text:
\section{Introduction}
Cell-free massive multiple-input multiple-output (MIMO) is one of the main candidate technologies for meeting the ambitious requirements of future wireless generation networks. Its main feature is the combination of the benefits of ultra-dense deployments and \textit{coordinated multi-point} (CoMP) methods, with the goal of offering a uniformly good quality of service to all users. Compared with classical cellular technologies, cell-free massive MIMO gives the opportunity to realize this goal in a significantly more efficient way in terms of bandwidth and energy consumption \cite{ngo2017cellfree,demir2021foundations}.

From a theoretical perspective, cell-free massive MIMO can be interpreted as an evolution of the well-known \textit{network MIMO} \cite{karakayali2006network} and \textit{cloud radio access network} (C-RAN) \cite{checko2015cran} concepts towards a more scalable, and hence practically feasible, implementation. This crucial enhancement has been essentially enabled by the analytical framework developed within the massive MIMO literature \cite{marzetta2016fundamentals,massivemimobook}, which allowed a more refined performance analysis especially in the presence of imperfect channel state information (CSI).

In fact, the development of cell-free massive MIMO was largely driven by the necessity of developing practical CoMP methods that do not require expensive network-wide information processing and sharing. Indeed, the early approaches recommended the use of time-division duplex (TDD) operations, and to run very simple distributed precoding/combining schemes at each access point (AP) on the basis of locally measured uplink (UL) channel samples only \cite{ngo2017cellfree}. The massive MIMO regime was then exploited to counteract the losses induced by this very limited CSI configuration. From this original idea, several improvements have been proposed involving more advanced processing and resource allocation techniques \cite{nayebi2017precoding,emil2020cellfree,buzzi2020usercentric,emil2020scalable,du2021cellfree}. The main objective of most of this subsequent literature is the definition of scalable and efficient architectures identifying which set of APs and computational units should serve a given user, with which precoding/combing scheme, and on the basis of which information.

\subsection{Optimal distributed precoding / combining}
One of the major issues behind moving from centralized to distributed processing is that limiting the CSI sharing makes the optimal precoding / combining design problem much more complicated. Therefore, previous works confined their analysis to the direct transposition of centralized methods taken from the massive MIMO literature such as \textit{maximum-ratio transmission / combining} (MRT / MRC), \textit{zero-forcing} (ZF), and \textit{minimum mean-square error} (MMSE) processing \cite{demir2021foundations}. On top of being heuristic, this approach is often not general enough, in the sense that it can be applied only to very specific CSI sharing patterns similar to the fully distributed setup in \cite{ngo2017cellfree}. This long-lasting problem has been solved only recently in \cite{miretti2021team} using the so-called \textit{team MMSE} (TMMSE) method. Building on powerful multi-agent control theoretical tools, and focusing on simple achievable rate bounds \cite{marzetta2016fundamentals,massivemimobook}, the TMMSE method provides rigorous yet practical guidelines for optimal distributed precoding  design under partial CSI sharing. As an important application, \cite{miretti2021team} derives the closed-form optimal \textit{local} precoders for the fully distributed setup studied in \cite{ngo2017cellfree}, improving upon previously known heuristics especially in the presence of pilot contamination and/or line-of-sight (LoS) components. Furthermore, \cite{miretti2021team} also derives the closed-form optimal precoders assuming that CSI is shared unidirectionally along a serial fronthaul, leading to an efficient recursive algorithm suitable for cell-free massive MIMO networks deployed using a so-called \textit{radio stripe} \cite{interdonato2019ubiquitous,shaik2020mmse}. An important remark is that, although presented in the context of downlink precoding, the results in \cite{miretti2021team} exploit the uplink-downlink (UL-DL) duality principle given by \cite{massivemimobook}, hence they also readily provide optimal UL combining schemes.

\subsection{Paper overview and summary of contributions}
The team MMSE method as exposed in \cite{miretti2021team} presents some limitations. First, it assumes that each user is served by all APs in the network, and hence it is not scalable. Second, the DL case assumes a rather unrealistic sum-power constraint, so that the UL-DL duality principle in \cite{massivemimobook} applies. In Section \ref{sec:TMMSE} of this work, we address the above limitations as follows:
\begin{itemize}
\item We show that the TMMSE method can be optimally merged with the \textit{user-centric} network clustering framework given by \cite{emil2020scalable}. This leads to a novel optimal distributed precoding / combining design jointly considering partial CSI sharing and arbitrary user-AP association rules.
\item We study the effect of a simple suboptimal technique for adapting the DL TMMSE solution to a per-TX power constraint. We argue that the resulting signal-to-noise ratio (SNR) penalty is negligible in practice, making the TMMSE method an attractive solution also under more realistic power constraints.
\end{itemize}
As a second main contribution, in Section \ref{sec:stripes}, we apply our results to an \textit{industrial internet-of-things} (IIoT) scenario with a cell-free massive MIMO system deployed using multiple radio stripes. Specifically, we derive a set of novel closed-form optimal distributed precoders under various information structures. These include the case of a fully distributed user-centric architecture as defined in \cite{buzzi2020usercentric,emil2020scalable,demir2021foundations}, but also more involved yet interesting cases. In particular, we obtain novel schemes that can be efficiently implemented using recursive algorithms along each stripe, significantly reducing the scalability issue of cell-free massive MIMO with respect to the number of APs. Note that, on top of covering scalable user-AP association rules, a relevant difference between this work and \cite{miretti2021team} is that the latter considers only a single radio stripe. The proposed schemes are finally  tested using numerical simulations.

The system model is provided in Section \ref{sec:model}. Similarly to \cite{miretti2021team}, we focus on DL precoding only, but we remark that our results can be readily applied to derive optimal UL combiners.

\textit{Notation:} We reserve italic letters (e.g., $a$) for scalars and functions, boldface letters (e.g., $\vec{a}$, $\vec{A}$) for vectors and matrices, and calligraphic letters (e.g., $\mathcal{A}$) for sets. Random quantities are distinguished from their realizations as follows: $\rvec{a}$, $\rvec{A}$ denote random vectors and matrices; $A$ denotes a random scalar, or a generic random variable taking values in some unspecified set $\set{A}$. The operators $(\cdot)^\T$, $(\cdot)^\herm$ denote respectively the transpose and Hermitian transpose of matrices and vectors. We denote the Euclidean norm by $\|\cdot\|$, and the Frobenius norm by $\|\cdot\|_\mathrm{F}$. Given $n>2$ random matrices $\rvec{A}_1,\ldots,\rvec{A}_n$ with joint distribution $p(\vec{A}_1,\ldots,\vec{A}_n)$, we say that $\rvec{A}_1\to \rvec{A}_2 \to \ldots \to \rvec{A}_n$ forms a Markov chain if $p(\vec{A}_i|\vec{A}_{i-1},\ldots,\vec{A}_1) = p(\vec{A}_i|\vec{A}_{i-1})$ $\forall i \geq 2$. We use $\mathrm{diag}(\vec{A}_1,\ldots,\vec{A}_n)$ to denote a block-diagonal matrix with the matrices $\vec{A}_1,\ldots,\vec{A}_n$ on its diagonal. We denote by $\vec{e}_n$ the $n$-th column of the identity matrix $\vec{I}$. We use $\prod_{i=l'}^{l}\vec{A}_i := \vec{A}_{l}\vec{A}_{l-1}\ldots\vec{A}_{l'}$ for integers $l \geq l' \geq 1$ to denote the \textit{left} product chain of $l-l'+1$ ordered matrices of compatible dimension, and we adopt the convention $\prod_{i=l'}^{l} \vec{A}_i = \vec{I}$ for $l<l'$.

\section{System Model}
\label{sec:model}
\subsection{Channel model}
Consider a network of $L$ transmitters (TXs) indexed by $\mathcal{L}:=\{1,\ldots,L\}$, each of them equipped with $N$ antennas, and $K$ single-antenna receivers (RXs) indexed by $\mathcal{K}:=\{1,\ldots,K\}$. Let an arbitrary channel use be governed by the MIMO channel law
\begin{equation}
\rvec{y} = \sum_{l=1}^L \rmat{H}_l\rvec{x}_l + \rvec{n},
\end{equation}
where the $k$-th element of $\rvec{y} \in \stdset{C}^{K}$ is the received signal at RX $k$, $\rmat{H}_l \in \stdset{C}^{K\times N}$ is a sample of a stationary ergodic random process modelling the fading between TX $l$ and all RXs, $\rvec{x}_l \in \stdset{C}^N$ is the transmitted signal at TX~$l$, and $\rvec{n}\sim \CN(\vec{0},\vec{I})$ is a sample of a white noise process. This channel model is relevant, e.g, for narrowband or wideband OFDM systems where transmission spans several realizations of the fading process. For most parts of this work, we do not specify the distribution of $\rmat{H}:=\begin{bmatrix}
\rmat{H}_1,\ldots,\rmat{H}_L
\end{bmatrix}$. However, we reasonably assume the channel submatrices corresponding to different TX-RX pairs to be mutually independent, and finite fading power $\E[\|\rmat{H}\|_{\mathrm{F}}^2]<\infty$. Furthermore, we focus on $N<K$, that is, on the regime where TX cooperation is particularly useful.

\subsection{Partial message and CSIT sharing}
In order to implement scalable cell-free massive MIMO networks, there is the need to limit the information sharing between the processing units controlling the distributed TXs.\footnote{In this work, we assume that each TX is controlled by a separate processing unit, but the results can be easily generalized to the case where multiple TXs are controlled by the same processing unit.} In particular, by focusing on two of the dominant components in the information sharing burden, we consider the following information constraints:

\textbf{Partial message sharing:}
Let $U_k \sim \CN(0,1)$ be a sample of the i.i.d. data bearing signal for RX $k \in \set{K}$. We assume the message $U_k$ to be available only at a subset $\set{L}_k \subseteq \set{L}$ of the TXs. We do not specify how the sets $\set{L}_k$ are formed, but we remark that scalable cell-free networks are expected to implement some kind of user-centric rule \cite{demir2021foundations} allowing each RX to be granted service without relying on the notion of cell. Given the sets $\set{L}_k$, we also define
\begin{equation}
\set{K}_l := \{k \in \set{K} \text{ s.t. } l \in \set{L}_k \}, \quad l \in \set{L},
\end{equation}
that is, the subset $\set{K}_l\subseteq \set{K}$ of RXs being served by TX $l$.

\textbf{Partial CSIT sharing:}
Consider a \textit{distributed} CSIT configuration \cite{miretti2021team}, i.e., where each TX has some local side information $S_l\in \set{S}_l$ about the channel state $\rmat{H}$. For example, $S_l$ may include local measurements of the local channel $\rvec{H}_l$,  and the output of some CSIT sharing procedure. We assume $(\rmat{H},S_1,\ldots,S_L)$ to be a sample of an ergodic stationary process with first order joint distribution fixed by nature/design, and known by all TXs. Note that, due to the looser time sensitivity, sharing statistical information is in practice less challenging than sharing estimates of $\rvec{H}$.

