacon?
If you've visited us at your local farmers market, you may have noticed that we offer pork belly, or fresh bacon, instead of regular bacon. Pork belly is the same cut as bacon, as both options come from the fatty, belly area of the pig. However, unlike regular bacon, pork belly is not cured using … Continue reading Why Pork Belly Instead of Bacon?


text:
dataset_type = 'CocoPanopticDataset'
data_root = 'data/coco/'
img_norm_cfg = dict(
    mean=[123.675, 116.28, 103.53], std=[58.395, 57.12, 57.375], to_rgb=True)
train_pipeline = [
    dict(type='LoadImageFromFile'),
    dict(
        type='LoadPanopticAnnotations',
        with_bbox=True,
        with_mask=True,
        with_seg=True),
    dict(type='Resize', img_scale=(1333, 800), keep_ratio=True),
    dict(type='RandomFlip', flip_ratio=0.5),
    dict(type='Normalize', **img_norm_cfg),
    dict(type='Pad', size_divisor=32),
    dict(type='SegRescale', scale_factor=1 / 4),
    dict(type='DefaultFormatBundle'),
    dict(
        type='Collect',
        keys=['img', 'gt_bboxes', 'gt_labels', 'gt_masks', 'gt_semantic_seg']),
]
test_pipeline = [
    dict(type='LoadImageFromFile'),
    dict(
        type='MultiScaleFlipAug',
        img_scale=(1333, 800),
        flip=False,
        transforms=[
            dict(type='Resize', keep_ratio=True),
            dict(type='RandomFlip'),
            dict(type='Normalize', **img_norm_cfg),
            dict(type='Pad', size_divisor=32),
            dict(type='ImageToTensor', keys=['img']),
            dict(type='Collect', keys=['img']),
        ])
]
data = dict(
    samples_per_gpu=2,
    workers_per_gpu=2,
    train=dict(
        type=dataset_type,
        ann_file=data_root + 'annotations/panoptic_train2017.json',
        img_prefix=data_root + 'train2017/',
        seg_prefix=data_root + 'annotations/panoptic_train2017/',
        pipeline=train_pipeline),
    val=dict(
        type=dataset_type,
        ann_file=data_root + 'annotations/panoptic_val2017.json',
        img_prefix=data_root + 'val2017/',
        seg_prefix=data_root + 'annotations/panoptic_val2017/',
        pipeline=test_pipeline),
    test=dict(
        type=dataset_type,
        ann_file=data_root + 'annotations/panoptic_val2017.json',
        img_prefix=data_root + 'val2017/',
        seg_prefix=data_root + 'annotations/panoptic_val2017/',
        pipeline=test_pipeline))
evaluation = dict(interval=1, metric=['PQ'])


Sheep industry plays an important role with its multipurpose utility of meat, wool, leather products and enriched manure thereby contributing a great deal towards our national economy. The accurate prediction of pregnancy in ewes would greatly increase efficiency of sheep farming.
A useful book for doctors & chemist, practitioners & the general public.
The book is very useful for all Veterinarians especially for Vety Surgeons of Haryana.
IGCSE Complete Chemistry NotesNotes for revising for 'O' Levels Chemistry Exam!


text:
Q: jquery - How to reference two div elements for a single function? I Have a function that references a specific input text box.  I would like to extend the function to be used by two specific input text boxes.  Rather than duplicate the code for the other text box, can anyone advise on how to reference the other?
Here it uses #Tags, but if i wanted it to reference #Tags2 also, how could I do that?

