text:
\section{Introduction}
Belyi's theorem says that any non-singular algebraic curve over a number
field is a covering of the complex projective line $P^1(\mathbf{C})$ ramified at
the three points $\{0,1,\infty\}$   [Belyi 1979] \cite[Theorem 4]{Bel1}.
The aim of our note is an analog of Belyi's theorem for the algebraic
surfaces based on an  approach of  \cite{Nik1}.
Namely, we associate to the countable division ring  an   avatar,
see definition \ref{def1.1}.
If the ring  is commutative (non-commutative, resp.),  then
its avatar is an algebraic curve (an algebraic surface, resp.) defined over the field
$\mathbf{C}$.
For example, an avatar of the ring of rationals   (rational quaternions, resp.)
is the complex projective line  $P^1(\mathbf{C})$  (complex projective plane  $ P^2(\mathbf{C}) $, resp.)
 Belyi's theorem follows from an embedding of rationals into the field of algebraic numbers
 \cite[Section 4]{Nik1}   and its analog for surfaces from an embedding of rational quaternions into a quaternion algebra,
 see Section 4 in below.  An extension of Belyi's theorem to  complex surfaces was studied independently in [Gonz\'alez-Diez 2008]
\cite{Gon1}.

 Recall that  an analogy between  the number fields
  and  complex algebraic curves is well  known  [Eisenbud \& Harris 1999] \cite[p. 83]{EH}.
 The  Grothendieck's  theory of schemes  cannot explain  this relation
 [Manin 2006] \cite[Section 2.2]{Man1}. The problem can be solved in terms of the
$C^*$-algebras  \cite{Nik1}. To explain the solution, let $R$ be a (discrete) associative ring,
let $M_2(R)$ be the matrix ring over $R$
and  let
\begin{equation}
\rho: M_2(R)\to \mathscr{B}(\mathcal{H})
\end{equation}
be a self-adjoint representation of $M_2(R)$  by the bounded linear operators
 on a Hilbert space $\mathcal{H}$.  Taking the norm-closure of $\rho(M_2(R))$
 in the strong operator topology,  one gets a $C^*$-algebra  $\mathscr{A}_R$.
 Likewise, let $B(V, \mathcal{L}, \sigma)$ be the twisted
homogeneous coordinate ring of a complex projective variety $V$, where $\mathcal{L}$ is an invertible sheaf and $\sigma$
is an automorphism of $V$ [Stafford \& van ~den ~Bergh 2001]  \cite[p. 173]{StaVdb1}.
Recall that the  Serre $C^*$-algebra, $\mathscr{A}_V$,   is the norm closure of a
self-adjoint representation of the ring  $B(V, \mathcal{L}, \sigma)$
in $\mathscr{B}(\mathcal{H})$  \cite[Section 5.3.1] {N}.
Finally, let $\mathscr{K}$ be the $C^*$-algebra of all compact operators on the Hilbert space
 $\mathcal{H}$.
 We refer the reader to \cite{Nik1} for the motivation and examples illustrating the following
 definition.

\begin{definition}\label{def1.1}
 The complex projective variety $V$ is called an {\it avatar}
 of the ring $R$,   if there exists  a $C^*$-algebra homomorphism:

 \begin{equation}\label{eq1.2}
  \mathscr{A}_V\to\mathscr{A}_R\otimes\mathscr{K}.
 \end{equation}

\end{definition}

\begin{theorem}\label{thm1.2}
{\bf (\cite{Nik1})}
Let $\overline{\mathbf{Q}}$ be the algebraic closure of the field  $\mathbf{Q}$.
Then:

\medskip
(i) $P^1(\mathbf{C})$ is an avatar of the field $\mathbf{Q}$;

\smallskip
(ii) the avatar of a field $K\subset \overline{\mathbf{Q}}$
is a non-singular algebraic curve $C(\overline{\mathbf{Q}})$;

\smallskip
(iii)  the field extension $\mathbf{Q}\subset K$ defines a covering
$C(\overline{\mathbf{Q}})\to P^1(\mathbf{C})$ ramified at the  points $\{0,1, \infty\}$.
\end{theorem}

 \medskip

\begin{remark}
Belyi's theorem follows from item (iii) of theorem \ref{thm1.2}. Roughly speaking,
it can be shown that each non-singular algebraic curve $C(\overline{\mathbf{Q}})$
is  the avatar of a field $K\subset \overline{\mathbf{Q}}$.
We refer the reader to \cite[Section 4]{Nik1} for the details.
\end{remark}

\medskip
To formalize our results, we use the following notation.
Denote by $\left({a,b\over F}\right)$ a quaternion algebra, i.e
the algebra over a field $F$,    such that $\{1,i.j, ij\}$ is a basis for
the algebra and
  \begin{equation}
  i^2=a, \quad j^2=b, \quad ji=-ij
  \end{equation}

   for some $a,b\in F^{\times}$ [Voight 2021] \cite[Section 2.2]{V}.
   The quaternion algebra with $a=b=-1$ will be written as $\mathbb{H}(F)$.
  The algebra  $\mathbb{H}(\mathbf{R})$ corresponds   to the Hamilton  quaternions and
   the algebra  $\mathbb{H}(\mathbf{Q})$  corresponds to the rational quaternions.
  Our main result is a generalization of theorem \ref{thm1.2} to the division rings $\left({a,b\over K}\right)$,
 where $K\subset\overline{\mathbf{Q}}$.

\begin{theorem}\label{thm1.4}
Let $\left({a,b\over K}\right)$ be a division ring, such that $K\subset\overline{\mathbf{Q}}$.
 Then:

\medskip
(i) $P^2(\mathbf{C}) $ is an avatar of the division ring $\mathbb{H}(\mathbf{Q})$;

\smallskip
(ii)  the avatar of a division ring  $\left({a,b\over K}\right)$ is a non-singular
algebraic surface  $S(\overline{\mathbf{Q}})$;

\smallskip
(iii)  the field extension $\mathbf{Q}\subset K$ defines a covering
$S(\overline{\mathbf{Q}})\to P^2(\mathbf{C})$ ramified at
  three  knotted two-dimensional spheres
$P^1(\mathbf{C})\cup P^1(\mathbf{C})\cup P^1(\mathbf{C})$.
\end{theorem}

\medskip
\begin{remark}
A relation between algebraic surfaces and division rings follows from \cite[Section 7.2]{N}.
Indeed, each non-singular algebraic surface is a smooth 4-dimensional manifold and
the arithmetic topology relates such manifolds to the cyclic division algebras
\cite[Theorem 7.2.1]{N}.
\end{remark}
\begin{remark}
The knotting type of $P^1(\mathbf{C})\cup P^1(\mathbf{C})\cup P^1(\mathbf{C})$  depends
on the arithmetic of the field $K$
and extends the Grothendieck's theory of {\it dessin d'enfant} to the case of algebraic surfaces.
\end{remark}

\medskip
The paper is organized as follows.  A brief review of the preliminary facts is
given in Section 2. Theorem \ref{thm1.4} is proved in Section 3.
An analog of Belyi's theorem for the algebraic surfaces is  proved
in Section 4.

\section{Preliminaries}
This section is a brief review of the quaternion and Serre $C^*$-algebras.
We refer the reader to [Voight 2021] \cite[Section 2.2]{V} and \cite[Section 5.3.1]{N}
for a detailed account.
\subsection{Quaternion algebras}
\begin{definition}
The algebra  $\left({a,b\over F}\right)$ over a field $F$ is called a quaternion algebra
  if there exists $i,j\in \left({a,b\over F}\right)$ such that $\{1,i.j, ij\}$ is a basis for $\left({a,b\over F}\right)$ and
  \begin{equation}
  i^2=a, \quad j^2=b, \quad ji=-ij
  \end{equation}

   for some $a,b\in F^{\times}$.
\end{definition}
\begin{example}
If $F\cong\mathbf{R}$ and $a=b=-1$, then the quaternion algebra
$\left({-1,-1\over \mathbf{R}}\right)$ consists  of the Hamilton quaternions $\mathbb{H}(\mathbf{R})$;
hence the notation.
If $F\cong\mathbf{Q}$, then the quaternion algebra
$\left({-1,-1\over \mathbf{Q}}\right)$ consists  of the rational quaternions $\mathbb{H}(\mathbf{Q})$.
\end{example}

\medskip
A $\ast$-involution on $\left({a,b\over F}\right)$ is defined by the formula
$(1,i,j,k)\mapsto (1, -i,-j,-k)$.  The norm $N(u)=uu^*$ of an element $u=x_0+xi+yj+ zk\in\left({a,b\over F}\right)$
is a quadratic form:
\begin{equation}\label{eq2.2}
N(x_0+xi+yj+ zk)=x_0^2-ax^2-by^2+abz^2.
\end{equation}

\medskip
Since $N(1)=1$ and $N(uv)=N(u)N(v)$, one concludes that the  $\left({a,b\over F}\right)$ is a division algebra if
and only if   quadratic form (\ref{eq2.2}) vanishes only at the zero element $u=0$.
Thus  (\ref{eq2.2}) must be a positive form
for all $x_0, x, y, z\in F$.