\subsection{Distributed linear precoding}
Given the above information constraints, we then let each TX $l$ form its transmit signal according to the following distributed linear precoding scheme:
\begin{equation}\label{eq:distributed_precoding}
\rvec{x}_l = \sum_{k\in \set{K}_l}\sqrt{p_k}\rvec{t}_{l,k}U_k,\quad \rvec{t}_{l,k} = \rvec{t}_{l,k}(S_l),
\end{equation}
where $(p_1,\ldots,p_K) =: \vec{p}\in \stdset{R}_+^K$ is a fixed power allocation vector, and where $\rvec{t}_{l,k}\in \stdset{C}^N$ for $k\in \set{K}_l$ is a linear precoder applied at TX $l$ to message $U_k$ based only on the local information $S_l$. More formally, by letting $(\Omega,\Sigma,\mathbb{P}) $ be the underlying probability space over which all random quantities are defined, we constrain $\rvec{t}_{l,k}$ for $k\in \set{K}_l$ within the vector space $\mathcal{T}_l$ of square-integrable $\Sigma_l$-measurable functions $\Omega \to \stdset{C}^N$, where $\Sigma_l\subseteq \Sigma$ denotes the sub-$\sigma$-algebra generated by $S_l$ on $\Omega$, called the \textit{information subfield} of TX $l$ \cite{yukselbook}. We finally denote the full precoding vector for message $U_k$ by $\rvec{t}_k^\T := \begin{bmatrix}
\rvec{t}_{1,k}^\T & \ldots & \rvec{t}_{L,k}^\T
\end{bmatrix}^\T $, and let $\rvec{t}_k \in \mathcal{T}^{(k)}:=\prod_{l=1}^L\mathcal{T}_l^{(k)}$, where
\begin{equation}
\set{T}_l^{(k)} := \begin{cases} \set{T}_l & \text{if } l \in \set{L}_k, \\
\{\rvec{t}_{l,k}(S_l) = \vec{0} \; \mathrm{a.s.}\} & \text{otherwise.} \end{cases}
\end{equation}

\subsection{Performance metric}
We measure the network performance under the specified transmission scheme by using Shannon (ergodic) achievable rates predicted by the popular \textit{hardening} bound \cite{marzetta2016fundamentals,massivemimobook},
\begin{equation}\label{eq:hardening_bound}
R_k^{\mathrm{hard}} :=  \log\left(1+\mathrm{SINR}_k^{\mathrm{DL}}\right),
\end{equation}
\begin{equation}\mathrm{SINR}_k^{\mathrm{DL}} := \dfrac{p_k|\E[\rvec{g}_k^\herm\rvec{t}_k]|^2}{p_k\mathrm{Var}[\rvec{g}_k^\herm\rvec{t}_k] + \sum_{j\neq k}p_j\E[|\rvec{g}_k^\herm\rvec{t}_j|^2]+1},
\end{equation}
where $\begin{bmatrix}
\rvec{g}_1 & \ldots & \rvec{g}_K \end{bmatrix} :=\rmat{H}^\herm
$.
We then let $\mathcal{R}(P_1,\ldots,P_L)$ be the union of all simultaneously achievable rate tuples $(R_1,\ldots,R_K)\in \stdset{R}_+^K$ such that $R_k \leq R_k^{\mathrm{hard}}$ $\forall k \in \mathcal{K}$ for some set of distributed precoders $\{\rvec{t}_k \in \set{T}^{(k)}\}_{k=1}^K$ and power allocation $\vec{p}\in \set{R}_+^K$ satisfying
\begin{equation}
\sum_{k\in\set{K}}p_k\E[\|\rvec{t}_{l,k}\|^2]\leq P_l<\infty, \quad \forall l \in \set{L}.
\end{equation}
The set $\mathcal{R}(P_1,\ldots,P_L)$ is an inner bound for the capacity region of the considered network with partial message and CSIT sharing, subject to a long-term per-TX power constraint $\E[\|\rvec{x}_l\|^2]\leq P_l$, $\forall l \in \set{L}$. The goal of this paper is to provide a method for designing distributed linear precoders spanning the largest possible region $\set{R}'\subseteq \set{R}(P_1,\ldots,P_L)$

\section{Team MMSE Precoding}
\label{sec:TMMSE}
\subsection{UL-DL duality and the MSE criterion}\label{ssec:duality}
In order to simplify the challenging problem of optimal distributed precoding design, we first focus on a relaxed version by assuming a \textit{sum} power constraint $\sum_{l=1}^L P_l \leq P$. Specifically, we focus on
\begin{equation}
\set{R}_{\mathrm{sum}}(P) :=  \bigcup_{\sum_{l=1}^{L}P_l \leq P} \set{R}(P_1,\ldots,P_L),
\end{equation}
which is an outer bound to $\set{R}(P_1,\ldots,P_L)$ $\forall (P_1,\ldots,P_L)$ s.t. $\sum_{l=1}^{L}P_l \leq P$.
This simplification allows us to exploit the UL-DL duality principle \cite[Th.~4.8]{massivemimobook}, and obtain a convenient design criterion as established by the following result.

\begin{theorem}\label{th:duality}
Let $\vec{w}:=(w_1,\ldots,w_K)$ be a vector of weights belonging to the simplex $\set{W} :=\{\vec{w} \in \stdset{R}_+^K \; | \; \sum_{k=1}^Kw_k = 1\}$, and define $\vec{W}:= \mathrm{diag}(\vec{w})$. Then, all rate tuples $(R_1,\ldots,R_K)$ satisfying
\begin{equation}\label{eq:MSE_bound}
R_k\leq \log(\mathrm{MSE}(\rvec{t}_k))^{-1},
\end{equation}
\begin{equation}
\mathrm{MSE}_k(\rvec{t}_k) := \E\left[ \left\|\vec{W}^{\frac{1}{2}}\rmat{H}\rvec{t}_k - \vec{e}_k\right\|^2 +\dfrac{1}{P}\|\rvec{t}_k\|^2 \right],
\end{equation}
for some $\rvec{t}_k \in \set{T}^{(k)}$,  belong to $\set{R}_{\mathrm{sum}}(P)$. Furthermore, if $\rvec{t}_k^\star$ minimizes $\mathrm{MSE}_k(\rvec{t}_k)$ over $\set{T}^{(k)}$, then $(R_1,\ldots,R_K)$, $R_k = \log(\mathrm{MSE}(\rvec{t}^\star_k))^{-1}$ is Pareto optimal w.r.t. $\set{R}_{\mathrm{sum}}(P)$, and every tuple in the Pareto boundary of $\set{R}_{\mathrm{sum}}(P)$ is achievable for some $\vec{w} \in \set{W}$.
\end{theorem}
\begin{proof}
The proof for the special case of perfect message sharing, i.e., by considering $\set{T} := \prod_{l=1}^L\set{T}_l$ instead of $\set{T}^{(k)}$ $\forall k \in \set{K}$, is given by \cite[Th.~1]{miretti2021team}. The proof for the general case follows by observing that none of the steps in the proof of \cite[Th.~1]{miretti2021team} (and, in particular, the UL-DL duality principle) is impacted if we replace $\set{T}$ with $\set{T}^{(k)}$.
\end{proof}
Theorem~\ref{th:duality} states that, if we consider a sum power constraint, the optimal distributed precoding design can be obtained by solving (for each RX $k \in \set{K}$)
\begin{equation}\label{eq:UC-TMMSE}
\underset{\rvec{t}_k\in \set{T}^{(k)}}{\text{minimize}} \;  \mathrm{MSE}_k(\rvec{t}_k),
\end{equation}
and where the operating point on the boundary of the performance region $\set{R}_{\mathrm{sum}}(P)$ is parametrized by the $K-1$ real coefficients $\vec{w}\in \set{W}$. The operating point $\vec{w}$ should be ideally selected by solving a dual UL power allocation problem optimizing some network utility. However, in practice, $\vec{w}$ is often chosen heuristically, for instance by interpreting its element as RXs' priorities. Given $\vec{w}\in \set{W}$ and a set of distributed precoders $\{\rvec{t}_k\}_{k=1}^K \in  \set{T}^{(k)}$, the desired achievable scheme is then obtained by computing a feasible DL power allocation vector $\vec{p}$ solving the linear system of equations in \cite[Theorem~4.8]{massivemimobook}.

Problem~\eqref{eq:UC-TMMSE} extends the so-called \textit{team} MMSE (TMMSE) precoding design criterion, studied in \cite{miretti2021team}, to the case of partial message sharing. Although more general, in this work we also refer to the solution of Problem~\eqref{eq:UC-TMMSE} as the optimal TMMSE precoders. This name originates from the specific solution approach that we adopt in this work, which is outlined in the following section.

\subsection{Team theory for distributed precoding design}
In this section we provide a useful set of necessary and sufficient conditions for optimal TMMSE precoding design. The key idea is that, by taking a user-centric perspective, we can optimize each precoder $\rvec{t}_k\in \set{T}^{(k)}$ by assuming full message sharing within a reduced network composed only by the TXs in $\set{L}_k$. Therefore, Problem \eqref{eq:UC-TMMSE} can be solved by means of the \textit{team theoretical} arguments \cite{yukselbook} developed in \cite{miretti2021team} for the full message sharing case.

\begin{theorem}\label{th:quadratic_teams}
If $\E[\|\rmat{H}^\herm\rmat{H}\|^2_{\mathrm{F}}]<\infty$,
then Problem~\eqref{eq:UC-TMMSE} admits a unique optimal solution, which is also the unique solution $\rvec{t}_k^\star \in \set{T}^{(k)}$ satisfying a.s. ($\forall l \in \mathcal{L}^{(k)}$)
\begin{equation}\label{eq:UC_stationary}
\E[\rmat{O}_{l,l}|S_l]\rvec{t}^\star_{l,k}(S_l) + \sum_{j \in \set{L}^{(k)}\backslash \{l\}}\E[\rmat{O}_{l,j}\rvec{t}^\star_{j,k}|S_l] = \E[\rvec{g}_{l,k}|S_l]\vec{W}^{\frac{1}{2}},
\end{equation}
where $\rmat{O}_{l,l} := \rmat{H}_l^\herm\vec{W}\rmat{H}_l + P^{-1}\vec{I}$, $\rmat{O}_{l,j} := \rmat{H}_l^\herm\vec{W}\rmat{H}_j$ $\forall l\neq j$, and $\rvec{g}_{l,k}$ is the subvector of $\rvec{g}_k$ corresponding to the channel of TX $l$.
\end{theorem}
\begin{proof}
We rewrite the objective of \eqref{eq:UC-TMMSE} by replacing $\rmat{H}$ with a reduced channel matrix $\rmat{H}^{(k)}$ containing only the columns related to the TXs in $\mathcal{L}_k$, and $\rvec{t}_k$ with a corresponding reduced distributed precoding vector $\rvec{t}_k^{(k)} \in \prod_{l\in\mathcal{L}_k}\set{T}_l$, yielding
\begin{equation}
\E\left[ \left\|\vec{W}^{\frac{1}{2}}\rmat{H}^{(k)}\rvec{t}_k^{(k)} - \vec{e}_k\right\|^2 +\dfrac{1}{P}\|\rvec{t}_k^{(k)}\|^2 \right].
\end{equation}
We then notice that the minimization problem over $\rvec{t}_k^{(k)} \in \prod_{l\in\mathcal{L}_k}\set{T}_l$ has exactly the same form as the TMMSE precoding design problem studied in \cite{miretti2021team}. Therefore, the results of \cite{miretti2021team} based on the theory of \textit{quadratic} teams \cite{yukselbook} apply, and the proof readily follows.
\end{proof}