$(function () {
$('#Tags').tagSuggest({
    separator: ", ",
    tagContainer: 'div',
    tags: ["tag1","tag2"]
  });
});

A: To do this just use a comma (a.k.a. the multiple selector), this works for any number of selectors.
$("#Tags, #Tags2").tagSuggest({
  separator: ", ",
  tagContainer: 'div',
  tags: ["tag1","tag2"] });
});

There's a list of all selectors here and a good start-up tutorial you should check out here.
There's another approach, not needed for your example really, but if you had a lot of elements you wanted to match, or an unknown number, etc...then use a class, like this:

And you can select all elements that have that class using the .class selector, like this:
$(".tags").tagSuggest({
  separator: ", ",
  tagContainer: 'div',
  tags: ["tag1","tag2"] });
});

redpajama_set_name: RedPajamaStackExchange


Aid - CPR First Aid Wall Charts - 4 Steps To CPR Cpr Posters Cpr Training Posters Procedure For Quick Features Poster.
Large size first aid posters for easy readability.
More from Aid - CPR First Aid Wall Charts - 4 Steps To CPR Cpr Posters Cpr Training Posters Procedure For Quick Features Poster.


text:
News Masters
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Teams set for 2022 WFG Masters in Oakville
Mouat wins third straight GSOC men's title at Masters
Fleury edges Jones to successfully defend Masters women's title
Jacobs to meet Mouat in Masters men's final
Fleury eliminates Einarson in Masters women's quarterfinals
Gushue, Mouat remain red-hot in Oakville sliding into Masters semifinals
Jones, Einarson and Kovaleva punch final tickets to Masters playoffs
Whyte qualifies for Masters men's quarterfinals in GSOC debut
Fleury upends Einarson to reach Masters quarterfinals
Bottcher, Jacobs and Edin move onto Masters quarterfinals
McEwen eliminates Epping in triple knockout stage of Masters
Undefeated Gushue, Mouat advance to playoffs at Masters
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text:
France squad to give bonuses to charity
By Community | November 10, 2010
The France squad want to give sponsorship bonuses to charity in a bid to improve their image following a poor display at the World Cup, ed according to captain Alou Diarra.
"We want to do a good deed, unhealthy " Diarra told French radio RTL on Tuesday. The squad are due an estimated two million euros in bonuses, their share of sponsorship revenue which is unrelated to footballing performance.
The players will now discuss with the French Football Federation their plan to give the money to charity.
France were eliminated in the first round of the World Cup in South Africa in June when the players also went on strike to support Nicolas Anelka after the striker was kicked out of the squad for insulting then-coach Raymond Domenech.


Brian T's and John's comments are important.
I do understand Brian's concern but I would worry about John's solution!
even I could "sail the Queen Mary" through it!
on what is the difference between, for example, CIF data and a CIF dictionary.
not be universal agreement on that within this group.. and I understand why!
Here is a rather primitive attempt to make these distinctions.
LAYER  LANGUAGE    PURPOSE          PROCESSOR       "PRODUCTS"
the CIF or STAR syntax requirements and still retain the overall functionality.
syntax is more concise and simpler to understand for the average scientist.
STAR/CIF standard* and the *regulator of crystallographic* dictionaries.
How does this sound as an "IUCr vision" for the future of data interchange?


You might be seeing Marvelous Beautiful Bedroom Ideas 175 Stylish Bedroom Decorating Ideas Design Pictures Of Beautiful Modern Bedrooms photograph of which are probably the perfect illustrations or photos from Beautiful Bedroom Ideas graphic collection. From Marvelous Beautiful Bedroom Ideas 175 Stylish Bedroom Decorating Ideas Design Pictures Of Beautiful Modern Bedrooms photo you can find inspirations to help you out realize a perfect home. Do not think twice to look at some ideas from Marvelous Beautiful Bedroom Ideas 175 Stylish Bedroom Decorating Ideas Design Pictures Of Beautiful Modern Bedrooms pic to become implemented to your house if you want to contain a dazzling house. Better most people study Marvelous Beautiful Bedroom Ideas 175 Stylish Bedroom Decorating Ideas Design Pictures Of Beautiful Modern Bedrooms image, you are going to get far more superb recommendations. You may build a captivating home are similar to Marvelous Beautiful Bedroom Ideas 175 Stylish Bedroom Decorating Ideas Design Pictures Of Beautiful Modern Bedrooms photograph indicates when you can add cosmetic factors perfectly. The balance within the formula of the household furniture, floor coverings, and additionally wall structure suggested just by Marvelous Beautiful Bedroom Ideas 175 Stylish Bedroom Decorating Ideas Design Pictures Of Beautiful Modern Bedrooms snapshot build a very calming environment.
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Vision: Achievement for All: a world in which all vulnerable and disadvantaged children and young people can develop their skills, interests and capabilities to achieve.
Mission: To transform the lives of vulnerable and disadvantaged children, young people and their families by raising educational aspirations, access and achievement.
We have bought into this scheme with Tregolls in order to raise the attainment, self-esteem and confidence in a select group of children.


