text:
\section{Introduction}\label{sec:introduction}}

\IEEEPARstart{R}{eversible}
data  hiding (RDH) is a technique where a payload is embedded into host data such that the consistency of the host is perfectly preserved and the host data are restored during the extraction of the payload \cite{shi2016reversible}. Nowadays, audio is widely spread on the Internet and has been one of the main digital multimedia carriers. Its associated Reversible Audio Watermarking (RAW) techniques are beneficial for archiving, transmitting, and authenticating high-quality audio data that contains metadata, secret data, and so forth \cite{DBLP:journals/sigpro/HuaHSGT16}.

Similar to other types of multimedia, a critical step of RAW is to design a proper reversible function.
Varying on how the reversible function is designed,
conventional RDH methods include difference expansion (DE) \cite{1227616}, prediction-error expansion (PEE) \cite{1421361,WU2014387}, histogram shifting (HS) \cite{ni2006reversible}. A common feature of these methods is to embed some clues of the cover object into the watermarked object, such that the cover object can be restored. Unfortunately,
these methods are mostly only suitable for a finite-alphabet cover domain (e.g., the domain of $\lbrace0,...,255\rbrace$ in a gray-scale pixel), which implies that they are more suitable for images rather than audio.

In recent years, the celebrated quantization index modulation (QIM) \cite{chen2001quantization} has also been adapted for RDH \cite{ko2012nested,peng2011effective,9328388}, in which the cover domain more generally includes the real-valued domain where the digital audio resides.
Ko \textit{et al.} \cite{ko2012nested} developed a reversible watermarking algorithm based on nested QIM via the iterative process that reduces the normalized error. Peng \emph{et al.} \cite{peng2011effective} made an improvement in RDH for one dimensional scalar-QIM by maintaining the relative distance, and extended it into $N$-dimensional region nesting model \cite{9328388}. These methods are collectively referred to as improved-QIM (IQIM), as is named in \cite{peng2011effective}. It is noteworthy that applying IQIM to digital audio is straightforward, although they generally fail to meet the demand of high robustness and imperceptibility. The reason of no robustness is that the scaling factor of IQIM is fixed as $1-\frac{1}{2^b}$. The reason of high distortion is more involved: i) The constructed difference vector is rather sub-optimal. ii) The embedding method is based on the integer lattice $\mathbb{Z}^n$, whose distortion performance is worse than other optimal lattices.

The robustness of the embedded message is important in the sense that
the cover object  may go through some attacks such as additive noises. In this regard, robust RAW has been investigated in \cite{nishimura2013reversible,LIANG2020107584,nishimura2016reversible}. To be concise,
Nishimura \textit{et al.} \cite{nishimura2013reversible} proposed a robust RAW scheme by combining quantization index modulation (QIM) and amplitude expansion, and also a scheme based on error-expansion of linear prediction \cite{nishimura2016reversible}  for segmental audio and G.711 speech. Liang \textit{et al.} \cite{LIANG2020107584} proposed a robust RAW scheme based on high-order difference statistics.  Nevertheless, these works overemphasize the robustness of embedded messages, but ignore or even sacrifice its imperceptibility.
Since the sensibility of human auditory system (HAS),
the watermarked cover object should not cause
perceivable changes.

To address the above issues, this paper makes a retrospective and prospective revisit to RDH from the perspective of lattices \cite{zamir2014lattice,DBLP:journals/tit/LingB14,DBLP:journals/tit/LyuC019}, with the hope of designing an efficient RAW scheme that simultaneously achieves good robustness and imperceptibility. Lattices are discrete additive subgroups of the Euclidean vector space, and QIM is in essence quantization based on nested lattice codes \cite{moulin2005data,zamir2014lattice}. The reversibility, robustness and imperceptibility features of QIM can then be better accommodated by using more advanced lattice coding skills. Specifically, the contributions of this paper, along with the highlights, are summarized as follows.

\begin{itemize}
	\item First, we propose a Meet-in-the-Middle Embedding (MME) RAW scheme. Within the QIM framework, there exists a difference vector between the
	cover vector and the quantized cover vector. By properly scaling the difference vector and adding it back to the quantized cover vector, it becomes possible for the receiver to estimate the cover vector with the aid of the scaled difference vector. As the reversibility of MME hinges on the properly choosing the scaling factor, we derive the feasible range of the scaling factor.
	\item Second, we analyze the performance of MME in terms of distortion and robustness.
	More specifically, we compare the signal-to-watermark ratio (SWR) and generalized signal-to-noise ratio (GSNR) between MME and IQIM \cite{peng2011effective}.
	\item Finally, we make a comprehensive comparison between MME and other state-of-the-art RAW methods, and the
	numerical simulations show that MME excels in the robustness and imperceptibility metrics such as
	SWR, GSNR, objective difference grade (ODG), and bit error rate (BER). The simulated results ideally align with our theoretical analyses.
\end{itemize}

Notation: Matrices and column vectors are denoted by
uppercase and lowercase boldface letters. We write $\lfloor \cdot \rfloor$ for the floor function, and $|\cdot|$ for the  absolute value.

\section{Preliminaries}
\subsection{QIM}\label{Sec.QIM}
The one-bit scalar-QIM is perhaps the most popular version of QIM in the data hiding community \cite{moulin2005data}. Its rationale can be explained by a one-bit embedding example in Fig. \ref{Fig. QIM embed model}. Denote circle and cross positions in Fig. \ref{Fig. QIM embed model} as two sets $\Lambda_0$ and $\Lambda_1$, respectively.
Given a host/cover sample $s\in\mathbb{R}$ and a one-bit message $m \in \{0,1\}$, the watermarked value is simply moving $s$ to the nearest point in  $\Lambda_0$ when $m=0$, and to the nearest point in  $\Lambda_1$ when $m=1$.

\begin{figure}[t!]
	\centering
	\includegraphics[width=0.4\textwidth]{fig/QIM_model.pdf}
	\caption{Embedding one bit into a sample with original QIM.}
	\label{Fig. QIM embed model}
\end{figure}

Define $Q(s)=\Delta\lfloor s/\Delta\rfloor$ with $\Delta$ being a step-size parameter.
Then the embedding process can be described as
\begin{equation}\label{Eq. conventional QIM embedding}
	s_{\mathrm{QIM}}\triangleq Q_m(s)=Q(s-d_m)+d_m,~m\in \{0,1\},
\end{equation}
where $d_0=-(\Delta/4)$, $d_1=\Delta/4$,  $\Lambda_0=d_0+\Delta\mathbb{Z}$ and $\Lambda_1=d_1+\Delta\mathbb{Z}$.

Assume that the transmitted $s_{\mathrm{QIM}}$ has undergone the contamination of an additive noise term $n$, then at the receiver's side we have: $y= s_{\mathrm{QIM}}+n$. A minimum distance decoder is therefore given by
\begin{equation}\label{Eq. QIM extract}
	\hat{m}=\mathop{arg\min}_{m\in\{0,1\}}\left[\mathop{\min}_{s\in\Lambda_m}|y-s|\right].
\end{equation}
If $|n|<\Delta/4$, the $\hat{m}$ is correct.

Regarding the embedding distortion, as shown in Fig. \ref{Fig. QIM distortion}, the maximum error caused by embedding is $\Delta/2$. If the quantization errors are distributed uniformly over $[-(\Delta/2),(\Delta/2)]$, then the mean-squared embedding distortion is $D=\Delta^2/12$.
\begin{figure}[t!]
	\centering
	\includegraphics[width=0.5\textwidth]{fig/QIM_distortion.pdf}
	\caption{Selection of watermarked signal $x$ with given $s$ and $m \in \{0,1\}$ in one-bit scalar-QIM. (a) Prototype symmetric function. (b) $x=Q_m(s)$ with $m = 0$. (c) $x=Q_m(s)$ with $m = 1$.}
	\label{Fig. QIM distortion}
\end{figure}

\subsection{IQIM}\label{IQIM}

Inspired by conventional QIM, a reversible version of QIM called improved-QIM (IQIM) has been proposed in \cite{peng2011effective}. Its embedding and extraction processes can be described as follows.

\subsubsection{Embedding}
\noindent \textbf{Step i)} Calculate the number of quantization interval $\gamma$ and relative distance of $s$ in the $\gamma^{th}$ quantization interval $r$ by:
\begin{equation} \label{prepare step}
	\left\{
	\begin{aligned}
		\gamma&=\left\lfloor\frac{s}{2^b\Delta}\right\rfloor\\
		r&=s-2^b\gamma\Delta
	\end{aligned},\right.
\end{equation}
where $b$ is the bit length of a watermark $m$, and $\Delta$ is again the step size of quantization.

\noindent \textbf{Step ii)} To embed the watermark $m$, the final embedded point $s_{\mathrm{IQIM}}$ is set as
\begin{equation}\label{Eq. REF of IQIM}
	s_{\mathrm{IQIM}}=2^b\gamma\Delta+m \Delta+\frac{r}{2^b}.
\end{equation}

\subsubsection{Extraction}
\noindent \textbf{Step i)} With either a clean or a noisy version of $s_{\mathrm{IQIM}}$ denoted as $y$, calculate the number of quantization interval $\gamma_w$ and the relative distance $r_w$ by
\begin{equation}
	\left\{
	\begin{aligned}
		\gamma_w&=\left\lfloor\frac{y}{\Delta}\right\rfloor\\
		r_w&=y-\gamma_w\Delta
	\end{aligned}
	.\right.
\end{equation}

\noindent \textbf{Step ii)} Estimate the watermark $m$ by
\begin{equation}
	\hat{m}=\gamma_w-2^b\lfloor\frac{\gamma_w}{2^b}\rfloor.
\end{equation}

\noindent \textbf{Step iii)} Estimate the   cover $s$ by
\begin{equation}
	\hat{s}=2^b\lfloor\frac{\gamma_w}{2^b}\rfloor\Delta+2^br_w.
\end{equation}

If $y$ is noiseless, one may verify that $\hat{m}=m$ and $\hat{s}=s$. For noisy $y$, although $\hat{s}$ becomes inaccurate, $\hat{m}$ may still be reliable if the noise pollution is small enough. In addition,
IQIM can also be described by an $N$-dimension integer set $\mathbb{Z}^N$, which is no more than independently performing embedding and extraction in each dimension. For instance, the embedding function w.r.t. the watermark $\mathbf{m}$ is given by
\begin{align}
	\mathbf{s}_{\mathrm{IQIM}}=\beta\left[2^b\Delta \left[\gamma_1~\cdots~\gamma_N\right]^\top+\frac{\Delta\mathbf{m}}{\beta}\right]+ (1-\beta)\mathbf{s},
\end{align}
where $\beta=1-\frac{1}{2^b}$ denotes the scaling factor in IQIM.

\subsection{Lattices}
This paper will use some concepts from lattices to arrive at simpler description of the algorithm and more elegant analysis. Hereby we review some basic concepts of lattices and nested lattice codes.

An $N$-dimensional lattice in $\mathbb{R}^N$ is defined as  $\Lambda=\left\lbrace \mathbf{Gz}|\mathbf{z}\in \mathbb{Z}^N\right\rbrace$, where the full-ranked matrix $\mathbf{G}\in\mathbb{R}^{N\times N}$ represents the generator matrix of $\Lambda$.
For any $\mathbf{x}\in\mathbb{R}^N$, finding its closest vector in a lattice $\Lambda$
is referred to as the closest vector problem (CVP). Based on efficient algorithms to solve CVP \cite{zamir2014lattice}, a nearest neighbor quantizer $Q_\Lambda(\cdot)$ is defined as
\begin{align}
	Q_\Lambda(\mathbf{x})=\mathop{\arg\min}_{\mathbf{\lambda} \in \Lambda} \|\mathbf{x}-\mathbf{\lambda}\|.
\end{align}
Details of some optimal low-dimensional lattices for quantization are listed in Table \ref{Tab. Appendix A}. Based on the CVP quantizer we also define $\rm{mod}(\mathbf{x},\Lambda) = \mathbf{x}-Q_{\Lambda}(\mathbf{x})$.

