text:
\section{Introduction}

Many authors have argued that gravity can be formulated as a gauge
theory~\cite{kib61,iva83,DGL98-grav}.  But there is a fundamental
difference between the Lagrangians of the electroweak and strong
interactions, and the Einstein--Hilbert action of gravity.  The
former are all quadratic in the field strength tensor, whereas the
latter is only linear.  It is therefore of interest to consider the
consequences of a theory of gravity based on a Lagrangian that is
quadratic in the Riemann tensor.  This is the theory we consider here.
We retain the gauge-theoretic framework of the
Einstein--Cartan--Kibble--Sciama theory~\cite{Grwsat}, so the tetrad
(vierbein) and connection are varied independently.  Furthermore, no
derivatives of the vierbein enter the Lagrangian, so that its
variation is straightforward and gives the quadratic analog of the
Einstein equations.

A problematic feature of the gravitational Lagrangian we consider is
that it is scale invariant.  This implies that the only matter
stress-energy tensors that can couple to gravity are trace-free.
Ultimately this symmetry would have to be broken in any physically
realistic theory.  But here we circumvent the problem by only
considering cosmological solutions where the matter is described by
radiation ($P=\rho/3$).  A more attractive property of a quadratic
Riemann Lagrangian is that torsion can be generated without an
accompanying source of spin~\cite{GADWBH}.  This is explicitly
prohibited in Ricci scalar Lagrangians \cite{Grwsat}.  The torsion is
not restricted in type, and can take the form of an isotropic field
appropriate for cosmology.  (For a review of cosmological models with
anisotropic torsion, see~\cite{Grwsat}.)

Here we construct the full cosmological field equations in a
straightforward manner, allowing for the presence of a torsion field.
The symmetries in the Lagrangian allow the equations to be expressed
in a variety of ways, and we show that one set of gauge choices leads
to a simple complex-valued differential equation.  This equations can
be solved explicitly in terms of elliptic functions, though the
accompanying evolution looks almost chaotic.  We find in particular
that the torsion couples to the Hubble parameter to produce
inflationary regimes in a quasi-periodic fashion.  While the present
day experimental upper bound on background cosmological torsion is
very small, on the order of $10^{-30}$ GeV~\cite{Shapiro,Lammer}, our
model shows that it could have been very large during some earlier
epoch, and could become large again in the future.

A further attractive feature of the theory presented here is that many
of the standard cosmological models (coupled to radiation) are
contained as special cases.  With zero torsion the equations are
solved by a standard radiation-dominated cosmology.  This set-up
illustrates neatly how the inclusion of a small amount of torsion
removes the big bang singularity by translating it into the complex
plane.  Minkevich~\cite{Minkevich} and Faria-Busto~\cite{Farina} have also
argued that a quadratic theory can remove the big bang singularity.
Furthermore, we are also able to find solutions that have a
cosmological constant present, despite the fact that is has not been
put in by hand in the original Lagrangian.  This happens because the
equations are now of higher order, and a cosmological constant arises
naturally as a constant of integration.

The paper begins with a derivation of the field equations.  Much of
the complexity of this derivation is avoided by working at the level
of the action.  We then study some of the general properties of
solutions, before considering some special cases.  Unless otherwise
stated we work in natural units where $G = c = 1$.

\section{The field equations}

Our starting point is the action integral
\begin{equation}
S = \int d^4x \sqrt{-g}
\left(\frac{1}{12}R^{\alpha}{}_{\beta\mu\nu}R_{\alpha}{}^{\beta\mu\nu}
+ \kappa{\cal L}_m\right)
\end{equation}
where $R^{\alpha}{}_{\beta\mu\nu}$ is the Riemann tensor, ${\cal L}_m$
is the matter Lagrangian, and $\kappa = 8\pi$.  The gravitational
degrees of freedom in this theory are a tetrad $\vb{_\mu}{^a}$ and the
connection $\sct{_\mu}{^a}{^b}$.  Throughout we use Greek letters for
coordinate components, and Latin for tetrad components.  The Riemann
tensor is constructed from the connection by
\begin{equation}
R^{ab}{}_{\mu\nu} = \partial_\mu\sct{_\nu}{^a}{^b} -
\partial_\nu\sct{_\mu}{^a}{^b} + \sct{_\mu}{^a}{^c}\sct{_\nu}{^b}{_c}
- \sct{_\nu}{^a}{^c}\sct{_\mu}{^b}{_c},
\end{equation}
and this can be thought of as the field strength of the connection
field.