text:
Pieces of the Past
Family history is passed in the most tangible way through an heirloom ring. These three local wedding vendors' rings stand out from those that they see every day because of their family significance.
Hallie King
Photo by Elizabeth Gelineau
Bridal vendors live and breathe weddings so constantly that when it comes to their own big day, they want to separate themselves from all the commonalities they're surrounded with in their work. The easiest way for them to stand out from their clients is with a one-of-a-kind family jewel to wear proudly on their finger.
A Father's Legacy
When local wedding photographer Debby Faught was ready to pick a diamond for herself, she knew she wanted something unlike anything she had seen before from photography clients.
Her fiancé, Richard Cullum, chose and purchased the center diamond for her ring (above). The surrounding stones, however, came from a grandmother's ring and one of her mother's necklaces that was a gift from her father, who passed away before Faught's wedding.
"My father passed away eight years ago this May, and having those diamonds that he gave to my mom in my ring means the world to me, " says Debby. "Although he hasn't been here to witness my love story with Richard, my dad still has had a part in it."
A Floral Connection
As the time came for Gray Fobes, husband of florist and designer Julia Greer Fobes, to prepare for a proposal in 2012, not just any ring would do. One ring in particular wielded enough history to truly shine as a piece of art.
The ring was originally a gift from Gray's great-grandfather to his wife, dating back to the late '60s. It was passed to their son and daughter-in-law, Gray's grandparents, upon their marriage. As their oldest grandson, Gray received the ring for his future bride.
The ring shines on its own, but its story is equally significant for Julia. "Gray's great-grandmother owned a flower shop in downtown Fairhope for years, which is the same profession that I practice, " says Julia, "so I love the connection with that and the history of the ring."
A Fairytale Fit
Marty and Rex Leatherbury now sell bridal pearls in their Fairhope antique shop, but when they got engaged in 1990, Marty's ring came straight from the family tree.
"The ring is one that my maternal grandfather gave my grandmother in 1925, " says Rex, whose grandmother later passed the nearly hundred-year-old ring to him for his future bride. "When I proposed to Marty, I put it in a big magnolia blossom and handed it to her."
The gesture screamed Southern romance, but was also aimed at making the ring seem larger than life. Rex would later realize, though, that it was actually the perfect fit.
"The ring size was very small, " Rex says, "but it fit Marty's finger like Cinderella's shoe."
Diamond Dos and Don'ts
Do: Get fitted. Rings can be adjusted if the size is wrong the first time, but it is best to be fitted before purchasing.
But Don't: Immediately resize. Our bodies go through many changes that affect our fingers. Unless you know your ring size is permanently changed, leave it to avoid over-working the band.
Do: Remove your ring during certain activities. When you have a safe place to store your ring while cooking, cleaning or exercising, set it to the side.
But Don't: Remove your ring in non-secured places. Restaurant bathroom, public beach or hotel table? Keep your rock on your finger. It is better than leaving it behind to wind up in a lost and found box.
Do: Utilize your jewelry box. The boxes or bags that rings come in are usually designed specifically for protecting that type of ring.
But Don't: Pull your ring from the top. Instead, remove your ring for storage by gripping your index finger and thumb around either side of your band for more protection.
Do: Know your rock. Learn what makes your ring special and make it known. Once you know the ins and outs of your ring, you'll be better equipped to recognize changes and avoid harmful damage.
But Don't: Hide your prize. Wear your ring and flaunt it with pride! No matter if it's vintage or brand new, you deserve to show off your stone, not let it waste away in a dust-proof box.