The optimality conditions \eqref{eq:UC_stationary} correspond to an infinite dimensional linear system of equations, which can be  solved via one of the many approximation methods available in the literature, such as the ones surveyed in \cite{yukselbook}. Importantly, \eqref{eq:UC_stationary} does not assume any particular CSIT acquisition scheme, and it only requires the mild condition $\E[\|\rmat{H}^\herm\rmat{H}\|^2_{\mathrm{F}}]<\infty$ on the fading distribution, which is satisfied, e.g., for all physically consistent distributions with bounded support, or for the classical Gaussian fading model. In the second part of this work, we focus on special yet relevant cases where \eqref{eq:UC_stationary} can be solved analytically. To this end, we first rewrite \eqref{eq:UC_stationary} under two additional assumptions, which are consistent with the canonical cell-free massive MIMO paradigm \cite{demir2021foundations}.

\begin{assumption}[Local channel estimation]\label{ass:TDD}
For every $l\in \mathcal{L}$, let $\hat{\rmat{H}}_{l}$ be the estimate of the local channel $\rmat{H}_l$ available at TX $l$, and $\rmat{E}_l:= \rmat{H}_l - \hat{\rmat{H}}_{l}$ be the local  estimation error. Assume that $\hat{\rmat{H}}_{l}$ and $\rmat{E}_l$ are independent. Furthermore, assume $\E[\rmat{E}_l] = \vec{0}$, and that $\E[\rmat{E}_l^\herm\vec{W}\rmat{E}_l] =: \vec{\Psi}_l$ has finite elements. Finally, assume that $(\hat{\rmat{H}}_{l},\rmat{E}_{l})$ and $(\hat{\rmat{H}}_{j},\rmat{E}_{j})$ are independent for $l\neq j$.
\end{assumption}

\begin{assumption}[CSIT sharing mechanism]\label{ass:CSIT_sharing}
For every $(l,j) \in \mathcal{L}^2$ s.t. $l\neq j$, assume the following Markov chain:
\begin{equation}
\rmat{H}_l \to \hat{\rmat{H}}_{l} \to S_l \to S_j \to \hat{\rmat{H}}_{j} \to \rmat{H}_j.
\end{equation}
\end{assumption}
Assumption \ref{ass:TDD} holds, e.g., for pilot-based MMSE estimates of Gaussian channels exploiting channel reciprocity in time-division duplex (TDD) systems \cite{demir2021foundations}.  Assumption \ref{ass:CSIT_sharing} essentially states that all the  available information about the local channel $\rmat{H}_l$ is fully contained in $S_l$ at TX $l$, and that TX $j$ can only obtain a degraded version of it through some arbitrary CSIT sharing mechanism.

\begin{lemma}\label{lem:stationarity_imperfect}
Suppose the assumption of Theorem~\ref{th:quadratic_teams}, Assumption~\ref{ass:TDD}, and Assumption~\ref{ass:CSIT_sharing} hold. Then, the unique solution to Problem~\eqref{eq:UC-TMMSE} is given by the unique $\rvec{t}_k^\star \in \set{T}^{(k)}$ satisfying ($\forall l \in \mathcal{L}_k$)
\begin{equation}\label{eq:stationary_imperfect}
\rvec{t}_{l,k}^\star(S_l) =  \rmat{T}_l\left(\vec{e}_k-\sum_{j \in \set{L}_k\backslash  \{l\}} \vec{W}^{\frac{1}{2}}\E\left[\hat{\rmat{H}}_{j}\rvec{t}^\star_{j,k}\Big|S_l\right] \right) \quad \mathrm{a.s.},
\end{equation}
where $\rmat{T}_l:=\left(\hat{\rmat{H}}_{l}^\herm\vec{W}\hat{\rmat{H}}_{l}+\vec{\Psi}_l + P^{-1}\vec{I}\right)^{-1}\hat{\rmat{H}}_{l}^\herm\vec{W}^{\frac{1}{2}}$.
\end{lemma}
\begin{proof}
The proof follows from simple manipulations of \eqref{eq:UC_stationary}. The details are similar to the full message sharing case given by \cite[Lem.~2]{miretti2021team}, hence they are omitted.
\end{proof}

\subsection{Per-TX power constraint}
The main drawback of the proposed TMMSE precoding design is that it relies on the UL-DL duality principle for fading channels given by \cite{massivemimobook}, which requires a sum power constraint. However, for deterministic channels, a weaker form of the UL-DL duality principle and of the Pareto boundary parametrization exists also under a per-TX power constraint (see, e.g., \cite{yu2007transmitter}). Although we do not rule out the possibility of establishing a similar result for fading channels, in the following we approximate the optimal distributed precoders spanning $\mathcal{R}(P_1,\ldots,P_L)$ by using a much simpler suboptimal approach.

Suppose $\rvec{x}_l^\star$ is the $l$-th TX signal obtained using optimal TMMSE precoding under a sum power constraint $\sum_{l=1}^LP_l = P$, and consider the trivial adaptation $(\forall l \in \set{L})$
\begin{equation}\label{eq:power_scaling}
\rvec{x}_l = \frac{1}{\nu} \rvec{x}_l^\star, \quad \nu^2 =  \max\left(1,\frac{\E[\|\rvec{x}^\star_1\|^2]}{P_1},\ldots,\frac{\E[\|\rvec{x}^\star_L\|^2]}{P_L}\right),
\end{equation}
which scales everything down until the per-TX power constraint is satisfied. In terms of performance, if $\{\rvec{t}^\star_k\}_{k=1}^K$ is the set of TMMSE precoders with corresponding power allocation $\{p_k^\star\}_{k=1}^K$ generating $\rvec{x}_l^\star$, the above method produces achievable rates given by $(\forall k \in \set{K})$
\begin{equation}
R_k = \log\left(1+ \dfrac{p^
\star_k|\E[\rvec{g}_k^\herm\rvec{t}^\star_k]|^2}{p^\star_k\V[\rvec{g}_k^\herm\rvec{t}^\star_k] + \sum_{j\neq k}p^\star_j\E[|\rvec{g}_k^\herm\rvec{t}^\star_j|^2]+\nu^2}\right),
\end{equation}
that is, compared to the optimal solution assuming a sum power constraint, there is a SNR loss $\nu^2$ proportional to the largest violation of the TX power constraints. Nevertheless, this loss may be marginal if the interference terms are still dominating the denominator in the rate expressions. Therefore, we argue that the simple power scaling method described above may be particularly suitable for the setup of this work, where partial message and CSIT sharing indeed often induce an interference limited regime.\footnote{The saturation of $R_k$ w.r.t. the SNR is due to the simple point-to-point coding scheme achieving \eqref{eq:hardening_bound} which treats interference as noise. The extension of our results to more advanced coding schemes based, e.g., on rate-splitting and (partial) interference decoding \cite{clerckx2016rate} is an interesting future direction.}

Other variations may be also considered, for example we can repeat the TMMSE precoders computation for decreasing values of $P$ until the per-TX power constraint is satisfied. Furthermore, power scaling coefficients coupled with clipping techniques can be also used to adapt long-term power constraints to short-term power constraints of the type $\|\rvec{x}_l\|^2\leq P_l$ almost surely. We leave further discussions on power constraints for future work.

\section{Case Study: Network of Radio Stripes}
\label{sec:stripes}
\subsection{Network architecture}
We consider an indoor IIoT scenario similar to \cite{interdonato2019ubiquitous} and depicted in Fig.~\ref{fig:IIoT}, where $L=100$ single-antenna TXs are arranged over a rectangular area (e.g., the ceiling of a warehouse) of $100 \times 50$ [$\mathrm{m}^2$] using $Q=5$ radio stripes of $M=20$ TXs each. For ease of exposition, we map all indexes $l \in \set{L}$ to pairs of indexes $(q,m) \in \set{Q} \times \set{M}$, where $\set{Q} :=  \{ 1,\ldots, Q \}$ and $\set{M} := \{1,\ldots, M \}$. For example, we denote the channel  $\rmat{H}_l$ between all RXs and the $m$-th TX of the $q$-th radio stripe by $\rmat{H}_{q,m}$. We assume each stripe $q$ is controlled by a separate master processing unit placed at the edge next to TX $(q,1)$, providing coded and modulated data bearing signals $U_k$ to all the TXs along the stripe. To limit the information processing and sharing burden, we let each RX $k$ be served only by the TXs belonging to the subset $\set{Q}_k \subset \set{Q}$ of its $Q_k = 2$ closest radio stripes. This implies that the message for RX $k$ is shared only within the master units controlling the $Q_k$ stripes in $\set{Q}_k$. Similarly, we assume that, at each TX $(q,m)$, the channel $\rvec{g}_{q,m,k}$ towards RX $k$ is perfectly estimated if $q \in \set{Q}_k$, and completely unknown otherwise.  Then, we study the following CSIT sharing patterns:
\begin{enumerate}
\item No CSIT sharing: $S_{q,m} = \hat{\rvec{H}}_{q,m}$;
\item Unidirectional CSIT sharing: $S_{q,m} = (\hat{\rvec{H}}_{q,1},\ldots,\hat{\rvec{H}}_{q,m})$;
\item Bidirectional CSIT sharing: $S_{q,m} = (\hat{\rvec{H}}_{q,1},\ldots,\hat{\rvec{H}}_{q,M})$.
\end{enumerate}
For all the above cases, CSIT sharing is limited within each stripe.
\begin{figure}[ht]
\centering
\includegraphics[trim=0.5cm 0 0.5cm 1.2cm, clip,width=0.8\columnwidth]{network}
\caption{Pictorial representation of an IIoT setup with $K=10$ RXs uniformly distributed within a rectangular service area, and a grid of $L=100$ single-antenna TXs arranged over $Q=5$ radio stripes of $M=20$ TXs each. The red crosses identify the set $\set{Q}_k$ of TXs serving an arbitrary RX, obtained from the $Q_k=2$ closest radio stripes.}
\label{fig:IIoT}
\end{figure}