Though the theory discussed here is clearly different from general
relativity, it is still often convenient to talk in terms of
Riemannian geometry and torsion.  The metric is defined in the
expected manner by
\begin{equation}
g_{\mu\nu} = \eta_{ab} \vb{_\mu}{^a}\vb{_\nu}{^b}.
\end{equation}
The metric defines a Christoffel connection $\Gamma^\lambda_{\mu\nu}$,
and from this we can write
\begin{equation}
\sct{_\mu}{^a}{_b} = \vb{_\alpha}{^a}
(\Gamma^\lambda_{\mu\nu} + \con{^\lambda}{_\mu}{_\nu}) \vb{^\beta}{_b}
- \partial_\mu\vb{_\beta}{^a}\vb{^\beta}{_b}.
\end{equation}
This equation defines the contorsion tensor
$\con{^\lambda}{_\mu}{_\nu}$ in terms of the pieces of
$\sct{_\mu}{^a}{_b}$ that would not be present in pure, torsion-free,
general relativity.

In this paper we are interested in cosmological solutions.  As the
underlying metric still gives rise to many of the observational
consequences of the theory, the standard cosmological arguments apply
and we can restrict to a homogeneous, isotropic line element of the
form
\begin{equation}
(ds)^{2} = dt^{2} - a(t)^2\left(\frac{dr^2}{1 - kr^2} +
  r^2 (d\theta^2 + \sin^2\!\theta\, d\bar{\phi}^2)\right).
\end{equation}
Here $k \in \{\pm 1,0\}$ sets the curvature, $a(t)$ is the scale
factor, and the bar on $\bar{\phi}$ is present as the $\phi$ symbol
will be used elsewhere.  A suitable tetrad for this metric is given by
\begin{equation}
\vb{_\mu}{^a} =
\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & a(1 -  kr^2)^{-\frac{1}{2}} & 0 & 0 \\
0 & 0 & ar & 0 \\
0 & 0 & 0 &  ar\sin\theta
\end{pmatrix}.
\end{equation}

The most general spin connection $\sct{_\mu}{_a}{_b}$ consistent with
isotropy and homogeneity has components
\begin{align}
&\sct{_1}{_0}{_1} = \frac{\phi}{\sqrt{1-kr^2}},& &\sct{_1}{_2}{_3} =
  -\frac{\psi}{\sqrt{1-kr^2}},& &\sct{_2}{_0}{_2} = r\phi, \nonumber \\
&\sct{_2}{_1}{_2} = \sqrt{1-kr^2},& &\sct{_2}{_3}{_1}= -r\psi,&
  &\sct{_3}{_0}{_3} = r\phi\sin\theta, \nonumber \\
&\sct{_3}{_1}{_2} = -r\psi\sin\theta,& &\sct{_3}{_1}{_3} = \sqrt{1 -
  kr^2}\sin\theta,& &\sct{_3}{_2}{_3} = \cos\theta,
\end{align}
together with further terms generated by the antisymmetry in the last
two indices.  Here $\phi$ and $\psi$ are scalar functions of time.
The theory therefore contains three gravitational degrees of freedom
--- $a(t)$, $\phi(t)$ and $\psi(t)$.  It is now a straightforward
matter to compute the Riemann tensor and, in terms of a tetrad basis,
we find the following nonzero components:
\begin{align}
R^{0}{}_{j0l} &= \frac{\dot{\phi}}{a}\delta_{jl}  &
R^{0}{}_{ijk} &= -\frac{2\phi\psi}{a^2}\epsilon_{ijk} \nonumber \\
R^{i}{}_{0k0} &= -\frac{\dot{\phi}}{a}\delta^i_k &
R^{i}{}_{0jk} &= -\frac{2\phi\psi}{a^2}\epsilon_{ijk} \nonumber \\
R^{i}{}_{j0k} &= \frac{\dot{\psi}}{a}\epsilon_{ijk} &
R^{i}{}_{jkl} &= \frac{(\phi^2 - \psi^2 + k)}
{a^2}\left(\delta^i_k\delta_{jl} - \delta^i_l\delta_{jk}\right)
\end{align}
(together with further terms generated by the antisymmetry in the last
two indices).

The spatial integrals are now irrelevant to the full action integral,
and the cosmological equations are generated by the reduced action
\begin{equation}
S = \int dt  \left(a(\dot{\phi}^2 -
\dot{\psi}^2) + \frac{1}{a}(\phi^4 - 6\phi^2\psi^2 + \psi^4 + 2k\phi^2
- 2k\psi^2 + k^2) + \frac{\kappa}{3} a^3\rho\right),
\label{CosmAct}
\end{equation}
where we have assumed that the matter content is pure radiation ($p =
\rho/3$).  This implies that the matter content does not contain any
direct coupling to the spin connection.