text:
Home » New Jersey adopts 2018 National Standard Plumbing Code
Market SectorsPlumbing NewsLatest News
New Jersey adopts 2018 National Standard Plumbing Code
KEYWORDS codes and standards / IAPMO / plumbers and pipefitters
New Jersey residents will continue to be protected by the National Standard Plumbing Code (NSPC), as the Garden State has adopted the 2018 edition of the NSPC, the first to be published by IAPMO.
The Division of Codes and Standards, which is part of the state's Department of Community Affairs, adopted the NSPC with state-specific amendments on Sept. 3.
The NSPC provides the latest information about common materials, fixtures, devices,and equipment systems used or installed in plumbing systems. Illustrations and supplementary notes make the NSPC an indispensable enforcement and training tool. For user convenience, IAPMO will have a separate book available that includes the New Jersey amendments embedded in the body of the text.
"The New Jersey version of the 2018 National Standard Plumbing Code is created in a fair and balanced process that includes plumbing contractors, engineers and inspectors, along with the United Association," said NSPC Code Committee Chair Frank Maddalon of F.R. Maddalon Plumbing and Heating. "The NSPC is an all-encompassing plumbing code with input from all aspects of the plumbing industry."
"The state of New Jersey has taken a step forward in protecting the health and safety of all its citizens by adopting the innovative 2018 NSPC," added Mike Maloney, NSPC code committee member and business manager of UA Local 9 in Englishtown, New Jersey.
"The 2018 NSPC provides cutting-edge technology and theories for the plumbing industry, along with a clear and concise tool for inspectors without requiring multiple code books," said NSPC Code Committee Member Mike Baker, an inspector for Wayne Township, New Jersey. "Protecting the health and safety of everyone in New Jersey is the highest priority for plumbers, engineers and inspectors, and the NSPC provides the guidance for the industry and ensures consistency throughout the state of New Jersey."
On June 1, 2017, IAPMO and the Plumbing-Heating-Cooling Contractors — National Association (PHCC) executed an agreement transferring ownership of the NSPC to IAPMO. The transfer encompasses all editions of the NSPC, including the 2018 edition. First published in 1933, the NSPC is designed to ensure the proper installation of plumbing systems, providing local and state governments, code administration bodies and the industry with a modern code to protect health and promote safety.
Source: IAPMO
IAPMO acquires National Standard Plumbing Code
IAPMO/ISO 30500 published as national adoption standard for the US and Canada
IAPMO announces 2018 edition of National Standard Plumbing Code Illustrated
2018 National Standard Plumbing Code Illustrated Now Available