\medskip
It is easy to see, that the form   (\ref{eq2.2}) admits non-trivial zeroes if and only if there are
such zeroes for the ternary quadratic form:
\begin{equation}\label{eq2.3}
\mathcal{Q}(x,y,z)=-ax^2-by^2+abz^2.
\end{equation}

\medskip
The substitution $a'={1\over b}, ~b'={1\over a}$ maps the zeroes of (\ref{eq2.3})  to the $F$-points of
a conic surface given by the equation:
\begin{equation}\label{eq2.4}
z^2=ax^2+by^2.
\end{equation}

\medskip
The following classification of the quaternion algebras is well known.
\begin{theorem}\label{thm2.3}
{\bf (\cite[Theorem 5.1.1]{V})}
The formula
\begin{equation}
\left({a,b\over F}\right)\mapsto \mathcal{Q}(x,y,z)
 \end{equation}

maps  isomorphic quaternion algebras to the similar ternary quadratic forms.
Equivalently, the quaternion algebras are classified by the isomorphism classes
of the conic surfaces (\ref{eq2.4}).
\end{theorem}

\subsection{Serre $C^*$-algebras}
Let $V$ be an $n$-dimensional complex  projective variety endowed with an automorphism $\sigma:V\to V$
 and denote by $B(V, \mathcal{L}, \sigma)$   its  twisted homogeneous coordinate ring  [Stafford \& van ~den ~Bergh 2001]  \cite{StaVdb1}.
Let $R$ be a commutative  graded ring,  such that $V=Proj~(R)$.  Denote by $R[t,t^{-1}; \sigma]$
the ring of skew Laurent polynomials defined by the commutation relation
$b^{\sigma}t=tb$  for all $b\in R$, where $b^{\sigma}$ is the image of  $\left({a,b\over \mathbf{Q}}\right)$ under automorphism
$\sigma$.  It is known, that $R[t,t^{-1}; \sigma]\cong B(V, \mathcal{L}, \sigma)$.

Let $\mathcal{H}$ be a Hilbert space and   $\mathscr{B}(\mathcal{H})$ the algebra of
all  bounded linear  operators on  $\mathcal{H}$.
For a  ring of skew Laurent polynomials $R[t, t^{-1};  \sigma]$,
 consider a homomorphism:
\begin{equation}\label{eq2.1}
\rho: R[t, t^{-1};  \sigma]\longrightarrow \mathscr{B}(\mathcal{H}).
\end{equation}
Recall  that  $\mathscr{B}(\mathcal{H})$ is endowed  with a $\ast$-involution;
the involution comes from the scalar product on the Hilbert space $\mathcal{H}$.
We shall call representation (\ref{eq2.1})  $\ast$-coherent,   if
(i)  $\rho(t)$ and $\rho(t^{-1})$ are unitary operators,  such that
$\rho^*(t)=\rho(t^{-1})$ and
(ii) for all $b\in R$ it holds $(\rho^*(b))^{\sigma(\rho)}=\rho^*(b^{\sigma})$,
where $\sigma(\rho)$ is an automorphism of  $\rho(R)$  induced by $\sigma$.
Whenever  $B=R[t, t^{-1};  \sigma]$  admits a $\ast$-coherent representation,
$\rho(B)$ is a $\ast$-algebra.  The norm closure of  $\rho(B)$  is   a   $C^*$-algebra
   denoted  by $\mathscr{A}_V$.  We  refer to  $\mathscr{A}_V$  as   the   Serre $C^*$-algebra
 of the complex projective variety $V$.

\section{Proof}
\subsection{Part I}
Let us prove item (i) of theorem \ref{thm1.4}.
Denote by $\mathcal{O}$ the ring of integers of the quaternion algebra  $\left({a,b\over \mathbf{Q}}\right)$.
Consider a polynomial ring:
\begin{equation}\label{eq3.1}
\mathfrak{R}=\mathbf{Z}[x,y,z]/[\mathcal{Q}],
\end{equation}
where $[\mathcal{Q}]$ is an ideal generated by the quadratic form $\mathcal{Q}(x,y,z)$ given by formula
(\ref{eq2.3}).  The proof of item (i) is based on the following lemma.

\begin{lemma}\label{lm3.1}
The  matrix rings $M_2(\mathcal{O})$ and  $M_2(\mathfrak{R})$  are isomorphic.
\end{lemma}
\begin{proof}
Roughly speaking, lemma \ref{lm3.1}  follows from the classification of the quaternion algebras given by  Theorem \ref{thm2.3}.
Namely, the quaternion algebras are classified by the conic surfaces defined by (\ref{eq2.4}) or, equivalently,  by their coordinate rings
 $\mathfrak{R}$. The same is true for the corresponding matrix rings.  Let us pass do a detailed argument.

\begin{figure}[h]
\begin{picture}(300,110)(-70,0)
\put(20,70){\vector(0,-1){35}}
\put(130,70){\vector(0,-1){35}}
\put(45,23){\vector(1,0){60}}
\put(45,83){\vector(1,0){60}}
\put(0,20){$\mathcal{Q}(x,y,z)$}
\put(55,30){${\sf similarity}$}
\put(45,90){${\sf isomorphism}$}
\put(117,20){$\mathcal{Q}'(x,y,z)$}
\put(7,80){$\left({a,b\over \mathbf{Q}}\right)$}
\put(115,80){$\left({a',b'\over \mathbf{Q}}\right)$}
\put(0,50){$F$}
\put(140,50){$F$}
\end{picture}
\caption
}
\end{figure}

\medskip
(i) One can recast theorem \ref{thm2.3} as a commutative diagram in Figure 1.
We wish  to upgrade the map $F$  to a ring isomorphism.
The simplest non-commutative ring attached  to the ternary quadratic form $\mathcal{Q}(x,y,z)$
is the matrix ring  $M_2(\mathfrak{R})$ over the ring $\mathfrak{R}$  defined by (\ref{eq3.1}).
On the other hand, the quaternion algebra  $\left({a,b\over \mathbf{Q}}\right)$ is simple and, therefore, cannot be isomorphic
to  $M_2(\mathfrak{R})$. However, the ring of integers $\mathcal{O}$ of the algebra $\left({a,b\over \mathbf{Q}}\right)$ admits non-trivial
two-sided ideals.  Here again, the ring $\mathcal{O}$  cannot be isomorphic to  $M_2(\mathfrak{R})$,
since $\mathcal{O}$ is a domain while  $M_2(\mathfrak{R})$ admits the zero divisors, e.g. the  projections.
Thus we must consider the matrix ring $M_2(\mathcal{O})$ as a candidate for the required
ring isomorphism.  Let us show that  $M_2(\mathcal{O})\cong M_2(\mathfrak{R})$  whenever $ \mathcal{Q}(x,y,z)=F\left({a,b\over \mathbf{Q}}\right).$

\bigskip
(ii)  Indeed, it follows from  [Voight 2021] \cite[Corollary 5.5.2]{V}  that the similar
quadratic forms $\mathcal{Q}(x,y,z)$ and $ \mathcal{Q}'(x,y,z)$ correspond to
 the isomorphic   conic surfaces  (\ref{eq2.4}) and, therefore, to
the isomorphic rings  $\mathfrak{R}$ and   $\mathfrak{R}'$.
Since $\mathcal{O}\subset \left({a,b\over \mathbf{Q}}\right)$, we conclude that an isomorphism between  $\left({a,b\over \mathbf{Q}}\right)$ and
$\left({a',b'\over \mathbf{Q}}\right)$
induces an isomorphism between  $\mathcal{O}$ and  $\mathcal{O}'$.  In other words,  the
diagram in Figure 2 must be  commutative.

\begin{figure}[h]
\begin{picture}(300,110)(-70,0)
\put(20,70){\vector(0,-1){35}}
\put(130,70){\vector(0,-1){35}}
\put(45,23){\vector(1,0){60}}
\put(45,83){\vector(1,0){60}}
\put(15,20){$\mathfrak{R}$}
\put(45,30){${\sf isomorphism}$}
\put(45,90){${\sf isomorphism}$}
\put(125,20){$\mathfrak{R}'$}
\put(17,80){$\mathcal{O}$}
\put(125,80){$\mathcal{O}'$}
\put(0,50){$F$}
\put(140,50){$F$}
\end{picture}
\caption
}
\end{figure}

\bigskip
(iii) The tensor product  with the matrix ring $M_2$ in Figure 2 gives us
 $\mathcal{O}\otimes M_2\cong M_2(\mathcal{O})$ and  $\mathfrak{R}\otimes M_2\cong M_2(\mathfrak{R})$.
The functor $F$ extends to the tensor product and  one gets  a
commutative diagram in Figure 3.