The set of vectors in $\mathbb{R}^{N}$ that are closer to $\lambda\in\Lambda$ than other vectors in $\Lambda$  is called the Voronoi region $\mathcal{V}_\lambda$, i.e.,
\begin{align}
	\mathcal{V}_\lambda=\{\mathbf{x}:Q_\Lambda(\mathbf{x})=\lambda\}.
\end{align}
The fundamental Voronoi region is represented as
\begin{align}
	\mathcal{V}_\Lambda=\{\mathbf{x}:Q_\Lambda(\mathbf{x})=\mathbf{0}\},
\end{align}
and the volume of the fundamental region is
\begin{align}
	\rm{Vol}(\mathcal{V}_\Lambda)=\int_{\mathcal{V}_{\Lambda}} d\mathbf{x}=|\rm{det} \mathbf{G}|.
\end{align}
The packing  radius  $r_{\rm{pack}\left(\Lambda\right)}$, represents the radius of the largest sphere contained in $\mathcal{V}_\Lambda$:
\begin{align}
	r_{\rm{pack}(\Lambda)} = \frac{1}{2} \rm{min}_{\lambda \in \Lambda \backslash \{\mathbf{0}\}}\|\lambda\|.
\end{align}
The covering radius $r_{\rm{cov}\left(\Lambda\right)}$ refers to the radius of the smallest sphere containing $\mathcal{V}_\Lambda$:
\begin{equation}
	r_{\rm{cov}\left(\Lambda\right)}=\mathop{\max}_{\mathbf{x} \in \mathbb{R}^N} \mathop{\min}_{\lambda \in \Lambda} \|\mathbf{x}-\mathbf{\lambda}\|.
\end{equation}

In the lattice quantization, a typical and efficient method is using the nested lattices based shaping, called coset coding \cite{zamir2014lattice,moulin2005data}. Two lattices $\Lambda_f$ and $\Lambda_c$ are regarded as nested when these two lattices have a inclusion relation, i.e., $\Lambda_c\subset \Lambda_f$. The lattice $\Lambda_f$ is called the \emph{fine/coding} lattice, and its subset  $\Lambda_c$ is called  the \emph{coarse/shaping} lattice. The generator matrices of $\Lambda_c$ and $\Lambda_f$ which are expressed by $\mathbf{G}_c$ and $\mathbf{G}_f$, respectively, have a relation
\begin{align}
	\mathbf{G}_c = \mathbf{G}_f \mathbf{J},
\end{align}
where the sub-sampling matrix $\mathbf{J}$ represents \emph{nesting matrix}.
When $\mathbf{J}$ is an identity matrix, it denotes a self-similar shaping \cite{Kurkoski2018SelfSimilar} operation. When $\mathbf{J}$ is a diagonal matrix with different elements, it denotes a rectangular shaping \cite{Lyu2021RectangularShaping} operation.

\newsavebox{\boxa
\savebox{\boxa}{$\mathbf{J}=\left[\begin{matrix}4&0\\0&4\end{matrix}\right]$}
\newsavebox{\boxb
\savebox{\boxb}{$\mathbf{J}=\left[\begin{matrix}2&0\\0&4\end{matrix}\right]$}

\begin{table*}[t!]
	\centering
	\renewcommand\arraystretch{2}
	\caption{The generator matrices of some optimal low-dimensional quantizers \cite{conway2013sphere}.}
	\label{Tab. Appendix A}
	\begin{tabular}{c c c c c c }
		\hline

		\textbf{N}& Quantizer& Generator Matrix& $r_{pack}(\Lambda)$&$r_{cov}(\Lambda)$& $G(\Lambda)$ \\
		\hline

		1& $\mathbb{Z}$& 1
		& $\frac{1}{2}$& $\frac{1}{2}$
		&0.083333 \\

		2 & $A_2$& $\left[\begin{matrix}\frac{\sqrt{3}}{2}&0\\\frac{1}{2}&1\end{matrix}\right]$
		& $\frac{1}{2}$& $\frac{\sqrt{3}}{3}$
		& 0.080188 \\

		3 & $A_3 \cong D_3$& $\left[\begin{matrix} -1&1&0\\-1&-1&1\\0&0&-1\end{matrix}\right]$
		& $\frac{\sqrt{2}}{2}$& $1$
		& 0.078745 \\

		4 & $D_4$& $\left[\begin{matrix} 2&1&1&1\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{matrix}\right]$
		& $\frac{\sqrt{2}}{2}$& $1$
		& 0.076603 \\

		8 & $E_8$
		& $\left[\begin{matrix}
		2&-1&0&0&0&0&0&\frac{1}{2}\\
		0&1&-1&0&0&0&0&\frac{1}{2}\\
		0&0&1&-1&0&0&0&\frac{1}{2}\\
		0&0&0&1&-1&0&0&\frac{1}{2}\\
		0&0&0&0&1&-1&0&\frac{1}{2}\\
		0&0&0&0&0&1&-1&\frac{1}{2}\\
		0&0&0&0&0&0&1&\frac{1}{2}\\
		0&0&0&0&0&0&0&\frac{1}{2}\\
		\end{matrix}\right]$
		& $\frac{\sqrt{2}}{2}$& $1$
		& 0.071682 \\
		\hline
	\end{tabular}
\end{table*}

\section{The Proposed Method}\label{Sec. Mathmetical Model}

\subsection{Lattice-QIM reformulation}\label{Sec.QIM improve}
Following \cite{moulin2005data,9455352,conway2013sphere},  we reformulate   QIM for arbitrary lattices and payloads from the perspective of lattice quantization and coset coding, based on which the description of the proposed RAW scheme can also be simpler.

\subsubsection{Embedding}

\noindent \textbf{Step i)} Choose a pair of nested lattices $\Lambda_f$ and $\Lambda_c \subset \Lambda_f$ in $\mathbb{R}^N$.
The fine lattice $\Lambda_f$ can be decomposed as the union of $|\rm{det} \mathbf{J}|$ cosets of the coarse lattice $\Lambda_c$:
\begin{align}\label{Eq. lambda f&c}
	\Lambda_f = \bigcup\limits_{i=0}^{|\rm{det} \mathbf{J}|-1} \Lambda_i
	=\bigcup\limits_{\mathbf{d}_i \in \Lambda_f \backslash \Lambda_c} (\mathbf{d}_i + \Lambda_c)
\end{align}
where each coset $\Lambda_i = \Lambda_c  + \mathbf{d}_i$ is a translated coarse lattice and $\mathbf{d}_i$ is called the coset representative of $\Lambda_i$.

\noindent  \textbf{Step ii)} Perform labeling to associate the $i\in \left\lbrace 0, 1, \ldots, |\rm{det} \mathbf{J}|-1 \right\rbrace $  to the $i$th message vector $\mathbf{m}_i \in \mathcal{M}$.

\noindent \textbf{Step iii)}
Consider a cover/host vector denoted as $\mathbf{s}$. To embed a message vector $\mathbf{m}_i$ over $\mathbf{s}$, the watermarked cover vector is set as
\begin{equation} \label{Eq. QIM_encode}
	\mathbf{s}_{\mathrm{QIM}} \triangleq	Q_{\Lambda_i}(\mathbf{s}) = Q_{\Lambda_c}(\mathbf{s}-\mathbf{d}_i)+\mathbf{d}_i.
\end{equation}

\subsubsection{Decoding}
Let the (possibly) noisy observation of $	\mathbf{s}_{\mathrm{QIM}}$ be $\mathbf{y}$.

\noindent \textbf{Step i)}   Estimate the coset representative $\mathbf{d}_{i}$ of $\Lambda_i$ by
\begin{equation}\label{Eq.qim_decode}
	\hat{\mathbf{d}}_{i}={\rm mod}(Q_{\Lambda_f}(\mathbf{y}),\Lambda_c).
\end{equation}

\noindent \textbf{Step ii)} Perform inverse labeling to turn $\hat{\mathbf{d}}_{i}$ into the estimated message vector   $\hat{\mathbf{m}}_i$.

The extracted message vector is correct as long as $Q_{\Lambda_f}(\mathbf{y})=\mathbf{s}_{\mathrm{MME}}$. Moreover, the information transmission rate per dimension of Lattice-QIM is simply
\begin{equation}
	R=\frac{1}{N}\log {|\rm{det} \mathbf{J}|}.
\end{equation}

\subsection{Meet-in-the-middle embedding}\label{SSec. GLMR}

Based on the above, we observe that there exists a difference vector  $\mathbf{e}$ between the cover vector $\mathbf{s}$ and its quantized watermarked vector $	\mathbf{s}_{\mathrm{QIM}}$, i.e.,
\begin{align}
	\mathbf{e} =  \mathbf{s} - Q_{\Lambda_i}(\mathbf{s}).
\end{align}
Obviously the information about $\mathbf{e}$ is lost if we only use $Q_{\Lambda_i}(\mathbf{s})$ as the watermarked vector.

Notice that QIM has certain error tolerance capability. If we treat $\mathbf{e}$ as the ``beneficial noise'' and add it back to $Q_{\Lambda_i}(\mathbf{s})$, then the information about the cover $\mathbf{s}$ can be maintained, and the scheme becomes reversible. The tricky part about adding  ``beneficial noise'' is that, they should be properly scaled to meet several demands.  First, the scaled $\mathbf{e}$  should be small enough such that it does not go beyond the Voronoi region of the fine lattice. Second, the scaled $\mathbf{e}$  should not be too small to avoid exceeding the used representation accuracy of numbers. Details of the proposed scheme is explained as follows.

\begin{definition}[MME Embedding]\label{Def.reversible lattice model definition}
	The watermarked cover vector is set as
	\begin{align}\label{Eq. REF}
		\mathbf{s}_{\mathrm{MME}} = \mathcal{W}(\mathbf{s}) &= Q_{\Lambda_i}\left(\mathbf{s}\right)+\left(1-\alpha\right)(\mathbf{s}-	Q_{\Lambda_i}\left(\mathbf{s}\right)) \notag\\
		&=  \alpha Q_{\Lambda_i}\left(\mathbf{s}\right) + \left(1-\alpha\right) \mathbf{s},
	\end{align}
	in which $\alpha$ is a chosen scaling factor such that
	$(1-\alpha)(\mathbf{s}-Q_{\Lambda_i}\left(\mathbf{s}\right))\in\mathcal{V}_{\Lambda_f}$.