text:
Aida- Saturday, June 22
Sat, June 22, 2019, 8:00 PM – 10:30 PM EDT
Sales Have Ended
Ticket sales have ended
We're sorry, this event is already past or has sold out. We hope you will come back for future shows.
The Seminole Theatre Players & Lorenzo Ford present
Elton John & Tim Rice's AIDA
Winner of four 2000 Tony Awards, Elton John and Tim Rice's Aida is an epic tale of love, loyalty and betrayal, chronicling the love triangle between Aida, a Nubian princess stolen from her country, Amneris, an Egyptian princess, and Radames, the soldier they both love.
An enslaved Nubian princess, Aida, finds her heart entangled with Radames, an Egyptian soldier who is betrothed to the Pharaoh's daughter, Amneris. As their forbidden love blossoms, Aida is forced to weigh her heart against the responsibility that she faces as the leader of her people. Aida and Radames' love for one another becomes a shining example of true devotion that ultimately transcends the vast cultural differences between their warring nations, heralding a time of unprecedented peace and prosperity.
Music by Elton John
Lyrics by Tim Rice
Book by Linda Woolverton and Robert Falls & David Henry Hwang
Directed by Mickey McGuire
Choreographed by Tiffany Hosch
Musically Directiom by Tony Seepersad
All tickets just $15. Performances run June 21 – 30, 2019.
AIDA is presented with the support of the City of Homestead Community Redevelopment Agency and with the support of the Miami-Dade County Department of Cultural Affairs and the Cultural Affairs Council, the Miami-Dade County Mayor and the Board of County Commissioners.
ELTON JOHN AND TIM RICE'S AIDA is presented through special arrangement with Music Theatre International (MTI). All authorized performance materials are also supplied by MTI. www.MTIShows.com
Tickets are also available at the Seminole Theatre box office, 786-650-2073 or 18 N Krome Ave, Homestead, FL (Tues-Sat 12-6pm)
Special Thanks to our very generous sponsor, Lorenzo Ford. Lorenzo Ford is a family owned Ford Dealership in Miami Dade, located in Homestead just minutes away from anywhere in Miami, but many customers come to us from all over Florida and even further. Why? Very simple. We can offer them the very best deals on a new Ford or a used vehicle from our large selection of most makes and models.
This page is only for tickets for the Saturday, June 22nd evening performance. For other performances, please click here: www.seminoletheatre.org/aida-musical
Aida- Saturday, June 22 at Seminole Theatre
Seminole Theatre Players
The Little Mermaid- Saturday, August 3
Seminole Theatre, Homestead
Fri, Aug 2 8:00 PM
The Little Mermaid - Friday, August 2
The Little Mermaid- Saturday, August 10
The Little Mermaid- Friday, August 9
Heroes Vs Villains Showdown! Presented by Camp Seminole
Summer Script Slam: An Open Mic For Writers And Actors! Hot Nights, Cold Readings.
Speak Easy Theater At Taquiza, Miami Beach
The Crow's Chronicle: Spontaneous Theater Inspired By True Stories
THE AMPARO EXPERIENCE CASTING!
221 NE 17th St, Miami
Les Ailes Du Désir, Miami
#Arts #Retreat


The VIP lounge and nightclub in Daytona is a hotspot for locals and tourists looking for a good time after the sun sets. Home to Daytonas largest dance floor and state of the art sound and lighting, weekly drink specials and ladies night, Razzle's Night Club in Daytona Beach guarantees a good time.
The jewel of the Seabreeze entertainment district in Daytona Beach, 509 is an upscale cocktail lounge and nightclub just one block from the beach. This venue truly has something for everyone - you can relax with a gourmet snack at the outdoor patio bar, enjoy a VIP bottle club experience, and shake your booty with the area's best DJs.
Featuring a spectacular view of the Atlantic ocean, this fun island-themed bar has a sister location in Honolulu. Mai Tai features a super tasty menu of tropical delights like seared rare Ahi tuna, Firecracker Thai Chili shrimp, traditional tiki drinks, and TWO happy hours Mondays through Fridays!
Once a historic 1920's bank building, this venue is now home to Daytona's internationally known Bike Week and Biketoberfest. The Bank and Blues Club offers a warm & friendly staff, ice cold beers, and live entertainment ranging from the Central Florida Burlesque Festival to blues phenom Victor Wainwright.
Known as "The Legendary", Boot Hill is the biker bar with a heart of gold. You'll enjoy great service, affordable drinks, and rockin' live music - and be sure to take home a souvenir from their cool gift shop!
Close to the beach and beloved of locals, The Oyster has been one of Daytona's best bars for nearly 30 years. This laid-back sports bar & gastropub offers more than 65 wide-screen televisions for all of your live sports needs. Dive into a huge menu of wings, sandwiches, burgers, and other delectable bar food favorites - or try the crab legs, clams, and of course, oysters.
There are tons of Daytona nightlife options in the area, so be sure to check 386area.com frequently for the latest updates on the coolest hangout spots, bars, and nightlife in Daytona Beach.