\bigskip
(iv) It remains to show that the map $F$ defines a ring isomorphism
  $M_2(\mathcal{O})\cong M_2(\mathfrak{R})$.
  Indeed,  let $x_0\in M_2(\mathcal{O})$. The left multiplication
  $y\mapsto x_0y$ (addition $y\mapsto x_0+y$, resp.)
  defines a morphism $\phi_{x_0}^{mult}$ ($\phi_{x_0}^{add}$, resp.)
  of the ring   $M_2(\mathcal{O})$.  Since the map $F$ preserves morphisms,
  we conclude that $F(\phi_{x_0}^{mult})$  ($F(\phi_{x_0}^{add})$, resp.)
  is a morphism of the ring  $M_2(\mathfrak{R})$.
  Namely, the morphism $F(\phi_{x_0}^{mult})$   ($F(\phi_{x_0}^{add})$, resp.)
  acts  by the formula $F(y)\mapsto F(x_0)F(y)$
  ($F(y)\mapsto F(x_0)+F(y)$, resp.)
  Thus one gets $F(x_0y)=F(x_0)F(y)$ and  $F(x_0+y)=F(x_0)+F(y)$
  for all $x_0,y\in M_2(\mathcal{O})$. In other words, the map $F$ defines
  an an isomorphism  between the rings
  $M_2(\mathcal{O})$ and $M_2(\mathfrak{R})$.

 \bigskip
  Lemma \ref{lm3.1} is proved.
   \end{proof}

\begin{lemma}\label{lm3.2}
Conic surface  (\ref{eq2.4}) is an avatar of the quaternion algebra  $\left({a,b\over \mathbf{Q}}\right)$.
\end{lemma}
\begin{proof}
(i)
According to definition \ref{def1.1},
we  must consider a self-adjoint representation
$\rho$ of the rings $M_2(\mathfrak{R})\cong M_2(\mathcal{O})$
by the bounded linear operators
on a Hilbert space $\mathcal{H}$.  We take the norm-closure
of $\rho$ in the strong operator topology.  Lemma \ref{lm3.1}
implies the following isomorphism of the $C^*$-algebras:
\begin{equation}\label{eq3.3}
\rho(M_2(\mathfrak{R}))\otimes\mathscr{K}\cong \rho(M_2(\mathcal{O}))\otimes\mathscr{K}.
\end{equation}

\bigskip
(ii) On the other hand, from the definition of the Serre $C^*$-algebra $\mathcal{A}_V$ one gets
the following isomorphisms:
\begin{equation}\label{eq3.4}
\begin{cases}
\rho(M_2(\mathfrak{R}))\cong \mathcal{A}_{V(\mathbf{Q})}&\cr
\rho(M_2(\mathfrak{R}))\otimes\mathscr{K}\cong \mathcal{A}_{V(\mathbf{C})}, &
\end{cases}
\end{equation}
 where  $V(\mathbf{Q})$ ($V(\mathbf{C})$, resp.) is the conic surface (\ref{eq2.4})
 over the field of rational numbers $\mathbf{Q}$ (complex numbers $\mathbf{C}$, resp.)
Thus the LHS of (\ref{eq3.3}) is the Serre $C^*$-algebra of the  conic surface  (\ref{eq2.4}).

\bigskip
(iii) It is immediate that the $\rho(M_2(\mathcal{O}))$ at the RHS of  (\ref{eq3.3}) is the $C^*$-algebra $\mathscr{A}_R$ of
the  ring  $R\cong \left({a,b\over \mathbf{Q}}\right)$.

\bigskip
(iv)  Using (ii) and (iii), we can write (\ref{eq3.3}) in the form:
\begin{equation}\label{eq3.5}
\mathcal{A}_{V(\mathbf{C})} \cong \mathscr{A}_R\otimes\mathscr{K}.
\end{equation}

\bigskip
(v) It remains to compare (\ref{eq3.5}) and  the definition \ref{def1.1},
where the connecting map in (\ref{eq1.2}) is an isomorphism between the  $C^*$-algebras.
We conclude that the conic surface  (\ref{eq2.4})
is an avatar of the quaternion algebra  $\left({a,b\over \mathbf{Q}}\right)$.

\bigskip
Lemma \ref{lm3.2} is proved.
\end{proof}

\begin{figure}[h]
\begin{picture}(300,110)(-70,0)
\put(20,70){\vector(0,-1){35}}
\put(130,70){\vector(0,-1){35}}
\put(45,23){\vector(1,0){60}}
\put(45,83){\vector(1,0){60}}
\put(0,20){$M_2(\mathfrak{R})$}
\put(45,30){${\sf isomorphism}$}
\put(45,90){${\sf isomorphism}$}
\put(115,20){$M_2(\mathfrak{R}')$}
\put(0,80){$M_2(\mathcal{O})$}
\put(117,80){$M_2(\mathcal{O}')$}
\put(0,50){$F$}
\put(140,50){$F$}
\end{picture}
\caption
}
\end{figure}

\begin{lemma}\label{lm3.3}
The  (\ref{eq2.4}) is a rational surface over the field $k\cong\mathbf{Q}(\sqrt{-1}, \sqrt{-a}, \sqrt{-b})$.
In particular, the complex points of (\ref{eq2.4}) define a simply connected 4-dimensional manifold.
\end{lemma}
\begin{proof}
(i) Let us show that the conic  (\ref{eq2.4}) is a rational surface over the field $\mathbf{Q}(\sqrt{-1}, \sqrt{-a}, \sqrt{-b})$.
Indeed, the reader can verify that a parametrization  $(u,v)\mapsto (x,y, z)$  of  (\ref{eq2.4})
is given by the formulas:
\begin{equation}\label{eq3.6}
\begin{cases}
x={u^2-v^2\over\sqrt{-a}}&\cr
y={2uv\over\sqrt{-b}}&\cr
z=\sqrt{-1}(u^2+v^2) &
\end{cases}
\end{equation}
We conclude that  the conic  (\ref{eq2.4}) is a rational surface $P^2(k)$
defined over the field  $k\cong \mathbf{Q}(\sqrt{-1}, \sqrt{-a}, \sqrt{-b})$.

\bigskip
(ii) It is well known that the rational complex projective variety is  simply connected as a manifold.
By item (i) surface (\ref{eq2.4}) is rational and therefore the underlying
4-dimensional manifold is simply connected.

\bigskip
Lemma \ref{lm3.3} is proved.
\end{proof}

\begin{remark}
Notice that  $k\ne \mathbf{Q}$.  For otherwise
the ternary quadratic form  (\ref{eq2.3}) admits (infinitely many) non-trivial  zeroes
and  $\left({a,b\over \mathbf{Q}}\right)$ is no longer a division
ring, see Section 2.1.
 \end{remark}

\begin{corollary}\label{cor3.5}
 $P^2(\mathbf{C}) $ is an avatar of the division ring $\mathbb{H}(\mathbf{Q})$.
\end{corollary}
\begin{proof}
Our proof is based on the result  [Piergallini 1995] \cite{Pie1} which
says that for each smooth 4-dimensional manifold $M^4$
  there exists a transverse immersion $X\hookrightarrow S^4$ of a 2-dimensional surface $X$
  into the 4-dimensional sphere $S^4$,  such that $M^4$ is the 4-fold PL  cover of  $S^4$ branched at the points of $X$.
  We pass to a detailed argument.

