text:
\section{Introduction}

Classical gravitational theories are gauge theories for which the principal symmetry is diffeomorphism invariance.
The study of symmetry in gauge theories has a long history going back to the seminal work of Noether \cite{Noether1918}.
While the first Noether theorem deals with global symmetries, Noether herself remarked that for a gauge symmetry, defined as a local symmetry acting differently at different spacetime points, the first theorem gives a current associated to the symmetry that necessarily vanishes on-shell up to total derivatives. It then follows that Noether charges for gauge symmetries must be defined as surface integrals of $d-2$ forms, where $d$ is the spacetime dimension, i.e., as surface charges. Thus codimension-2 surfaces play a central role in gravity and other gauge theories. We will refer to them here as {\it corners} \cite{Donnelly:2016auv,Speranza:2017gxd,Freidel:2020ayo,Freidel:2020svx,Freidel:2020xyx,Ciambelli:2021vnn,Freidel:2021cjp} for brevity.

The first discussion of the role of gauge symmetries and their surface charges appeared using the Hamiltonian formalism in the seminal work of Regge and Teitelboim \cite{Regge:1974zd}. Later, Wald and others \cite{Wald:1993nt,Iyer:1994ys,Wald:1999wa}, using the covariant phase-space formalism, and  Barnich and Brandt \cite{Barnich:2001jy}, using Anderson's variational bicomplex \cite{MR1188434, Anderson:1996sc}, formulated the Lagrangian analysis of gauge symmetries and their conserved quantities. The theory of asymptotic symmetries and surface charges following from these works has been shown to give the same results, modulo ambiguities, as reviewed for example in \cite{Compere:2019qed}.

In any diffeomorphism-invariant classical theory on a manifold $M$, in the absence of any extra structure we are free to perform any diffeomorphism, as it corresponds to a gauge redundancy. However, in the presence of some geometric structure, such as a subregion of $M$ or a corner,
some diffeomorphisms will become physical symmetries. This is a familiar feature of other gauge theories as well, where in the corresponding quantum theory, non-trivial physics is involved in the gluing of subregions and is implicated in entanglement properties. Often one addresses such geometric structures through the mathematical construction of embeddings \cite{Donnelly:2016auv,Speranza:2017gxd,Ciambelli:2021vnn}.
In particular, in \cite{Ciambelli:2021vnn} we explored the consequences of carefully treating such embeddings, and found a theory-independent finite
sub-algebra of $\mathfrak{diff}(M)$, compatible with the presence of an embedded submanifold $S$, whose Lie brackets close on itself, which we referred to as the maximal embedding symmetry, ${\cal A}_k=(\mathfrak{diff}(S)\loplus \mathfrak{gl}(k,\mathbb{R}))\loplus\mathbb{R}^k$.  Applied to corners ($k=2$), this algebra includes the so-called extended corner algebra \cite{Freidel:2021cjp}, which in turn includes notable sub-cases, such as the BMSW algebra \cite{Freidel:2021fxf}, the generalized BMS algebra \cite{Campiglia:2014yka,Compere:2018ylh,Campiglia:2020qvc}, the extended BMS algebra \cite{Barnich:2010eb,Barnich:2011mi}, as well as the original BMS algebra \cite{doi:10.1098/rspa.1962.0161,doi:10.1098/rspa.1962.0206,Sachs:1962wk}.

In diffeomorphism-invariant theories, a basic construction is the integration of a Noether charge density over  a corner. An important issue in this regard is {\it integrability}, whether or not a diffeomorphism is equivalently associated with a Hamiltonian vector field on the space of fields of the theory and a function on field space. If integrability pertains, then diffeomorphisms are represented by such functions and the algebra of charges reproduces canonically the vector field algebra via the Poisson bracket, possibly with central extension \cite{Brown:1986nw}. A separate issue is how the possible non-conservation of charge in a given region is associated with the flow of flux in or out of the region.
As advocated in \cite{Donnelly:2016auv}, such features can be obtained in general if one extends the field space of the theory to include effects associated with embedded submanifolds.
However, in that and subsequent analyses, it was found that diffeomorphisms that do not preserve a corner are on a much different footing than those that do: only the latter were found to correspond to integrable charges. The diffeomorphisms that do not preserve a corner are its normal translations, which appear in the $\mathbb{R}^2$ factor in the extended corner symmetry ${\cal A}_2=(\mathfrak{diff}(S)\loplus \mathfrak{gl}(2,\mathbb{R}))\loplus\mathbb{R}^2$. In the context of asymptotic symmetries, it is this factor that gives rise to the so-called supertranslations, and so it is certainly of central interest to fully understand it.

In \cite{Ciambelli:2021vnn} by carefully treating embeddings we found that the maximal embedding algebra corresponds precisely to the set of those diffeomorphisms that become physical in the presence of a corner and furthermore that the variation of the charge with respect to any diffeomorphism gives precisely $\delta_{\un\eta}H_{\un\xi}=H_{[\un\xi,\un\eta]}$, which appears ready-made for an interpretation in terms of Poisson brackets. This result was obtained purely geometrically without reference to the covariant phase space formalism beyond a specification of the Noether charge density.

In this letter, we will show how to extend the field space of diffeomorphism-invariant theories such that the entire extended corner symmetry is realized by integrable charges. This is achieved by introducing the same careful treatment of embeddings into the covariant phase space methodology, which leads to a natural extension of the symplectic structure of the theory which differs from that introduced in \cite{Donnelly:2016auv}.
We stress that integrability is achieved on the entire field space (on-shell) without a need for first setting some flux to zero. The existing literature contains many examples where integrability is achieved only in this sense.
Here we propose a universal resolution and the consequences are far-reaching:  we find that the algebra of charges associated with the full extended corner symmetry (and thus any of its subalgebras appropriate to any particular physical situation) is represented in terms of Poisson brackets on the extended phase space, without central extension.
As a further consequence, the flux is accounted for fully by the field-space contraction of the Hamiltonian vector field associated to the symmetry and the extended pre-symplectic potential.

\section{Embedding Maps}

In this section, we describe in detail embedding maps. This material of course is standard but it is important to carefully establish our notation. We are concerned entirely here with classical diffeomorphism-invariant theories. We thus suppose that we have a spacetime manifold $M$ of dimension $d$ that we endow locally with coordinates via the trivialization $\Phi_i:U_i\to \mathbb{R}^d, U_i\subset M$, giving $\Phi_i:p\mapsto y^\mu$. An embedded submanifold of $M$ of codimension $k$ is the image of a (smooth)  map  $\phi_k:S_k\to M$, where $S_k$ is a manifold of dimension $d-k$. We introduce coordinates $\{\sigma^\alpha\}$ on $S_k$ with the embedding described by $\phi_k:\{\sigma^\alpha\}\mapsto \{y^\mu(\sigma)\}$, the latter thought of as the locus of points of the embedded manifold in $M$. Given the embedding, differential forms $\alpha\in\Gamma(\wedge^{d-k}T^*M)$ can be pulled back to a top form $\phi_k^*\alpha\in\Gamma(\wedge^{d-k}T^*S_k)$ on $S_k$. Such a form can then be integrated over $S_k$.

We will be interested in describing a variation of such an embedding $\phi_k\to\phi_k+\delta\phi_k$, promoted to an arbitrary variation from the perspective of covariant phase space. Given such, we can then express the response of the embedding to a diffeomorphism as a contraction\footnote{Throughout the paper, we use the notation $i_{\un\xi}$ for the contraction of a spacetime vector field with a differential form and $I_{V_{\un\xi}}$ for the corresponding contraction on field space; here $V_{\un\xi}$ denotes the vector field on field space associated with the spacetime diffeomorphism generated by $\un\xi$. Similarly, Lie derivatives are denoted ${\cal L}_{\un\xi}=di_{\un\xi}+i_{\un\xi}d$ and $\mathfrak{L}_{V_{\un\xi}}=\delta I_{V_{\un\xi}}+I_{V_{\un\xi}}\delta$.} of $\delta\phi_k$ with a vector field on phase space, i.e., $\delta_{\un\eta}\phi_k = I_{V_{\un\eta}}\delta\phi_k$.
Essentially, this idea was implemented originally in \cite{Donnelly:2016auv} by writing the corresponding change of the embedding coordinates as
\begin{eqnarray}\label{varyembk}
 \{\sigma^\alpha\}\rightarrow \{y^\mu(\sigma^\alpha)+{{\chi}}^\mu(\sigma^\alpha)\}
\end{eqnarray}
which we  interpret as defining a vector field on $M$, ${\underline{\chi}} \in TM$ defined at all points on the embedded manifold. Thus we have $\delta\phi_k \leftrightarrow \un\chi$ and we will consequently regard $\un\chi$ as a 1-form on field space, the details of which we will review below.