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Hayden Gallery
Nairy Baghramian: Fluffing the Pillows
ShowingMay 9, 2013 - July 14, 2013
The MIT List Visual Arts Center presents Nairy Baghramian: Fluffing the Pillows (Moorings, Gurneys, Silos, Mops News Rack, Railing) an exhibition by Iranian born, Berlin-based artist Nairy Baghramian. Baghramian uses disparate tropes and motifs drawn from a variety of sources—from interior design to physiology—in her investigation of sculptural form. With a keen sense of traditional sculptural concerns such as material and volume, her work plays on the supposed distinctions between decoration and function, industrial and handmade, commodity and art object. Her work has also centered on the political and social relations implied by objects and the site of display, in particular on the exhibition space as a type of interior, where affect and experience increasingly conflict with luxury and leisure.
For this commissioned installation, Baghramian abstracts materials and forms derived from utilitarian and maritime objects, drawing out the formal and creative processes that define notions of the 'sculptural.' The exhibition centers on groups of forms, such as Silos, Gurneys, and Moorings, each sited in relation to the museum's architecture. Her Silos share their name with a container or structure used to store bulk or industrial materials. These seemingly soft yet solid forms, like those used to hold or transport materials, are created out of sailing fabric, rubber, and pleather. Made from chrome-plated poles, Gurneys—a term to describe wheeled stretchers—are used to support the formless sacks. Baghramian's Moorings are named after objects that are used to moor, or secure, boats in place at port. Cast in aluminum, their shape is derived from the large hooks that crane operators use to lift commercial cargo containers. A news rack displays a glossy publication, Baghramian's exhibition catalog, disguised as an upscale boating magazine. The artist brings these forms and their complex associations—boating and sailing, trade and cargo, the labor of industry, service, and stevedores—into the museum as a means to investigate gendered notions of labor and craft.
Nairy Baghramian was born in Isfahan, Iran in 1971, and has lived and worked in Berlin since 1985. Her work has been shown in numerous internationally recognized solo and group exhibitions, including recent solo exhibitions at the Sculpture Center, Long Island City, NY (2013); Galerie Buchholz, Köln (2012); Contemporary Art Gallery Vancouver (2012); Neuer Aachener Kunstverein (2008); Staatliche Kunsthalle Baden-Baden (2008); and Kunsthalle Basel (2006). Baghramian had a two-person show with Phyllida Barlow at Seprentine Gallery, London (2010), and her work was in Illuminations, 54th Venice Biennial (2011); Glasgow International Festival of Visual Art (2011); Temporary Stedelijk 2, Stedlijk Museum (2011); Berlin Biennial (2008); and Sculpture Project Münster (2007). In 2012, she was awarded the Hector Kunstpreis, which included an artist publication and exhibition at the Kunsthalle Manheim.
Nairy Baghramian: Fluffing the Pillows is made possible through the generous support of Julian and Barbara Cherubini, the Council for the Arts at MIT, the Massachusetts Cultural Council, the Office of the Associate Provost at MIT, the MIT List Visual Arts Center Advisory Committee, the Friends of the List, and the Consulate General of the Federal Republic of Germany in Boston.
Installation View:
Nairy Baghramian: Fluffing the Pillows (Moorings, Gurneys, Silos, Mops News Rack, Railing)
Photo: Peter Harris