\end{definition}

\begin{definition}[Noiseless MME Extraction]
	If the receiver's side has $\mathbf{s}_{\mathrm{MME}}$,
	the estimated cover vector can be accurately restored by
	\begin{align}\label{Eq. RF}
		\hat{\mathbf{s}}
		=\mathcal{W}^{-1}\left(\mathbf{s}_{\mathrm{MME}}\right)
		&=\frac{\mathbf{s}_{\mathrm{MME}} -
			Q_{\Lambda_f}\left(\mathbf{s}_{\mathrm{MME}}\right)
		}{1-\alpha} + Q_{\Lambda_f}\left(\mathbf{s}_{\mathrm{MME}}\right)
		\nonumber \\
		&= \frac{1}{1-\alpha}\mathbf{s}_{\mathrm{MME}}-\frac{\alpha}{1-\alpha} Q_{\Lambda_f}\left(\mathbf{s}_{\mathrm{MME}}\right).
	\end{align}
	In this case, the message vector can also be accurately decoded by using the decoder of QIM.
\end{definition}

In the noisy setting,
consider an additive white Gaussian noise (AWGN) channel in the form of $\mathbf{y}=\mathbf{s}_{\mathrm{MME}}+\mathbf{n}$, where the entries of $\mathbf{n}$ admit a standard Gaussian distribution $\mathcal{N}(0,\sigma_{\mathbf{n}}^2)$. In this case, accurately restring the cover vector is impossible, but the message vector may be accurately decoded by using the decoder of QIM.
Compared with IQIM, MME is advantageous in the following aspects.
\begin{itemize}
	\item As shown in  Figs. \ref{Fig. embeddin process comparison one dimension} and  \ref{Fig. embeddin process comparison two dimension}, the difference vector of MME can be confined to a small Voronoi cell (hence the name ``meet-in-the-middle'') while IQIM cannot. In the distortion analysis we will shown that this brings certain performance gains.
	\item
	MME can be applied to general lattices while IQIM is only feasible for the standard integer lattice.
\end{itemize}

\begin{figure}[t!]
	\linespread{1}
	\centering
	\subfigure[]{\includegraphics[width=.45\textwidth]{fig/fig_embeddin_process_comparison_05.pdf}}
	\quad
	\subfigure[]{\includegraphics[width=.45\textwidth]{fig/fig_embeddin_process_comparison_15.pdf}}

	\caption{Comparison of embedding process between IQIM and MME in one-dimension with different host vector $\mathbf{s}$. (a) $\mathbf{s}=0.5$. (b) $\mathbf{s}=1.5$.}
	\label{Fig. embeddin process comparison one dimension}
\end{figure}
\begin{figure}[t!]
	\linespread{1}
	\centering
	\includegraphics[width=.45\textwidth]{fig/fig_embeddin_process_comparison_2_dimension.pdf}

	\caption{Comparison of embedding process between IQIM and MME in two-dimension with $\mathbf{s}=(1.61,0.73)$.}
	\label{Fig. embeddin process comparison two dimension}
\end{figure}

\subsection{Correctness analysis}
\subsubsection{Reversibility}\label{SSec. Reversibility of GLMR}
For the embedding function Eq. (\ref{Eq. REF}), its definition field $\mathcal{A}$ is noted as
\begin{equation}
	\mathcal{A}=\{\mathbf{s}|\mathbf{s}\in\mathbb{R}^N\}.
\end{equation}
And the value field $\mathcal{B}$ is defined as
\begin{equation}\label{defsujection}
	\mathcal{B}=\{\mathbf{s}_{\mathrm{MME}}|\mathbf{s}_{\mathrm{MME}}=\mathcal{W}\left(\mathbf{s}\right),\mathbf{s}\in\mathcal{A}\}.
\end{equation}
Hereby we introduce a theorem about the one-to-once correspondence between about the cover and the watermarked cover.

\begin{theorem}[Noiseless Recovery]
	\label{Lem. lemma one to one}
	The function $\mathcal{W}$ in MME is bijective.\end{theorem}
\begin{proof}
	It suffices to prove that $\mathcal{W}$ is both injective and  surjective.
	``Injective'' means no two elements in the domain of the function gets mapped to the same image, i.e.,
	for any cover vectors $\mathbf{s}_a,\mathbf{s}_b\in\mathcal{A}$,
	\begin{equation}
		\mathbf{s}_a\neq\mathbf{s}_b\rightarrow \mathcal{W}\left(\mathbf{s}_a\right)\neq\mathcal{W}\left(\mathbf{s}_b\right).
	\end{equation}
	With
	$\mathbf{s}_a\neq\mathbf{s}_b$, we analyze the relationship between their output $\mathcal{W}\left(\mathbf{s}_a\right)$ and $\mathcal{W}\left(\mathbf{s}_b\right)$ in three cases:
	\begin{itemize}
		\item[1.]$\mathbf{s}_a$ and $\mathbf{s}_b$ belong to two different Voronoi regions $\mathcal{V}_{\lambda_a}$ and $\mathcal{V}_{\lambda_b}$ of the coarse lattice $\Lambda_c$.  It follows from  $\mathcal{V}_{\lambda_a}\cap\mathcal{V}_{\lambda_b}=\emptyset$ that
		$\mathcal{W}\left(\mathbf{s}_a\right)\neq\mathcal{W}\left(\mathbf{s}_b\right)$.
		\item[2.]   $\mathbf{s}_a$ and $\mathbf{s}_b$ belong to the same Voronoi region in $\Lambda_c$ but different watermarks ($Q_{\Lambda_i}\left(\mathbf{s}_a\right)\neq Q_{\Lambda_i}\left(\mathbf{s}_b\right)$). Since the ``self-noise'' does not go beyond the Voronoi cell of a fine lattice, i.e., $(1-\alpha)(\mathbf{s}-Q_{\Lambda_i}\left(\mathbf{s}\right))\in\mathcal{V}_{\Lambda_f}$, then obviously  $\mathcal{W}\left(\mathbf{s}_a\right)\neq\mathcal{W}\left(\mathbf{s}_b\right)$.
		\item[3.]   $\mathbf{s}_a$ and $\mathbf{s}_b$ belong to the same Voronoi region in $\Lambda_c$ and watermark ($Q_{\Lambda_i}\left(\mathbf{s}_a\right)= Q_{\Lambda_i}\left(\mathbf{s}_b\right)$). Since $\mathbf{s}_a\neq\mathbf{s}_b$, one has $(1-\alpha)\mathbf{s}_a\neq(1-\alpha)\mathbf{s}_b$, and they are still unequal after both adding $Q_{\Lambda_i}\left(\mathbf{s}\right)$.
	\end{itemize}
	Combining the above three cases, the injection is proved.

	``Surjective'' means that any element in the range of the function is hit by the function.  We prove this by using contradiction.	If $\mathcal{W}$ is  not surjective, i.e., $\exists \mathbf{s}_{\mathrm{MME}}\in\mathcal{B}$, $\forall \mathbf{s}\in\mathcal{A}$ \textit{s.t.} $\mathcal{W}(\mathbf{s})\neq\mathbf{s}_{\mathrm{MME}}$, then we obtain $\mathbf{s}_{\mathrm{MME}}\notin\mathcal{B}$ which   contradicts Eq. (\ref{defsujection}).

\end{proof}
The above theorem says that $\mathcal{W}$ is a
reversible function, where each element of one set is paired with exactly one element of the other set. Thus the correctness of the estimated covers is guaranteed.

In the noisy scenario of $\mathbf{n}\neq \mathbf{0}$ in $\mathbf{y}=\mathbf{s}_{\mathrm{MME}}+\mathbf{n}$, we argue that the cover vector is also approximately reversible if  $
Q_{\Lambda_f}\left(\hat{\mathbf{v}}\right)=\mathbf{0}$,
where
\begin{equation}\label{Eq. whole noise2}
	\hat{\mathbf{v}} =  (1-\alpha)\mathbf{e}
	+ \mathbf{n}
\end{equation}
is referred to as the composite noise vector at the receiver's side.
To be concise, by using the estimation function
\begin{align}
	\hat{\mathbf{s}}_{\mathrm{noisy}}
	=\mathcal{W}^{-1}\left(\mathbf{y}\right)
	&=\frac{\mathbf{y} -
		Q_{\Lambda_f}\left(\mathbf{y}\right)
	}{1-\alpha} + Q_{\Lambda_f}\left(\mathbf{y}\right),
\end{align}
we have
\begin{equation}
	\hat{\mathbf{s}}_{\mathrm{noisy}}-\mathbf{s}=\frac{1}{1-\alpha}\mathbf{n}.
\end{equation}
It says that, if the composite noise $\hat{\mathbf{v}}$ is small enough to ensure the correctness of the message, then the distance from the noisy estimated cover and the clean cover is only $||{1}/{(1-\alpha)}\mathbf{n}||$.

\subsubsection{Correctness of the estimated messages}\label{SSec. RF}
We have the following theorem about the robustness of the watermarking scheme. Since the ``self-noise'' is within the boundary of the Voronoi region, the estimated messages in the noiseless setting is correct for sure. More generally in the noisy setting, if the composite noise is small, the correctness of the estimated messages is also guaranteed.

\begin{theorem}\label{Lem. lemma recover function 1}
	If $\hat{\mathbf{v}}$ satisfies
	\begin{equation}\label{Eq. noise condition}
		Q_{\Lambda_f}(\hat{\mathbf{v}})=\mathbf{0},
	\end{equation}
	then the estimated message by using MME is correct.
\end{theorem}
\begin{proof}
	At the receiver's side, the noisy observation can be written as   $\mathbf{y}=Q_{\Lambda_i}\left(\mathbf{s}\right)+\hat{\mathbf{v}}$.
	Since $Q_{\Lambda_i}\left(\mathbf{s}\right)\in\Lambda_f=\cup_{\mathbf{d}_i \in \Lambda_f \backslash \Lambda_c} (\mathbf{d}_i + \Lambda_c)$, $Q_{\Lambda_f}(\mathbf{y})$ can be written as
	\begin{equation}
		Q_{\Lambda_f}(\mathbf{y})=Q_{\Lambda_f}(Q_{\Lambda_i}\left(\mathbf{s}\right))+Q_{\Lambda_f}(\hat{\mathbf{v}}).
	\end{equation}
	Then we have
	\begin{align}\label{Eq. decode proof}
		&{\rm mod}(Q_{\Lambda_f}(\mathbf{y}),\Lambda_c)\notag\\
		=&{\rm mod}(Q_{\Lambda_f}(Q_{\Lambda_i}\left(\mathbf{s}\right))
		+Q_{\Lambda_f}(\hat{\mathbf{v}}),\Lambda_c)\notag\\
		=&{\rm mod}({\rm mod}(Q_{\Lambda_f}(Q_{\Lambda_i}\left(\mathbf{s}\right)),\Lambda_c)
		+{\rm mod}(Q_{\Lambda_f}(\hat{\mathbf{v}}),\Lambda_c),\Lambda_c)\notag\\
		=&{\rm mod}(\mathbf{d}_i+Q_{\Lambda_f}(\hat{\mathbf{v}}),\Lambda_c).
	\end{align}
	Thus ${\rm mod}(Q_{\Lambda_f}(\mathbf{y}),\Lambda_c)=\mathbf{d}_i$ if $Q_{\Lambda_f}(\hat{\mathbf{v}})=\mathbf{0}$. Since each coset representative $\mathbf{d}_i$ corresponds a unique message $\mathbf{m}_i$,  the lemma is proved.
\end{proof}

\subsection{Setting the scaling factor} \label{SSec. proposed lower bound}
In this subsection, we will discuss the feasible range of $\alpha$.
\subsubsection{Lower bound}
The lower bound of $\alpha$ is determined by ensuring the correctness of estimated messages.  As mentioned in Definition 1, one should have
$(1-\alpha)(\mathbf{s}-Q_{\Lambda_i}\left(\mathbf{s}\right))\in\mathcal{V}_{\Lambda_f}$. This implies that
\begin{equation}\label{Eq. radius inequality}
	(1-\alpha)\mathcal{V}_{\Lambda_c}\subseteq\mathcal{V}_{\Lambda_f}.
\end{equation}
It suffices to have
\begin{equation}
	(1-\alpha)r_{cov}(\Lambda_c)\leq r_{pack}(\Lambda_f),
\end{equation}
which means
\begin{equation}\label{alphabound1}
	\alpha\geq 1-\frac{r_{pack}(\Lambda_f)}{r_{cov}(\Lambda_c)}.
\end{equation}

For the special case of self similar shaping, a tighter bound can be derived. To be concise, let $\Lambda_c = \Gamma \Lambda_f$.  It follows from $	(1-\alpha) \Gamma \mathcal{V}_{\Lambda_f}\subseteq\mathcal{V}_{\Lambda_f}$ that
\begin{equation}\label{alphabound2}
	\alpha \geq 1- 1/\Gamma.
\end{equation}

\newsavebox{\boxxa
\savebox{\boxxa}{$\mathbf{J}=\left[\begin{matrix}4&0\\0&4\end{matrix}\right]$}
\newsavebox{\boxxb
\savebox{\boxxb}{$\mathbf{J}=\left[\begin{matrix}4&0\\0&4\end{matrix}\right]$}
\newsavebox{\boxxc
\savebox{\boxxc}{$\mathbf{J}=\left[\begin{matrix}10&0\\0&11\end{matrix}\right]$}
\newsavebox{\boxxd
\savebox{\boxxd}{$\mathbf{J}=\left[\begin{matrix}2&0\\0&4\end{matrix}\right]$}
\newsavebox{\boxxe
\savebox{\boxxe}{$\mathbf{J}=\left[\begin{matrix}2&0\\0&4\end{matrix}\right]$}

\begin{figure}[t!]
	\linespread{1}
	\centering
	\subfigure[]{\includegraphics[width=.22\textwidth]{fig/fig_absolute_correct.pdf}}

	\subfigure[]{\includegraphics[width=.22\textwidth]{fig/fig_self-similar_shaping_correct.pdf}}
	\caption{Distribution of the watermarked cover vector $\mathbf{s}_{\mathrm{MME}}$ with $\Lambda_f$ being the $A_2$ lattice and $\Lambda_c = 4 \Lambda_f$.
		(a)  $\alpha = 1 - \frac{\sqrt{3}}{6}$ based on Eq. (\ref{alphabound1}).
		(b)  $\alpha = 3/4$ based on Eq. (\ref{alphabound2}).}

	\label{Fig. Cases of overstep lower bound}
\end{figure}

Fig. \ref{Fig. Cases of overstep lower bound} depicts the distribution of the watermarked cover vector $\mathbf{s}_{\mathrm{MME}}$ based on the general bound in Eq. (\ref{alphabound1}) and the special-case bound in Eq. (\ref{alphabound2}).