Consider a $(d-k)$-form $\alpha[g,y]$ where $g$ collectively denotes the fields of a theory and $y$ denotes the coordinates on $M$ in which we are working. Given
an embedding $\phi_k:S_k\to M$, we can pull back $\alpha$ to $S_k$ and integrate
\begin{eqnarray}\label{genericform}
A[g,\phi] := \int_{S_k} \phi_k^*\Big(\alpha[g,y]\Big).
\end{eqnarray}
Often in the literature these details are not expressed clearly and instead integrals are expressed directly in the coordinates of $M$. We will see that keeping track of such details will have important consequences for the covariant phase space formalism. An important result that we will use repeatedly is Stokes' theorem, which in the notation we are using reads
\begin{eqnarray}
\int_{S_k}\phi^*_k\Big(d\beta[g,y]\Big)=\int_{\partial S_k}\phi^*_{k-1}\Big(\beta[g,y]\Big)
\end{eqnarray}
where $\partial S_k$ is the boundary of $S_k$, its embedding given by $\phi_{k-1}:\partial S_k\to M$.

In \cite{Ciambelli:2021vnn}, we made use of this formalism in a simple setting, in which we simply integrated the Noether charge density in this way over a corner, corresponding to the case $k=2$,
\begin{eqnarray}\label{firstCH}
H_{\un\xi}=\int_{S_2} \phi_2^*(Q_{\un\xi})=\int_{S_2} \phi_2^*(*di_{\un\xi}g),
\end{eqnarray}
where $\un\xi\in TM$ is an arbitrary vector field on $M$ and $Q_{\un\xi}$ is the Noether charge density, making no further reference to any other aspects of the covariant phase space formalism. In the second equality we inserted the specific representation of the  Noether charge for the Einstein-Hilbert theory. We found that only those vector fields in the maximal embedding symmetry\footnote{The tilde denotes the fact that whereas the maximal embedding algebra is the algebra of the group $\Big(Diff(S)\ltimes GL(k,\mathbb{R})\Big)\ltimes \mathbb{R}^k$, only the group $\Big(Diff(S)\ltimes SL(k,\mathbb{R})\Big)\ltimes \mathbb{R}^k$ is realized in the Einstein-Hilbert theory.} $\tilde{\cal A}_k=\Big(\mathfrak{diff}(S)\loplus \mathfrak{sl}(k,\mathbb{R})\Big)\loplus \mathbb{R}^k$ give rise to non-zero charges. Thus all other diffeomorphisms remain pure gauge, even in the presence of a corner. We then showed
that
\begin{eqnarray}
\delta_{\un\xi}H_{\un\eta}
=-H_{[\un\xi,\un\eta]}.
\end{eqnarray}
It is tempting to interpret this result as a bracket
\begin{eqnarray}
\brac{ H_{\un\xi}}{H_{\un\eta}}=-H_{[\un\xi,\un\eta]}.
\end{eqnarray}
If this bracket were to coincide with the Poisson bracket of the covariant phase space formalism for all $\tilde{\cal A}_2$ diffeomorphisms, then we would conclude that the symmetry is represented on phase space without central extension.

We will show in the remainder of the paper that precisely this pertains if we correctly enlarge the field space to include the degrees of freedom associated with embedding maps corresponding to subregions of $M$ and hypersurfaces, and extend the symplectic structure accordingly.  Such a correction is in the spirit of \cite{Donnelly:2016auv} but differs in a crucial way. In particular we will show that the correct extension of the symplectic structure yields integrable charges for {\it all} of $\tilde{\cal A}_2$  and furthermore, non-conservation of the charges associated with  flux is fully accounted for by the extended symplectic structure.

Consider the variation of \eqref{genericform}
\begin{eqnarray}
\delta A[g,\phi]=\delta \int_{S_k} \phi_k^*(\alpha[g,y]).
\end{eqnarray}
 The variation receives two contributions, one from the variation of $\alpha$, and one from the variation of the embedding $\phi_k$,
\begin{eqnarray}
\delta A[g,\phi]= \int_{S_k} \phi_k^*\Big(\delta\alpha[g,y]\Big)+\int_{S_k} \delta\phi_k^*\Big(\alpha[g,y]\Big)
\end{eqnarray}
where as usual
\begin{eqnarray}
\label{variation2}
\delta \alpha[g,y] := \alpha[g+\delta g,y] - \alpha[g,y]
\end{eqnarray}
while the variation of the embedding is given by  \begin{eqnarray}
\label{variation3}
(\delta \phi_k^*) (\alpha[g,y]) &:=& \phi_k^*\Big(\alpha[g,y+\chi] - \alpha[g,y]\Big)\\
&=&\phi_k^*\Big( {\cal L}_{\un\chi} \alpha[g,y] \Big)
\end{eqnarray}
where we are using the notation introduced in eq. \eqref{varyembk}.
Thus
\begin{eqnarray}\label{variationA}
\delta A[g,\phi]= \int_{S_k} \phi_k^*\Big(\delta\alpha[g,y]+{\cal L}_{\un\chi} \alpha[g,y]\Big).
\end{eqnarray}
The variation with respect to a diffeomorphism in particular is given by
\begin{eqnarray}
I_{V_{\un\eta}}\delta g = \mathfrak{L}_{V_{\un\eta}}g = {\cal L}_{\un\eta}g,\qquad
I_{V_{\un\eta}}\un\chi=-\un\eta\Big|_{\phi_k(S_k)}
\end{eqnarray}
which implies in particular that $\delta_{\un\eta}\phi_k = I_{V_{\un\eta}}\delta\phi_k$.
Essentially similar relations have also appeared in  \cite{Donnelly:2016auv,Speranza:2019hkr} for example.
Before moving on to covariant phase space formalism, we consider the implication of the nilpotency of $\delta$,
\begin{eqnarray}
0=\delta^2A[g,\phi]=\int_{S_k}\phi_k^*\Big({\cal L}_{\delta\underline{\chi}}\alpha[g,y]+\tfrac12 {\cal L}_{[\underline{\chi},\underline{\chi}]}\alpha[g,y]\Big)\nonumber
\end{eqnarray}
from which we conclude
\begin{eqnarray}\label{delta_chi}
\delta \un\chi = -\tfrac12[\un\chi,\un\chi].
\end{eqnarray}
Thus $\un\chi$ is not an exact form in field space generally. We note that this result resembles a property of  ghosts, which is by no means an accident. Indeed this is another sign that in the presence of an embedding, a `vertical` degree of freedom becomes physical. Related ideas appear in \cite{Gomes:2016mwl,Speranza:2017gxd}.

\section{Covariant Phase Space}

In the case where one integrates a Lagrangian density over all of the manifold $M$, no embedding is required because the Lagrangian is a top-form on $M$. However, suppose we consider integrating the Lagrangian over some subregion $R$ of $M$; we will regard that subregion as embedded in $M$ via $\phi_0:R\to M$, with the boundary of the subregion  regarded as an embedded hypersurface in $M$. So we write
\begin{eqnarray}
S_{R}[g,\phi]=\int_R \phi^*_0\Big(L[g,y]\Big).
\end{eqnarray}
Given this, we then write
\begin{eqnarray}
\delta S_{R}[g,\phi]&=& \int_{R} \phi_{0}^*\Big(\delta L[g,y] \Big)
+   \int_{R} \delta\phi_{0}^*\Big( L[g,y]\Big)
\nonumber\\
&\hat{=}& \int_{ \partial R} \phi_{1}^* \Big( \theta[g,\delta g, y]\Big)
+   \int_{R} \phi_{0}^* \Big({\cal L}_{\un\chi} L[g,y] \Big)
\nonumber\\
&\hat{=}&
\int_{\partial R} \phi_1^*\Big(\theta[g,\delta g,y]+i_{\un\chi}L[g,y]\Big).
\end{eqnarray}
where $\theta$ is the usual pre-symplectic form satisfying $\delta L\,\hat{=}\,d\theta$.
This result suggests a  corresponding extended pre-symplectic potential,
\begin{eqnarray}
\label{extended_potential}
\Theta^{ext.}_\Sigma  \equiv \int_{\Sigma} \phi^*_1\left (\theta[g,\delta g,y]+i_{\un\chi}L[g,y] \right)
\end{eqnarray}
where $\phi_1$ now embeds a hypersurface $\phi_1:\Sigma\to M$, possibly with boundary. This extension is different than the one first introduced in \cite{Donnelly:2016auv}. To understand its properties, we consider the corresponding extended pre-symplectic structure, which can be shown to be of the form
\begin{eqnarray}\label{OmegaExt}
\Omega^{ext.}_\Sigma &:=& \delta \Theta^{ext.}_\Sigma
=\int_{\Sigma} \phi^*_1\Big(\delta\theta[g,\delta g,y]\Big)
\\
&&+\int_{\partial\Sigma}\phi^*_2\Big(i_{\un\chi}\theta[g,\delta g,y]+\tfrac12i_{\un\chi}i_{\un\chi}L[g,y] \Big).\nonumber
\end{eqnarray}
We then identify
\begin{eqnarray}
\Omega^{ext.}_\Sigma[g,\delta g,\un\chi,y] = \Omega_\Sigma[g,\delta g,y]+\Omega^{cor.}_{\partial\Sigma}[g,\delta g,\un\chi,y].
\nonumber\end{eqnarray}
Note that if embeddings are not considered as in the standard treatment, then the result would reduce to the first line of \eqref{OmegaExt}. This is only consistent however if we restrict attention to diffeomorphisms that preserve the corner $\partial\Sigma$.
On the other hand,
similar extended structures were given in \cite{Donnelly:2016auv,Speranza:2017gxd} but the prescription used there differs from ours in an important way, the details of which we will discuss below.