The transition from one presidential administration to the next is inevitably a time of uncertainty. This is amplified when the transition is being made from one political party to another. Typically, the campaign season includes a significant degree of discussion about the policies of the candidates, so there are some broad expectations regarding the direction the new administration will take on major policy issues. In this respect, as in many others, the 2016 presidential campaign differed from the norm.
While some topics, such as immigration, were subject to debate and discussion during the primaries and the campaign itself, the issue of climate change was almost wholly absent, receiving a brief mention during the Democratic primary debates and no mention at all in the presidential debates. The topic was frequently addressed, instead, in the candidates' campaign speeches. Secretary Clinton vowed to support the United States' commitment to the Paris Accords and to pursue an energy and development agenda focused on reducing impacts on the environment. President Trump, in contrast, emphasized a renewed commitment to fossil fuels and pledged to exit he Paris Accords as quickly as possible.
As a result, the nation has been attempting to discern the potential impact on climate change policy of the new Trump administration. Will President Trump's campaign rhetoric become policy or will the new administration embrace something closer to the current administration's approach to the issue?
In reviewing Trump's Cabinet picks thus far, we believe a new approach is coming. The nominees are largely represented by a number of climate change skeptics and/or picks that lack a definitive position on the issue. These choices appear to indicate a bias in the new administration toward appointing officials who oppose prudent action on the issue.
As confirmation hearings have begun, there has been some focus on climate change in the questions posed to Trump's nominees for Cabinet positions.
The responses demonstrate a lack of a unified policy on the issue of climate change. There is a philosophical congruence among the appointees that suggests what the administration will likely prioritize, what will be amended, and what will be abandoned.
It is becoming clearer the Trump administration will likely seek to reduce regulatory oversight of many industries by the federal government, shifting it to the states. Only where clear federal legislative mandates are in place will the new administration continue to enforce regulatory compliance. On issues related to water quality, air quality, pollutants, particulate matter, and non-federally regulated toxic emissions the onus will shift to states to ensure that their residents are safe from potentially dangerous environmental pollution. The nomination of Scott Pruitt for head of the Environmental Protection Agency is confirmation of this approach, particularly given his history of fighting for states' rights to regulate environmental issues and his repeated litigation with the EPA to limit its powers of enforcement during his tenure as Attorney General of Oklahoma.
The new administration's approach to global agreements related to the environment and climate change remains unclear. Based on remarks by Trump and his transition team to date, it is likely that the administration will seek to amend a number of these agreements to secure more favorable positioning for U.S. business interests. Where such amendment is impractical, such as in the Paris Accords, it is expected that the administration will follow through with campaign promises and exit the agreement as quickly as possible. Moreover, due to disclosed policy positions, we see support for abandoning the Clean Power Plan. Conversely, the administration has made it a priority to increase the extraction of fossil fuels, including coal and oil, as a component of its economic and energy plans. This commitment was reflected in the Trump campaign's policy priority to "unleash America's $50 trillion in untapped shale, oil, and natural gas reserves, plus hundreds of years in clean coal reserves." The position has been further articulated in the 'America First Energy Plan,' with the administration committing to "embrace the shale oil and gas revolution to bring jobs and prosperity to millions of Americans," and "take advantage of the estimated $50 trillion in untapped shale, oil, and natural gas reserves, especially those on federal lands that the American people own." An immediate example of the administration's policy regarding fossil fuels can be seen in the issuance of executive orders by President Trump on January 24th to push forward the Keystone XL and Dakota Access pipelines.
These policies and actions by the new administration run counter to how most of the world is approaching environmental issues. Globally, governments have demonstrated a willingness to continue to invest in renewable energy, to achieve greenhouse gas reductions through energy efficiency and technology updates, and to pursue strategic climate resiliency policies. This approach is reflected in actions such as China's recent commitment of $360 billion by 2020 for new and expanded clean energy projects, India's commitment of $1 trillion by 2030 to attain 40% of its energy from renewables, and Germany's continued commitment to produce 80% of its electricity from renewable sources by 2050 (the Energiewende).