\subsubsection{Upper bound}
The upper bound of $\alpha$ is related to the correct extraction of the covers.  Recall that
the audio data is stored as single or double precision floating-point numbers (as shown in Table \ref{Tab. Appendix B}), and it cannot represent arbitrary real-valued numbers without loss of accuracy. Overflow occurs when the magnitude of a number exceeds the range allowed by the size of the bit field.
To avoid the effect of overflow, we need to have
\begin{equation}\label{alphaupperbound}
	\alpha\leq 1-2^{-(\mathcal{L}+1)},
\end{equation}
where  $\mathcal{L}$ denotes the mantissa bit length. For example, we have $\alpha \leq 1-2^{-53}$ when using double precision floating-point numbers.

\begin{table*}[t!]
	\centering
	\renewcommand\arraystretch{2}
	\caption{The storage structure of floating-point numbers.}
	\label{Tab. Appendix B}
	\begin{tabular}{c c c c c }
		\hline

		Data Type& Total length (bit)& Sign length (bit)& Order length (bit)& Mantissa length (bit)\\
		\hline
		Float & 32& 1& 8& 23\\
		Double & 64& 1& 11& 52\\
		\hline
	\end{tabular}
\end{table*}

\section{Performance metrics}\label{SSec. Theoretical Analysis}

\subsection{Embedding distortion}
To evaluate the embedding distortion, we adopt the signal to watermark ratio (SWR) metric defined as
\begin{align}\label{Eq. SWR1}
	{SWR}~(\mathrm{dB})=10\times lg\left(\frac{\sigma^2_\mathbf{s}}{\sigma^2_\mathbf{w}}\right),
\end{align}
where $\sigma^2_\mathbf{s}$, $\sigma^2_\mathbf{w}$ represent the power of the host and the additive watermark, respectively. For MME, we have
\begin{align}
	\sigma^2_\mathbf{w} 	&=   E(\|\alpha \mathbf{e}\|^2)\notag\\
	&=\alpha^2 E(\| \mathbf{e}\|^2)\notag \\
	&= \alpha^2 N G({\Lambda_c}) \rm{Vol}(\mathcal{V}_{\Lambda_c})^{2/N}, \label{eq_sigma_w2}
\end{align}
in which $G(\Lambda_c)$ represents the normalized second moment of the chosen coarse lattice $\Lambda_c$, and Eq. (\ref{eq_sigma_w2}) is derived from the widely adopted flat-host assumption \cite{DBLP:journals/tcsv/WangZLCH21}. For
the simplest setting of $\Lambda_f = \Delta \mathbb{Z}^N$ and $\Lambda_c = \Delta 2^b \mathbb{Z}^N$, since $G(\Delta 2^b \mathbb{Z}^N)=1/12$, we have
\begin{equation}\label{cubic_dist}
	\sigma_{\mathbf{w}}^2
	=\frac{N\alpha^2 2^{2b}\Delta^2}{12}.
\end{equation}

\begin{proposition}\label{The. greater SWR}
	By setting $\Lambda_f = \Delta \mathbb{Z}^N$, $\Lambda_c = \Delta 2^b \mathbb{Z}^N$, and $\alpha = \beta$,
	MME has a larger SWR than IQIM.
\end{proposition}
\begin{proof}
	Based on the inequality that
	\begin{equation}
		x-1<\left\lfloor x\right\rfloor\leq x,
	\end{equation}
	the embedding distortion of IQIM can be bounded as
	\begin{align}
		&	\sigma_{\mathbf{w},\rm{IQIM}}^2 \notag\\
		&=E\left(\beta^2 \left\lVert \mathbf{s} - \left[2^b\Delta \left[\gamma_1~\cdots~\gamma_N\right]^\top+\frac{\Delta\mathbf{m}}{\beta}\right] \right\rVert^2 \right)\notag\\
		&=\frac{\beta^2}{2^b}\sum_{q=1}^{N}\sum_{m_{i,q}=0}^{2^b-1}\int_{0}^{2^b\Delta}\left[2^b\Delta\gamma_q+\frac{m_{i,q}\Delta}{\beta}-s_q\right]^2\notag\\
		&\cdot f(s_q) ds_q\notag\\
		&>\frac{\beta^2}{2^b}\sum_{q=1}^{N}\sum_{m_{i,q}=0}^{2^b-1}\int_{0}^{2^b\Delta}\left[\frac{m_{i,q}\Delta}{\beta}-2^b\Delta\right]^2 f(s_q) ds_q \notag\\
		&=\frac{\left(2^b\right)^2\left(2\cdot 2^b-1\right)}{6\left(2^b-1\right)}N\beta^2\Delta^2.
	\end{align}
	Letting $\alpha = \beta$ in Eq. (\ref{cubic_dist}), we have
	\begin{equation}
		\sigma_{\mathbf{w},\rm{IQIM}}^2 - 	\sigma_{\mathbf{w}}^2 > \frac{\beta^2 2^{2b} \left(3\cdot 2^b-1\right)N\Delta^2}{12\left(2^b-1\right)}>0.
	\end{equation}
	As IQIM has a larger denominator in SWR, the proposition is proved.
\end{proof}
Proposition \ref{The. greater SWR} justifies the advantage of MME over IQIM: by using a
better meet-in-the-middle approach to construct the ``beneficial noise'', it enjoys a larger SWR.

\subsection{Robustness of messages}\label{SSec. gsnr}
In addition to the distortion/imperceptibility metric, it is also necessary to evaluate the robustness of MME against additive noises.
Following \cite{moulin2005data}, we define the
generalized signal-to-noise ratio (GSNR) as
\begin{align}
	{\rm GSNR}&\triangleq\frac{\min_{i,j\in\mathcal{I},i\neq j}\|\mathbf{d}_i-\mathbf{d}_j\|^2}{ E(\| \hat{\mathbf{v}}\|^2) }\notag\\
	&=\frac{4r_{{\rm{pack}}(\Lambda_f)}^2}{E(\| \hat{\mathbf{v}}\|^2)}, \label{eqgsnr_std}
\end{align}
where $\hat{\mathbf{v}}$ is the composite noise vector defined in Eq. (\ref{Eq. whole noise2}).

Due to the independence of $\mathbf{e}$ and $\mathbf{n}$, we have
\begin{align}
	E(\| \hat{\mathbf{v}}\|^2) &= 	E(\|(1-\alpha)\mathbf{e}
	+ \mathbf{n} \|^2) \notag \\
	&=(1-\alpha)^2 	E(\| {\mathbf{e}}\|^2) + E(\| {\mathbf{n}}\|^2) \notag \\
	&=(1-\alpha)^2 N G({\Lambda_c}) {\rm{Vol}}(\mathcal{V}_{\Lambda_c})^{2/N} + N \sigma_{\mathbf{n}}^2.\label{eq3GSNR}
\end{align}

By substituting (\ref{eq3GSNR}) into (\ref{eqgsnr_std}), the
GSNR of MME can be expressed as
\begin{equation}
	{\rm GSNR} = \frac{4r_{{\rm{pack}}(\Lambda_f)}^2}{(1-\alpha)^2 N G({\Lambda_c}) {\rm{Vol}}(\mathcal{V}_{\Lambda_c})^{2/N} + N \sigma_{\mathbf{n}}^2}.
\end{equation}

Since the energy of the self-noise $(1-\alpha) \mathbf{e}$ is smaller than that of IQIM, its composite-noise also features a smaller energy. Therefore, MME has a larger GSNR than IQIM.

\section{Simulations}\label{Sec. equipment}
We carry out some simulations in this section to verify the effectiveness of MME. The simulation setups are summarized as follows.

\begin{table}[t!]

	\renewcommand{\arraystretch}{1}
	\centering
	\caption{The level of objective difference grade scores \cite{xiang2017digital}.}
	\label{Tab. objective difference grade}
	\begin{tabular}{l l l}
		\hline
		ODG &Quality & Impairment\\
		\hline
		~0 & Excellent & Imperceptible\\
		-1 & Good & Perceptible but not annoying\\
		-2 & Fair & Slightly annoying\\
		-3 & Poor & Annoying\\
		-4 & Bad & Very annoying\\
		\hline
	\end{tabular}\label{ta_odg3}
\end{table}

\noindent \textbf{Datasets:} In the experiments, two online datasets \cite{database1} and \cite{database2} are adopted, which contain ringtone, natural sound, absolute music, songs, and speeches. They consist of $5$ and $70$ bipolar $16$-bits Waveform Audio File Format (WAV) files, respectively, which are  labeled as No. 1001-1005 and 2001-2070. The cover vectors are generated from these datasets, and the
messages are generated from uniform random distributions.

\noindent \textbf{Distortion metrics:}
In addition to the SWR metric, the objective difference grade (ODG) \cite{xiang2017digital} is also introduced in the experiments, which is a popular metric to assess accurately the objective auditory perception and is produced by the Perceptual Evaluation of Audio Quality (PEAQ) measure standardized in the ITU-R BS. 1387 \cite{itu20011387}.  The ODG scores are computed by the software downloaded from \cite{PEAQsoftware}, which is the Matlab version of Evaluation of Audio Quality (EAQUAL) \cite{lerch2002zplane}. ODG gives a score in the range of  $[-4.5,0.5]$.
As shown in Table \ref{ta_odg3}, the audio quality is said to be excellent, good, fair, poor, and bad based on the respective ODG scores.

\noindent \textbf{Robustness metrics:}
In addition to the GSNR metric, we also introduce the bit error rate (BER) metric to exactly show the decoding error rates.
BER is defined as
\begin{equation}
	BER=\frac{\sum_{k=1}^{M}\sum_{q=1}^{N}\left(\mathbf{x}_{k,q}\oplus \mathbf{x}'_{k,q}\right)}
	{M*N},
\end{equation}
where $\mathbf{x}$ and $\mathbf{x}'$ separately represent the original and estimated messages, while $q$ and $k$ are dimensional and sample identifiers respectively.