We now turn our attention to the question of integrability, and so we compute
\begin{eqnarray}
I_{V_{\un\eta}}\Omega^{ext.}_\Sigma =
I_{V_{\un\eta}}\Omega_\Sigma+I_{V_{\un\eta}}\Omega^{cor.}_{\partial\Sigma}.
\nonumber\end{eqnarray}
For the first term, we have the standard result
\begin{eqnarray}
I_{V_{\un\eta}}\Omega_\Sigma=\int_\Sigma \phi_1^*\Big(I_{V_{\un\eta}}\delta\theta\Big)
\hat{=}\int_\Sigma \phi_1^*\Big(di_{\un\eta}\theta
-\delta dQ_{\un\eta}\Big)
\end{eqnarray}
where here we have assumed that $\un\eta$ is an arbitrary field-independent vector field as well as the covariance of $\theta$,  $\mathfrak{L}_{V_{\un\eta}}\theta={\cal L}_{\un\eta}\theta$ \cite{Iyer:1994ys} (see also \cite{Chandrasekaran:2020wwn}).
Here $Q_{\un\eta}$ is the Noether charge density, defined as usual by
\begin{eqnarray}
dQ_{\un\eta}=I_{V_{\un\eta}}\theta-i_{\un\eta}L.
\end{eqnarray}
Next, we consider the corner contribution,
\begin{eqnarray}
I_{V_{\un\eta}}\Omega^{cor.}_\Sigma
&=&
\int_{\partial\Sigma}\phi^*_2\Big(I_{V_{\un\eta}}i_{\un\chi}\theta+\tfrac12I_{V_{\un\eta}}i_{\un\chi}i_{\un\chi}L \Big)\nonumber
\\
&=&
-\int_{\partial\Sigma}\phi^*_2\Big(i_{\un\eta}\theta
+i_{\un\chi}I_{V_{\un\eta}}\theta
+\tfrac12i_{\un\eta}i_{\un\chi}L
-\tfrac12i_{\un\chi}i_{\un\eta}L
\Big)\nonumber
\\
&=&
-\int_{\partial\Sigma}\phi^*_2\Big(i_{\un\eta}\theta
+i_{\un\chi}(dQ_{\un\eta}+\tfrac12i_{\un\eta}L )
+\tfrac12i_{\un\eta}i_{\un\chi}L
\Big)\nonumber
\\
&=&
-\int_{\partial\Sigma}\phi^*_2\Big(i_{\un\eta}\theta
+i_{\un\chi}dQ_{\un\eta}
\Big)
\end{eqnarray}
and so
\begin{eqnarray}
I_{V_{\un\eta}}\Omega^{ext.}_\Sigma\hat{=}
-\int_{\Sigma}\phi^*_1\Big(
\delta d Q_{\un\eta}
+{\cal L}_{\un\chi}dQ_{\un\eta}\Big)
=-\delta\int_{\partial\Sigma}\phi^*_2\Big(
 Q_{\un\eta}\nonumber
\Big)
\end{eqnarray}
where we made use of eq. \eqref{variationA} in reverse. Thus the charge is integrable, and we write
\begin{eqnarray}
I_{V_{\un\eta}}\Omega^{ext.}_\Sigma
=-\delta\int_{\partial\Sigma}\phi^*_2
 (Q_{\un\eta})=-\delta H_{\un\eta}
\end{eqnarray}
Thus $V_{\un\eta}$ is the Hamiltonian vector field on field space corresponding to the Hamiltonian function $H_{\un\eta}$, the latter coinciding precisely with that appearing in \eqref{firstCH}. Continuing in the same vein, it can be shown that
\begin{eqnarray}
I_{V_{\un\xi}}I_{V_{\un\eta}}\Omega^{ext.}_\Sigma
=-I_{V_{\un\xi}}\delta\int_{\partial\Sigma}\phi^*_2
 (Q_{\un\eta})=\int_{\partial\Sigma}\phi^*_2
 (Q_{[\un\xi,\un\eta]})= H_{[\un\xi,\un\eta]}\nonumber
\end{eqnarray}
which coincides with the result of \cite{Ciambelli:2021vnn}.
Thus we have the Poisson bracket
\begin{eqnarray}
\Big\{H_{\un\xi},H_{\un\eta}\Big\}=\delta_{\un\xi}H_{\un\eta}=-H_{[\un\xi,\un\eta]}.
\end{eqnarray}
This proves that the charges are canonically represented, given the choice \eqref{extended_potential}. This is achieved without any restriction on the field space, without boundary conditions being imposed and without involvement of ambiguities that would alter the definition of the Noether charge.

Finally we note that $\Theta^{ext.}_\Sigma$ correctly accounts for  flux. Consider for example a `pillbox' with spacelike boundaries $\Sigma_{1,2}$ which have boundaries $S_{1,2}$ and a timelike boundary $B$ (whose boundary is $S_1\cup S_2$). Then
\begin{eqnarray}
H_{\un\xi}\Big|_{S_2}-H_{\un\xi}\Big|_{S_1}&=&
\int_B \phi^*_1(dQ_{\un\xi})\\
&=& \int_{B}\phi^*_1\Big(I_{V_{\un\xi}}\theta-i_{\un\xi}L\Big)
\\
&=& I_{V_{\un\xi}}\int_{B}\phi^*_1\Big(\theta+i_{\un\chi}L\Big)
\\
&=& I_{V_{\un\xi}}\Theta_B^{ext.}
\end{eqnarray}
where we used again our definition \eqref{extended_potential} applied to $B$. Thus the flux of the extended symplectic form precisely accounts for possible non-conservation of the charges. This applies to all vector fields $\un\xi$, whether it be tangential or orthogonal.

\subsection{Comparison to Previous Treatments}

In the usual treatment, where embeddings are not considered at all, one has $\Theta_\Sigma=\int_\Sigma \theta$ and $I_{V_{\un\eta}}\Omega_\Sigma
=- \int_{\partial\Sigma}\Big(\delta Q_{\un\eta}-i_{\un\eta}\theta\Big)
$ as above. Thus, one says that the charge is integrable if $i_{\un\eta}\theta$ is either zero, or is set to zero by imposing some condition. Note that it is automatically zero if $\un\eta$ is tangent to $\partial\Sigma$, but not if $\un\eta$ is normal.
In fact, this is precisely the problem that we have resolved by including the embedding -- the charges are then integrable for all $\un\eta$.

Finally we consider the relationship of our treatment to that of   \cite{Donnelly:2016auv,Speranza:2017gxd}. In fact, they chose a different extension by making use of an ambiguity in the pre-symplectic form
\begin{eqnarray}
\Theta^{DF}_{\Sigma}
&=&\Theta^{ext.}_{\Sigma}+ \int_{\partial\Sigma}\phi_2^*\Big(Q_{\un\chi}\Big)
\\
&=& \int_{\Sigma}\phi_1^*\Big(\theta+i_{\un\chi}L+dQ_{\un\chi}\Big).
\end{eqnarray}
This has the property that $I_{V_{\un\eta}}\Theta^{DF}_\Sigma=0$, and thus all diffeomorphism charges have been made to vanish. However, as we have seen, it is  the pre-symplectic structure $\Theta^{ext.}_\Sigma$ that gives rise to the actual Noether charges that generate the extended corner symmetry.

\section{Conclusions}

In this letter, we have emphasized the need for an interpretation in which physical symmetries are associated with corners and we have found the description of field space that gives rise to that interpretation. We plan to follow up this work with a more extensive account in which we study many of the examples of current interest and extend the construction to field-dependent vector fields and the corresponding modified brackets. For example, one may anticipate that our formalism has important implications when applied to the case of  black hole horizons.