  \bigskip
  (i)  Recall that if  $J$ is the complex conjugation,  then  $P^2(\mathbf{C})/J\cong S^4$.
  Using Piergallini's Theorem,  we conclude that $J$  acts on the conic  surface  (\ref{eq2.4})
  so that it becomes a branched cover of  $P^2(\mathbf{C})$.
  In view of lemma \ref{lm3.3},  the  conic surface is rational over the field
 $k\cong \mathbf{Q}(\sqrt{-1}, \sqrt{-a}, \sqrt{-b})$.
Thus there exists a regular map:
\begin{equation}
P^2(k)\to \mathbb{P}^2(k_0),
\end{equation}
where $k_0\subset k$ is the minimal non-trivial subfield of $k$.

\bigskip
(ii) But the minimal non-trivial subfield of $k\cong \mathbf{Q}(\sqrt{-1}, \sqrt{-a}, \sqrt{-b})$
independent of the parameters $a$ and  $b$ coincides with the field  $k_0\cong \mathbf{Q}(\sqrt{-1})$.
Clearly, the  $k_0$ corresponds to the case $a=b=-1$.
All other possible combinations $a=\pm 1, ~b=\pm 1$ must be
excluded since the ternary quadratic form (\ref{eq2.3}) must be  positive-definite.

\bigskip
(iii) It remains to notice that the quaternion algebra with  $a=b=-1$ corresponds to the
rational quaternions $\mathbb{H}(\mathbf{Q})$.

\bigskip
Corollary \ref{cor3.5} is proved. \end{proof}

\smallskip
Item (i) of theorem \ref{thm1.4} follows from corollary \ref{cor3.5}.

\bigskip
\subsection{Part II}
Let us prove item (ii) of theorem \ref{thm1.4}.  We proceed with construction of  an algebraic
surface $S(\overline{\mathbf{Q}})$ from the quaternion algebra  $\left({a,b\over K}\right)$
with $K\subset \overline{\mathbf{Q}}$.
From Part I  if  $K\cong\mathbf{Q}$,    then  $S(\overline{\mathbf{Q}})$ is given
by the equation $\mathcal{Q}(x,y,z)=0$,  where
\begin{equation}\label{eq3.8}
\mathcal{Q}(x,y,z)=-ax^2-by^2+abz^2.
\end{equation}

\bigskip
(i) Let $K\subset \overline{\mathbf{Q}}$ be a number field and let $a,b\in K$. Denote by $p\in\mathbf{Z}[u]$ and  $q\in\mathbf{Z}[w]$  the minimal
polynomials of $a$ and  $b$, respectively.  We  set $a=h, ~b=w$ and  we write (\ref{eq3.8}) in the form:
\begin{equation}\label{eq3.9}
F(x,y,z, u, w)=-ux^2-wy^2+uwz^2\in \mathbf{Z}[x,y,z,u,w].
\end{equation}

\bigskip
(ii)  Solving the equation $F(x,y,z, u, w)=0$,   one gets:
\begin{equation}\label{eq3.10}
u={wy^2\over wz^2-x^2}, \quad w={ux^2\over uz^2-y^2}.
\end{equation}

\bigskip
(iii) The required algebraic surface  $S(\overline{\mathbf{Q}})$ is defined  as an intersection of two  hyper-surfaces
given  the equations:
\begin{equation}\label{eq3.11}
\begin{cases}
p\left( {wy^2\over wz^2-x^2}  \right)=0,&\cr
q\left( {ux^2\over uz^2-y^2}\right)=0. &
\end{cases}
\end{equation}

\bigskip
(iv) The reader can verify that the surface (\ref{eq3.11}) is defined over the field $\overline{\mathbf{Q}}$
and coincides with the conic surface  (\ref{eq3.8}) when $K\cong \mathbf{Q}$.

\bigskip
Item (ii) of theorem \ref{thm1.4} is proved.

\bigskip
\subsection{Part III} Let us prove item (iii) of theorem \ref{thm1.4}.
For the sake of clarity, we  consider the case $K\cong \mathbf{Q}$ first,
and then the general case $K\subset\overline{\mathbf{Q}}$.

\bigskip
\subsubsection{Case $K\cong \mathbf{Q}$}
(i)  Lemma \ref{lm3.2} says that  conic surface  (\ref{eq2.4}) is an avatar of the quaternion algebra  $\left({a,b\over \mathbf{Q}}\right)$. On the other hand, it is known that (\ref{eq2.4})
is a rational surface $P^2(k)$ over the number field $k\cong\mathbf{Q}(\sqrt{-1}, \sqrt{-a}, \sqrt{-b})$, see lemma \ref{lm3.3}.

\bigskip
(ii)  Let $k_1\cong\mathbf{Q}(\sqrt{-1}), ~k_2\cong\mathbf{Q}(\sqrt{-a})$ and
$k_3\cong\mathbf{Q}(\sqrt{-b})$.
Consider  a regular map $P^2(k_i)\to P^2(\mathbf{Q})$
between the rational surfaces   $P^2(k_i)$ and  $P^2(\mathbf{Q})$
shown at the lower level in Figure 4.

\begin{figure}[h]
\begin{picture}(300,140)(-70,0)

\put(63,100){$P^2(k)$}

\put(75,90){\vector(0,-1){20}}
\put(55,90){\vector(-1,-1){20}}
\put(95,90){\vector(1,-1){20}}

\put(20,50){$P^2(k_1)$}
\put(60,50){$P^2(k_2)$}
\put(110,50){$P^2(k_3)$}

\put(75,40){\vector(0,-1){20}}
\put(35,40){\vector(1,-1){20}}
\put(115,40){\vector(-1,-1){20}}

\put(60,0){$P^2(\mathbf{Q})$}

\end{picture}
\caption
}
\end{figure}

\bigskip
(iii) Using  [Piergallini 1995] \cite{Pie1} (see proof of corollary \ref{cor3.5}),
we conclude that each $P^2(k_i)\to P^2(\mathbf{Q})$
is a covering map ramified over an embedded 2-dimensional surface $X$.
To determine the genus of $X$, recall that the group of deck transformations
of the covering $P^2(k_i)\to P^2(\mathbf{Q})$ is isomorphic to the Galois group
$Gal~(k_i | \mathbf{Q})\cong \mathbf{Z}/2\mathbf{Z}$ of the field $k_i$.
In particular,  the ramification set $X$ is fixed by the deck transformations
and, therefore, corresponds to the field $\mathbf{Q}$ fixed by the group
$Gal~(k_i | \mathbf{Q})$. But the avatar of $\mathbf{Q}$ is a
projective line $P^1(\mathbf{C})\cong X$,  see item (i) of theorem \ref{thm1.2}.
We conclude that the surface $X$ has genus zero.

\bigskip
(iv)   Since $k\cong\mathbf{Q}(\sqrt{-1}, \sqrt{-a}, \sqrt{-b})$,
one gets for each $i=1,2, 3$  a regular map $P^2(k)\to P^2(k_i)$ as shown at the upper level of diagram in Figure 4. Composing these  maps  with the maps $P^2(k_i)\to P^2(\mathbf{Q})$, one concludes the algebraic surface $P^2(k)$
is a covering of  $ P^2(\mathbf{C}) $ ramified over three  knotted two-dimensional spheres
$P^1(\mathbf{C})\cup P^1(\mathbf{C})\cup P^1(\mathbf{C})$ embedded in $ P^2(\mathbf{C})$.
\begin{remark}
The knotting type of $P^1(\mathbf{C})\cup P^1(\mathbf{C})\cup P^1(\mathbf{C})$  depends  on the arithmetic of the fields $k_i$
and extends the Grothendieck's theory of {\it dessin d'enfant} to the case of algebraic surfaces.
\end{remark}

\bigskip
\subsubsection{Case  $K\subset\overline{\mathbf{Q}}$}
(i)  Let  $S(\overline{\mathbf{Q}})$ is an avatar of the quaternion algebra
$\left({a,b\over K}\right)$ constructed in Part II.
It follows from formulas (\ref{eq3.9})-(\ref{eq3.11}) that there exists
a regular map:
\begin{equation}\label{eq3.12}
f:  S(\overline{\mathbf{Q}})\to P^2(k).
\end{equation}

\bigskip
(ii)  Let $f^{-1}(P^1(\mathbf{C})\cup P^1(\mathbf{C})\cup P^1(\mathbf{C}))$
be the pre-image of the three knotted two-dimensional spheres embedded in $P^2(\mathbf{C})$
under the map (\ref{eq3.12}).  It is not hard to see, that such a pre-image
consists again of  three  spheres $P^1(\mathbf{C})\cup P^1(\mathbf{C})\cup P^1(\mathbf{C})$ but knotted differently when compared
to the case of the surface  $P^2(k)$.