\subsection{Optimal distributed precoding and recursive implementations}
The optimal solution to \eqref{eq:UC-TMMSE} can be obtained in closed form for all the considered information structures. We start with the most involved case, that is, undirectional CSIT sharing:
\begin{theorem}\label{th:unidirectional}
The TMMSE precoder applied at the $m$-th TX of the $q$-th radio stripe to the message for RX $k$ under unidirectional CSIT sharing is given by
\begin{equation}\label{eq:TMMSE_stripes}
\rvec{t}_{q,m,k}(S_{q,m}) = \rmat{T}_{q,m}\rmat{V}_{q,m}\prod_{n=1}^{m-1} \bar{\rmat{V}}_{q,n}\vec{c}_{q,k}, \quad \forall q \in \set{Q},
\end{equation}
where we use the following short-hands:
\begin{itemize}
\item $\rmat{V}_{q,m} := (\vec{I}-\vec{\Pi}_{q,m}\rmat{P}_{q,m})^{-1}(\vec{I}-\vec{\Pi}_{q,m})$;
\item $\bar{\rmat{V}}_{q,m} := \vec{I}-\rmat{P}_{q,m}\rmat{V}_{q,m}$;
\item $\rmat{P}_{q,m} := \vec{W}^{\frac{1}{2}}\hat{\rmat{H}}_{q,m}\rmat{T}_{q,m}$;
\item $\vec{\Pi}_{q,m} := \E\left[\rmat{P}_{q,m+1}\rmat{V}_{q,m+1}\right] + \vec{\Pi}_{q,m+1}\E\left[\bar{\rmat{V}}_{q,m+1}\right]$;
\end{itemize}
and where we let $\vec{\Pi}_{q,M} := \vec{0}_{K\times K}$, and $\{\vec{c}_{q,k}\}_{q=1}^Q$ be the unique solution of the linear system of equations
\begin{equation}
\begin{cases}\vec{c}_{q,k} + \sum_{j \in \set{Q}_k \backslash \{q\}}\vec{\Pi}_{j,0} \vec{c}_{j,k} = \vec{e}_k & \forall q \in \set{Q}_k, \\
\vec{c}_{q,k} = \vec{0}_{K\times 1} & \text{otherwise.}
\end{cases}
\end{equation}
\end{theorem}
\begin{proof}
We need to verify that the proposed solution satisfies the optimality conditions given by Lemma \ref{lem:stationarity_imperfect}. Replacing \eqref{eq:TMMSE_stripes} in \eqref{eq:stationary_imperfect}, after some simple manipulations, we observe that it suffices to verify ($\forall (q,m) \in \set{Q}_k \times \set{M}$)
\begin{equation}\label{eq:stationarity_stipes}
\begin{split}
&\rmat{V}_{q,m}\prod_{n=1}^{m-1} \bar{\rmat{V}}_{q,n}\vec{c}_{q,k} + \sum_{l \neq m} \E\left[ \rmat{P}_{q,l}\rmat{V}_{q,l}\prod_{n=1}^{l-1} \bar{\rmat{V}}_{q,n}\vec{c}_{q,k} \middle| S_{q,m}\right] \\
& + \sum_{j \in \set{Q}_k \backslash \{q\}} \sum_{l=1}^M\E\left[ \rmat{P}_{j,l}\rmat{V}_{j,l}\prod_{n=1}^{l-1} \bar{\rmat{V}}_{j,n}\vec{c}_{j,k} \middle| S_{q,m}\right] = \vec{e}_k.
\end{split}
\end{equation}
The first and second term in \eqref{eq:stationarity_stipes} correspond to the contribution of the $q$-th radio stripe, seen by TX $(q,m)$. Using the result in \cite[Th.~5]{miretti2021team} for a single radio stripe, which exploit in its proof the recursive structure of the equations and of the information structure at hand, it can be shown that
\begin{align}
\rmat{V}_{q,m}\prod_{n=1}^{m-1} \bar{\rmat{V}}_{q,n} + \sum_{l \neq m} \E\left[ \rmat{P}_{q,l}\rmat{V}_{q,l}\prod_{n=1}^{l-1} \bar{\rmat{V}}_{q,n} \middle| S_{q,m}\right] = \vec{I}_K,
\end{align}
which simplifies \eqref{eq:stationarity_stipes} to
\begin{equation}
\vec{c}_{q,k} + \sum_{j \in \set{Q}_k \backslash \{q\}} \sum_{l=1}^M\E\left[ \rmat{P}_{j,l}\rmat{V}_{j,l}\prod_{n=1}^{l-1} \bar{\rmat{V}}_{j,n}\vec{c}_{j,k} \middle| S_{q,m}\right] = \vec{e}_k.
\end{equation}
The second term in the above equation corresponds to the contributions of the other radio stripes $j \neq q$. Since $S_{q,m}$ contains no information about the channels at the other radio stripes $j\neq q$,  the optimality conditions can be further simplified to
\begin{equation}
\vec{c}_{q,k} + \sum_{j \in \set{Q}_k \backslash \{q\}} \E\left[ \sum_{l=1}^M\rmat{P}_{j,l}\rmat{V}_{j,l}\prod_{n=1}^{l-1} \bar{\rmat{V}}_{j,n} \right]\vec{c}_{j,k} = \vec{e}_k.
\end{equation}
Following again the same approach as in \cite[Th.~5]{miretti2021team} for a single radio stripe, it can be shown via recursive arguments that
\begin{align}
&\E\left[\sum_{l=1}^M \rmat{P}_{j,l}\rmat{V}_{j,l}\prod_{n=1}^{l-1} \bar{\rmat{V}}_{j,n} \right] \\
&= \E\left[ \rmat{P}_{j,1}\rmat{V}_{j,1} \right] + \E\left[\sum_{l=2}^M \rmat{P}_{j,l}\rmat{V}_{j,l}\prod_{n=2}^{l-1} \bar{\rmat{V}}_{j,n} \right]\E\left[\bar{\rmat{V}}_{j,1} \right]\\
&= \vec{\Pi}_{j,0}.
\end{align}
The proof is concluded by showing that the resulting system of equations $\vec{c}_{q,k} + \sum_{j \in \set{Q}_k \backslash \{q\}}\vec{\Pi}_{j,0} \vec{c}_{j,k} = \vec{e}_k$, $\forall q \in \set{Q}_k$, always has a unique solution. This can be done by following the same lines as in the proof of \cite[Th.~4]{miretti2021team}.
\end{proof}
Interestingly, \eqref{eq:TMMSE_stripes} can be implemented through a recursive procedure from the $q$-th master unit to TX $(q,M)$ involving the sequential update and forward of a $K$-dimensional complex vector $\rvec{u}^{(q,m)} = \bar{\rmat{V}}_{q,m}\rvec{u}^{(q,m-1)}$, where $\rvec{u}^{(q,0)}:= \sum_{k\in \set Q_k} \vec{c}_{q,k}U_k$ is a vector of statistically precoded messages computed at the $q$-th master unit using $\{\vec{\Pi}_{q,0}\}_{q\in \set{Q}_k}$ for all the RXs $k$ that it is serving. Furthermore, to compute $\bar{\rmat{V}}_{q,m}$, each TX $(q,m)$ needs only the local estimate $\hat{\rmat{H}}_{q,m}$ and $\vec{\Pi}_{q,m}$. The required statistical information can be easily tracked through another recursive procedure involving the sequential update and forward of $\vec{\Pi}_{q,m} \in \stdset{C}^{K\times K}$, in the reverse direction. This leads to a very efficient implementation which requires only some local information exchange scaling with the number of RXs $K$.

The bidirectional CSIT sharing case can be readily obtained from the proof of Theorem~\ref{th:unidirectional} by omitting the expectation in the summands over $l\neq m$, since $S_{q,m}$ makes these terms deterministic.
\begin{corollary}
The TMMSE precoder applied at the $m$-th TX of the $q$-th radio stripe to the message for RX $k$ under bidirectional CSIT sharing is given by \eqref{eq:TMMSE_stripes}, with $\vec{\Pi}_{q,m}$ replaced by $\bar{\rvec{P}}_{q,m} := \rmat{P}_{q,m+1}\rmat{V}_{q,m+1} + \bar{\rvec{P}}_{q,m+1}\bar{\rmat{V}}_{q,m+1}$ in the computation of $\rvec{V}_{q,m}$.
\end{corollary}
Similarly to \eqref{eq:TMMSE_stripes}, the above scheme can be also implemented using a recursive procedure. The main difference is that, in contrast to $\vec{\Pi}_{q,m}$, $\bar{\rvec{P}}_{q,m}$ needs to be computed for every channel realization. Note that all $\vec{\Pi}_{q,0}$ still need to be acquired for the computation of the statistical precoders $\vec{c}_{q,k}$.

We finally consider the no CSIT sharing case. This case is better covered by remapping $\set{Q}\times \set{M}$ to the original index set $\set{L}$, and defining the sets $\set{L}_k$ from $\set{Q}_k\times \set{M}$ accordingly.
\begin{theorem}
The TMMSE precoder applied at the $l$-th TX to the message for RX $k$ under no CSIT sharing $S_l = \hat{\rmat{H}}_{l}$ is given by
\begin{equation}\label{eq:TMMSE_local}
\rvec{t}_{l,k}(S_l) = \rmat{T}_l\vec{c}_{l,k}, \quad \forall l \in \set{L},
\end{equation}
where we define $\vec{\Pi}_l := \E\left[\vec{W}^{\frac{1}{2}}\hat{\rmat{H}}_l\rmat{T}_l\right] $ and let $\{\vec{c}_{l,k}\}_{l=1}^L$ be the unique solution of the linear system of equations
\begin{equation}
\begin{cases}\vec{c}_{l,k} + \sum_{j \in \set{L}_k \backslash \{l\}}\vec{\Pi}_j \vec{c}_{j,k} = \vec{e}_k & \forall l \in \set{L}_k, \\
\vec{c}_{l,k} = \vec{0}_{K\times 1} & \text{otherwise.}
\end{cases}
\end{equation}
\end{theorem}
\begin{proof}
The proof follows by verifying that \eqref{eq:TMMSE_local} satisfies the optimality coditions \eqref{eq:stationary_imperfect}. The details are similar to the full message sharing case given by \cite[Th.~4]{miretti2021team}, hence they are omitted.
\end{proof}
As for \cite[Th.~4]{miretti2021team}, it can be seen that under certain conditions typically modeling non line-of-sight (NLoS) channels and no pilot contamination, \eqref{eq:TMMSE_local} coincides with the known \textit{local} MMSE solution $\rvec{t}_{l,k}(S_l) = c_{l,k}\rmat{T}_l\vec{e}_k$ with optimized \textit{large-scale fading} coefficients $c_{l,k}$ given, e.g., in \cite{demir2021foundations}. However, \eqref{eq:TMMSE_local} outperforms local MMSE precoding in the general case. Note that \eqref{eq:TMMSE_local} can also be used to derive an equivalent scheme for bidirectional CSIT sharing, by simply interpreting all the TXs of stripe $q$ as a single TX with $NM$ antennas, and assume no CSIT sharing. However, this interpretation does not easily lead to a recursive implementation, and it is more suitable for a setup where each master unit is responsible for the computation of all the precoders for its stripe, instead of distributing the task.

\begin{figure*}[!ht]
\centerline{
\subfloat[]{\includegraphics[trim=0.5cm 0 0.5cm 1.2cm, clip, width = 0.45\linewidth]{comparison_info_100mW_kappa6_Ic2} \label{fig_first_case}}
\hfil
\subfloat[]{\includegraphics[trim=0.5cm 0 0.5cm 1.2cm, clip, width = 0.45\linewidth]{comparison_info_1W_kappa6_Ic2} \label{fig_second_case}}}
\caption{CDF of the rate achieved by TMMSE precoding under different CSIT sharing patterns, and by assuming a symmetric per-TX power constraint (a) $P_l = 1$ mW, and (b) $P_l = 10$ mW, $\forall l \in \set{L}$. As expected, sharing CSIT leads to performance gains, and the unidirectional case strikes an interesting compromise between the considered examples. Furthermore, the sum-power upper bound is approached as the system becomes interference limited, e.g., for lower interference suppression capabilities and/or higher power budget. Finally, the local MMSE baseline is outperformed by the competing TMMSE solution under no CSIT sharing, due to the presence of LoS components ($\kappa = 6$).} \label{fig:sim}
\end{figure*}

\subsection{Numerical simulations}
We let each channel coefficient $H_{l,k}$ between TX~$l$ and RX~$k$ be independently distributed as $H_{l,k} \sim \CN\left(\sqrt{\frac{\kappa}{\kappa+1}\rho^2_{l,k}}, \frac{1}{\kappa+1}\rho^2_{l,k}\right)$, where $\kappa$ denotes a common Ricean factor, and $\rho^2_{l,k}$ denotes the channel gain between TX $l$ and RX $k$. We follow the 3GPP NLoS-DH path-loss model for IIoT applications \cite{jiang2021iiot}
\begin{equation}
\mathrm{PL}_{l,k} = 21.9 \log_{10}\left(\dfrac{d_{l,k}}{1 \; \mathrm{m}}\right) + 33.6 + 20\log_{10}\left(\dfrac{f_c}{1 \; \mathrm{GHz}}\right) + Z_{l,k} \; [\text{dB}],
\end{equation}
where $f_c = 4.9$ GHz is the carrier frequency, $d_{l,k}$ is the distance between TX $l$ and RX $k$ including a difference in height of $7$ m, and $Z_{l,k}\sim \CN(0,\sigma^2)$ is an independent shadow fading term with standard deviation $\sigma = 4$. We let the noise power at all RXs be given by
$
P_{\mathrm{noise}} = -174 + 10 \log_{10}(B) + F$ dBm,
where $B = 100$ MHz is the system bandwidth, and $F = 7$ dB is the noise figure. Finally, we let $\rho^2_{l,k} := 10^{-\frac{\mathrm{PL}_{l,k} +P_{\mathrm{noise}}}{10}}$ $\text{mW}^{-1}$, and $\kappa = 6$.