\paragraph{Acknowledgements} We thank L. Freidel for communication about this result and for sharing an unpublished note containing a related discussion.
The research of LC was partially supported by a Marina Solvay
Fellowship, by the ERC Advanced Grant ``High-Spin-Grav" and by
FNRS-Belgium (convention FRFC PDR T.1025.14 and convention IISN 4.4503.15).
The work of RGL was supported by the U.S. Department of Energy under contract DE-SC0015655.

redpajama_set_name: RedPajamaArXiv


text:
August 19, 2021 Uncategorized
Malaysia is a country in Southeast Asia consisting of peninsular Malaysia and east Malaysia. Peninsular Malaysia is located to the south of Thailand while the states of Sabah and Sarawak are on the Island of Borneo, which is located across the South China Sea. They share borders with the small country of Brunei and the Indonesian province of Kalimantan.
Malaysia is made up of thirteen states with three federal territories and each state has its own written constitution law, legislative assembly, and executive council, which reports to the the legislative body of a country or state and is led by a chief minister. The 3 federal territories are Kuala Lumpur's capital city region, Putrajaya's administrative capital, and the island of Labuan. The heads of state of Melaka, Penang, Sarawak, and Sabah are known as Yang di-Pertuan Negeri, meaning the state rulers. The state ruler acts on the recommendation of the state government and the constitution calls for federal parliamentary elections and state legislature elections to be held at least every five years. Hereditary rulers dominate the majority of the peninsular states. Sultans reign in Johor, Kedah, Kelantan, Pahang, Perak, Selangor, and Terengganu, while Rajas rule in Perlis and the Yang di-Pertuan Besar rule in Negeri Sembilan.
The state of Selangor is often mentioned in news, especially on twitter due to the low supply of vaccines provided by the state. The number of supply and demand does not match evenly as the state of Selangor currently has more people living inside of and thus, many of the people cannot get their vaccine appointment as early as they want even though the dangerous wave of the pandemic has swept through the country with the 3rd wave. As of now, the situation is getting much better with more vaccines given to the people through various incentives such as, through walk-in appointments. Thus, one cannot help but think of the places used to give the vaccines needs some adjustable wall panel to separate each and every person for the vaccines to be given. With the Selangor Operable Wall System, the places can be divided much easier to accommodate the upcoming vaccine appointment.
A proper access to safe and effective vaccines is vital to eliminating the COVID-19 pandemic, so seeing so many vaccines in testing and development is quite encouraging. WHO is collaborating with multiple partners to develop, manufacture, and distribute safe and effective vaccinations so that is why there are vaccines such as Astrazaneca, Pfizer and others. Being vaccinated is not the reason for not exercising caution and putting ourselves and others at risk, especially as research is still ongoing into how well vaccines protect not just against diseases but also with infection and ongoing transmission. Although vaccines are a game-changer, for the time being, people must continue to wear masks, wash their hands, ensure proper ventilation indoors, and physically distance themselves and avoid the crowds. With that in mind, immunisation at the end will put an end to the epidemic and not the vaccine. Nonetheless, people must be assured of a fair and equitable access to vaccines, as well as that every country obtains them and can use them to safeguard its citizens.
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redpajama_set_name: RedPajamaCommonCrawl


Pictures taken while camping at Potholes Resevoir in Eastern Washington.
I threw a few new pics up on flickr yesterday... Nothing spectacular, but I like them.
These are four of my favorites out of almost three hundred snaps of my shutter. I would have taken many more, but I was busy fishing or drinking beer. We had a good time out there!
BTW, I was much more successful at snapping photos than catching fish. I caught five fish, only one was keeper sized (barely). ...Still, it was on of my better performances this year. Cut me some slack, it's been some twenty years that I have cast a lure in anger before 2008.


text:
Home Uncategorized Former communist guerrilla blasts state intervention in the economy
Former communist guerrilla blasts state intervention in the economy
Juan Cristobal Nagel
Juan Cristóbal says:
(With my apologies to Teodoro-groupie Quico, but that headline wrote itself.)
In today's Tal Cual, Teodoro Petkoff sensibly butchers the Chávez administration for involving itself directly in every last corner of the economy and making a mess wherever it pokes its nose. I was stratled by the tone of the piece, specially considering who the messenger is.
The Venezuelan government has a knack – the understatement of the day – for involving itself in the direct production of goods and services that could be supplied better and more cheaply by private industry. Every time, yes, every time it does so, the results are sub-par and all Venezuelans end up poorer for it. Teodoro echoes this idea more strongly than I recall him ever doing so, and for that he earns two thumbs up from me.
It's funny that a right-wing talking point like that could come from a man like Petkoff, no ifs, ands, or buts. It's not just that he's correctly framing Chávez as the anti-Midas that he is, it's that he does it so vehemently. It's as if he's channeling his inner Margaret Thatcher.
Now, the issue with this argument has always been how to sell it. How can we convince Venezuelans that state-owned enterprises are a waste of money, that when the chavista heads of the Venalums, the Banco Industriales and the Venirans of the world call for the government to "capitalize" their companies, we all end up paying? Where is the outrage when the government announces its foray into the hospitality industry? Where is the outcry when we hear our tax money will be used to sell cars?
After all, explaining this is just a matter of math: it's a whole lot easier to simply pay workers in these companies wages for doing nothing than have them be a part of a company where you also have to pay bribes, managers, distributors and foreign suppliers, with all the "surplus" pricing that comes with it.
It's also a lot less time consuming for government decision-makers who, instead of focusing on these empty shells, should be thinking about education, national security and crime. How much time does Chávez spend coming up with funky names for his new companies?
The fiscal and welfare consequences of a badly-run state-company are unequivocally sub-optimal relative to simply giving the workers cash.
This is an issue some Venezuelan politicians have meekly tried to sell, and time and again, they retreat. Ultimately, it always proves easier to just continue doing what we're used to and keep feeding the statist beast.
But how can we break this vicious cycle?
We may never find out.
Previous articleThe curious case of the missing panic
Next articleSpeaking truth to power, Cuba-style
Teaches Economics at Universidad de los Andes in Santiago, Chile. Former editor of Caracas Chronicles.
Humanitarian Catastrophe
The Defection That Turned into Exile
FAO Warns About a Real Possibility of Famine in Venezuela
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Verifies dimensions and shapes of cores for conformance to specifications, using straightedge, gauges, and calipers: Places cores in fixtures, manually or using hoist. Moves straightedge along surface of cores to verify contours. Verifies dimensions, using gauges and calipers. Records tally of inspections on standard forms. May file high spots from cores. May repair defects, such as cracks and broken edges. May clean flask from cores, using wire scrapers or files. May inspect molds and be designated Mold Checker (foundry).


Northfield Public Schools would like to remind parents of the Wednesday one-hour late starts for our Professional Learning Communities. All buses will run one hour later than normal and classes will begin one hour later than normal each Wednesday, beginning Sept. 7.
We hope your child had a great first day of school!


There are total 13 letters in Recriminative, Starting with R and ending with E.
Recriminative is a scrabble word? Yes (20 Points) Recriminative has worth 20 Scrabble points.
In Recriminative R is 18th, E is 5th, C is 3rd, I is 9th, M is 13th, N is 14th, A is 1st, T is 20th, V is 22nd letters in Alphabet Series.


text:
Q: I want to remove app.php from url, but how? I have a symfony project and I uploaded it to my host. Here is my folders order:
www
-------vendor
-------bin
-------src
-------app
-------html
--------------(my web content is inside html folder including .htaccess)
--------------app.php

When I type ip_address/app.php in browser it brings my homepage. But I want to remove app.php from all request urls. Please help me to do that.
I searched for solutions but because I don't know anything about apache configuration I couldn't solve my problem.
Please give me an straight solution or a complete code for .htaccess.

A: Here is an example of vhost for Symfony in the last versions of Apache:
# /etc/apache2/sites-available/my-app.conf

<VirtualHost *:80>
    ServerName my-app.local.fr
    DocumentRoot /home/me/Workspace/MySymfonyApp/web

    <Directory /home/me/Workspace/MySymfonyApp/web>
            Options Includes FollowSymlinks
            AllowOverride none
            Require all granted
            RewriteEngine On
            RewriteCond %{REQUEST_FILENAME} !-f
            RewriteRule ^(.*)$ app.php [QSA,L]
    </Directory>

    ErrorLog ${APACHE_LOG_DIR}/my_app_error.log
    # Possible values include: debug, info, notice, warn, error, crit,
    # alert, emerg.
    LogLevel warn
    CustomLog ${APACHE_LOG_DIR}/my_app_access.log vhost_combined
</VirtualHost>

Note the three lines which are the ones that will "remove" app.php:
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^(.*)$ app.php [QSA,L]

To active this url rewriting for all your vhosts, you have to execute the following commands:
$ sudo a2enmod rewrite
$ sudo service apache2 restart

Finally, I wouldn't recomment to use .htaccess because of associated security problems.