Scale invariance is still present in this action, though in the
slightly modified form of a combined rescaling and reparameterisation.
The effect of these is that the scale factor $a$ transforms as the
inverse of an einbein,
\begin{equation}
a(t) \mapsto a'(t) = \frac{dt}{dt'} a(t'),
\end{equation}
with $\phi$ and $\psi$ transforming as scalar fields, $\phi(t) \mapsto
\phi'(t) = \phi(t')$.  The result of this symmetry is that the
scale factor $a$ is essentially an arbitrary function and, after
variation, can be chosen in any convenient manner.  Two choices of $a$
are particularly attractive.  The first is the `cosmological' gauge
choice, for which
\begin{equation}
\phi = \dot{a},
\label{defphi}
\end{equation}
where the overdot represents differentiation with respect to $t$.
This is the gauge that most closely resembles a standard FRW
cosmology.  The evolution parameter $t$ measures cosmic time, and the
equations can be expressed in terms of the Hubble function $H(t)$,
where
\begin{equation}
 H = \frac{\dot{a}}{a}.
\end{equation}
The second gauge of interest is the `conformal' gauge in which we set
$a=1$.  In this case the evolution parameter $t$ measures conformal
time, which we denote by $\eta$.  The conformal gauge turns out to be
most convenient for solving the field equations.

\section{Equations of motion and their general solution}

The Euler--Lagrange equations for $\phi$ and $\psi$ from the action
integral~\eqref{CosmAct} are
\begin{align}
\partial_t(a\dot{\phi}) &= \frac{2}{a}(\phi^3 - 3\phi\psi^2 + k\phi) \\
-\partial_t(a\dot{\psi}) &= \frac{2}{a}(-3\phi^2\psi + \psi^3 - k\psi)
\end{align}
The $a$ variation produces a form of Hamiltonian constraint equation,
\begin{equation}
a(\dot{\phi}^2 - \dot{\psi}^2) = \frac{1}{a}(\phi^4 - 6\phi^2\psi^2 +
\psi^4 + 2k\phi^2 - 2k\psi^2 + k^2) - \kappa a^3\rho.
\label{Ham}
\end{equation}
An immediate consequence of these equations is that we recover the
expected conservation law for radiation,
\begin{equation}
a^4 \rho = \mbox{constant}.
\end{equation}
In the absence of torsion $\psi=0$ and, working in the cosmological
gauge, the dynamics reduces to the pair of equations
\begin{align}
\ddot{H} + 4 H \dot{H} &= 2H \frac{k}{a^2} \label{torfree1} \\
(\dot{H} + H^2)^2 &= \left(H^2 + \frac{k}{a^2} \right)^2 - \kappa
\rho.
\label{torfree2}
\end{align}
We return to these equations in section~\ref{cases}.

The full equations of motions are simplest to analyse in the conformal
gauge.  Setting $a=1$, so that all derivatives are with respect to
conformal time, we arrive at the pair of equations
\begin{align}
\phi'' &= 2\phi^3 - 6\phi\psi^2 + 2k\phi \label{phieqn} \\
\psi'' &= -6\phi^2\psi + 2\psi^3 - 2k\psi. \label{psieqn}
\end{align}
Henceforth we use dashes to denote derivatives with respect to
conformal time, and retain overdots for derivatives with respect to
cosmic time.  We now introduce the complex variable
\begin{equation}
Z = \phi + i\psi
\end{equation}
so that the equations of motion are contained in the single
complex-valued differential equation
\begin{equation}
Z'' = 2Z^3 +2kZ.
\end{equation}
This equation has a trivial first integral,
\begin{equation}
{Z'}^2 = Z^4 + 2kZ^2 + A_0
\label{firstint}
\end{equation}
where $A_0$ is a complex-valued constant.  The real part of $A_0$ is
determined by the conserved energy density $a^4 \rho$ and the
curvature via
\begin{equation}
\mbox{Re}(A_0) = k^2 - \kappa a^4 \rho.
\end{equation}
The imaginary part of $A_0$ can similarly be thought of a source term
for the torsion.  The first integral~\eqref{firstint} illustrates that
the system is essentially Hamiltonian, but the complex structure
drives a mixed signature in momentum space (going as
${\phi'}^2-{\psi'}^2$), which has some unusual consequences.