Fig.~\ref{fig:sim} reports the empirical cumulative density function (CDF) of the rates \eqref{eq:hardening_bound} achieved by TMMSE precoding under the considered CSIT sharing patterns, for $100$ realizations of the RX positions. Each RX position is independently and uniformly drawn within the considered service area. We study both the sum-power upper bound and the suboptimal adaptation \eqref{eq:power_scaling} to a per-TX power constraint. We focus on the boundary point of $\set{R}_{\mathrm{sum}}(P)$ given by $\vec{w} = \vec{1}/K$. For the sum-power constraint, the DL power allocation $\vec{p}$ is obtained using the UL-DL principle \cite{massivemimobook}, by interpreting $\vec{w}$ as  dual UL powers. For the per-TX power constraint, $\vec{p}$ is further scaled by $\nu^2$. As a baseline, we also report the performance of local MMSE precoding with optimized large-scale fading coefficients \cite{demir2021foundations}.

The first remarkable observation is that, while having roughly the same information sharing overhead on the order of $K$ complex symbols per channel use and stripe span, the TMMSE solution under unidirectional CSIT sharing significantly improves upon the no CSIT sharing case. Therefore, it can be seen as a promising intermediate solution between no CSIT sharing and bidirectional CSIT sharing. However, this comes at the expense of additional computational complexity at each TX to implement the recursive routine.

A second observation is that, as expected, the approach of scaling the TMMSE solution to satisfy the per-TX power constraint is basically optimal whenever the dominant performance limit is the residual interference. This is evident for the schemes with lower interference suppression capabilities, and/or for higher power budgets. However, the gap w.r.t. the sum-power upper bound increases for low powers and for the better performing information structures. In this case, further research is needed to understand whether this gap is close to the fundamental limit or only an artifact of the suboptimal approach.

Finally, we observe that the baseline local MMSE method is not optimal under no CSIT sharing. This is motivated by the fact that, similarly to other local methods such as MRT, local MMSE does not handle well the interference originating from the channel mean.

\bibliographystyle{IEEEbib}

redpajama_set_name: RedPajamaArXiv


Judas is about a man whose name is synonymous with betrayal; a man who has been universally vilified for centuries. But without this man and without his Judas' kiss, Christianity would never have become one of the great religions in the world. Every age has speculated about Judas and his motives. After two thousand years it is about time for Judas to have his own say: He stages a last effort to reduce his act to a human level and to take the audience where they rather would not be: to the Judas in themselves. – Steven Scharf was voted "Actor of the Year" for this role in 2013.
Steven Scharf gives the apostle a gruff, straightforward diction with which he makes it clear that it was he who took all the blame for the betrayal. Scharf is a Judas of impressive clarity. In the artistic underexposure of the room he is a man of pain as if painted on the Iron Curtain. At the end of the German premiere, there was long applause for an extraordinary piece of acting.
Johan Simons has transformed the lucid text into a strong scenic form without any naturalistic gesture. But above all, he has a great actor. Steven Scharf's aura does not blow up the scenic corset, but it towers above it. It is an exciting evening and the evening of a formidable actor, who is rightly showered with applause.
An act of violence, both physically and mentally, for Steven Scharf, who only has to keep the tension through his voice. It is full and space-filling, but without pathos, although it always sounds as if he is about to burst into tears. (...) After the hour-long performance there is intense applause from a deeply moved audience.


text:
One final Belk Bowl before new sponsor steps in
The retail chain ended its affiliation with its hometown bowl, but the Charlotte Sports Foundation said the game will live on with a new corporate backer
December 4, 2019 Brett Friedlander Article, College Football, Sports
The Belk Bowl — which began in Charlotte in 2011, replacing the Meineke Car Care Bowl — will be played for the final time this year, leaving the Charlotte Sports Foundation searching for a new title sponsor. (Chuck Burton / AP Photo)
The relationship between Charlotte and Belk dates back to 1909 when William Henry Belk and his brother John moved first their department store from nearby Monroe to the Queen City.
But the two entities have slowly drifted apart since the Belk brothers' great-grandchildren sold the company to a New York-based private equity group for $3 billion in 2015.
While Belk's headquarters remain in Charlotte, the company's bond with the city has diminished since the sale. Last week, Belk made another break by announcing plans to discontinue its sponsorship of the college football bowl that bears its name.
This year's game, scheduled for New Year's Eve, will be the last one known as the Belk Bowl. It won't be the last postseason event the Charlotte Sports Foundation puts on at Bank of America Stadium, though.
With a new six-year deal with the ACC, SEC and Big Ten signed last summer and a lucrative television contract with ESPN already in place, the bowl will live on with a new title sponsor executive director Danny Morrison is confident will be secured soon.
"With the expansion of our ties to the strongest conferences in college football, the future of our bowl has never looked brighter," Morrison said "Dating back to 2002, the Charlotte bowl game has historically been in the top tier of all bowls from an attendance and ratings standpoint and we are excited about working with a new title sponsor as we continue to elevate the game on the field and the fan experience surrounding the event."
This isn't the first time the Charlotte bowl has changed title sponsors.
Originally certified as the Queen City Bowl in 2002, it was played as the Continental Tire Bowl for its first three years before becoming the Meineke Car Care Bowl in 2004. Belk signed on six years later and helped the game become one of the most popular on the college football postseason schedule beyond the New Year's Six bowls.
In addition to the obligatory banquets and hospital visits, the bowl has treated its participants to such unique experiences as a NASCAR ride-along at Charlotte Motor Speedway and a $400 shopping spree for each player at Belk's flagship store in Charlotte's South Park Mall.
"Belk has been an exceptional partner since signing on to sponsor the first Belk Bowl in 2011," Morrison said. "This bowl has become a great Charlotte sports tradition that has a significant economic impact on the Charlotte region, and we could not have achieved the success we have enjoyed without Belk's commitment and the support of our other community partners."
According to the Sports Business Journal, Belk paid $400,000 for the rights to sponsor the Charlotte game.
Belk CEO Lisa Harper, in a prepared statement, called the Charlotte Sports Foundation a "first-class organization" and said her company "is proud to have been part of (the bowl's) tradition."
While the bowl is ending one partnership, another remains strong. ACC spokesperson Amy Yakola said the conference is firmly committed to continuing its relationship with not only Charlotte's postseason game but also the Sports Foundation's opening week kickoff event in September that is also included in the title sponsorship package.
Next year's Charlotte Kickoff game will match Wake Forest against Notre Dame. Teams for the final Belk Bowl later this month will be announced on Sunday.
"The Charlotte-ACC relationship is a long one. It's stronger now than it's ever been," ACC commissioner John Swofford said at the league's preseason football media event last July. "It's interesting, with the growth of our league, as it's expanded, Charlotte has remained sort of the epicenter of the footprint."
Bank of America Stadium
Belk Bowl
Charlotte Sports Foundation
John Swofford
Wake Forest Football
Unbeaten Lenoir-Rhyne reaches final eight of Division II football tournament
App State eyes Sun Belt title, Drinkwitz's coaching future
Five questions to ponder before kickoff
September 9, 2017 Brett Friedlander College Football, Sports
For all the anticipation and buildup, the opening week of the college football season in North Carolina sure turned out to be a letdown. With the exception of Duke and Wake Forest, which put up […]
Trent Jr. has best game on slow day at Vegas Summer League
July 13, 2018 Brett Friedlander Article
Thursday was a slow day for players with North Carolina ties at the NBA's Las Vegas Summer League. Although the tournament is in its playoff phase, many of the 30 teams involved have seen all […]
ACC announces early-season football kickoff times
May 18, 2018 Brett Friedlander Article
North Carolina's ACC football teams will get off an an early start this fall, both in the dates of their season openers and the starting times for their games over the first three weeks, according […]
Chief Justice John Roberts sworn in to preside over impeachment trial
RALEIGH — The United States Senate was in session today as articles of impeachment against President Donald J. Trump were delivered from the House of Representatives. On Wednesday, the House voted to send two articles [...]

redpajama_set_name: RedPajamaCommonCrawl


Like most writers, I've always got some tunes going in the background as I write and work on IN MAPS & LEGENDS.
So I thought I'd share some of the tunes that have inspired me, including some key lyrics that leaped out at me (and in some cases inspired me to even greater weirdness).
"Bodysnatchers," Radiohead — this song is solely responsible for the creation of those weird rat-squirrels at Bartamus' feet on pages 4-8 and 11.
Thanks for listening, and for reading, too!


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There are three aspects of a successful professional negligence claim which consist of proving that you were owed a duty of care, that this duty of care was breached and that you have directly lost out as a result as well as that the services provided to you fell below the standards expected of a competent professional.
If you feel that you have a valid case, call us today to appoint professional negligence solicitors in Ely and Crewe who will work on your behalf to ensure that you receive the compensation you are entitled to. Alternatively, you can visit us at our Crewe or Ely offices to discuss your case in person.
Get the professional negligence compensation you deserve with Bentley Solicitors. Call 01270 509800 or 01353 865333.


text:
package org.terasology.input;

public final class ControllerId {

    public static final int NONE = -1;

    public static final int ZERO = 0;
    public static final int ONE = 1;
    public static final int TWO = 2;
    public static final int THREE = 3;
    public static final int FOUR = 4;
    public static final int FIVE = 5;
    public static final int SIX = 6;
    public static final int SEVEN = 7;
    public static final int EIGHT = 8;
    public static final int NINE = 9;
    public static final int TEN = 10;
    public static final int ELEVEN = 11;

    public static final int X_AXIS = 100;
    public static final int Y_AXIS = 200;
    public static final int Z_AXIS = 300;

    public static final int RX_AXIS = 500;
    public static final int RY_AXIS = 600;

    public static final int POVX_AXIS = 800;
    public static final int POVY_AXIS = 900;