A: Copy the .htaccess file to your webspace. There is the rewrite to app.php.
# Rewrite all other queries to the front controller.
RewriteRule .? %{ENV:BASE}/app.php [L]

A: Add this to the top of your htaccess file:
RewriteEngine On
RewriteCond %{THE_REQUEST} \ /+app\.php([^\?\ ]*)
RewriteRule ^ /%1 [L,R]

RewriteRule ^$ /app.php [L]

A: So basically what you want is that when you load http://ip_address you want the content in html/app.php to get loaded. This you can do with DirectoryIndex directive. More information about this can be found here.
DirectoryIndex index.html index.php app.php

The above configuration will make apache to search for index.html file first, index.php file second and the app.php third. If it finds any of these files then it will be loaded.
You can add this directive withing <VirtualHost> section if you want different behavior for different virtual hosts.

A: Thanks for all of my friends here. I solved my problem by allowing override with AllowOverride All in /etc/apache2/sites-available/000-default.conf file.

redpajama_set_name: RedPajamaStackExchange


Bidirectional motors - those that can rotate in either direction – are of two classes: 1. Reversing motors , which can change from full speed in one direction to full speed in the opposite direction. 2. Reversible motors , which can be reversed only when the motor is not running, or is running below cut out speed. Some motor manufacturers distinguish between quick reversing and instant reversing. A quick reversing motor requires a time delay of approximately 1/25th of a second or more for the switching circuitry to react. An instant reversing motor requires absolutely no time delay. The standard SINPAC Switch can be used on reversible and reversing motors. The SINPAC IR Series Switch provides the function of a direction sensing centrifugal switch and makes a reversible capacitor start motor into an instant reversing motor.
In order to reverse a single-phase motor, it is necessary to reverse the polarity of either the start or main winding, but not both at the same time. The reversal of the winding is accomplished with an external reversing switch or contactor that is not part of the SINPAC Switch. SINPAC Instant Reverse Switch is not dependent upon how quickly the user operates the reversing switch, but only that the reversing switch did change states, i.e., forward to reverse, or vice versa. The SINPAC Switch detects the change in the phase shift between the main and start windings, and the logic circuit instantly actuates the starting switch, causing the start circuit to be reconnected to line voltage. This connection causes the motor to decelerate and then reaccelerate in the opposite direction. The SINPAC IR Series Switch interrupts the start circuit current after the motor has accelerated to the cut out speed, and reconnects the start circuit whenever the circuit senses the motor speed has fallen to cut in speed (usually about 50% of synchronous motor speed).


Weinbrenner is the outdoor lifestyle brand within the global umbrella of the Bata shoe organization. American in heritage, the present day Wienbrenner is European in focus. This modern, muscular website evoked the durable workmanlike quality of the product, and provided simple cues to navigate the collection. Aspirational photography set an approachable human tone against the clean interface.


Maria Abreu's research group at the University of Miami's Miller School of Medicine in the USA found that the incidence of colon cancer was linked directly to expression of the Toll‐like receptor 4 (TLR4) gene []. TLRs are crucial in alerting the immune system to microbial infection, triggering acute inflammatory responses that clear invading pathogens. However, TLR4 can also maintain chronic inflammation, for example by responding to commensal bacteria in the gut. As such bacteria are constantly replenished through food intake, and therefore cannot be permanently cleared by the immune system, this can lead to persistent chronic infection maintained by TLRs. Abreu's work suggests that TLR4 not only plays a role in setting up chronic inflammation—which seems to trigger cancer formation—but also promotes subsequent tumorigenesis. She found that suppressing the TLR4 gene protects mice from colon cancers that usually arise from chronic inflammation, and that overexpression of TLR4 increases susceptibility to colon cancer. Interestingly, humans with colitis‐associated cancer have elevated TLR4 levels, which raises the possibility of using this highly conserved receptor as a therapeutic target.
Rosana Risques, a specialist in inflammatory processes at the University of Washington in Seattle, USA, said that it is becoming clear that chronic inflammation is implicated at every level of tumorigenesis. This includes initiation, promotion, malignant conversion, invasion and final metastasis. Risques explained that the initial process involves DNA damage caused by reactive oxygen species that are produced by immune cells. The role of inflammation in the subsequent processes that lead to terminal cancer is less clear, and presumably involves signalling and cross‐talk between the tumour cells and the host immune system. Indeed, a study from the Istituto Clinico Humanitas in Milan, Italy, suggests that an inflammatory microenvironment is essential for all cancers [], although the causal mechanisms have yet to be established.
According to Maija Kohonen‐Corish from the Garvan Institute of Medical Research, Sydney, Australia, chronic inflammation causes cancer through tissue destruction and scarring, and reshaping of the tissue architecture, as well as contributing to changes in gene expression that sustain tumorigenesis. The permanent presence of inflammatory proteins also maintains an environment in which tumour cells can proliferate. "In a nutshell, it is believed that inflammatory mediators such as cytokines and chemokines, when persistent in the inflamed tissue, can induce proliferation, survival and growth of cells and modify their differentiation status, 'forcing' them to undergo transformation," Kohonen‐Corish explained. In some cases, cancer might arise in the absence of inflammation—as a result of an oncogenic change caused by an environmental exposure, for example—but even in those cases, low‐level inflammation is crucial in sustaining the processes of tumorigenesis. Thus, environmental factors that trigger both oncogenic changes and inflammation are probably particularly potent causes of cancer; this certainly seems to be the case for tobacco smoke. In addition to the established role of tobacco smoke in tumour initiation, owing to its high concentration of carcinogens, research shows that smoking also promotes lung cancer by causing chronic inflammation [].
Another major group of diseases in which chronic inflammation has been implicated are disorders that involve progressive and irreversible damage to the central nervous system. Work in this field has already led to clinical trials for a drug to treat amyotrophic lateral sclerosis (ALS), a common and fatal motor neuron disease. The drug was developed by Arturo Zychlinsky and colleagues at the Max Planck Institute for Infection Biology in Berlin, Germany, who suspected that in addition to a combination of inherited and environmental factors that cause ALS, inflammatory processes might also be involved in causing the death of neurons. They discovered that the signalling molecule interleukin‐1 is integral to the pathogenesis of ALS and showed that, by blocking its production, they could enhance the motor performance and increase the lifespan of mice suffering from a disease similar to ALS. Their results suggested that the same blocking agent might work in ALS patients []. "[T]ogether with the ALS clinic at the Charité, we have started a clinical trial," Zychlinsky explained. The team is optimistic that the patients will have enhanced motor performance, even if it is still too early to say whether they will also live longer.
If chronic inflammation does underlie so many diseases, it would make sense to recognize it as a condition that should be treated in its own right as a preventative therapy. One problem with promoting this approach, however, is that chronic inflammation does not always cause disease; it requires additional genetic and environmental factors. As such, attempts to alleviate chronic inflammation are confined to cases where it is already clear that disease has resulted.
This is the case for severe asthma, which Peter Barnes and colleagues at Imperial College in London, UK, have shown is associated with insensitivity to the action of corticosteroids []. Corticosteroids are effective in treating most patients suffering from mild or moderate asthma, but Barnes has found that 5–10% of patients retain severe symptoms even after treatment with high doses of corticosteroids. This group of patients accounts for about 50% of total healthcare cost for asthma in the UK. Barnes and his team have found that the reduced responsiveness to corticosteroids is associated with reduced nuclear translocation and hyperphosphorylation of the glucocorticoid receptor. Normally, corticosteroids bind to glucocorticoid receptors that then translocate to the nucleus to regulate the expression of genes involved in immune responses. Barnes and colleagues have identified a mechanism by which the administration of long‐acting adrenergic agonists restores the activity of the glucocorticoid receptor in severe asthma patients, by inhibiting phosphorylation and increasing nuclear translocation. The result is improved sensitivity to corticosteroids, opening up a potential treatment for severe asthma.
In some cases, existing drugs with anti‐inflammatory effects are being found to be effective against a variety of diseases resulting from chronic inflammation. The long‐term use of aspirin to reduce the risk of cardiovascular disease is well known, but a study at the John Radcliffe Hospital in Oxford, UK, found that people taking aspirin over long periods also had a lower incidence of death from cancer [].
Clinical evidence suggests that some traditional remedies, such as curcumin—an active component of turmeric, the yellow spice used widely in Indian cuisine—are effective against inflammatory bowel disease (IBD). A study from the Father Muller Medical College in Karnataka, India, reported that several experimental models of IBD responded to curcumin, which seems to work by scavenging free radicals, increasing anti‐oxidants and influencing multiple signalling pathways []. The authors recommend the initiation of large‐scale clinical investigations to determine the potential for the oral use of curcumin to treat IBD.
There is growing evidence that diseases with an inflammatory component can be treated through physical exercise, rather than pharmacology. The positive effect of exercise on inflammatory processes has long been known, but there was little evidence of a direct link with specific conditions. This year, however, a multi‐agency US study looked in detail at 45 articles published between 1950 and 2011 that relate physical activity, cancer survival and biomarkers potentially relevant to cancer []. Although the data were inconclusive for most cancers, there was consistent evidence from 27 of the studies that physical activity reduced mortality from breast and colon cancers of all causes. Furthermore, the authors pointed out that randomized controlled trials designed to correlate exercise with specific biomarker endpoints suggest that physical activity might beneficially change the circulating levels of insulin, insulin‐related pathways, inflammation and, possibly, immunity.
The entire field of inflammation and disease has reached a point where large controlled studies are needed to identify specific targets for therapeutic intervention. There is also hope of establishing a common framework for understanding a variety of conditions previously considered to be unrelated, through the underlying inflammatory mechanisms. One study at Carnegie Mellon University in the USA attempted to link stress, inflammation and the risk of infectious disease by looking at glucocorticoid receptor resistance, which is known to have a role in other inflammation‐related diseases such as asthma. The study, led by Sheldon Cohen, Director of the university's Laboratory for the Study of Stress, Immunity and Disease, focused on the common cold to assess the link between chronic psychological stress and the risk of contracting upper respiratory infections in general. The researchers found that reduced glucocorticoid receptor sensitivity leads to increased levels of circulating leukocytes and neutrophils, triggered by the increased release of pro‐inflammatory cytokines. The authors concluded that this same inflammatory process upregulates immunity to the cold virus and is responsible for well‐known cold symptoms such as increased mucus production in the nose. The implication is that stress does not necessarily increase the probability of infection, but it does amplify the symptoms. This suggests that anti‐inflammatory rather than anti‐viral mechanisms might constitute the most effective remedy for many upper respiratory infections. Cohen pointed out that these findings were consistent with the viral‐challenge theory, which suggests a positive association between pro‐inflammatory cytokine levels and the expression of symptoms.
More fundamentally, Cohen argued that this model might help to understand the development of many other conditions associated with prolonged stress, including cardiovascular disease, diabetes, autoimmune conditions and even clinical depression. It might also lead to a new and better understanding of the interplay between the immune system, inflammation and infectious disease, and how they trigger chronic inflammation leading to other conditions.
↵† Philip Hunter is a freelance journalist in London, UK.