From the first integral form of the equations of motion, the full
solution can be written down as
\begin{equation}
\eta = \int \frac{dZ}{(Z^4 + 2kZ^2 + A_0)^{1/2}}.
\label{IntSol}
\end{equation}
This integral can be solved analytically in terms of the Weierstrass
elliptic function $\wp(\eta) =
\wp(\eta;g_2,g_3)$~\cite{Whittaker,Elliptic,Weierstrass}.  This
function requires two constants, $g_2$ and $g_3$.  These are defined
in terms of the quartic polynomial
\begin{equation}
f(Z) = Z^4 + 2kZ^2 + A_0.
\end{equation}
From this we compute the pair of elliptic invariants $g_2$ and $g_3$,
obtaining
\begin{align}
g_2 &= A_0 + 12k^2 \\
g_3 &= 4kA_0.
\end{align}
The integral
\begin{equation}
\eta = \int^{Z}_{Z_0} \frac{dZ'}{\sqrt{f(Z')}}
\end{equation}
now has the general solution
\begin{equation}
Z = Z_0 + \frac{\sqrt{f(Z_0)}\wp'(\eta) +
  \frac{1}{2}f'(Z_0)\left(\wp(\eta) - \frac{1}{24}f''(Z_0)\right) +
  \frac{1}{24}f(Z_0)f'''(Z_0)}{2\left(\wp(\eta) -
    \frac{1}{24}f''(Z_0)\right)^2 - \frac{1}{48}f(Z_0)f^{(4)}(Z_0)}.
\label{gensoln}
\end{equation}
The Weierstrass $\wp(\eta)$-function has a second order pole at $\eta
= 0$, and the derivative of the Weierstrass function, $\wp'(\eta)$, is
itself an elliptic function with pole of order 3 at $\eta = 0$.  The
constant $Z_0$ is arbitrary, and it is sometimes convenient to chose
it at one of the zeros of $f(Z)$.  With $f(Z_0) =0$ the solution
simplifies to
\begin{equation}
Z = Z_0 + \frac{1}{4}f'(Z_0)\left(\wp(\eta; g2, g3) -
  \frac{1}{24}f''(Z_0)\right)^{-1}.
\end{equation}
Given generic initial conditions, the behavior of the general
solution~\eqref{gensoln} is extemely complicated, as the following
plots illustrate.  Figures~\ref{Agraph} and~\ref{Bgraph} show sample
behaviour both without and then with matter.  We can generally
characterize the general solution as describing periods of fairly
stable behaviour, which are quasi-periodically driven by the torsion
to produce very large, but generally finite, peaks.

\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=11cm]{Z0_1-I_a0_-I.eps}
\end{center}
\caption{\textit{Evolution of $Z$ without radiation.} The plot shows
    the real (solid) and imaginary (dashed) components of $Z(\eta)$ as
    a function of conformal time $\eta$.  For these plots we have
    $f(Z) = Z^4 - i$, $Z_0 = 1 - i$ and the sign for the initial value
    of $Z'$ is chosen so that $\phi$ is decreasing.  Also highlighted
    are the regions in which inflation is occurring, where $0< \phi' <
    \phi^2$.  The magnitude of the inflation is desribed by $\phi'$.  }
\label{Agraph}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=11cm]{Z0_1-I_a0_1-I.eps}
\end{center}
\caption{\textit{Evolution of $Z$ with radiation.}  A similar graph to
    figure~\ref{Agraph}, but now with matter present.  This in
    incorporated by setting $A_0= 1 - i$.  We keep the initial
    value of $Z_0 = 1 - i$.}
\label{Bgraph}
\end{figure}

The plots~\ref{Agraph} and~\ref{Bgraph} also highlight the regions
where inflation is occurring.  To define the regions of inflation we
must first recall how to switch between the conformal and cosmological
gauges.  Given $\phi(\eta)$ we can introduce a scale factor via
equation~\eqref{defphi}, the solution of which is
\begin{equation}
a(\eta) = \exp \left(\int_{\eta_0}^\eta \phi(\eta') \, d\eta' \right).
\end{equation}

With $a$ computed, we then compute the Hubble function by
\begin{equation}
H(\eta) = \frac{\phi(\eta)}{a(\eta)}.
\end{equation}
If necessary, $H(\eta)$ can be converted back to a function of cosmic
time, though it is easier to compute $H(t)$ from the differential
equations in the cosmic gauge.  Typical behaviour for $H(t)$ is shown
in figure~\ref{Hplot}

\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=11cm]{Hgraph.eps}
\end{center}
\caption{\textit{Hubble function $H$ as a function of cosmic time
    $t$.} The initial conditions are chosen to match those of
    figure~\eqref{Agraph}.  Also plotted is the torsion $Q(t)$, where
    $Q=\psi/a$.  Inflationary regions are also highlighted.}
\label{Hplot}
\end{figure}

In the theory as it stands it makes no sense to distinguish one gauge
as being preferred over another, as we have no way of measuring $H$,
for example.  One would have to find some way of breaking the
conformal invariance and including matter with mass.  However, it is
still interesting to compute whether the solutions could represent an
inflating universe.  The standard condition for inflation is
$\ddot{a}>0$, and we also impose the further restriction that
$\dot{H}<0$.  Combined, these produce the restriction $0<-\dot{H}
<H^2$.  In terms of the conformal gauge, the equivalent condition is
\begin{equation}
0< \phi' < \phi^2.
\end{equation}
The regions for which this occurs are marked on figures~\ref{Agraph}
and~\ref{Bgraph}.