    private ControllerId() {
    }
}

redpajama_set_name: RedPajamaGithub


Every day is a new chance to have new business opportunities and ideas, because of globalization and the continuous improvement of technology, it has now become easier for people to do businesses.
Even if your customers are halfway across the world you can make a transaction with them.
What you need to get started? Is just a right inspiration and some ideas to lead you? So, here are 17 best business ideas you can start right now.
These days' people are so busy that they do not have time to go shopping they need in their lives, right from grocery shopping to gift buying or anything.
People are mostly depended on personal shopping industry and it is really taking over traditional marketing.
You can offer your buyer to buy your products and deliver by yourself or you can work remotely and give information and links that your clients might be interested and your clients will pay for the convenience as they do not have to do the research by themselves.
Becoming a consultant is a wonderful business to get started because it does not require any capital to start.
What you have to do is, if you have knowledge about anything no matter what your background is and if your knowledge is useful for others then you can start a consulting business and people are going to pay for your service.
You can also build a website for free in Google BlogSpot.
Many people these days are facing many types of problems and issues, the problems faced by the people might be successful or unsuccessful but they want their problems and issues to be solved.
They may be going through marriage issues or may be struggling for self-esteem and many of these people want help.
If you have the skill to listen and solve their problems and issues and give them practical pieces of advice and ideas, you can start a life coaching business or service, like starofservice.com.
Large business owners of all types are now investing in art industries. The art industry is increasing and is now becoming the more profitable investment for businesses.
But if you start an art business you have to be passion for art and understand the art. You can also try to become a local arts and crafts vendor and support your clients and also launch a website on your art dealer service.
You may take examples like Kamel Mennour, Thaddaeus Ropac, they have started up going door-to-door, but now they are one of the world's best art dealers.
Now a day's social media has become the greatest platform for advertising business products and services and get traffic to your site which then ultimately turns them into customers.
So, if you are good at social media like Facebook, Twitter, etc. you can start becoming a social media consultant and help business owners by promoting their products and services on social media sites.
Every person does not have time to prepare and organize for parties or event. If you have qualities and skills to organize the meeting or social gathering and arranged on behalf of your client's then event planning service is a great ideal business for you.
Event planning business is best suitable for women as they are natural organizer and planner and can perform the job easily. You can even start your website for free by using Google BlogSpot where you do not even have to pay a penny.
Laundry services if another ideal home based business you can start right off. People these days do not have time for washing their clothes on weekends because they do not want to ruin their weekends by washing clothes.
Starting laundry service is on the top of any business to get started with low capital and does not require much knowledge, you only need to purchase necessary equipment and get going.
Network marketing is also known as MLM or multi-level marketing. Network marketing is increasing with the craze on the internet or the digital marketing trends. You can get going new marketing formulas with passion.
Almost every computer is linked with an internet connection. The computer technology has increased so much this days that there are hundreds of students taking up computer courses.
But for some students, the complex subjects are not understandable. If you can master on operating systems and have pretty good knowledge in programming languages, then you can become an online tutor and earn some bucks.
If you are an internet savvy, then you can become a virtual assistant for online clients. You just have to complete some easy task of replying to your client's emails, writing some marketing messages or such similar works and you can earn $5 to $150 or much.
You can find virtual assistance jobs at upwork.com, virtualassistancejobs.com.
If you are excited to take photos of your friends and families during any get-together or during a picnic.
Then why not turn this excitement into some profitable business. You can start exposing your skills by voluntarily going to various weddings and parties or in some corporate events where people will notice you.
You can even sell your photographs or videos online like in vimeo.com, contributor.freepik.com, and shutterstock.com.
Building website and these days have become quite easy as just drinking a glass of water. All you need is a desktop or a laptop and a place to sit.
But if you want to really give service for building a website and making it your business then you have to have some knowledge and skills of web development.
You can sell your products online by buying some items form wholesales and then selling them online like jewelry, accessories, clothing material or any products that you can get at a cheaper rate and be able to earn some profit.


text:
<?php

namespace Symfony\Component\Locale\Stub\DateFormat;

@trigger_error('The '.__NAMESPACE__.'\SecondTransformer class is deprecated since Symfony 2.3 and will be removed in 3.0. Use the Symfony\Component\Intl\DateFormatter\DateFormat\SecondTransformer class instead.', E_USER_DEPRECATED);

use Symfony\Component\Intl\DateFormatter\DateFormat\SecondTransformer as BaseSecondTransformer;

/**
 * Alias of {@link \Symfony\Component\Intl\DateFormatter\DateFormat\SecondTransformer}.
 *
 * @author Bernhard Schussek <bschussek@gmail.com>
 *
 * @deprecated since version 2.3, to be removed in 3.0.
 *             Use {@link \Symfony\Component\Intl\DateFormatter\DateFormat\SecondTransformer}
 *             instead.
 */
class SecondTransformer extends BaseSecondTransformer
{
}


Provide comfort for the family of Valerie Terrance with a meaningful gesture of sympathy.
AKWESASNE – "Kanonsisakhe" Valerie Francis Terrance, Mohawk Nation – Snipe Clan, 67, entered back into the Spirit World on her journey to the Creator on Saturday, February 2, 2019 at Ottawa Civic Hospital.
Kanonsisakhe was the daughter of Mary Herne Francis and the late Michael H. Francis; loving wife of Robert Phillip Terrance; mother of Jarrad (Wendy), Brooke (Mike), Lenard (Charlene); and stepmother to Cindy (Lyle Lazore). She was the grandmother of Trevor, Edwin, Mercedes, Brodie, Krysten, Tevin, Tye, Kahentase, Kawisahawi, Nolan, Mitchell, Lenni, Lyric, Lenard Jr. "Rawi", Lantana, and Lotus and great grandmother to Treyton, Taniyah, Kaiden, Kamery, Hendrix, and Barrett.
She was also a loving sister to, Mike Francis Jr. (Ann), Robin Barnes (Jim), Thomas Francis (Marilyn), Joseph Francis (Lorna), John Francis (Carolyn), Dave Francis, James T. Francis (Corleen), LeeAnn Jock (Steve), Cindy Francis Mitchell (Keith), Kathy Francis-Roundpoint (Frank), and the late Donna Hopps (Jake); as well as an aunt to many nieces and nephews.
Friends may call at the Donaldson Funeral Home, Massena on Wednesday from 2-4 and 7-9 PM and Thursday from 8-9:30 AM. Her funeral ceremony will be held Thursday 11:00 AM at the Mohawk Nation Longhouse, with cremation to follow.
At her request, please omit flowers, those wishing may bring a basket in her honor.
To send flowers in memory of Valerie L. "Kanonsisakhe" Terrance (Francis), please visit our Heartfelt Sympathies Store.
We encourage you to share your most beloved memories of Valerie here, so that the family and other loved ones can always see it. You can upload cherished photographs, or share your favorite stories, and can even comment on those shared by others.
Mike and Ruth Devine sent flowers to the family of Valerie L. "Kanonsisakhe" Terrance (Francis).
My Condolences to the Terrance Family. Val was a great Lady who I had the pleasure of knowing for many years. She taught me patience and alot about the culture. Val spoke with high regard about her family. We spent a lot of time together countless lunch breaks. We even went to the Casino and that was fun! Many laughs shared. Val was one special Lady.
My heartfelt condolences to Val's entire family. I worked with Val at Scotiabank for years. She was a nice lady. She will be missed.


text:
La Portorriqueña és una botiga de Barcelona del barri de Raval dedicada a la torrefacció de café i fundada el 1902.

Es va obrir com a petit establiment de queviures situat al carrer del Bonsuccés, al costat de la Rambla, per l'indià Miquel Ferrer i la seva dona Graciales, nascuda a Puerto Rico. El 1908 les seves especialitats eren el sucre, la xocolata La Arabia-Chocolates de la Trapa i el cafè portat de les plantacions de San Felipe i Limón, situades a Ciales, Puerto Rico, propietat d'en Miquel Ferrer. El 1920, La Portorriqueña va obrir una sucursal al carrer Xuclà. Fins a mitjans d'aquella dècada van coexistir les dues botigues, tot i que finalment només va sobreviure la del carrer Xuclà.

Amb la jubilació de Graciales es va fer càrrec de la botiga un empleat seu, Eloy Álvarez, que va deixar la venda de queviures i es va concentrar en el cafè que es torrava cada dia entre les onze del matí i la una del migdia. Després el negoci va passar a mans del seu fill, Jordi Álvarez. El 2006 va passar a la seva viuda, Carme Rigata, fins al 2019 quan va ser comprat per la família Sans, fundadors dels cafès El Magnífico.

Referències

Comerços de Barcelona
Cafè

redpajama_set_name: RedPajamaWikipedia


text:
DOLE PUSHES BILL TO MOVE EMBASSY TO JERUSALEM
New York Times News ServiceCHICAGO TRIBUNE
Sen. Bob Dole on Friday reintroduced a bill to move the U.S. Embassy in Israel from Tel Aviv to Jerusalem by May 1999 but he dropped his earlier provision that groundbreaking should begin in 1996.
The Clinton administration said Friday night it still opposed the proposal.
"Any efforts to try to legislate the Jerusalem issue now risk doing very serious damage to the process of implementing the Israeli-Palestinian peace agreement," said Nicholas Burns, a State Department spokesman.


Back in 2013, two weeks into a federal government shutdown that would eventually last 16 days, MeetingsNet published "5 Ways the Government Shutdown Hurts Meetings." Today, the article is as true as it was then, but now, three and a half weeks into the longest government shutdown in history, there's more to the story.
Meeting professionals who plan events with a large contingent of government workers are seeing a major drop in attendance. For example, the American Astronomical Society held its 233rd meeting January 6-10 in Seattle and had to make accommodations for hundreds of furloughed workers who couldn't attend. Similarly, earlier this month, 500 attendees missed the American Institute of Aeronautics and Astronautics' SciTech Forum and Exposition in San Diego, and 700 couldn't attend the American Meteorological Society conference in Phoenix.
Similarly, government speakers have been forced to cancel their appearances during the shutdown. For example, according to reports, at least 11 speakers canceled on last week's CES tech expo, including Federal Communications Commission Chairman Ajit Pai and Transportation Secretary Elaine Chao.
The Department of Homeland Security canceled its 2019 Cybersecurity and Innovation Showcase expecting about 1,000 participants at the Washington Marriott Wardman Park January 8-10. At the University of Montana, a three-day conference for fire researchers at the end of January has been canceled because participants from Forest Service, National Park Service, and Bureau of Land Management cannot attend because of the shutdown.
Consider the progress that has been slowed and the critical ideas that have not been shared around cybersecurity, fire safety, astronomy, and many more topics as federal workers miss critical events.
TSA staff shortages as a result of unpaid worker "call outs" have resulted in airport delays and terminal closures at some airports around the country. At Houston Bush Intercontinental, for example, the ticketing counter and security checkpoints at Terminal B, home to United Airlines, were closed over the weekend and remained closed Monday. Atlanta's Hartsfield-Jackson International Airport advised passengers on Monday to leave three hours to clear security.
With TSA workers expected on the job without pay, one Florida airport is taking steps to alleviate some of the hardship. On Monday, Tampa International Airport teamed up with Feeding Tampa Bay and United Way Suncoast to set up a food bank to provide food and toiletries to the security professionals in an effort to make their life easier during the shutdown.
Groups with special events planned at federally owned venues have had to make alternative plans since the institutions closed their doors in early January. From the Smithsonian's elegant banquet rooms in the National Portrait Gallery to the 20,000 square feet of event space at the U.S. Institute for Peace, government venues are a no-go until the government reopens.
Meeting organizers can't communicate with attendees who are furloughed if their primary way to keep in touch is their work e-mail. That hurts an organization's ability to publicize upcoming meetings, and to be a resource for them in their profession. In this situation, communicating through social media is critical, but not as direct.
During the government shutdown, the Food and Drug Administration is inspecting about a third of the products they normally would. While there have been no ill effects seen from the drop off in monitoring, high-profile food safety alerts, like the January 2019 E. coli infections linked to romaine lettuce in northern and central California, remind meeting professionals what can go wrong.