\bigskip
(iii)  Since our surface is an avatar of the quaternion algebra
$\left({a,b\over K}\right)$, it  is defined over $\overline{\mathbf{Q}}$, see item (ii)
of theorem \ref{thm1.4}.  This argument finishes the proof of item (iii)
of theorem \ref{thm1.4}.

\bigskip
Theorem \ref{thm1.4} is proved.

\section{Belyi's theorem for algebraic surfaces}
The aim of this section is an analog of Belyi's theorem for algebraic surfaces.
Our approach is geometric and  follows from  theorem \ref{thm1.4}.
We refer the reader to  [Gonz\'alez-Diez 2008] \cite{Gon1}
for an analytic treatment to this problem.
\begin{theorem}\label{thm4.1}
A non-singular algebraic surface is defined over a number field $K$
if and only if it is a covering  of the complex projective plane $P^2(\mathbf{C}) $
ramified at three knotted two-dimensional spheres
$P^1(\mathbf{C})\cup P^1(\mathbf{C})\cup P^1(\mathbf{C})$.
\end{theorem}
\begin{proof}
Our proof is based on item (iii) of  theorem \ref{thm1.4} and the following lemma.
\begin{lemma}\label{lm4.2}
For each algebraic surface $S(\overline{\mathbf{Q}})$
 there exists a quaternion algebra  $\left({a,b\over K}\right)$
 such that the avatar of $\left({a,b\over K}\right)$ is isomorphic to  $S(\overline{\mathbf{Q}})$.
\end{lemma}
\begin{proof}
(i) In view of [Piergallini 1995] \cite{Pie1} (see proof of corollary \ref{cor3.5}),
the algebraic surface  $S(\overline{\mathbf{Q}})$ is a covering of the
projective plane $P^2(\mathbf{C}) $ ramified over a knotted 2-dimensional surface  $X\subset P^2(\mathbf{C})$.
In particular, there exists a regular map $\phi: S(\overline{\mathbf{Q}})\to  P^2(\mathbf{C}) $.

\bigskip
(ii) Recall that the  $ P^2(\mathbf{C}) $ is an avatar  of the division ring $\left({-1,-1\over \mathbf{Q}}\right)$,
see item (i) of theorem \ref{thm1.4}.  Moreover, the field  inclusion
$\mathbf{Q}\subset\overline{\mathbf{Q}}$ gives rise to a regular map
$\psi_0: S_0(\overline{\mathbf{Q}})\to  P^2(\mathbf{C}) $, where   $S_0(\overline{\mathbf{Q}})$
is an avatar of the quaternion algebra $\left({-1, -1\over \overline{\mathbf{Q}}}\right)$.

\begin{figure}[h]
\begin{picture}(300,140)(-70,0)

\put(35,100){$S(\overline{\mathbf{Q}})$}
\put(90,100){$S_0(\overline{\mathbf{Q}})$}

\put(65,103){\vector(1,0){20}}
\put(50,90){\vector(0,-1){70}}
\put(105,90){\vector(0,-1){20}}

\put(100,90){\vector(-2,-3){40}}

\put(85,50){ $\left({-1, -1\over K}\right)$}

\put(105,40){\vector(0,-1){20}}

\put(30,0){$P^2(\mathbf{C})$}
\put(90,0){$\left({-1,-1\over \mathbf{Q}}\right)$}
\put(65,3){\vector(1,0){20}}

\put(35,50){$\phi$}
\put(70,110){$\psi$}
\put(70,70){$\psi_0$}
\end{picture}
\caption
}
\end{figure}

\bigskip
(iii)  One gets a regular map $\psi:  S(\overline{\mathbf{Q}})\to S_0(\overline{\mathbf{Q}})$
by closing arrows of the commutative diagram in Figure 5. Notice that $\psi$ is a finite covering of
the surface $S_0(\overline{\mathbf{Q}})$, since $\phi$ and $\psi_0$ are mappings of finite degree.

\bigskip
(iv) On the other hand, it follows from  equations (\ref{eq3.9})-(\ref{eq3.11})
that each finite covering   $S(\overline{\mathbf{Q}})$ of
the avatar $S_0(\overline{\mathbf{Q}})$
of the algebra  $\left({-1, -1\over K}\right)$ must
be  avatar of an algebra  $\left({a, b\over K}\right)$
for some $a,b\in K$. Thus  there exists
a quaternion algebra   $\left({a, b\over K} \right)$,
such that  algebraic surface $S(\overline{\mathbf{Q}})$ is the
avatar of  $\left({a, b\over K}\right)$.

Lemma \ref{lm4.2} is proved.
\end{proof}

\bigskip
Returning to the proof of theorem \ref{thm4.1},  one combines lemma \ref{lm4.2} with the conclusion of
item (iii) of theorem \ref{thm1.4}.  This argument finishes the proof of theorem \ref{thm4.1}.
\end{proof}