\noindent \textbf{Benchmarks and settings:} The state-of-the-art methods in \cite{peng2011effective,LIANG2020107584,nishimura2013reversible} are adopted as the benchmarks, which are respectively named as ``IQIM'', ``Liang'' and ``Nishimura''.
For IQIM, Nishimura and the proposed MME, unless stated otherwise, we set  $\alpha=0.6569$, $\Delta=2000$, $\Lambda_f=\Delta\mathbb{Z}^2$, and $\Lambda_c=\Delta2^R\mathbb{Z}^2$.
In addition, ``Liang'' is configured with parameters
$S=300,~T=7500,~G=20000$.

\subsection{Imperceptibility performance}

\begin{figure}[t!]
	\linespread{1}
	\centering
	\subfigure[]{\includegraphics[width=.35\textwidth]{fig/all_SWR.pdf}}
	\quad
	\subfigure[]{\includegraphics[width=.35\textwidth]{fig/all_ODG.pdf}}

	\caption{The comparisons between methods in \cite{peng2011effective,LIANG2020107584,nishimura2013reversible} and the proposed MME with different metrics (a) SWR. (b)ODG.}
	\label{Fig. experiment_1}
\end{figure}

Fig. \ref{Fig. experiment_1}(a) and Fig. \ref{Fig. experiment_1}(b) have respectively depicted the average value of SWR and ODG for the whole dataset.  The blue and black bars represent the confidence interval (CI)  and the range of standard deviation (SD). Fig. \ref{Fig. experiment_1}-(a) shows that the proposed method attains the highest SWR of $32.9891$dB, which is better than the $31.6769$dB of Liang, and the $28.3758$dB of IQIM. Moreover, the Nishimura method fails to work in this setting. Regarding ODG, the proposed method, IQIM and Nishimura work well, and they all belong the the class of QIM-based methods.

\begin{figure}[t!]
	\linespread{1}
	\centering
	\subfigure[]{\centering{\includegraphics[width=.35\textwidth]{fig/GLMR_IQIM_SWR.pdf}}}
	\quad
	\subfigure[]{\centering{\includegraphics[width=.5\textwidth]{fig/GLMR_IQIM_ODG.pdf}}}

	\caption{The impact of code rate $R$ of the performance of (a) SWR. (b)ODG.}
	\label{Fig. experiment_1_2}
\end{figure}

More in-depth comparisons are made with the most related IQIM method hereby.
Fig. \ref{Fig. experiment_1_2} shows the performance of SWR and ODG with different code rate $R$.
We have the following observations:
i) For the SWR performance, MME is strictly better than IQIM regardless of the code rate $R$.
ii) In terms of ODG, when the performance is above the bar of ``fair'', MME generally outperforms IQIM, but falls short when both methods become unreliable.

The advantages of using more general lattices
for MME are further examined in Table \ref{ta_swr4}. In addition to the simple integer lattice $\mathbb{Z}$, the optimal lattices in $2$, $4$, and $8$ dimensions are respectively $A_2$, $D_4$ and $E_8$. The Conway-Sloane type labeling technique  \cite{conway2013sphere} can be used for these lattices.  Specifically, we have the following observations from the table.
i)MME outperforms IQIM in all the metrics (SWR and ODG), regardless of the chosen type of lattices. For instance, the SWR of proposed lower bound in $A_2$ $(R=1)$ is $34.3771$dB, which is greater than the $28.3758$ SWR in IQIM.
ii) Choosing larger-dimensional optimal lattices is more desirable. Steady improvements can be observed by increasing the dimensions of the lattices from $\mathbb{Z}$ to $A_2$, $D_4$ and $E_8$.
iii) Since the fine lattices are fixed to feature unit volumes while the coarse lattices grow as the code rate $R$ increases, the SWR/ODG decreases with $R$.

\begin{table}[t!]
	\setlength{\tabcolsep}{1.5mm}
	\centering
	\renewcommand\arraystretch{1.5}
	\caption{The performance of MME with different lattices.}
	\label{Tab. experiment 2}
	\begin{tabular}{c c c c c c c }
		\hline
		\multirow{2}{*}{\textbf{Rate} $R$} & \multirow{2}{*}{\textbf{Metrics}} & \multicolumn{4}{c}{\textbf{MME with $\alpha=1-\frac{r_{pack}(\Lambda_f)}{r_{cov}(\Lambda_c)}$}} & \multicolumn{1}{c}{\multirow{2}{*}{\begin{tabular}[c]{@{}c@{}}\textbf{IQIM \cite{peng2011effective}} \end{tabular}}} \\ \cline{3-6}
		& & $\mathbb{Z}$ & $A_2$ & $D_4$ & $E_8$  & \multicolumn{1}{c}{}
		\\ \hline
		\multicolumn{1}{c}{\multirow{4}{*}{1}} & $\alpha$
		& 0.5 & 0.5670 & 0.6464 & 0.6464
		& 0.5
		\\ \cline{2-7}

		& SWR(dB)
		&34.5727	&34.3771	&34.2464	&36.0888
		&28.3758

		\\ \cline{2-7}

		& ODG
		&-1.3185	&-1.3237	&-1.3316	&-1.2840
		&-1.4659
		\\ \hline

		\multicolumn{1}{c}{\multirow{4}{*}{2}} & $\alpha$
		&0.75&0.7835&0.8232&0.8232
		&0.75
		\\ \cline{2-7}

		& SWR (dB)
		&25.2209	&25.75211	&26.3638	&28.3057
		&20.2369
		\\ \cline{2-7}

		& ODG
		&-1.5459	&-1.5290	&-1.5132	&-1.4723
		&-1.6339
		\\ \hline
	\end{tabular}\label{ta_swr4}
\end{table}

\subsection{Robustness performance}
With the same setting as in Fig. \ref{Fig. experiment_1}-(a), we further investigate the robustness performance of the watermarking algorithms against AWGN attacks. Fig. \ref{BERfigure} has depicted the BER comparison for MME, Liang and IQIM. The Nishimura method has been excluded as its robustness performance is weak.
The reason for  MME's better BER performance is that, by adjusting the scaling factor $\alpha$, it's watermarked vector can be tuned further away from the boarder of the decoding regions.

Fig. \ref{Fig. experiment_1_3}-(a) and  Fig. \ref{Fig. experiment_1_3}-(c) have drawn the GSNR for MME and IQIM for various SNR and $\alpha$. The GSNR of MME can go well beyond $10^{12}$, while IQIM flattens at about $3\times 10^{11}$. Fig. \ref{Fig. experiment_1_3}-(b) and Fig. \ref{Fig. experiment_1_3}-(d) are also attached to show the better GSNR performance of MME is not generated by scarifying the SWR performance.
The simulation results above are remarkable: compared with other QIM-variants, MME can simultaneously achieve smaller distortion and better robustness.

Since both the BER and SWR metrics are related to the $\Delta$ in MME, we plot the trade-off relations of BER versus SWR in Fig. \ref{RDfigure} by changing $\Delta$ and letting SNR=$25$dB. We have the following observations: i) The trade-off capability becomes better when $\Delta$ increases, where the curve rises smoothly when $\Delta=500$ and become sharper when $\Delta$ increases. ii) The ratio of SWR/BER decreases when $\Delta$ increases, which means larger distortion and higher robustness is achieved with a larger $\Delta$.

\begin{figure}[t!]
	\linespread{1}
	\centering{\includegraphics[width=.44\textwidth]{fig/fig_BER_whole.pdf}}
	\caption{BER versus SNR.} \label{BERfigure}
\end{figure}

\begin{figure}[t!]
	\linespread{1}
	\centering
	\subfigure[]{\centering{\includegraphics[width=.23\textwidth]{fig/fig_GSNR_IQIM_GLMR_SNR.pdf}}}

	\subfigure[]{\centering{\includegraphics[width=.23\textwidth]{fig/fig_SWR_IQIM_GLMR_SNR.pdf}}}

	\subfigure[]{\centering{\includegraphics[width=.23\textwidth]{fig/fig_GSNR_IQIM_GLMR_ALPHA.pdf}}}

	\subfigure[]{\centering{\includegraphics[width=.23\textwidth]{fig/fig_SWR_IQIM_GLMR_ALPHA.pdf}}}
	\caption{GSNR and SWR comparisons between MME and IQIM with different parameters. (a), (b) SNR ($\alpha=0.6569$, $R=1$). (c), (d) $\alpha$ (SNR$=25$, $R=1$).}
	\label{Fig. experiment_1_3}
\end{figure}

\begin{figure}[t!]
	\linespread{1}
	\centering{\includegraphics[width=.44\textwidth]{fig/fig_MME_R_D.pdf}}
	\caption{BER versus SWR.} \label{RDfigure}
\end{figure}

\subsection{Reversibility}

\begin{figure*}[t!]
	\linespread{1}
	\centering
	\includegraphics[width=.9\textwidth]{fig/fig_main.pdf}

	\caption{The signal waveforms at different stages of MME.
		(a) Original signals.
		(b) Watermarked signals by using MME, whose SWR are $38.0775$dB, $33.2487$dB, $34.0998$dB and	$35.1670$dB.
		(c) Restored signals.
		(d) The differences between the original signals and the restored signals.}
	\label{Fig. experiment_4}
\end{figure*}

Due to the sensibility of HAS, the human awareness of sounds from different sources is also diverse, which may cause a distinct feeling for heterogeneous sounds.
To vividly demonstrate the actual effect of embedding, we draw the original, watermarked and restored signal of four typical audio host signals in Fig. \ref{Fig. experiment_4}. They are absolute music, songs, speeches and white noises, respectively. These host signals are labeled as No. 2002, 2003, 2040 and 2050.
Judging by the naked eye, the wave forms of the original and  the restored signals  are basically the same. In terms of watermarked signals, MME achieves the SWRs of  $38.0775$dB, $33.2487$dB, $34.0998$dB and $35.1670$dB for these host signals. Lastly, Fig. \ref{Fig. experiment_4}-(d) shows that are basically no difference between the original cover signals and the restored cover signals.

\section{Conclusions}
In this paper, a novel reversible audio watermarking method referred to as Meet-in-the-Middle Embedding (MME) has been proposed. We have justified its correctness, and make comparisons with existing methods, which show that MME exhibits less distortion and better robustness. Theoretical analyses on the SWR and GSNR have been presented.  Simulations show that the proposed method features a smaller amount of distortion and probability of decoding errors compared with   IQIM and other representative methods in RAW.

\ifCLASSOPTIONcaptionsoff
  \newpage
\fi

\bibliographystyle{IEEEtranMine}

redpajama_set_name: RedPajamaArXiv


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Home National People climb up rooftops to catch supermoon's rare glimpse
People climb up rooftops to catch supermoon's rare glimpse
ISLAMABAD, Nov 14 (APP): People across the country Monday climbed up to rooftops Monday night for catching the peculiar glimpse of 'supermoon', which was happening after 70 years.
According to a spokesman of Pakistan Meteorological Department, on Monday evening at 18:52 PST, the moon was very close to the earth and force of attraction was strongest resulting in high tides than usual full moon.
He said that the moon was seen bigger and brighter because it was at the closest distance from the earth.
He said when the moon comes close to the earth, it appears 14% bigger and 30% brighter than the normal full moon, which is called the 'supermoon'.
He said as orbit of the moon around the earth is elliptical, it causes to change the distance between earth and moon.
He advised the general public to remain careful on Tuesday along the shore.
Last such type of supermoon was seen in 1948. People can experience such a brighter supermoon again on November 25, 2034.
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We supported Thames Water in the design of their solution, providing strategic advice and thought leadership. Using our unique Transformation Approach, we ensured that people, process and technology were aligned, so as to embed the necessary changes and new ways of working.
Phase 1 of the programme focused on the consolidation of the seven regional offices into the two centres. This include supporting over 300 field and office personnel to define and create a single set of working practices. Phase 2 focused on the use of technology to improve the flow of information between the office and field-based teams, improving the schedule optimisation tool to increase field team productivity.
As a result of the programme, Thames Water saved around £2m per annum from improved productivity and efficiency. The programme delivered the centres of excellence that Thames Water had envisaged and provided process standardisation and a performance-oriented business model to drive continuous improvement across their workforce management processes.