Recently we came across following error when mobile app was trying to upload images using backend API.
"POST /api_endpoint HTTP/1.1" 502 1051 "-"
"Mozilla/5.0 (iPhone; CPU iPhone OS 9_1 like Mac OS X) AppleWebKit/601.1.46 (KHTML, like Gecko) Mobile/13B143 (366691552)"
The backend API was developed using Ruby on Rails and was powered using NGINX HTTP server along with unicorn application server.
Notice the the http response received was 502 which is documented in RFC as shown below.
10.5.3 502 Bad Gateway The server, while acting as a gateway or proxy, received an invalid response from the upstream server it accessed in attempting to fulfill the request.
From the first look it seemed that the client_max_body_size parameter for nginx was too less, which might cause the request to fail if the uploaded filesize is greater than the allowed limit.
But that was not the case with our NGINX configuration. The NGINX was configured to accept file size upto 250 megabytes, while the file being uploaded was around 6 megabytes.
In our Rails code we are forcing all traffic to use HTTPS by having production.rb to have following setting.
Here is how our nginx.conf is configured.
NGINX is configured to accept both HTTP and HTTPS requests. This is a pretty standard setting so that application can support both HTTP and HTTPS. What it means is that nginx will accept both HTTP and HTTPS request. It would not force HTTP request to be HTTPS. It would forward HTTP request to rails backend api.
When we upload a file then NGINX takes that request and passes that request to Rails. NGINX expects a response from Rails only when NGINX is done sending the whole request.
Let's see what happens when a user visits login page using HTTP. NGINX takes the request and passes the request to Rails. When NGINX is done handing over the request to Rails then NGINX expects a response from Rails. However in this case rather than sending 200 Rails sends a redirect over HTTPS. So now NGINX takes up the request again over HTTPS and then hands over request to Rails. Rails processes the request and returns 200. Everything works out.
Now let's see what happens when a file is uploaded over HTTP.
User uploads a file over HTTP. NGINX takes up the request and starts sending the file to Rails. More details about the file upload process can be see at RFC. The data is sent to server in chunks. When first chunk is sent to server then server notices that data is being sent over HTTP and it immediately sends a response that data should be sent over HTTPS.
In the meantime on the client side , client is still pushing rest of the data to the server. Client expects a response from the server only when it is done pushing all the data. However in this case server sends a response when client is not expecting it.
NGINX at this time is all confused and thinks something has gone wrong with the gateway and returns HTTP/1.1 502 Bad Gateway and aborts the upload operation. And that how we get the 502 error.
So next time you see an error like this make sure that you are using https to upload the file if server is enforcing https.


Legacy Kitchens is committed to giving back to the community. We work with local, national and international communities to provide aid to the less fortunate.
In just one month, teams of Legacy Kitchens staff turned $1,300 in seed money into $19,000 for one of Legacy's charities of choice, Opportunity International, which makes short-term loans to small businesses in developing countries.
Our friends Dennis Plintz and the Calgary Dream Centre teamed up to send a group of young men to camp. The results are inspiring.
Here's a great video introduction to one of our favorite charities, Opportunity International, a non-profit organization dedicated to helping the working poor.
With your help we were able to raise over $6,500 to help those affected by the devastating earthquakes in Nepal. Thank you!
As you may be aware a second earthquake has struck Nepal, two weeks after the first deadly one. We invite all of you to participate in a matching donation campaign to help those affected by these devastating earthquakes.
Doris is Vice President of Opportunity International (OI) Canada, a micro-finance organization dedicated to transforming the lives of the poor that Legacy Kitchens has supported since 2007. This is Part 1 of Doris' transformation journey, in her own words.
40 people from Legacy Kitchens participated in the Ice Bucket Challenge, all of them donating to ALS and passing the challenge on to our friends at Decor Cabinets.
Elvira is described as "persistent" and a "leader in her community" by Astrid, the program manager of the Opportunity International program that we support in Cartagena, Colombia. Astrid sent us a note about Elvira's business and the kitchen expansion she completed with the help of a Roof & Floor program loan.
A group of 10 from Legacy Kitchens has just returned from an Opportunity International insight trip to Bogota and Cartagena, Colombia where we saw how microfinance and loving relationships can transform the lives of the working poor. The following recap will highlight the heroic stories of some of the people that we interacted with in a significant way, touching our spirits and in turn transforming us.
We are excited to announce that the 12th Annual 'Music for a Winter Evening' benefit concert and 'Save a Life Campaign' has raised $117,000 for the Calgary Dream Centre.
Rosiris is a hard working, dependable Opportunity International client whose dream it is to have a well-constructed home. Astrid, the program manager of the Opportunity International program that we support in Cartagena, Colombia, sent us this update to let us know that Rosiris is halfway to fulfilling her dream.
Legacy Kitchens is partnering with Corpus Christi Male Chorale again this year for the 12th Annual "Music for a Winter Evening" concert. Over the past 11 years, this event has raised over 1 million dollars for Calgary charities. This year all proceeds will benefit The Calgary Dream Centre.
Astrid sent us this update on the Opportunity International Roof & Floor Program in Cartagena, Colombia. Deny and her family installed floors in their home and remodeled the bathroom to make it safer and more sanitary.
Here's the latest Opportunity International Roof & Floor Program update from Astrid in Cartagena, Colombia. Luz runs a small business and is active in her community.
Astrid, the program manager of the Opportunity International Roof & Floor program that we support in Cartagena, Colombia, sent us this update about Wilfrido whose story we shared last Summer. Wilfrido's house was threatened by mudslides and flooding so he salvaged materials and rebuilt his home on a friend's property while maintaining his coffee business.
Nancy is a participant in the Opportunity International Roof & Floor program that we support in Cartagena, Colombia. Astrid, the program manager, sent along this story about how Nancy's business and family have benefitted from their rebuilt kitchen.
This is another inspiring update from Astrid, manager of the Opportunity International program that we support in Cartagena, Colombia. She sent us this story about Candelaria who was able to reconstruct her home after it was destroyed.
We are excited to announce that the 'Music for a Winter Evening' benefit concert and 'Save a Life Campaign' has raised over $100,000 for the Calgary Dream Centre.
Legacy Kitchens is partnering with Corpus Christi Male Chorale again this year for the 11th Annual "Music for a Winter Evening" concert. Over the past 10 years, this event has raised over $950,000 for Calgary charities. This year all proceeds will benefit The Calgary Dream Centre.
Here's the latest update from the Opportunity International program that we support in Cartagena, Colombia. The program manager, Astrid, writes about how Sara and her family have overcome major medical expenses and time off work to fulfill their financial obligations.
Here's the latest update from Astrid, manager of Opportunity International's Roof & Floor program that we support in Cartagena, Colombia. She sent us this story about Wilfrido who was able to build his new home with the help of the Roof & Floor program.
Opportunity International's local Roof & Floor program manager, Astrid, sent us an update about Carmen, a participant in the program that we support in Cartagena, Colombia.
We're closely involved with the non-profit microfinance organization Opportunity International and their work in Cartagena, Colombia. Recently the Roof & Floor program manager, Astrid, sent us an update about Mrs. Rosa, a participant in the new program.
Legacy Kitchens is partnering with Corpus Christi Male Chorale and The Mustard Seed again this year for the 10th Annual "Music for a Winter Evening" concert. Over the past 9 years, this event has raised over $500,000 for one of Legacy's charities of choice: The Mustard Seed.
In January 2010 Legacy Kitchens staff members returned to Cartagena, Colombia to get a first-hand update on the remarkable people and programs that we support there through one of our preferred charities, Opportunity International. Please take a moment to watch our latest short-format documentary "Opportunity: Colombia, Part 2".
Legacy Kitchens sponsored Calgary's Corpus Christi Male Chorale's 9th annual 'Music for a Winter Evening' concert to benefit The Mustard Seed. The Mustard Seed's Winter 2010 Newsletter included an article about the concert.
Legacy Kitchens is partnering with Corpus Christi Male Chorale and The Mustard Seed again this year for the 9th Annual "Music for a Winter Evening" concert. Over the past 8 years, this event has raised over $500,000 for one of Legacy's charities of choice: The Mustard Seed.
Legacy Kitchens is a proud supporter of Habitat for Humanity. Did you know that instead of throwing away your old cabinets you can sell them on consignment to Habitat for Humanity? If the cabinets are sold, Habitat for Humanity will give you a tax receipt in the amount of the purchase price of your old cabinets.
During the summer of 2008, Legacy Kitchens staff members visited Cartagena, Colombia to see first-hand the work of one of our charities of choice: Opportunity International. Please take a moment to watch our short-format documentary "Opportunity: Colombia".
Legacy Kitchens partnered with Corpus Christi Male Chorale and The Mustard Seed again last year for the 8th Annual "Music for a Winter Evening" concert. Over the past 7 years, this event has raised over $500,000 for one of Legacy's charities of choice: The Mustard Seed.