\bibliographystyle{amsplain}

redpajama_set_name: RedPajamaArXiv


text:
GOVERNMENT / CAG AUDIT
NREGA workers kept waiting for wages
A performance audit of the National Rural Employment Guarantee Act in Karnataka reveals delayed payment of wages, sometimes by three months or more, to nearly five lakh workers under the scheme during the period 2009-12. Himanshu Upadhyaya looks at the key audit findings and connects the dots.
18 September 2013 -
The performance audit report on the implementation of the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) in Karnataka was tabled in the State Assembly on 30 July 2013. An earlier article reviewed several anomalies, delays and variance with what had been originally envisioned in respect of planning processes, realistic labour budget estimation, registration and issue of job cards, monitoring mechanisms, social auditing and grievance redressal.
What stands out equally starkly, if not more, from the report are the performance audit findings related to payment of wages and compensation to workers employed under the scheme. The audit notes that in 2010-11, almost half of all payments made were recorded beyond the stipulated 15-day period and while workers should have been paid compensation for such delays, no such compensation was paid.
If one wonders why and how such a sad state of affairs came about, one only needs to look at the way in which Information, Education and Communication activities to empower MGNREGA workers about their rights have been undertaken by the state.
Delayed payment of wages
MGNREGA workers are entitled to being paid on a weekly basis, and in any case within a fortnight of the date on which the work was done. In case payment of wages is not made within the period specified under the scheme, workers must receive compensation as per the provisions of the Payment of Wages Act, 1936 with the cost of such compensation being borne by the state government.
Audit scrutiny of data extracted from the MIS throws up a significant number of cases where wages were paid after a delay of more than the stipulated period of 15 days. In the year 2010-11, delayed wage payments amounted to as high as almost half the total wages paid. During the years 2009-10 and 2010-11, a very high number of muster rolls showed payments of wages with a delay of more than 91 days.
The audit observes that though wages belatedly paid as a proportion of total wages showed a decline in the year 2011-12, the percentage still remained significantly high at 23 per cent. In its reply to this audit finding, the state government has accepted its failure.
MGNREGA researchers would perhaps do well to look at MIS data for the year 2012-13 and analyse the payment of wages reported therein to verify if the state government has merely stopped at acknowledgement of its failure or if it has indeed learnt any lessons from the above audit observation.
Non-payment of unemployment allowance
The CAG's performance review of MGNREGA implementation in Karnataka has also revealed that the state government had made no payments towards unemployment allowance. The Operational Guidelines stipulate that any person having a job card can apply for work to the Gram Panchayat in writing. On receiving such an application, which is also called 'demand for work,' the official shall issue a dated receipt to the applicant. In case work is not provided within 15 days from the date of demand for work, an unemployment allowance is to be paid to the applicant by the state government.
In a significant number of cases, wages were paid after a delay of more than the stipulated period of 15 days. In the year 2010-11, delayed wage payments amounted to as high as almost half the total wages paid.
• Six months for a job card?
• MIS=Too many mistakes
Audit scrutiny of MIS data showed that in a majority of cases, the demand for work had been entered as the same date on which the person was engaged as MGNREGA worker as per the muster rolls, or the preceding day of the engagement of worker. This pattern of data entry in MIS, accompanied by the conspicuous absence of what I term 'flesh and blood employment registers,' indicate the scope for manipulating the date of demand for work.
The neat records at the MIS level in a state where a beneficiary survey has seen many workers reporting delays of up to six months in acquiring a job card itself does seem to indicate that we can't take the MIS claims at face value.
In those relatively less number of cases, where the MIS data broke away from the pattern narrated above, the number of person-days for which unemployment allowance should have been paid to workers is as mentioned in the table below:
Year	Number of person-days for which unemployment allowance was payable
In all 30 districts       In 8 test-checked districts
2007-'08          65,415                    5,097
2008-'09        3,12,574                1,49,840
2009-'10        1,01,952                  46,166
2011-'12         22,493                     10,098
Total               6,52,220                2,60,656
However, during audit scrutiny it was found that no unemployment allowance had been paid to workers, either as per MIS data or as per records in test-checked data.
It is worth looking at what the state government says in reply to this audit observation, in its communication dated January 2013. In its reply, the state government sought to argue that as per the Operational Guidelines, the question of unemployment allowance arises only when the labourer applies for it in writing. The state government also added in its reply that the whole process of record maintenance was being computerised now, which would resolve these issues.
The CAG however pronounced that "the reply was not acceptable, as the state government, instead of educating the labourers through Information, Education and Communication (IEC) activities, had taken shelter under the ignorance of the intended beneficiaries."
It would, therefore, be interesting to explore the amount of resources that the Karnataka government has spent from its MGNREGA budget on such IEC activities. The following is what the audit has to say on this.
Information, Education and Communication Activities under MGNREGA
Audit scrutiny revealed that the state government had not drawn up any Information, Education and Communication (IEC) plan. IEC activities were taken up in a limited manner through street plays, radio programmes, pamphlets and wall writing in public places. Towards this, the state government incurred expenditure worth Rs. 74.78 lakh during 2007 to 2012. Since June 2010, the state government has engaged consultants for IEC activities and paid them an amount of Rs 1.5 crore till March 2012.
The CAG performance review also noted that the financial management of the scheme was deficient, as monthly squaring and reconciliation of accounts at all levels was not being attempted at all. It also indicted the State Employment Guarantee Council (SEGC), Governing Council and Executive Council, stating that they failed to meet regularly. The SEGC had met only four times as of 31 March 2012, while the Governing Council had met only two times during the period 2009 to 2012 and the Executive Council had met only once since its constitution.
With a change of the guards, will things improve for MGNREGA workers in Karnataka in the year 2012-13? We will have to wait and watch, but meanwhile civil society organisations and MGNREGA researchers could go a long way by insisting that the Public Accounts Committee of the State Assembly takes up the present audit report for discussion soon.
Himanshu Upadhyaya
Himanshu Upadhyaya is a researcher at the Azim Premji Foundation, Bangalore.
DRIVERS OF GROWTH : India's new growth recipe: Larger firms
A PACHYDERM'S DIET : Elephants need to eat a lot, but are selective
REPRODUCTIVE RIGHTS : SC opens the door to autonomy in abortions
INDIAN GIANT SQUIRREL : IGS numbers decline as forests become less dense
FINANCE REGULATION : How well are securities laws enforced in India?
RENEWABLES AND JOBS : Can DRE projects stem the tide of migration?
SUNDARBANS MANGROVES : Satellite images reveal impact of frequent cyclones
INEQUALITY : The need to spatialise human rights in cities
TRADITIONAL FOODS : Re-seeding the past for a better future
YIELDS AND LIVELIHOODS : Has precision farming's moment arrived
TAX TRIBUNAL : GSTAT: An urgent necessity and opportunity
AFFORESTATION : Missing the forest for the CAMPA trees
WELFARE STATE : RJ, TN move towards universal health care
WIND FARMS : Lands, jobs and a new way of life
ORANGE GROVES : Orange growers face an uncertain future
on similar topics ...
India's new growth recipe: Larger firms
How well are securities laws enforced?
The need to spatialise human rights in urban India
Shaping our streets for people
Wildlife-friendly land use: Would incentives work?
Dual lesson plans can bridge the digital divide
Migrant women find moving up is still hard
Household appliances: Fruits of labour
Why aren't more women working?
ESG: A lot more S needed
Higher funding alone doesn't improve urban services
Can governments let go of fossil-fuel revenues?
Month-wise GST collections
Why doesn't the CAG look at its own past work?

redpajama_set_name: RedPajamaCommonCrawl


Suppose a patient loses faith in the potential of any treatment to cure them. They will become sicker and soon die.
What applies to our physical health applies much more to our moral and spiritual health. Why much more? Because when we become morally and spiritually sick, we can hurt not just ourselves but also others.
Let's backtrack to better understand this inner dynamic.
However, even if we stop trying to improve, the inner self-destructive force won't allow us to stay where we are; it will attack us with greater force and drag us down to actions of depravity and even brutality. The Bhagavad-gita (03.37) states that the inner self-destructive force degrades us till it devours completely everything we hold sacred.
Thankfully, Gita wisdom assures that our potential to improve is never lost. It is intrinsic to who we are: pure souls, parts of the all-pure source of everything.
If we don't want to become cowardly or malicious, we need to unsentimentally understand that in our inner war, we can't stay on neutral ground. Committing ourselves to resisting our inner enemy, we seriously seek inner empowerment, thereby increasing our receptivity to spiritual insights and practices.
Why can't we maintain the status quo in the inner war?
How does losing faith in our potential lead to cowardice and malice?
Why is our potential to improve never lost?


This past weekend I went to the NY NJ Gem Show, held in Edison NJ. There are very few gem shows in the northeast. I am lucky this one is a short travel distance from me. I go every year and always find a few treasures.
Blue stones ready for custom made jewelry. Lapis, turquoise, Shattuckite and Herkimer Diamonds.
My favorite colors are blues of the water and sky. There are three Lapis stones here that I find magical. I can't wait to set them into something beautiful. There are also two incredible turquoise triangles that will make a great pair of earrings. The rough, raw turquoise I will use for rings. The two stones on top right are Shattuckite from Congo. In the center is a sprinkle of clear Herkimer Diamonds (quartz) that are only found in New York state.
Earth Tones stones ready for custom made jewelry. Cross shaped pearls, amber, Dinosaur bones, Royal Imperial Jasper and Picture jasper.
Here are more earthy colored stones. I couldn't resist them. The two cross shapes are cultured pearls. They will be perfect for something to add to the Crosses and Saints Collection. In the center are sprinkles of warm Amber from Poland. An interesting Dinosaur Bone stone is top right , in reds and gray. The two large oval stones on bottom are brown Picture Jasper and a Royal Imperial Jasper from Mexico.
Do you have any ideas for what I should make to set these stones? Let me know if anything here speaks to you.


Each year, on Memorial Day weekend, America stops what it's doing and takes a moment to honor the fallen.
But what about those who went missing in action?
Data from the Defense Department's POW/MIA Accounting Agency (DPAA) outlines the scale of the number of those still considered lost in action. The missing originated from each of the 50 states and any number of U.S. territories — including the Philippines, which was an American commonwealth at the time of the war. The three states with the most missing native sons and daughters are New York, California and Pennsylvania. (Were it a state, the Philippines would rank fourth on this list, with 4,533 service members listed as missing.) Relative to population, West Virginia, the District of Columbia and Iowa are missing the most service members.
There is a silver lining, however. The same agency that tracks data surrounding POW/MIA continues to make updates, sometimes locating the remains of service members decades after they were reported missing (Marine Corporal Henry Andregg, Jr. was found on May 19 — he was last seen fighting in the Pacific Theater in World War II in 1943).