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Preheat oven to 400 degrees. Line a baking sheet with parchment paper. Place the puff pastry on the lined cooking sheet. I separated mine into three pieces, because it didn't want to stay together. Bake for 15 minutes or until golden brown.
Remove from oven and allow to cool for 5 minutes. Divide the cream cheese between the three pieces and spread evenly. Top with bacon, arugula and tomatoes. Enjoy!
Check out all the other great recipes in this week's reveal!
I used to eat lots of BLT sandwiches in my youth in one of our favorite bars… never had one since….This puff pastry version sounds and looks delicious!!!
What a great way to use all the tomatoes we have growing in our garden this year! I love using the chive-flavored cream cheese as the base … it adds a ton of flavor with no extra work. Brilliant! And of course bacon makes everything better LOL.
The cream cheese definitely was a great flavor in it.
I LOVE BLT's, I can just imagine how tasty this was! Definitely going to try this for one of our weekly pizza and movie nights.
This puff pastry pizza looks delicious and so perfect for a weeknight! I love the blt combination.
BLT is my favorite sandwich – I love this idea! great SRC pick!
We've been eating BLTs at least once a week. Love them!
What a great idea! And I love that it uses the flavored cream cheese. Can't wait to try this with some tomatoes from the farmers market.
This looks so good and so light!


text:
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    left: 0px;
    display: block;
    padding: 5px;
    border-width: 0px;
    border-color: blue;
    border-style: solid;
    background: lightblue;
}

div.PLUGINmessage{
    height: 30px;
    width: 512px;
    padding: 2px;
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redpajama_set_name: RedPajamaGithub


text:
A suite of five lessons on the water cycle, illustrated with a PowerPoint presentation and accompanied by suggestions for activities and experiments to carry out in the classroom, suitable for Key Stage 2 classes.
Themes covered by the lessons are:
Where does water come from?
What is the water cycle?
Why do evaporation and condensation happen ?
Why is it important not to waste water?
How can we stop wasting water?
Download Lesson Plan & Presentation (85.9 MB)
If you have found our lesson plans useful, please donate £1 to help YPTE to continue its work of inspiring young people to look after our world.
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Plastic found in tap waterArticle
Paddleboarding environmentalist highlights plastic pollution in England's waterwaysArticle
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High profile climate change clash in Davos Yesterday at the 2020 World Economic Forum, held in Davos, Switzerland, US President Donald Trump...
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text:
Q: Create a native Flashlight Android Java plugin for unity 3D I have an issue, I don't know how to access to my java plugin from Unity.
Here is the Java Code :
package fr.vincentmazet.utilslibrary;

import android.content.Context;
import android.hardware.camera2.CameraAccessException;
import android.hardware.camera2.CameraManager;
import com.unity3d.player.UnityPlayerActivity;

public class FlashLight extends UnityPlayerActivity {
private CameraManager camManager;
private Context context;

public void FlashLight(Context context){
    this.camManager = (CameraManager)    context.getSystemService(context.CAMERA_SERVICE);
    this.context = context;
}

public boolean enableFlash(){
        try {
            camManager.setTorchMode("0", true);
        } catch (CameraAccessException e) {
            e.printStackTrace();
    }
    return true;
}

public boolean stopFlash(){
        try {
            camManager.setTorchMode("0", false);
        } catch (CameraAccessException e) {
            e.printStackTrace();
    }
    return true;
}
}

And here my c# func :
public bool startFlash(){
    if (Application.platform == RuntimePlatform.Android) {
        using (var javaUnityPlayer = new AndroidJavaClass     ("com.unity3d.player.UnityPlayer")) {

            using (var currentActivity = javaUnityPlayer.GetStatic<AndroidJavaObject> ("currentActivity")) {

                using (var androidPlugin = new AndroidJavaObject ("fr.vincentmazet.utilslibrary.FlashLight", currentActivity)) {

                    return androidPlugin.Call<bool> ("enableFlash");
                }
            }
        }
    }
    return false;
}

But it failed when I enter in :
var androidPlugin = new AndroidJavaObject  ("fr.vincentmazet.utilslibrary.FlashLight", currentActivity)

And I don't know how to debug, access to the stack-trace from my android.
Any ideas is appreciated thank's you by advance.

A:
And I don't know how to debug, access to the stack-trace from my
  android.

Debugging your Android plugin yourself is a must. You can do this with Debug.Log from Unity/C# and Log.V from Android/Java side.
Use Android Monitor from Android Studio to view the Logs and also Exception Log from Unity.

I don't know how to access to my java plugin from Unity

You need to send instance of Context from Unity to the Android Plugin. You also don't have to extend from UnityPlayerActivity. Totally unnecessary here.
Permission:
<uses-permission android:name="android.permission.CAMERA" />
<uses-feature android:name="android.hardware.camera" />
<uses-permission android:name="android.permission.FLASHLIGHT"/>
<uses-feature android:name="android.hardware.camera.flash" android:required="false" />

Java:
public class FlashLight{
private CameraManager camManager;
static Context myContext;

// Called From C# to get the Context Instance
public static void receiveContextInstance(Context tempContext) {
        myContext = tempContext;

 this.camManager = (CameraManager)   myContext.getSystemService(context.CAMERA_SERVICE);
    }

public static boolean enableFlash(){
        try {
            camManager.setTorchMode("0", true);
        } catch (CameraAccessException e) {
            e.printStackTrace();
    }
    return true;
}

public static boolean stopFlash(){
        try {
            camManager.setTorchMode("0", false);
        } catch (CameraAccessException e) {
            e.printStackTrace();
    }
    return true;
}
}

C#:
AndroidJavaClass unityClass;
AndroidJavaObject unityActivity;
AndroidJavaObject unityContext;
AndroidJavaClass customClass;

void Start()
{
    //Replace with your full package name
    sendActivityReference("fr.vincentmazet.utilslibrary.FlashLight");

    //Enable Flashlight
    enableFlash();

   //Disable Flashlight
   //stopFlash();
}

void sendActivityReference(string packageName)
{
    unityClass = new AndroidJavaClass("com.unity3d.player.UnityPlayer");
    unityActivity = unityClass.GetStatic<AndroidJavaObject>("currentActivity");
    unityContext = unityActivity.Call<AndroidJavaObject>("getApplicationContext");

    customClass = new AndroidJavaClass(packageName);
    customClass.CallStatic("receiveContextInstance", unityContext);
}

bool enableFlash()
{
   return customClass.CallStatic<bool>("enableFlash");
}

bool stopFlash()
{
   return customClass.CallStatic<bool>("stopFlash");
}

redpajama_set_name: RedPajamaStackExchange


text:
Tag Archives: Birthers Movement
Deathers: The New Birthers
Christopher Beam writes on Slate.com:
First came the "birthers." Now, as President Obama makes a final push for health care reform, we have the deathers.
Many senior citizens are concerned that health care reform would mean cuts to Medicare. That much was clear at a town-hall meeting hosted Tuesday by the American Association of Retired Persons at which Obama fielded questions from seniors who don't want to give up their benefits.
But one question stood out. It addressed what the host from the AARP called the "infamous" Page 425 of the House health care bill. "I have been told there is a clause in there that everyone that's Medicare age will be visited and told to decide how they wish to die," said Mary from North Carolina. "This bothers me greatly, and I'd like for you to promise me that this is not in this bill." The host elaborated: "As I read the bill, it's saying that Medicare will, for the first time, cover consultation about end-of-life care, and that they will not pay for such a consultation more than once every five years. This is being read as saying every five years you'll be told how you can die."
"Well, that would be kind of morbid," Obama said.
The audience laughed. Many observers aren't so amused. To them, the House bill and health care reform in general are the legislative equivalent of euthanasia.
"Obama's not going to say, 'Let's kill them,' " says Charlotte Allen, a conservative commentator and author of The Human Christ: The Search for the Historical Jesus. "But he seems to be perfectly comfortable with the idea that a lot more old people are going to die a lot sooner."
Deathers point to several parts of the House bill as evidence that health care reform means letting old people die. Most prominent is the end-of-life consultation provision mentioned above. An article on World Net Daily argues that the proposal "specifically calls for the consultation to recommend 'palliative care and hospice' for seniors in their mandatory counseling sessions." In fact, the bill says the meeting must include "an explanation by the practitioner of the end-of-life services and supports available, including palliative care and hospice"—not a recommendation of it. (Emphasis added.) Still, Obama pointed out that it's not too late to remove the language: "If this is something that really bothers people, I suspect that members of Congress might take a second look at it."
Another seemingly scary provision is one that permits "the use of artificially administered nutrition and hydration"—or, more accurately, the withholding of it. Betsy McCaughey, founder of the Committee To Reduce Infection Deaths and former lieutenant governor of New York, wrote an influential (and, to many, misleading) critique of Hillarycare in the New Republic 15 years ago. She told me that the provision is a disturbing example of the government making decisions for the patient. But the bill specifically says that an order to withhold, say, an IV drip, must be one that "effectively communicates the individual's preferences regarding life sustaining treatment, including an indication of the treatment and care desired by the individual." In other words, a doctor can't make you do it.
Read the rest of the article here.
Filed under Birthers, Deathers, Health Care, Politics
Tagged as AARP, Barack Obama, Betsy McCaughey, Birthers, Birthers Conspiracy, Birthers Movement, Christopher Beam, Committee to Reduce Infection Deaths, Congress, Deathers, Deathers Conspiracy, Deathers Movement, Democrats, Euthanasia, Health Care, Health Care Reform, Healthcare, Healthcare Reform, Hillarycare, House Health Care Bill, Media, New Republic, news, Obama Health Care, Obama Healthcare, Page 425, Politics, President Obama, Republicans, Senior Citizens, Slate, World Net Daily


We all have heard (and asked) the dreaded question, "What's for dinner?" When it comes to the most planned of the three daily meals, what it's served on is just as important. That's where we come in. We're here to inspire you to dress up your dinnertime spread and make it exciting, so you won't dread planning it.
So, what's on tonight's menu for us, you ask? One of our favorites… Ybor Chicken. We chose our Brushed Dot Dinner Plate because the scoop shape makes it perfect for rice and pasta dishes. With this recipe, we're going back to our Miami roots. Want to take the trip with us? See below for the recipe.
Here's a take on Ybor Chicken, a recipe adapted from The Tampa Treasures Cookbook.
Mix flour, salt and pepper, and coat the chicken. Heat olive oil in a large skillet on medium heat. Brown the chicken slowly.
Preheat the oven to 325 degrees. Place chicken in a casserole dish. Sautée green pepper, onion, garlic, tomato, bay leaf, raisins, and olives in the skillet with the remaining oil. Add wine and simmer for 5 minutes. Pour over the chicken and add chorizo. Cover and bake until chicken is tender, 1 ¼ to 1 ½ hours. Serve with white rice.
P.S. Be on the lookout for your meal inspiration in the future!