text:
Arthur B. McDonald - Explore Facts
Takaaki Kajita
Arthur B. McDonald
Arthur B. McDonald - Facts
Arthur B. McDonald - Biographical
Arthur B. McDonald - Nobel Lecture: The Sudbury Neutrino Observatory: Observation of Flavor Change for Solar Neutrinos
Share on Facebook: Arthur B. McDonald – Facts Share this content on Facebook Facebook
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© Nobel Media AB. Photo: A. Mahmoud
Born:	29 August 1943, Sydney, Canada
Affiliation at the time of the award: Queen's University, Kingston, Canada
Prize motivation: "for the discovery of neutrino oscillations, which shows that neutrinos have mass."
Arthur McDonald was born in Sydney, Nova Scotia, Canada. He studied at Dalhousie University, Nova Scotia and then at the California Institute of Technology, Pasadena, United States, where he earned his doctorate in 1969. His doctoral advisor was future Nobel Laureate William Fowler. He worked at the Chalk River Nuclear Laboratories near Ottawa until 1982 when he became a professor at Princeton University. Since 1989 he is affiliated with Queen's University at Kingston, Ontario. Arthur McDonald is married with four children.
The Standard Model used by modern physics has three types of a very small and elusive particle called the neutrino. In an experimental facility in a mine in Canada in 2000, Arthur McDonald studied neutrinos created in nuclear reactions in the sun. Measurements showed deviations, which were explained by the neutrinos switching between the different types. This means that they must have mass. The Standard Model, however, is based on neutrinos lacking mass and the model must be revised.
MLA style: Arthur B. McDonald – Facts. NobelPrize.org. Nobel Media AB 2021. Thu. 14 Jan 2021. <https://www.nobelprize.org/prizes/physics/2015/mcdonald/facts/>


text:
Q: How to check what components an object consists of? When I receive an object, I want to know how to check what components the value consists of.
inputData?.let {
   val detail: MutableState<Any?> = mutableStateOf(null)
   detail.value = inputData
}

I want to read components of inputData.
I'd like to check how the components of input data are made.
---Edit
class SelectDetail (
    private val purchaseDao: PurchaseDao,
    private val purchaseEntityMapper: PurchaseEntityMapper
) {
    fun execute(
        type: String,
        id: Int
    ): Flow<DataState<Any>> = flow {
        try {
            emit(DataState.loading())
            when(type) {
                "purchase" -> {
                    val cacheResult = purchaseDao.getPurchaseById(id)
                    val data = purchaseEntityMapper.fromEntity(cacheResult)
                    emit(DataState.success(data))
                }
            }
        }catch (e: Exception) {
            emit(DataState.error<Any>(e.message?: "Unknown Error"))
            e.printStackTrace()
        }
    }
}

And then call from viewModel,
private fun selectDetail() {
    selectDetail.execute(type = type.value, id = detailId.value).onEach { dataState ->
        loading.value = dataState.loading

        dataState.data?.let { inputData ->
            -----In here-----
        }

        dataState.error?.let { error ->
            Log.d(TAG, "message: $error")
        }
    }.launchIn(viewModelScope)
}

Here is the DataState
data class DataState<out T>(
    val data: T? = null,
    val error: String? = null,
    val loading: Boolean = false,
) {
    companion object {

        fun <T> success(
            data: T
        ): DataState<T> {
            return DataState(
                data = data
            )
        }

        fun <T> error(
            message: String
        ): DataState<T> {
            return DataState(
                error = message
            )
        }

        fun <T> loading(): DataState<T> = DataState(loading = true)
    }
}

I'm sorry for the lack of explanation.


This article was published 31/10/2012 (2364 days ago), so information in it may no longer be current.
PARAMEDICS and firefighters have been ordered to put away their personal cellphones when they're on the job.
The City of Winnipeg says the new rule is part of its "electronics and camera use in the workplace" policy that took effect Oct. 25.
"The purpose of this policy is to ensure that legislation such as the Highway Traffic Act and the Personal Health Information Act are adhered to by all employees of the Winnipeg Fire Paramedic Service," a city spokeswoman said in an email Wednesday.
"The policy serves to prevent distractions in the workplace and help ensure the safety and privacy of all personnel, the public and patients."


Under the Constitution, before police can get a warrant to search someone's home, they need probable cause of unlawful activity. But due to the U.S. Supreme Court's abdication of its duty to enforce this command, cities like Red Wing, Minn., have passed rental inspection ordinances that allow government officials to barge in on someone's home without probable cause of a crime or code violation. Thanks to this rental inspection loophole, criminals actually have more constitutional rights than law-abiding renters.
In order to rent out property in Red Wing, the property needs to be licensed. But a license requires an on-site inspection. If the proprietor or tenant refuses, the city can obtain an "administrative warrant" from a judge. So the notion that these inspections can be considered "consensual" is an illusion.
Represented by the Institute for Justice, nine landlords and two tenants have been fighting the city of Red Wing ever since the rental inspection ordinance passed in 2006. In August 2012, the Minnesota Supreme Court decided to hear the case.
"[t]he City will not share information regarding the condition of the unit or its occupants obtained through inspections conducted pursuant to this Section with any current member of the Red Wing Police Department or any law-enforcement agency of another jurisdiction, or enable their discovery by such person or agency …." RDLC § 4.31, subd. 1(3)(q) (emphasis added).
But this restriction has exemptions. Rental inspectors are allowed to report information from an inspection about meth labs (either active or inactive), and evidence of mistreatment of children, vulnerable adults, and animals.
There are two major problems with this. First, the rental inspectors would not originally have had probable cause to search and enter the property for those crimes. Second, the exemptions are rather arbitrary. Why can rental inspectors disclose evidence of wannabe Walter Whites but not terrorists or thieves?
Cities that have passed rental registration and inspection ordinances usually claim they're necessary to crack down on code violations and punish slumlords. But violating the Fourth Amendment is an excessive response.
Rental inspections are even less justified in Richardson, Tex. The town's city council passed a rental inspection ordinance in November 2011 that requires an inspection to be done within 30 days of a new tenant moving in. According to the Dallas Morning News, "In 2012, the city inspected 644 properties, and only one failed." In other words, that's a pass rate of 99.8%. Clearly, rental inspections are completely unnecessary in Richardson.
There can also be a financial interest behind rental inspections. Rochester, Mich. passed a rental inspection ordinance as a way to "protect property values" after the housing market crash of 2008. Meanwhile, the town of Sharon, Penn. recently tripled rental inspection fees, jacking fees up from $15 to $50. Back in 2010, these fees were just $3 per dwelling, with the inspection done every two years. This fee increase is estimated to generate an extra $12,000 for this small town.
But there are other alternatives to mandatory rental inspections. Tenants can ask for inspection if they're concerned about a property. In addition, inspections could avoid infringing renters' privacy by conducting them only when a property is vacant. Cities could also incentivize landlords and landladies by offering seal of approvals or quality standards. These could then be used in marketing to promote better properties. These options would both protect the health and safety of renters, without sacrificing their civil liberties.
Indeed, more cities and jurisdictions are eliminating warrantless rental inspections. The Board of Supervisors in Chesterfield County, Va. voted unanimously to scrap its rental inspection ordinance in October 2009, after pressure from the ACLU.
Brett White, a landlord and Air Forces spec-ops veteran in Elizabethville, Penn., won in federal court in August 2012 after he sued the borough for its rental inspection ordinance. The court dismissed $450 in fines and nine citations Brett received for refusing to comply with the ordinance.
Garland, Tex. mandated rental inspections in order to be licensed. Anyone who rented property without a license or refused rental inspections would face up to $2000 in fines, per day.
In response, Garland amended its ordinance. Renters and landlords in Richardson are hoping their city will follow suit.
In addition, the Institute for Justice has already won two cases against unconstitutional rental inspections. IJ successfully defended property and privacy rights of tenants in Park Forest, Ill., forcing the village to drop its rental inspection program in the late 1990s. After IJ sued the City of Yuma, AZ for its suspicionless rental inspections, city officials amended the ordinance in 2003 so that inspectors need to have a warrant before snooping around on someone's property. Let's hope Red Wing, too, can apply the Constitution to renters.