text:
Life and Arts ›
UT basketball alumnus makes '100 most important burgers' for Austin's homeless
UT alumnus Drew Gressett, the founder of Hat Creek Burger Co., paired his restaurant with nonprofit and church organizations in order to provide burgers to the Austin homeless population. Gressett said that giving back to the community with the "100 most important burgers project" creates a culture of caring within the Austin community.
Photo Credit: Rachel Zein | Daily Texan Staff
Published on March 28, 2016 at 12:06 am Last update on March 28, 2016 at 1:06 am
By Elena Mejia
Each day, UT alumnus Drew Gressett's burgers help improve the lives of 100 members of Austin's homeless community.
In 2009, Gressett's Hat Creek Burger Co. partnered with the Austin Ridge Bible Church and nonprofit Mobile Loaves and Fishes to distribute his "100 most important burgers" to homeless people six days a week. Hat Creek employees cook the burgers in the afternoon, and up to 700 volunteers distribute them every month.
"There aren't enough burgers out there," Gressett said. "Putting food in empty stomachs and the opportunity to go out and serve [the homeless population of Austin] creates a culture of caring about others. That, for me, is the most important thing."
Gressett played basketball for the Longhorns before graduating in 2004. Four years later, he opened his first food truck, which later evolved into four restaurants around Austin. During that transition, Gressett met Matt Freeman, ex-pastor at Austin Ridge Bible Church, and Alan Graham, CEO and co-founder of Mobile Loaves and Fishes, at the Austin Ridge Bible Church. As Gressett's food trailers evolved into brick-and-mortar restaurants, the church began looking into connecting with the homeless community.
The trio united under a shared desire to give back, and Gressett and Freeman co-founded the "100 most important burgers project."
"It really all began with [Gressett] as the chief visionary," Freeman said. "He's an entrepreneur with compassion."
Four to five volunteers show up to Hat Creek Burger Co. on Burnet Road every morning to cut vegetables and, with the help of Hat Creek employees, load the burgers into Mobile Loaves & Fishes' trucks before driving to regions around Austin with the highest homeless rates. Hat Creek, Mobile Loaves & Fishes and the church's partnership now feed more than 30,000 people every year.
"This project has had the most [impact] of any project I've been involved in," Freeman said. "It's not only about the hamburgers, it's about the human-to-human, heart-to-heart interaction."
Gressett said people tend to think the homeless population is made up of lazy people who choose to not work or suffer from mental illness, but it is more common for Austin's homeless to wind up on the streets after losing family.
"When I think about the friend and family support that I have and how they don't have it, that's heartbreaking," Gressett said. "That allows you to go out to the streets and develop relationships."
Hat Creek Burger Co. will open a fifth location in Lakeway this year.
"I always wanted Hat Creek to grow and build a company, but I never really knew the twist and turns it would take," Gressett said. "By the time you come back from handing out the burgers, you've blessed yourself and you've blessed them."


text:
Storm Therapeutics
Exelixis and STORM Therapeutics Enter into Exclusive Collaboration and License Agreement to Discover and Develop Inhibitors of Novel RNA Modifying Enzymes.
California, USA and Cambridge, UK. 14 October 2021. STORM to deliver small molecule ADAR1 clinical candidate compounds discovered using its proprietary RNA modifying enzyme drug discovery platform. Exelixis, Inc. (Nasdaq: EXEL) and STORM Therapeutics (STORM) today […]
Storm Therapeutics and Evotec Leverage Indigo Platform to Progress Oncology Project.
Storm's First-in-Class clinical candidate against an RNA Methyltransferase for use in Cancer was identifed with support from Evotec's Drug Discovery Engine. Storm will progress the compound towards the clinic using indigo, Evotec's integrated Ivestigational New Drug […]
STORM Therapeutics selects first-in-class clinical candidate targeting METTL3
Cambridge, UK. 22 October 2020. Seroba's investee company, STORM Therapeutics, the leading biotechnology company focused on the discovery and development of small molecule therapies modulating RNA epigenetics, has announced that STC-15, its first-in-class drug candidate targeting […]
FutureNeuro partners with STORM Therapeutics to explore the role of RNA epigenetics in epilepsy.
Dublin, Ireland. 9 September 2020. FutureNeuro has announced that it has entered into partnership with Seroba's portfolio company, STORM Therapeutics, the leading biotechnology company focused on the discovery and development of small molecule therapies modulating RNA […]
STORM Therapeutics Presents Breakthrough Data at RNA Epigenetics Conference.
Cambridge, UK. 18 September 2019. STORM Therapeutics, the biotechnology company focused on the discovery of small molecule therapies modulating RNA epigenetics, announced today that Oliver Rausch, Chief Scientific Officer of STORM Therapeutics, will present first […]
Seroba Invests in Storm Therapeutics.
Cambridge, UK. 20 May 2019. STORM Therapeutics ("STORM"), the drug discovery company tackling disease through modulating RNA modifying enzymes, has announced that it has raised an additional £14 million bringing its total Series A financing to […]
Seroba Life Sciences 18 Herbert Street, Dublin 2
T: 353 (0)1 633 4028
Copyright © 2022 Seroba. All rights reserved.
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text:
Will push classes which hopefully simplify the coding of some things.

## Sqlite3.nut
Wrapper for LH-MP [sqlite3_* functions](http://lh-mp.eu/wiki/index.php/Functions#SQLite), created this to simplify the usage of the sqlite3_ functions.

**Usage** (more usage examples can be found in the file):

```squirrel
// Create a new sqlite instance
local sql = SQLite( "filename.db" );

// Create new table
sql.create( "table_name( SOME_ID int(10), FIRST_VALUE varchar(20) UNIQUE, SECOND_VALUE varchar(50) )" ).finalize();

// Insert value into table
sql.insert( "table_name", [1, "My first value", "My second value!"] ).finalize();

// Update existing value in table
sql.update( "table_name", {"FIRST_VALUE": "My new first value"}, {"SOME_ID": 1} );

// Selecting existing values from table
local value = sql.query( "SELECT * FROM table_name WHERE SOME_ID = '1'" ).finalize();

// Using the values
value.count; // Returns the result count
value.results; // Returns an array containing values inside a table
value.results[0].FIRST_VALUE; // This is how you would fetch the FIRST_VALUE from Database

// Deleting existing value from table
sql.query( "DELETE FROM table_name WHERE SOME_ID = '1'" ).finalize();
```

**NOTICE**

Remember to always use .finalize() when you are done with your query requests!

redpajama_set_name: RedPajamaGithub


text:
Q: How do programs like PhotoShop, Word, etc. run forever and react to the mouse? This is a general question, and one that I have yet to find a good solution.
First, some pretext. I'm new to programming and all I have done (mainly anyway) are sequential    programs in C.
This leads me to wonder how do big programs such as word, photoshop,visual studio etc. work.
To be less vauge, how do they remain open for one? All the programs I have written are top to bottom, the code runs and then the program terminates. Also What always user to say click save and the file writes or to click font and change the font. Clearly these operations can be performed in any order, infintely many times.
In general I do not see from my limited experiecne how real world applications are made. I want to try and make something "real" or useful, but school has not yet begun to teach me where to start.

A: Most desktop applications are programmed using a style called event-driven programming.  In this setup, the program usually looks (at a very high level) like this:
while (true) {
    wait for an event to occur.
    react to that event.
}

These "events" tend to be things like mouse clicks, keyboard events, window resizings, etc.  Typically, event-driven programs set up windows and attach pieces of code to them so that when an event occurs, the given piece of code can run.  Each piece of code that's attached tends to look exactly like what you've seen - it executes from the top to the bottom in a normal fashion.  The fact that different events can happen in different orders just means that they run when the user asks them to.
Every language and framework has their own way of handling events, so I'd recommend consulting the documentation for your favorite language / system for more details.
Hope this helps!

redpajama_set_name: RedPajamaStackExchange


text:
A Year of Awards for Sarah Mildred Long
5/21/2019 8:07:00 AM |
Since completing the $162 million Sarah Mildred Long (SML) Bridge Replacement in Kittery. Maine, Cianbro received two impressive awards for this project: one from the Associated General Contractors (AGC) of Maine and the other from the Post-Tensioning Institute (PTI).
In April 2019, Cianbro was one of only five construction companies to receive a Build Maine Award from AGC. The SML Bridge Replacement was recognized in the bridge division for its innovation, uniqueness, and complexity.
Immediately following the Build Maine Award, Cianbro received even more recognition in May when the SML Bridge Replacement received an Award of Excellence in the bridges category from PTI. This award is given to the top project in each category that demonstrates excellence in post-tensioning applications. Major evaluation factors included creativity, innovation, ingenuity, cost-effectiveness, functionality, constructability, and aesthetics.
Not only did we successfully construct a quality project worthy of recognition, but Cianbro's own project team members were also deservedly recognized for their significant safety milestone achievements throughout the project. In particular, Cianbro Safety Manager, Mike Franck, received a Safety Leadership Award from the Associated Builders and Contractors (ABC) of Connecticut in 2017 for his outstanding leadership in ensuring a safe workplace.
In excess of 20 subcontractors and 185 team members working simultaneously on site, the project was completed with more than 660,000 safe hours, only one recordable injury, and zero lost time incidents
Nearly 500 Precast superstructure and lift tower segments were erected
92 lift tower segments were precast on site
More than 40,000 cubic yards of concrete
Nearly 8,000,000 pounds of rebar
More than 300 miles of post-tensioning strand
The majority of the work was performed off temporary work trestles and barges, including the erection of the tower segments
Little Bay Bridge Team Celebrates Milestones 4/30/2012
Destiny Tech Summit 10/28/2008
Little Bay Bridge Project Successfully Completes Span Float-In 5/1/2012
Bright News at Brightman 6/18/2009
Cianbro's PNSY Bridge #1 Repairs Project Celebrates Milestone 9/10/2015
Cianbro's Oxford Casino Project Wins AGC Build Maine Award 4/17/2013