Choosing white on your rest room is always the safest option. It looks clean and refined within any sort of loo. You will get that fresh feeling each time you're looking at a white rest room. There are people, nonetheless, who find white a boring colour. Sustaining a white toilet also poses a problem to a lot of people. Stains can be harder to remove when the surface is white. Even products that don't usually stain can already leave a big mark on this mild surface. So as to avoid making the room look boring, it's a must to use brightly coloured equipment and loo fixtures.
Today, drugs cupboards are extremely useful products – yes, they now have fog-proof mirrors – which might be as a lot an announcement about the rest room as are vanities or bathtubs. Gone are the days when the only derivation from the everyday metal drugs cabinet was one with three plain doorways wrapped in chrome trim as an alternative of 1. In truth, medicine cabinets mirror, and sometimes even decide, the type of the bathroom as a lot as any furniture or artwork may.
Having a superb seal, often alongside magnetic strips on the inner wall of shower door is a major necessity for retaining the water inside. Another main benefit of bathe seals is that it makes the enclosure a lot more pleasing, especially in an aesthetic method. Strong metal door handles and fixtures are approach better than fancy, chrome platted plastic made fixtures. Plastic chrome fixtures may look fancy, however give an inexpensive look upon contact, and now have a small life.
Although septic tanks are comparatively low-maintenance, solids that are not digested by the anaerobic micro organism (sludge) accumulate and should be removed to prevent expensive problems. If the tank goes over it's optimum capacity, uncooked sewage waste can end up in the leach subject. Overflow can rapidly and easily clog the drainage piping. There can also be an issue with the filtration of the sludge as the process is significantly slowed.


text:
Windows Mobile smartphone sales plunge 20% in Q3
Decline occurs despite overall smartphone growth
By Matt Hamblen
Senior Editor, Computerworld |
Sales of smartphones running the Window Mobile operating system declined by 20% in the the third quarter at the same time that smartphone sales with all operating systems surged 13%, according to an analysis of newly released sales data from Gartner Inc.
The fact that Windows Mobile sales declined may not be a surprise, but the size of the decline is. The third quarter ended before an upgraded operating system, Windows Mobile 6.5, began shipping in October, too late to have an effect on sales figures.
But even sales of version 6.5 look lackluster.
Gartner analyst Carolina Milanesi, asked by e-mail today if Windows Mobile will get a boost in the fourth quarter from the new Windows Mobile 6.5, responded: "No, not really ... you might see enough traction that might stabilize the decline."
Microsoft CEO Steve Ballmer criticized Windows Mobile in late September, saying that Microsoft had "screwed up with Windows Mobile." The company had recently reorganized the Windows Mobile team in advance of the 6.5 release and next year's 7.0 release.
Several industry analysts have questioned whether Windows Mobile will last beyond version 7.0.
They have explained their pessimism by noting that the operating system has been in the market far longer than the popular Apple Inc. iPhone but is still fourth in global rankings for smartphones. Some say that Microsoft might want to focus more on its Office applications as a money maker, rather than Windows Mobile.
Windows Mobile runs on dozens of different cell phones and smartphones by several device manufacturers. Only 3.2 million smartphone units running the OS were sold in the third quarter, Gartner said, down 20% from the 4.05 million phones sold in the third quarter of 2008.
As such, Windows Mobile had 7.9% of the total smartphone OS market in the third quarter, out of a total of 41 million smartphones sold to end users, Gartner said. Symbian, the OS used by Nokia devices, finished first with 44.6%, while Research in Motion's BlackBerry OS finished second with 20.8%, and the iPhone finished third with 17.1%.
Phones running Google's Android operating system began appearing on only a few smartphone models, including the G1, by the third quarter and sold 1.4 million devices, giving it a 3.5% share, Gartner said.
Android is expected to gain steady ground in the fourth quarter and speed up in 2010 with several manufacturers offering dozens of different models. The Motorola Droid, which launched last Friday with Verizon Wireless, runs Android 2.0.
Gartner in September forecast that by 2012, Android will have 18% of the smartphone market with 94 million units sold, zipping upward into the second spot behind Symbian, with BlackBerry in third, the iPhone in fourth and Windows Mobile ranking fifth.
Gartner explained the phenomenal gains its expects for Android as stemming from the influence of Google applications and services and the open nature of Android. Some other analysts, including those at ABI Research Inc., have significantly lower forecasts for Android in 2012 than Gartner, although they still see strong Android growth.
Gartner's Milanesi noted that while Android is an open OS, it will be far from uniform on all devices, even though the Android OS share data will be reported by Gartner together as the data for Windows Mobile is. Manufacturers want to differentiate themselves within the Android platform, sometimes with software services and layers, she said.
For example, HTC has launched its "Sense" user interface with Android while Motorola has announced Motoblur, its Web-based service, on the Cliq device using Android. Meanwhile, Motorola's Droid smartphone, which runs Android, does not include Motoblur, even though some analysts and reviewers said it should, to make managing contact information easier.
Matt Hamblen is a multi-media journalist covering mobile, networking and smart city tech. He previously was a senior editor at Computerworld.


Perhaps the relative truth is that there are too many immature game board tossers in general, who also perhaps play very well and keep the site busy. likely, some of them also purchase slots and piece decorations and generate such profit. Resolution issues such as these usually boil down to profit over customer service anyway, not some absurd sleeping better at night excuse which defaults to the perpetrator, not the victim and says alot about where the truth of the matter may actually lie. Perhaps some moderators/staff/abusers/friends of all these people enjoy the occasional disconnect while using the site under anon names where elo isn't of concern-as stated here already by others. if you are not a poor sport, you will simply need exercise a little more of that exceptional grace and patience to allow for various child-like a-holes of the world to come and participate along with you because some of them are actually in charge of decisions sometimes. many great solutions have already been suggested so why not employ them? the answer seems obvious.
Those decision makers are likely thinking, You cant please everyone all the time anyway, so why bother?
He means that he registered for QB's tourney, not that he is QB.
Thanks, guys! You know, without a context, I didn't think roeczak was responding to my post, but I believe that both of you are correct. I was looking at RGillis' post about Hammer04...I'd forgotten about 84CA. roeczak is absolutely correct! I checked my records and lo and behold, 84CA had registered, and then left the queenbee high and dry. Not to worry...anyone who participated in the Queenbee Invitational knows that it was a smash hit.
WonderAboutWomen. https://imgur.com/a/ciMgDkb. Player starts game by attacking me for being a disconnecting loser and a time waster during set up. Accuses me of being player 12. Who they just played and were annoyed by their actions. I explain I am not 12 and to just ask nicely if you want me to start game and not accusing me of false information and incorrect facts. We play game, I beat them, and wham disconnect! What a hypocrite!! I thought Canadians were nicer than this...LOL sore loser.
Just got done with a match against WAW. They won I did mention this post and player admitted to doing disconnect on purpose. I buffered out against them as I was in a chat about who was really behind acct. I generally don't worry that much about mult. accts I am to low in rank for such things. I did ask directly if this was Jookiya ? they did not reply then they did accusing me of making things up and being a loser. Last part not that far off but first part player refused to answer yes or no. Another player thought I was suspicious today, they were correct !
Hey brother Ray! I don't think this one is jookiyaya for the simple reason the jooks could easily make gold with a much better ratio and record than WonderAboutWomen, and the one tell-all is missing from chat...he didn't call you or Indiana Knights cheaters!
Yes KMC my BS meter not as well tuned as Unladen Swallows. The player had the time to say no but did not--odd. They did recall Indiana Knights apparently we are just losers not cheaters according to WAW.
UW must have needed to go some where quickly.
Susan DD thanks for posting but could you make this a tad clearer for me. Are you upset with these disconnections or the folks posting or the site owners for not addressing the concerns of players ?
I just played with my account PSYCHOPATH against KingTubby and destroyed him. He couldn't do anything and started doing lotto with majors, general and Marshal. He found only bombs and then i chatted him "only lotto" . Probably he got angry and then like a noob he left all of his time buffer like a child... So in these 5 minutes i was eating my pop corn!
I've recorded little of this to remember it !!
P.S Please learn to lose!!! Its a game!!!
Edited by ☆OVERLORD☆, 07 July 2018 - 04:47 PM.
General Pancho-- needed to leave quickly it was an emergency---they lost the trade off of pieces.
Player 217 I think this is a second or third time. Marshal is just a piece, play it out for a while I say.
Just played Kingtubby and the game was shorter than the 5 minutes I had to wait after I destroyed him. What a noob get him back to bronze or off the site.
Edited by ☆OVERLORD☆, 08 July 2018 - 08:29 PM.
Extremely sore loser this dude. Both times I played him, he took captains/majors with marsh/gen to be taken by my spy/marsh, and immediately started abusing me, and disconnecting about 3 times to run out the 2 minutes.


We live in an age of technology and as such we are always looking for ways to make life easier or ways to make things look better. In the home or office (or even the home office) making things look better involves getting rid of clutter. This is where the wireless desktop comes into play. No wires means less clutter and because when using Bluetooth wireless devices line of sight is not needed, you can use your desk space to its optimum with no worries.
There is more to the wireless desktop than you might think as well. You will all be aware that you can get a wireless keyboard and mouse. But wireless technology and Bluetooth in particular stretches much further than that. Your mobile phone if a recent one will probably have Bluetooth technology built into it. This means that you can easily connect it to your PC. Companies such as Logitech offer software that really gets your mobile phone and your PC working together. Synchronization is just one aspect of this, but how about being able to type an SMS text message on your keyboard and send it without having to touch your phone. This is all possible with the power of Bluetooth. Communication with your mobile phone is not the only method of contact with Bluetooth. You can also get Bluetooth headsets that work with Microsoft Messenger so you can add an easy chat functionality to your desktop. As new products come on the market Bluetooth becomes more and more popular. Peripheral devices such as Printers and Scanners can now be found.
This is the first device that you will probably buy for your wireless desktop. This is the basic starting point and probably the most effective. The keyboard and mouse wires cannot be hidden away from sight as they have to be straight in front of you. plus limiting the mouse wire can mean limiting the mouse movement as well. So A wireless keyboard and mouse will give you a better looking desktop as well as freedom to move your keyboard where you want it. You can have it on your lap or anywhere else in range. Having a wireless mouse will also help in gaming. Most wireless mice are just as responsive as corded ones and your wire wont snag at that vital moment when online gaming.
While printers are not being produced as wireless as yet. The idea is very much being worked on. Currently what you can by for your USB connected printers is a two small connecters that plug into your printer and USB port which connect together like a wireless network. Its almost a wireless USB connection if you like. I doubt that is how it will be described though. The advantages of the wireless printer as well as the lack of wires behind your PC is the range can be increased as well as you being able to place your printer in a place where a USB cable would be unsuitable to travel. A second advantage would be that connecting your printer to a wireless network for sharing will be much easier.
I think the biggest advantage of wireless technology has to be Wireless Networking. While Bluetooth technology is does not have the range in which to be affective at networking computers together. RF technology is still used however and is very easy to setup. For a simple network (peer to peer) on two computers all you need is two wireless networking cards setup to the same channel. More complex networks can also be setup using a server and workstations. Anything you can do with a wired network you can do with wireless technology.
While we keep saying that the main advantage of wireless technology is that you don't have wires lying around everywhere, this is more true than ever when we are talking about wireless networking. When your computers are likely to be located in different room, the last thing you want is for wires to be laid around your home or office being an eyesore. Plus should you wish to move your computer at anytime, you don't have to re-route the wires connecting your network together.
Security on Wireless networks is set by adding a name for your network which all computers on that network must be assigned to connect to, plus then you can add a password to keep unwanted intruders out from your files. Software firewalls are also recommended on wireless connections (as well as wired) just for added security against unwanted virus' or Adware/Spyware.
Wireless headphones are readily available from many manufacturers. These are really one of the most practical uses of wireless technology behind the networking. Wireless headphones allow you to freely listen to your music, game or whatever noise your PC is making anywhere in your room without the restriction of wires. Even if your wires are long enough they will still be a little dangerous stretched across the room. And we all know you like to dance around your room listening to your favourite tracks. A set of wireless headphones could save you a few quid on broken items that your headphone wires have snagged on and brought crashing down to the floor :).
Wireless speakers are poking out of the woodwork and those of you that have a 5.1 or above sound system will just how many wires are involved in that setup. Not only do you have connection to the computer but each speaker is connected to the sub / power box and and you also have the volume control to deal with. At time of writing this the US seem to have a decent supply of wireless speakers where as only a few can be found in the UK. I am very sure that wireless speakers will become a lot more popular in the UK over the next couple of months. Wireless speakers will remove loads of wires from the back of your computer. Using a 5.1 wireless system will allow you to place your speakers in the perfect position without any restrictions or ugly wires running along your walls or floor.