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Spain-Georgia (21.00). Andres Iniesta's home town of Albacete hosts Spain's final group game, with a point against Georgia sufficient to guarantee top spot – as indeed would any slip up by France at home to Finland, should the Georgians pull off an unlikely result against the current World and European Champions.
Chile-Equador (01.30). After letting a win slip away against Columbia last Friday, Alexis Sanchez's Chile have another chance to qualify for Brazil, with a point at home to Ecuador enough to see them and Ecuador both through. Success would mean Chile reaching their second successive World Cup.
Brazil-Zambia (13.45). The day's football kicks off with a friendly in Beijing between Brazil and Zambia, where both Alves and Neymar, starters in the 0-2 win over South Korea, again look likely to get some game time.


In the 1851 census, Henry and Sarah are living in Islington, Middlesex.� Henry's occupation is that of Coppersmith and Engineer.� His son Henry S. is listed as Brewer and Charles is a coppersmith and Engineer.� They are living at 4 Alymn Road.
Found Henry and Sarah in the 1861 census.� Harriet, their daughter is living with them in their home in Middlesex along with a servant Mary Ann Clark.
In the 1881 census, Henry Daniel is a widower. He is living with two servants in the house.� One of the servants, Jane Kidgell becomes his wife in 1884.
In the 1861 census, Frederick and Elizabeth are living in Islington, Middlesex.� Frederick is employed as a clerk to an Engineer.


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Head Shop Music
Gurellias Girl Singing Song
On their new album "Guerrilla" they've abbreviated their name to SFA, and when I trudged home with the record under my arm I was concerned. SFA sounds like some boy- or girl-band collective. Noel's.
Her sweet vocals on tracks like "Sunshine/Pretty Girls," which is perhaps the best song on the album (download it for free. is of the rare breed of musicians known as the singing drummer. Knowing.
feminist artist group Guerrilla Girls will present a culture jamming evening of performance. White Rabbits will open with their signature one-minute wonder songs. Don't miss the year's last.
radio-ready new songs: another instant soundtrack hit for delighted fans. Pleasant as it was, though, a certain something was missing from "Begin Again": something that has become obvious with the.
The low-budget 2007 indie, featuring Markéta Irglová and The Frames' Glen Hansard as musicians who sing together as a substitute for the relationship they can't have, became an international hit, and.
They're done with humor, but also makes you cringe a little bit at the songs that you used to worship. that I realized I knew every strip club in America because of singing "Girls, Girls, Girls.".
Pink Martini Live Concert Jun 20, 2019 · Pink Martini are the class of their own. For those who don't like rap or techno, and don't necessarily go to hard rock or heavy metal concerts Pink Martini are a perfect solution. The live in Lyon was Pink Martini at its best. Solid proper perfect performance – they sound exactly like
Husson uses this bond to create sentimental but touching shots of guerrilla. Girls of the Sun adopts a narrative that seems interesting and appealing, also for the western audience: brown feminist.
Middle East Eye travels in a pick-up truck alongside five young girls in camouflage uniforms. discussing the events of the day, and dancing and singing Kurdish nationalist songs. When the sun sets.
At first listen, the electro-punk outfit Guerilla Toss is an appealing. eight to 10 hours a day and just work on these songs." Carlson, who hails from Cape Cod, grew up playing the violin and.
Imagine a scene where in one corner Poison Ivy danced with a cowboy while in the other a sexy girl scout was getting. For the first song Arm came out with a lounge singer's croon singing on top of.
Nijmeijer's European background makes her stand out among the FARC's thousands of female recruits (about a third of the guerrilla. a "pretty girl" who decided to join the revolution. The FARC have.
When he wasn't botching lyrics he was singing out of time with the music. they were also relatively minor and didn't prevent songs like "Somebody Get Me A Doctor," "Beautiful Girls," "Panama" and.
Now they are singing at each other. a crack team of performers who specialise in 'guerrilla opera' – posing as chefs, waiters and guests before bursting into song. If you are lucky enough to be.
Musical Fidelity A100 For Sale Rapper Died On On Instagram Update: June 9, 1:32 p.m. Eastern: After reports spread about the death of Bushwick Bill, the rapper's son released a statement on Instagram confirming that the Geto Boys icon is still alive. "My dad. In his May 1 video message, Bill said he wanted to record some new music before
Good Appeal Obedience Hymns The outbreak of the crisis severely damaged the electoral appeal of New Democracy. The markets did indeed reward Tsipras. Musical Fidelity A100 For Sale Rapper Died On On Instagram Update: June 9, 1:32 p.m. Eastern: After reports spread about the death of Bushwick Bill, the rapper's son released a statement on Instagram confirming that the
UniWorld also created three videos shown at the concerts about three girls who use Sync to play Mr. Brown's music. Ecast's first BarPulse survey of the most popular songs played in U.S. nightclubs.
This remarkable account gives a face and personality to that shadowy stereotype which we so often read about and fear, and which we understand so little: the ANC guerrilla. choir welcomed him by.
Somewhere between the slight goofiness of the barbershop quartet and the life-or-death dramatics of the opera, there lies a cappella, a form of harmonized singing usually reserved. we started the.
The buried bombs are used by guerrillas and drug traffickers, who are often allied, to protect coca fields and guerrilla encampments. At one point, the girl stepped off the road to relieve herself.


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Rusal raises China aluminium exports with Australian government
in Aluminum, Australia, Oceania March 16, 2015 1,342 Views
Reuters – Top global aluminium producer Rusal said it has raised China's swelling aluminium exports with the Australian government, and wants the issue tabled at the next meeting of the world's top customs body.
John Hannagan, chairman of Rusal Australia, and a director of the Australian Aluminium Council, said he had alerted the Australian government to China's rising exports.
"I have contacted both Customs and the Trade minister's office seeking to have the matter of China semis … put on the agenda of the next meeting of the World Customs Organisation," Hannagan told Reuters.
China is the world's top producer and consumer of aluminium, as well as semis, semi-manufactured shapes used in everything from window frames to beer cans.
Exports of primary aluminium ingots attract heavy export duties in China, but producers have been sidestepping the tax and other costs by ramping up shipments of lightly processed metal, which is often remelted at its destination.
Swelling semis exports have seeped into Asia, hurting the export markets of regional producers such as Australia, as well putting downard pressure on prices and premiums – the surcharge paid to obtain physical metal.
China's exports of aluminium products grew about 19% last year, a trend expected to continue in 2015, given Chinese domestic prices compared with international markets.
Benchmark London Metal Exchange aluminium prices have fallen around 15% in the past three months while high global aluminium premiums – the delivery cost to obtain metal – have begun to crumble.
China's primary aluminium exports attract a 15% tariff on top of a 17% VAT, however exports of semi-manufactured shapes don't attract the tariff, and are eligible for a 13% VAT refund, making them more competitive.
The World Customs Organisation is a Brussels-based body that represents 179 customs administrations governing around 98 percent of world trade. It is involved in the definition of goods for the application of tariffs, according to its website.
Strong Chinese participation in Aluminium Middle East 2015
Middle East holds high potential for Aluminium downstream facilities