The Trump administration's potential policy shifts come with certain risks. Climate change models clearly point to an increase in the frequency and severity of extreme weather events such as hurricanes, blizzards, droughts, and heat waves. In 2016 the U.S. experienced fifteen such extreme weather events with total damages of over $46 billion, compared to eight such events in 2015 resulting in only $19 billion in damage. This increased risk is problematic for residents, communities, and businesses. It will also begin to be priced into markets, as more investors demand to be compensated for taking such risk when investing in communities. Credit rating agencies such as Moody's and S&P have already begun to evaluate risk resulting from extreme weather when assigning credit ratings to issuers in at-risk geographies.
It is clear that investors are not ignoring climate change issues. Increased attention to the issue of climate change will produce winners and losers in the public markets. According to the US SIF Foundation's 2016 Report on U.S. Sustainable, Responsible and Impact Investing Trends, the number of investors including climate change related criteria in their investment evaluation has increased by 400% from 2014. There is currently at least $2.15 trillion in U.S. markets that is invested with such criteria in mind. Globally, there are over 1,500 signatories to the United Nations Principles for Responsible Investment, representing $60 trillion in assets under management. This level of concern, and the resulting pressure on the equity or debt pricing of entities with negative outcomes in a climate aware world, will create challenges for companies, municipalities, and nations that fail to address climate impacts.
As a result of investor pressure, it is expected that market exchanges and financial regulatory bodies will continue to push for more disclosure and action on environmental issues, including climate change. According to the Sustainable Stock Exchanges Initiative's 2016 Report on Progress, "Fifty-eight stock exchanges, representing over 70% of listed equity markets, have made a public commitment to advancing sustainability in their market…12 exchanges currently incorporate reporting on environmental, social, and governance (ESG) information into their listing rules and 15 provide formal guidance to issuers…23 additional stock exchanges have committed to introducing new ESG reporting guidance for their listed companies in the past year." U.S. companies operating abroad, and foreign companies with U.S. operations, must be aware of these emerging requirements and comply with them so as to ensure continued access to global capital markets. This is aside from regulatory frameworks, such as the EU Emissions Trading System, designed to encourage not just transparency, but credible action on the reduction of greenhouse gas emissions. As countries work toward lower total emissions, carbon constraints will become a reality of business.
Another risk created by ignoring more environmentally conscious policies will be the likely loss of business opportunities and associated jobs. According to Bloomberg New Energy Finance, global investments in renewable energy totaled $315 billion in 2014, $348.5 billion in 2015, and $287.5 billion in 2016. As countries implement commitments like those outlined above, economies that embrace the production of equipment for renewable energy will benefit. Depending on the path the new administration takes, the U.S. could either capitalize on this opportunity by taking a progressive approach to renewable energy and technology or risk being left behind.
The number of people employed in the renewable energy industry surpassed that employed by the oil and natural gas extraction industry for the first time in 2015. Green jobs accounted for 3.6 million openings in 2013, 3.8 million openings in 2014, and over 4 million openings in 2015. With renewable energy now representing over 13% of the total energy generated in the United States, and with the U.S. making up 17% of the global investment total for renewables, any policies that put the growth of this sector at risk also risk the loss of associated job growth and investments.
What does all this mean for investors concerned about the environment and about climate change? And in particular, what does it mean to fixed income investors who are seeking positive environmental outcomes as part of their investment strategy?
We believe the bright spot for 2017 will be the municipal bond market. A large number of states and municipalities have been vocal since the presidential election about their continued commitment to address climate change and to meet renewable energy targets. These states and municipalities will be looking to the public markets for financing support for many of their environmentally responsible projects, giving investors the opportunity to support such approaches both regionally and nationally. SNW will continue to assess and invest in these opportunities for our clients, helping to ensure that there is a market for issuers committed to positive environmental outcomes.
That is the short-term answer to the question, "What does all this mean for investors concerned about the environment and about climate change?" The answer over the long term is more complicated and will depend on how the new administration's policies are worded and implemented, not just regarding climate change but also for tax structures and infrastructure investment. As the country moves further into 2017 and begins to receive more clarity on both policy wording and implementation, the longer-term picture will become clearer.