text:
Q: How do I output the number of times a certain button was clicked in the shell in python tkinter? So my gui is fully functional except I would like to be able to keep a counter in the console of how many times each different button was clicked (e.g "the like button was clicked x times" & "the um button was clicked y times"). I've tried unsuccessfully, my problem is that nothing is actually printing in the console. Can someone point out how to properly execute this? Thank you.
from tkinter import *
import tkinter as tk

window = tk.Tk()
window.geometry('900x900')
window.config(bg = 'honeydew2')
window.title('The Speech Filler Counter')

like = 0
def likes():
  global like
  like = like + 1
  likelabel.configure(text=like)

likelabel = tk.Label(window, text = like, bg = 'honeydew2', fg = 'red')
likelabel.place(x = 22, y = 1)

likebutton = tk.Button(window, text="Like", activebackground= 'blue', activeforeground = 'honeydew2', bg = 'deep sky blue', fg = 'red', command=likes).place(x= 2, y = 25)

um = 0
def ums():
  global um
  um = um + 1
  umlabel.configure(text = um)

umlabel = tk.Label(window, text = um, bg = 'honeydew2', fg = 'cyan')
umlabel.place(x = 122, y = 1 )

umbutton = tk.Button(window, text="Um", activebackground= 'brown', activeforeground = 'honeydew2', bg = 'light pink', fg = 'blue', command=ums).place(x= 100, y = 25)

basically = 0
def basicallys():
  global basically
  basically = basically + 1
  baslabel.configure(text = basically)

baslabel = tk.Label(window, text = basically, bg = 'honeydew2', fg = 'deep pink')
baslabel.place(x = 235, y = 1 )

basbutton = tk.Button(window, text="Basically", activebackground= 'red', activeforeground = 'black', bg = 'gold', fg = 'brown', command=basicallys).place(x= 200, y = 25)

uh = 0
def uhs():
  global uh
  uh = uh + 1
  uhlabel.configure(text = uh)

uhlabel = tk.Label(window, text = uh, bg = 'honeydew2', fg = 'lime green')
uhlabel.place(x = 350, y = 1 )

uhbutton = tk.Button(window, text="Uh", activebackground= 'purple2', activeforeground = 'goldenrod1', bg = 'firebrick1', fg = 'blue2', command=uhs).place(x= 335, y = 25)

youknow = 0
def youknows():
  global youknow
  youknow = youknow + 1
  youknowlab.configure(text = youknow)

youknowlab = tk.Label(window, text = youknow, bg = 'honeydew2', fg = 'SlateBlue1')
youknowlab.place(x = 455, y = 1 )

youknowbutton = tk.Button(window, text="You know", activebackground= 'DarkOrange1', activeforeground = 'DeepSkyBlue1', bg = 'hot pink', fg = 'lemon chiffon', command=youknows).place(x= 425, y = 25)

ok = 0
def oks():
  global ok
  ok = ok + 1
  oklabel.configure(text = ok)

oklabel = tk.Label(window, text = ok, bg = 'honeydew2', fg = 'blue2')
oklabel.place(x = 595, y = 1 )

okbutton = tk.Button(window, text="Ok", activebackground= 'midnight blue', activeforeground = 'SeaGreen2', bg = 'SlateBlue2', fg = 'magenta2', command=oks).place(x= 575, y = 25)

print(f"um: {(um)}")
print(f"like: {like}")
print(f"uh: {uh}")
print(f"basicallly: {basically}")
print(f"ok: {ok}")
print(f"youknow: {youknow}")

window.mainloop()

redpajama_set_name: RedPajamaStackExchange


text:
CH hvězda je hvězda, která se vyznačuje přítomností velmi silných CH absorpčních čar ve svém spektru. Patří sem hvězdy populace II, což znamená že jejich věk je ve srovnání s jinými hvězdami průměrný, obsahují málo kovů a jejich jas ve srovnání s C-N uhlíkatými hvězdami je podprůměrný. Mnohé známé CH hvězdy patří mezi dvojhvězdy a předpokládá se, že všechny CH hvězdy mohou být dvojhvězdy. Podobně jako baryové hvězdy, jsou pravděpodobně výsledkem přemístění hmoty z bývalé klasické uhlíkové hvězdy, ze které se stal bílý trpaslík.

Související články
 Bílý trpaslík

Reference

Typy hvězd


Final plans for new electoral arrangements in West Wiltshire are being submitted to The Electoral Commission today. The recommendations from The Boundary Committee for England mark the end of a review which began in July 2005. They include changes to ward boundaries across the district.
As part of its final recommendations, the Committee proposes the council size remains the same, with 44 councillors.
1. PDFs of maps are available on The Boundary Committee's website www.boundarycommittee.org.uk For copyright permission, contact Ordnance Surveys helpline on 023 8030 5092.


This dish is quick, simple and very tasty.
Preheat oven to 475 degrees. Drain marinade from artichokes into a 9 inch diameter glass pie dish. Add fish; turn to coat with marinade. Sprinkle fish with salt and pepper. Scatter artichokes, tomatoes, zucchini, basil and garlic around fish. Pour clam juice over the fish and back until fish is just opaque in the center–about 20 minutes. Serves 2. Calories 208 with 3 g. fat. ENJOY!


Women(Ska-De-La-De-Da)-clean vg/vg(+) Vinyl Promo! (marker on label)--Top Shelf Teen Popcorn!
Garage Rock / Surf / ACID / British Invasion / Bubblegum / Pop Psych / Sunshine Pop & More!
Girl From New York City -Visual VG/VG-(lots of suface scuffs)-Still has Gloss And Plays Fine! --RARE PROMO! -Written by Brian Wilson!
It's Not Gonna Take Too Long / The Day Turns Me On(The Bufferin Song) -old stock -M(-) -Non Chart Sunshine Pop!
Lonely Littls Girl -Clean High Gloss VG PROMO!
Little Miss Sad / Artificial Rose -old stock M(-) Vinyl Promo!
What Is The Reason / You're On My Mind -Unplayed Old Stock Mint(-) -PROMO!
I Can't Get Enough Of You Baby / Smokes! - Light Gloss VG Vinyl! --Killer 2 sider!
Fire / Foxey Lady (Live @ The Miami Pop Festival)--Factory Sealed Unopened Mint Condition! -Limited Edition #0637- One of the first 1,000 pressed!
So I'm Wrong And You Are Right / Wild About My Lovin' / The People Had No Faces -M(-) -Nice 2012 Sundazed Release on Verve Folkways Records Label!
Parchman Farm / Bright Lights, Big City - -M(-) -Nice 2012 Sundazed Release on Verve Folkways Records Label!
Lizbeth Peach / Forever And A Day -clean VG(+) --Vinyl Promo! --vintage store sticker and DJ date stamped(July 13 1967)on flip side label!
One In A Hundred -M(-) --Nice 2012 Sundazed Release on A&M Records Label!
Why Not Your Baby -M(-) --Nice 2012 Sundazed Release on A&M Records Label!


text:
Le couvent des Carmes (Convento do Carmo en portugais) est situé sur le Largo do Carmo à Lisbonne, au Portugal. Il domine le Rossio.

L'ancienne principale église gothique de la capitale s'écroula lors du violent tremblement de terre de 1755, et ne fut jamais reconstruite. Ces ruines visibles de loin restent comme un des principaux témoins de la catastrophe de 1755. De nos jours, elles abritent le musée archéologique du Carmo.

Histoire

Le couvent fut fondé par Nuno Álvares Pereira en 1389, et occupé à l'origine par les frères carmélites de Moura, appelés par Don Nuno pour revenir au couvent en 1392. En 1404, Don Nuno donna ses biens au couvent, et, en 1423, il y entra lui-même comme religieux.

Le couvent et l'église furent érigés approximativement entre 1389 et 1423 dans un style gothique, influencé par le Monastère de Batalha. Ce dernier, fondé par Don João I était en construction à la même époque.

Le 1er novembre 1755, le tremblement de terre détruisit une grande partie de l'église et du couvent, qui ne furent jamais entièrement reconstruits. Une nouvelle aile du couvent fut construite sous le règne de Marie  de Portugal, sans se préoccuper du style original. Elle fut occupée par les frères carmes jusqu'à l'expulsion des ordres religieux, en 1834. Elle fut ensuite convertie en installation militaires en 1836.

Ce fut dans la caserne du Carmo, siège du commandement général de la gendarmerie portugaise, que se réfugia le président du conseil de l'Estado Novo, Marcelo Caetano, pendant la révolution des œillets. L'encerclement de la caserne fut conduit par le capitaine Salgueiro Maia.

Au Largo do Carmo, en face du couvent, on trouve la fontaine du Carmo, conçue au  par Ângelo Belasco, et décorée de quatre dauphins.

Caractéristiques

La façade de l'église possède un portail de plusieurs archivoltes lisses avec des chapiteaux décorés.

La rosace qui surplombait le portail est détruite. La face sud de l'église est soutenue par cinq arcboutants, ajoutés en 1399, après un effondrement durant la construction de l'église. Les trois nefs de l'intérieur se prolongent en une abside et quatre absidioles. Le toit de la nef s'est effondré lors du tremblement de terre, et seuls les arcs en ogives transversaux qui le soutenaient sont encore visibles.

Musée archéologique

Le corps principal de l'église et le chœur (dont le toit résista au tremblement de terre), furent réhabilités et abritent aujourd'hui un musée archéologique avec une petite collection. Les principales pièces datent du Paléolithique et du Néolithique portugais, et proviennent de fouilles d'une fortification préhistorique près d'Azambuja  (3500 av. J.C. - 1500 av. J.C.).

Les sarcophages gothiques principaux comprennent celui de D. Fernando Sanches (début du ), décoré avec des scènes de chasse au sanglier. On note aussi une statue d'un roi du  (peut-être Alphonse I de Portugal), à côté d'objets romains, wisigoths, et même deux momies peruviennes.

Le tombeau du roi Ferdinand  de Portugal (1367-1383), transféré d'un couvent à Santarém, se trouve dans le Musée archéologique.

Galerie

Voir aussi

Articles connexes
 Sé de Lisbonne
 Ordre du Carmel
 Nuno Álvares Pereira
 Ferdinand  de Portugal
 Liste des nécropoles royales

Liens externes
  Portail officiel de l'Ordre du Carmel
  Direction Générale des Monuments Nationaux
  Institut Portugais du Patrimoine Architectural

Notes et références

Lisbonne
Carmes
Lisbonne
Monument national au Portugal
Lisbonne, Carmes


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