Dabo is a Python based desktop application framework. The talk will demonstrate creating a simple application using the three tiers (database, business objects, ui) of the framework. I create my applications by hand coding. There is a GUI interface available and it will be introduced.


text:
Q: Negative power spectrum I've got a set of 780 monthly temperature anomalies over 65 years and I want to analyse it for frequencies that are driving the anomalies. I've used the spectrum package to do this, I've included pictures of the series before and after the analysis.
from spectrum import *

p = Periodogram(anomalies, sampling=1/12)
p.run()
plt.title('Power Spectrum of Monthly Temperature Anomalies')
p.plot(marker='.')
plt.show()

The resulting spectrum has several clear negative spikes. Now I understand that a negative value in Db isn't actually a negative absolute value, but why is this happening? Does it imply there's some specific frequency missing from my data? Because a positive spike implies one is present.
Also, why are most of the frequencies displayed negative? What is the reference value for Db to be an amplification of?
A part of me thinks I should be taking the absolute value of this spectrum but I'd like to understand why if that's the case. Also I put in the value for sampling as 1/12 because the data points are monthly so hopefully the frequency scale is in per year?
Many thanks, this is my first post here so let me know if I need to be clearer about anything.
Negative Energies

The Series being Analysed

A: As you can see in the plots, on the y-axis, the units are in dB (decibel, https://en.wikipedia.org/wiki/Decibel). so what is see is not the raw data (in the frequency domain) but something like 10*log10(data). This explains the presence of negative values and is perfectly normal.
Here you have positive and negative values but in  general, you would normalise the data (by the maximum) so that all values are negative and the highest value is set to 0. This is possible using :
p.plot(norm=True)

You can plot the raw data (without the log function) but you would need to use the raw data (in the frequency domain). For instance to reproduce the behaviour of p.plot function, you can use:
from pylab import plot
plot(p.frequencies(), 10*log10(p.psd/p.psd.max())

So, if you do not want to use the decibel unit, use:
from pylab import plot
plot(p.frequencies(), p.psd)

disclaimer: I'm the main author of Spectrum (http://pyspectrum.readthedocs.io/).


text:
Home Essays Mormons
Topics: Joseph Smith, Jr., Christianity, The Church of Jesus Christ of Latter-day Saints Pages: 7 (2583 words) Published: June 18, 2013
In this paper I will discuss about the history of the Mormon religion also called the church of Jesus Christ of the latter day saints, also the doctrine that they as church follow. How were the founder and how they lived back in beginning of the Church, also how they live in today society and how other people see this religion, is some of the subjects that this paper will talk about. The Mormon religion used and still has different doctrine as all the Christian religions in the United States and the essay will discuss some of them and the problems that have in the past and today society.
1. Mormon History……………………………………………...……4 2. Differences of Mormons and Other Christians Religions………....5 3. Doctrine……………………………………………………………7 4. Life During History………………………………………………..9 5. References………………………………………………………..12
MORMONS HISTORY
Mormonism is a religion that was founded in 1830 by six members in Fayette New York. This religion is viewed as a cult by other religions. It has since gained worldwide popularity where over three million people are members. It was founded by a young man called Joseph Smith who was born on December twenty third in the 1805 Vermont. According to him, he was chosen to restore the church of Jesus Christ which had been corrupted. (Meldrum and Stephens, 2003) The followers of this religion do not like to be called Mormons but prefer be known as the church of Jesus Christ of the latter day saints. It was initially called the church of Christ when it was founded in 1830 but was later changed to the church of the latter day saints dropping the name of Christ in 1834.One of the Mormon apostles later in 1838 declared that the church was to be called the church of Jesus Christ of the latter day saints (Quinn, 1994). According to Joseph Smith, he was saw many visions where a person who resurrected from the dead called Moroni came to him and gave him golden plates that were to be the authority of the new church of Christ of the latter day saints. These plates came to be the book of Mormons. Joseph Smith also claimed that John the Baptist came and ordained him into the priesthood of Aaron called the Aaron priesthood in 1829.He was latter ordained by other disciples of Christ like John, James and Peter to become a spokesman of God. (Padfield, 2003) The Mormons believe that there is no salvation when one is not ordained into the Melchizedek Priesthood. This is why Joseph Smith was ordained into this priesthood by the three disciples Peter, James and John. This meant that the church had been fully authorized to restore true religion that had been lost through corruption. The religion was established in America.
DIFFERENCES OF MORMONS AND OTNER CHRISTIANS RELIGIONS
They therefore view America as holy and divine land and believe that the first resurrection will happen in Missouri in America. Mormons have beliefs that differ from the orthodox Christianity. They do not view the Holy book as the only source of authority like the Christians. They believe in the bible, the book of Mormons and the visions of their prophet Joseph Smith. They dwell on covenants and doctrines. They see the bible as incomplete and needs additional information. They refer to the King James Version which they say is well translated. (Meldrum and Stepgens, 2003) The point of argument when it comes to the bible is the mode of translation. They say as long as it is correctly translated then it is a source of authority. However, they do not see it as a strong authority so they refer to other sources. According to the history, the battle that caused the destruction of the Tower of Babel brought to existence two nations that are the Lamanites and the Nephites (Leavitt, Marshall and Crandall, 2003). The Nephites became true Christians because they were civilized but the Lamanites were cursed. They became dark skinned and were extremely poor. They later perished and the Nephites were...
References: Mormons had racist's beliefs because they believed that black skin is a sign of sin and the curse. This belief was held strongly such that black people were viewed as inferior and were never put into consideration religion wise until 1978 (Padfield,2003).
Leavitt D. H., Marshall J. C., and Crandall K. A. (2003)," Dialogue: A Journal of Mormon Thought 36:4 (2003), 133-150.
Quinn D
Padfield D. (2005) 'the truth about Mormons' http://www.fairlds.org/apol/Book of Mormon/Book of Mormon08.html
Prince, G
Whiting M. F., (2003) "Book of Mormon:," Journal of Book of Mormon Studies 12:1 (2003).
...Excommunication In The Mormon Church Kate Kelly, a feminist, civil rights activist and faithful member of The Church of Jesus Christ of Latter Day saints, was recently notified that she might possibly be excommunicated, pending a trial in absentia. Ms. Kelly is being tried as an apostate, due to her vocal presence online and for begging the question- why can't women have the same rights as men within the church? It is morally and ethically apprehensible to excommunicate a faithful and active member of the church, simply because the member is asking for growth, progress and equality. Excommunication is considered the highest punishment that the Church can impose on its members. It consists of "…cutting the person off from the Church, so that he is no longer a member. Every blessing of the gospel is thereby lost, and unless the person repents and gains his church status again, he cannot be saved in the Celestial Kingdom." (McConkie, 1979). Cause for excommunication includes apostasy, rebellion, cruelty to wives and children (just a hint of sexism), immorality, and "all crimes involving moral turpitude". (McConkie, 1979). The Mormon faith is known for several things- kindness, community, family, service, charity, sobriety, etc. But a closer look also shows blatant sexism, a history of racism, intolerance, antiquated world-views, corporate greed and an alarming amount of cognitive dissonance, avoidance issues and lasting psychological...
What Is Particularly American About the Mormon Religion? Essay
...Dufie Nsia-Debrah March 6 2013 History 3329*01 What is particularly American about the Mormon religion? The Mormons faith was founded and created on the soil of America but one cannot help but to wonder what is particularly American about this religion. To answer this question we must traveled to the past and witness how the church of Mormon came into existence. In the 19th century to call someone a Mormon is close to calling someone a Muslim terrorist. Today Mormon is one of the world's fastest religions regardless of the enormous of repression Mormons endured over the past two generations. The Mormons religious practice has always put them in a suspicious or outcast position. In the Mormon Faith, the Bible is considered the word of God, but Mormons also believe God did not stop speaking and that he also spoke to Joseph Smith, the founder of Latter-Day Saint. Smith encounter with God is said to have happened when he was a young man in upstate New York. Smith claimed a Colum of light came to his room then a glowing angle informed him about the book of Mormon. The Angel led him to the nearby hill where he dug up a pair of golden plates. But he was forbidden to take the plate's home until he is married with children. After he married, he and his wife returned to the hill, dug the golden plates from which he translated the...
Mormon Church: Restricts Access to Holocaust Victims Essay
...Scott Young Mr. Bizga ARE; period 7 March 8, 2012 A.M.D.G. Mormon Church responds to criticism of proxy baptisms, restricts access to Holocaust victims This article is about the practice of the Mormon religion where they baptize holocaust victims. The members of this religion believe that the baptism allows the deceased to move on to the afterlife. This is a controversial issue among other religions, especially the Jewish population. They are very upset because they believe that the Mormons are trying to alter the religion of the Holocaust victims. This has caused the Jewish population to call an end of these religious practices. The Mormons have now closed their online database that contained all of the names of the Holocaust victims. This will keep the public from accessing this database and should stop these baptisms. But the Jewish population believes that this is just a cover up and that the Mormons will continue to practice these baptisms. This firewall does not help the problem. These practices do not even make sense. Why would they want to baptize these Holocaust victims? What is the point? This is basically defiling the dead. The Jewish population has every right to be angered by this. The Holocaust victims were murdered for being Jewish, not Mormon. They have absolutely no right to baptize these Jews. This should be totally illegal and the government should put an end to...
Paradoxical Statements in the Book of Mormon Essay
...Robert Fry Book of Mormon as Sacred Literature Professor Swift 11/14/2011 "He who hath ears to hear, let him hear" Paradoxes in the Book of Mormon As with all great literary works, more content is often present than first meets the eye. The Book of Mormon is no exception. One such way that the Book of Mormon proves its literary worth is through the use of paradox. In fact, the Book of Mormon uses paradox strategically to help the reader further ponder the meaning of the scriptures in his or her life, and thus discover statements of deeper doctrine. In our theological dive into paradoxes found within the Book of Mormon, it is first important to understand what a paradox is and in what contexts it is used. The word itself can be derived from its Greek roots, para and doxa, meaning "beyond belief" (Parsenios). According to K. S. Kantzer in Evangelical Dictionary of Theology, a paradox is "(1) an assertion which is self-contradictory, or (2) two or more assertions which are mutually contradictory, or (3) an assertion which contradicts some very commonly held position on the matter in question." (Kantzer) Most experts choose to break paradoxes into rhetorical paradoxes and logical paradoxes—the former being the juxtaposition of two seemingly incompatible ideas for the sake of striking an unconventional insight, and the latter "arises from the attempt by the human mind to unify or to...
Essay about Mormons: the Church of Jesus Christ of Latter-day Saints and Salt Lake City
..."Go west young Man" The American Frontier during the 19th century Character #3: Mormons INSTRUCTIONS: Your group must present the Mormons and their role in the settlement of the Great Plains • Your presentation must be about 20 minutes. • Your presentation must be structured in main parts (titles included in the PPT) • Your must create a PowerPoint Presentation (a few slides) underlining the main parts and notions of your presentation. Use it to present some documents (source and analysis). • Work, analyze and present to the rest of the class the document (s) included in this worksheet. • Don't forget to explain the major notions and the key vocabulary. • Each member of your group must talk in front of the class. Key questions you have to address during your presentation. • Who are the Mormons? Present quickly their main beliefs and religious practices. • Present their main leaders in the 1840s (Joseph Smith and Brigham Young). • Why did they decide to move West? • What were the main steps of their westward migration? • Why did they settle around the Great Salt Lake? How did they organize the territory? • What were the relations between the Mormons and the US government? • Why did they play an important role in the Westward expansion? Documents you have to use during your presentation: Doc 1: Source : First vision of Joseph Smith, stained...
Book of Mormon: Study Guide Essay
...Book of Mormon 122 Exam 1 Study Guide Brother Merrill People to know: Alma Korihor Amulek Helaman Pahoran Amalickiah Morianton Ammoron Zenock Moroni Corianton Moronihah Shiblon Lehi Teancum Zerahemnah Zenos Zeezrom Scriptures: Study the doctrines of chapters 32, 34, 36-42, 60 Review the following passages: 30:14-18, 37-49; 31:5, 15-17, 26-35; 32:14-16, 21, 27-42; 33:3-16; 34:8-10, 13-28, 31-40; 36:12-21; 37:6, 12, 15-16, 33-37, 41; 38:9-15; 39:5-14; 40:11-14; 41:2-3, 1015; 42: 6-15, 21-25, 29-30; 43:45-47; 45:2-11; 46:11-13, 19-21; 48:11-17; 50:21-23; 53:16-22; 56:44-48; 57:21, 26-27; 58:10-12; 60:6-14, 21-24, 33-36. Sample Essay Questions: Why did Mormon include the war chapters? What lessons did he intend to be learned from them? Be specific. What doctrines did Alma discuss with Corianton in chapters 39-42? Why did he address these specific doctrines? Given the gravity of Corianton's transgression, why do you suppose Alma went into such doctrinal detail on these matters? Define the Lord's position on war. What is His law of self-defense? Use specific examples to support your explanation. What specific things did Korihor preach? What are the counterparts of such philosophies in modern society? Why are they so appealing? What responses did Alma give to such ideas? ...
Essay about Mormons
...society ideals. The integration of religion in a secular age can be more closely examined through research of the modern Church of Jesus Christ of Latter-Day Saints. The Latter-Day Saints (LDS), inoffensively known as Mormons, is a religion that began in the 1820's during a period of religious revival and has now become the fourth largest Christian denomination ("NCC"). Founded by Joseph Smith Jr. and believed to be a restoration of the Christian church that focused on the atonement of Jesus Christ. Despite the fact that both religions focus on salvation in the name of Jesus Christ, Mormons have received much discrimination due to their alleged beginnings. Members believe that American-born prophets, Joseph Smith being the preliminary prophet, were anyone with a testimony of Jesus Christ. Joseph Smith was said to have been visited by the Heavenly Father and His Son Jesus Christ, and was told that "none of the churches on the earth had the fullness of truth" ("Newsroom"). The idea was misconstrued and lead to persecution from fear of religious threat when the authenticity of Joseph Smith's revelations was questioned. He was said to have been led by God himself to ancient writings and given means to translate them into what became known as The Book of Mormon. Later revelations became the doctrines and covenants used to better understand the 13 articles of faith. To Christians, this 're-writing' of biblical text discredited the...
Mormon Essay
...Bluffing Case Study Ta olso Bluffing in business revolves around the ethics of the specific business or person. Bluffing is often times viewed as deceiving, which usually corresponds to lying. Although some people believe bluffing in certain situations may be more acceptable than in others such as on a resume, or to make a deal, is it truly ethical? Oppositely, there is a true benefit from an honest reputation in business making bluffing unnecessary. The case study suggests that the nature of business is similar to the game of poker. The author explains that business has an element of chance; the winner in the long run is often one who plays with steady skill and well planned bluffs. While it may be true that the honest businessman receives more respect, the author suggests that bluffing in business is simply the same as a game strategy. Similar to poker, business bluffing does not reflect the ethics of the bluffer. The author believes that the ethics of business are game ethics, which differ from the ethics of religion. His view suggests that bluffing has nothing to do with ethics; rather they are merely a business practice. This introduces the question, do I personally agree with bluffing in the business world? I do not. I truly believe honesty is the key to being successful in the business world. I believe if success can be achieved through honesty, goes much further than success through bluffing. The case study explains an example of an older man who lies on his...
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This is the dungeon of Olaus Magnus, High Dread Sorceror of the Seventh Spire. He was said to have died years ago, leaving his fortification ripe for plundering. Nearby monarchs are trying to lay claim to the dungeon and the magical treasures within. Unbeknownst to them, on his deathbed Magnus made a pact with Thanuu, a demon of the pestilence realm. Now Magnus lives as a half beast, gathering his forces to invade nearby kingdoms and bring them under the rule of Thanuu.
Madness is claiming the settlement around the dungeon. Thanuu is creating visions of pestilence in people's minds. They are heavily religious and have taken to self-flagellation. Trying to stop them will cause them to attack - but they welcome a beating from the religious.
This is Gimlet Sneeve, a rogue, rabble-rouser and drunk. He is posing as a monk to get villagers to pay him for blessings. If he's rumbled, he'll help the PCs get into the dungeon and will join the for a cut. At some point reveal he's a werebear. As a clue, villagers have been found torn apart. Some report a hairy beast prowling the moors they call a devil. He doesn't know he's a werebear.
Balthazar is the demonic blacksmith in the dungeon, creating infernal weapons for Thanuu's soldiers. He wants human bone and hair to will forge a morbid blade. If PCs refuse, he will try to make the blade from their bodies.
1. 1d6 PCs become sexually aroused by the smell of demon bile and smear it on themselves. This can attract fester devils.
4. The PCs are teleported into a pit of demon feces.
Savnoc the Elder One wishes to feast on fester beasts, but the PCs will do nicely. Throwing an item into its hat enchants it, allowing the user to smell secret doors (they smell like wet moss).
Olaus Magnus sits on his damned throne. He is particularly weak to venom or the blessings of the clergy. He claws eyes out and lays hexagonal eggs that hatch into fester demons. All he wants to do is die, but Thanuu won't allow it.
Thanuu makes an appearance once Magnus is killed, or decides against killing the PCs. He has the appearance of a blasphemous bishop. The face on his chest can hypnotise PCs to believe they are babies again. He can fly, cast sleep and cause two or more fester demons to merge into a Dreadwalker - which feeds on wisdom.