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29 November 2010, at 11:16a.m.
EU - The European Food Safety Authority (EFSA) says that feathers can be collected from geese without welfare implications if the process is carried out at particular times and in certain ways.
EFSA's opinion on the welfare implications of collecting feathers from live geese concludes that this practice can be carried out without causing pain, suffering or injury to the birds if done at a time when the birds are moulting and if brushing and combing techniques are used. Experts on the Animal and Welfare (AHAW) Panel said, however, that under current commercial conditions, plucking feathers, a way of collecting feathers which causes pain, is unavoidable. They therefore recommended that a control system should be put in place to ensure that only moulting feathers are gathered from live geese.
In the opinion, the Panel points out that brushing or combing live geese to collect moulting feathers causes no tissue damage, whereas plucking feathers (that is pulling them out) will result in pain and other forms of suffering, such as bleeding and skin damage. However, as different parts of the body moult at different times, some feathers may be unavoidably plucked when brushing and combing techniques are used. Furthermore, not all the birds in a flock moult at the same time, so those which are not at the appropriate stage in the moulting process may also have their feathers plucked.
EFSA experts recommended that only feathers at the appropriate moulting phase should be gathered and that a control system be put in place to ensure this is carried out in practice, such as by checking for the presence of skin tears or for any blood or tissue on the feathers. Operators should be familiar with the difference between feathers that are ripe for collection and those that are not.
The Panel also concluded that suffering should be avoided or minimised when catching and handling the geese and that operators should be aware of good animal handling methods. The presence of bloody feathers, skin injuries, posture changes (e.g. hanging wings), and broken or dislocated bones can be used to assess the welfare of geese submitted for feather collection. They also suggested that further animal-based indicators should be developed and that future research in the field should be carried out to establish methods to evaluate the maturity of feathers.
The opinion follows a request from the European Commission to assess the welfare of live geese from which feathers are collected for down production. In order to collect the best available data, the Panel looked at all relevant scientific studies and consulted stakeholders from Member States and beyond. A technical meeting attended by representatives from industry and animal welfare organisations was held in May 2010. In addition, a public consultation of the draft opinion took place in August 2010.


You are here:Home » Arizona DUI Law » Can I Refuse a Field Sobriety Test when Pulled Over for DUI?
Refusing to take a field sobriety test may be misconstrued as an admission of guilt. But a DUI defense attorney can explain the refusal away as part of a defense case for a DUI violation trial. By refusing a field sobriety test, you are not providing law enforcement with any new evidence of driving while under the influence, aside from an initial admission of guilt. By not taking the test, the potential of self-incrimination is reduced.
Although field sobriety tests are useful in some situations, these tests are over 40 years old. They have not been updated, thus do not provide the necessary versatility for the variances between types of individuals who are able to safely drive on the roads today.
Roadside field sobriety tests are purposefully more difficult than other types of tests. There is an inherent factor toward failure in these tests, with each field test requiring dexterity many people do not have, even when completely sober. The tests have a small base of stability that can cause balance issues, potential for falling over and other failures that may be seen as intoxication.
For people with a normal or broad base of balance, fewer issues will occur under sobriety. But walking in a line with heel and toe together is much more difficult for many people than it sounds, especially so when one must follow a straight line while retaining the number of steps the officer requested. The leg raise test can make test takers shaky, nervous, jittery and prone to falling over or needing assistance in remaining balanced. All of these issues are exacerbated by unsteady ground, gravel, darkness in night, passing traffic and other factors.
Field sobriety tests have set instructions for officers to follow. But there is no standard for determination of the results, as to whether or not someone is impaired. The officer is the sole judge of this and uses his or her judgment in the balancing test to make a determination toward inebriation. A law enforcement officer can judge someone as drunk or otherwise impaired if that person has difficulty walking the line or performing other tasks to which they are unaccustomed.
When a police officer is making a judgment on driver performance of a roadside test, he or she is not considering the emotional stress of the driver or other issues causing the driver to not perform well. Many drivers become nervous when asked to perform this type of test, particularly after feeling anxious about being pulled over in the first place. Officers often ignore weather, traffic, lighting, driver stress and other factors. Even if other portions of the test are completed successfully, the officer's statement that the test was failed cannot be overridden by the driver.
Drivers do not know which field sobriety test officers will ask them to perform until suspected of driving under the influence of alcohol or other substances. If the driver agrees to take the test, he or she is provided with quick, often confusing set instructions and no explanation of movement or how to perform the test effectively. Following officer instructions can be intimidating and even simply walking a straight line may need to be performed without any kind of visual reference to direct the driver straight ahead. If you have been pulled over, and find yourself performing these tests, there are some tips on taking a sobriety test that you can follow.
Officers look for physical cues from suspected DUI drivers such as swaying from side to side, swerving while walking, raising one's arms, turns or other clues they assign to intoxication.
Do Sober Persons Pass Field Sobriety Tests?
According to a recent study investigating whether sober people are able to perform field sobriety tests effectively as compared to when they are intoxicated, many sober participants could not pass the tests. These people would have been arrested in most instances, despite being completely sober. This is why it is best for people who are pulled over to refuse taking the tests by calmly and politely answering, "No thank you" to the law enforcement officer when the test is requested. By being polite and answering in this manner with a calm demeanor, you are not further incriminating yourself.
We can help you when you are wrongly accused of DUI because of refusal to take a field sobriety test. Our experienced attorneys will be able to guide you through criminal defense when you are charged with DUI due to a breathalyzer or other chemical test. It is important to have an effective lawyer's help in these situations, as even a first offense DUI can have serious, life-changing results that limit your ability to drive, work and pursue your personal goals for the future. Even your freedom can be affected.
When you are accused of this charge in Arizona, call the experienced and effective lawyers of the Law Offices of David Michael Cantor at 602.307.0808 for a free, initial consultation and recommendations regarding your case.


text:
Q: Python copy bitvise ssh client profiles with different IP Trying to change the IP address of a Bitvise SSH Client profile with python, but every time I change the IP address (along with the length byte before the IP address itself) and load the profile into Bitvise, it seems like the profile is corrupted or something.
The process I am following:

*

*Create a SSH profile manually and saved it as TEMPLATE_PROFILE.tlp.

*Run my python script (code below) to copy the template into another file and change the IP address (with the length byte before it).

*Load both the profiles in HxD (hex editor) to verify the only difference is the IP I've changed (to my eyes, it is).

*Load the profile into Bitvise SSH Client where it fails to show the changed IP address in the appropriate field and throws an error in the log window (screenshot below).

My python script (the IP address shown is for dev purposes only):
import shutil

allowedLen = [
    '\x01',
    '\x02',
    '\x03',
    '\x04',
    '\x05',
    '\x06',
    '\x07',
    '\x08',
    '\x09',
    '\x0a',
    '\x0b',
    '\x0c',
    '\x0d',
    '\x0e',
    '\x0f'
]

shutil.copyfile(r"TEMPLATE_PROFILE.tlp", r"C:\\Users\\MyUsername\\Desktop\\Bitvise Profiles\\FINAL.tlp")

with open(r"C:\\Users\\MyUsername\\Desktop\\Bitvise Profiles\\FINAL.tlp", "rb") as binaryFile:
    byteData = binaryFile.read()

byteData = byteData.replace(b'\x08\x41\x53\x44\x46\x48\x4F\x53\x54', bytes("{}{}".format(allowedLen[len("12.32.12.15") - 1], "12.32.12.15"), 'utf-8'))

with open(r"C:\\Users\\MyUsername\\Desktop\\Bitvise Profiles\\FINAL.tlp", 'wb') as file:
    file.write(byteData)
print("Created BitVise profile for the host: FINAL")

Screenshot with the FINAL.tlp loaded on Bitvise SSH Client
Edit to add notes: \x41\x53\x44\x46\x48\x4F\x53\x54 is the "ASDFHOST" in plaint text and the first byte (\x08) is the length of the hostname. This is the hostname I've put in the template tlp file.


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The vinyl soffit we install has the additional advantage of being too slick for wasps or migratory swallows to affix their nests to. It also can help safeguard your home from a potential fire by preventing drifting wildfire embers from entering your attic and setting your home's insulation ablaze.
In short, this innovative soffit and fascia solution addresses many of the problems homeowners in the San Clemente, CA, experience with their roofs. Contact Ameriside today to schedule a free, in-home consultation. We'll also be happy to tell you about the vinyl siding options we have available for installation on your home.


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