text:
Armstrong State and USCB pick up Wednesday Baseball wins
College Baseball Season is underway
Updated: 12:08 AM EST Feb 9, 2017
Frank Sulkowski
The Armstrong State University baseball squad picked up an 8-1 win over visiting Morehouse College in its home opener of the 2017 season on Wednesday at Pirate Field. The Pirates evened their record at 2-2 after the win, while Morehouse falls to 2-5. Armstrong State returns to action on Saturday, hosting Paine College in a 1:00 p.m. non-conference contest at Pirate Field. Armstrong State put up a pair of runs in the first inning to take a 2-0 lead. Senior Ryan Patterson drove in a run with an RBI groundout and frehsman Mark Felton drove in a run with a single back to the pitcher. Morehouse cut the lead in half with a single run in the fourth inning as Percy Walters was hit by a pitch, Austin Jeter followed with a dobule down the left field line, then Zachary Lowe drove in Walters with a groundout to short. The score remained 2-1 until the late innings. The Pirates plated one run in the sixth on a passed ball, then also plated a run in the seventh on an error. Armstrong State then put the game out of reach with four runs in the eighth inning, highlighted by RBI doubles from Patterson and junior Mike Warren. Senior Aaron Bentley (1-0) picked up the win in his first start of the season, hurling seven innings of two-hit, one-run ball, walking one while striking out nine. Daron Bowling (1-2) took the loss for the Maroon Tigers, giving up eight hits and five runs - two earned - in seven innings of work, walking four while striking out two. Patterson finished the day 3-for-5 with a pair of doubles and two RBI to pace the 11-hit Pirate attack. Warren went 2-for-5 with a double and two runs scored, while freshman Trey Polewski went 2-for-3. Jeremy Christian's debut as USCB's head baseball coach was a rousing success Wednesday, as the Sand Sharks were sharp in every facet of the game in a 19-4 rout of visiting St. Andrews at Richard Gray Sports Complex. Every eligible position player on USCB's roster appeared in the game and 14 different players collected hits, as Christian took advantage of an early lead to display his team's depth. USCB took a 1-0 lead in the first on Bobby Wenthe's sacrifice fly and took advantage of an error and a pair of passed balls to plate three runs in the second before breaking it open in the third. The Sand Sharks sent 13 batters to the plate in the 10-run third inning, which Alex Murphy capped with a grand slam to left-center to make it 14-0. The Sand Sharks emptied the bench the next time through the order, but the offense kept rolling. Michael Grunder and Charlie McGinnis each knocked in runs in the fourth, and Grunder added a two-run single in the three-run fifth. Murphy led the way with four RBIs, while Grunder went 2-for-2 with three RBIs off the bench. Thomas Estopare, Wenthe and Mclean Hartz each drove in two runs, and Noah Matthews, Kal Davis and Brandon Joyce joined Murphy and Grunder with multi-hit games. The offensive outburst overshadowed a solid showing from the pitching staff, as junior right-hander Zac Burke limited the Knights to one hit and two walks over three scoreless innings to earn the win, and Nick Constan and Michael Biasello each worked a scoreless inning in relief.
SAVANNAH, Ga. —
The Armstrong State University baseball squad picked up an 8-1 win over visiting Morehouse College in its home opener of the 2017 season on Wednesday at Pirate Field.
The Pirates evened their record at 2-2 after the win, while Morehouse falls to 2-5. Armstrong State returns to action on Saturday, hosting Paine College in a 1:00 p.m. non-conference contest at Pirate Field.
Armstrong State put up a pair of runs in the first inning to take a 2-0 lead. Senior Ryan Patterson drove in a run with an RBI groundout and frehsman Mark Felton drove in a run with a single back to the pitcher.
Morehouse cut the lead in half with a single run in the fourth inning as Percy Walters was hit by a pitch, Austin Jeter followed with a dobule down the left field line, then Zachary Lowe drove in Walters with a groundout to short.
The score remained 2-1 until the late innings. The Pirates plated one run in the sixth on a passed ball, then also plated a run in the seventh on an error. Armstrong State then put the game out of reach with four runs in the eighth inning, highlighted by RBI doubles from Patterson and junior Mike Warren.
Senior Aaron Bentley (1-0) picked up the win in his first start of the season, hurling seven innings of two-hit, one-run ball, walking one while striking out nine. Daron Bowling (1-2) took the loss for the Maroon Tigers, giving up eight hits and five runs - two earned - in seven innings of work, walking four while striking out two.
Patterson finished the day 3-for-5 with a pair of doubles and two RBI to pace the 11-hit Pirate attack. Warren went 2-for-5 with a double and two runs scored, while freshman Trey Polewski went 2-for-3.
Jeremy Christian's debut as USCB's head baseball coach was a rousing success Wednesday, as the Sand Sharks were sharp in every facet of the game in a 19-4 rout of visiting St. Andrews at Richard Gray Sports Complex.
Every eligible position player on USCB's roster appeared in the game and 14 different players collected hits, as Christian took advantage of an early lead to display his team's depth.
USCB took a 1-0 lead in the first on Bobby Wenthe's sacrifice fly and took advantage of an error and a pair of passed balls to plate three runs in the second before breaking it open in the third. The Sand Sharks sent 13 batters to the plate in the 10-run third inning, which Alex Murphy capped with a grand slam to left-center to make it 14-0.
The Sand Sharks emptied the bench the next time through the order, but the offense kept rolling. Michael Grunder and Charlie McGinnis each knocked in runs in the fourth, and Grunder added a two-run single in the three-run fifth.
Murphy led the way with four RBIs, while Grunder went 2-for-2 with three RBIs off the bench. Thomas Estopare, Wenthe and Mclean Hartz each drove in two runs, and Noah Matthews, Kal Davis and Brandon Joyce joined Murphy and Grunder with multi-hit games.
The offensive outburst overshadowed a solid showing from the pitching staff, as junior right-hander Zac Burke limited the Knights to one hit and two walks over three scoreless innings to earn the win, and Nick Constan and Michael Biasello each worked a scoreless inning in relief.


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New Zealand Prime Minister Jacinda Ardern has called for the arrest of Turkish President Recep Erdogan for flashing white supremacist hand signals and sharing video of the Christchurch terror attack at recent campaign events.
While New Zealand is arresting people for "possessing" or "distributing" the first-person video of the shooting, President Erdogan has shown footage of the murders to thousands of Turkish citizens to whip up his pious Islamic supporters ahead of local elections scheduled for March 31.
Waleed Shahid, spokesman for America's Justice Democrats — who elected Ilhan Omar, Rashida Tlaib, and Alexandria Ocasio-Cortez to Congress — strongly criticized Erdogan and his Justice and Development Party.
An analysis of America's Justice Democrats and Turkey's Justice and Development Party shows that the names of their political parties are similar, they run the same kinds of Islamist candidates, and their policies are analogous.
Experts say Turkey looks like your average one-man autocracy found everywhere in the Middle East, American Democrats feel increasingly comfortable with anti-Semitic rhetoric, and white supremacists are shooting up mosques just like Islamist terrorists.
As for Erdogan, no one — not journalists, government officials, or analysts — can figure out how he became a modern case study for authoritarianism, but everyone agrees he should be arrested for hate speech.