A further way of viewing the dynamics is shown in
figure~\ref{complexspace}.  This plot shows the trajectory of $Z(t)$
in complex space over a finite time interval.  The plot further
illustrates how the complex dynamical evolution can arise from a
simple complex ordinary differential equation.  The plot concentrates
on the fine structure around the origin and does not show the large
excursions that occur aperiodically.

\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=11cm]{PhaseZ0_1-I_a0_-I.eps}
\end{center}
\caption{\textit{Complex space trajectory of $Z$.} The plot shows the
  trajectory in complex space of $Z(\eta) = \phi + i\psi$ over a
  finite interval of conformal time.  The plot is for $f(Z) = Z^4 - i$
  with initial condition $Z_0 = 1 - i$.  The plot illustrates how the
  trajectory of $Z(\eta)$ generally stays in the vicinity of the
  origin, but occasionally moves far away.  The horiztonal line
  illustrates one such excursion.}
\label{complexspace}
\end{figure}

\section{Special cases}
\label{cases}

In this section we consider some of the special case solutions to the
general cosmological equations.  First, returning to the torsion-free
equation~\eqref{torfree1} and integrating we find that
\begin{equation}
\dot{H} + 2H^2 = -\frac{k}{a^2} + c_0
\end{equation}
where $c_0$ is a constant of integration.  It then follows from
equation~\eqref{torfree2} that the density is given by
\begin{equation}
\frac{\kappa}{2c_0} \rho = H^2 + \frac{c_0}{2} + \frac{k}{a^2}.
\end{equation}
But, following a redefinition of $\rho$, this is precisely the
standard FRW equation with a cosmological constant $c_0/2$.  Indeed,
in order to include matter into this model, a term representing the
cosmological constant is \textit{forced}!  This is clear from the fact
that $c_0=0$ implies $\rho=0$.

If we continue to specialise by further setting $k$ and $\rho$ to
zero, the cosmological equations reduce to
\begin{equation}
\dot{H} + H^2 = \pm H^2.
\end{equation}
This has two solutions.  The positive root corresponds to constant
$H$, representing a de Sitter space.  The negative root has
$\dot{H}=-2H^2$ and is solved by $H=1/(2t)$.  This corresponds to a
simple big bang model.  So we see that many standard cosmological
solutions are contained in the quadratic Lagrangian framework.

It is instructive to see how we recover the simple big bang solution
$H=1/(2t)$ from the general solution~\eqref{gensoln}.  In the
conformal gauge, this solution is characterised by
\begin{equation}
 Z = \frac{1}{2\eta}.
\end{equation}
To recover this solution we first set $f(Z) = Z^4$, which removes the
matter and curvature contributions.  The general solution now reduces
to (\ref{gensoln}) to
\begin{equation}
Z = Z_0 + \frac{Z_0^2\wp'(\eta) + 2Z_0^3\wp(\eta)}{2\wp^2(\eta) -
  2Z_0^2\wp(\eta)}.
\end{equation}
(Selecting the opposite sign for the square root in this expression
only changes the overall sign in the result.)  With $g_2 = g_3 = 0$ we
have
\begin{equation}
\wp(\eta) = \eta^{-2},
\end{equation}
and it follows that
\begin{equation}
Z = \frac{1}{\eta + Z_0^{-1}}.
\end{equation}
By choosing $Z_0 \mapsto \infty$  we recover the big bang model.
An interesting effect occurs if we include some initial torsion by
setting by setting $Z_0 = -i/b$.  Now the general
solution becomes
\begin{equation}
 Z = \frac{\pm \eta - ib}{(\eta^2 + b^2)}.
\end{equation}
We see now that the initial big bang singularity has been removed by
the torsion and the evolution is entirely finite.  In effect, the
torsion term has moved the singularity to a complex value of the
conformal time.

We can find further interesting models within the general solution.
Choosing $f(Z) = Z^4 + 1$ and $Z_0 = 1$ then the solution produces big
bang and big crunch singularities in a periodic manner (see figure
\ref{BangCrunch}). For this configuration, $g_2 = 1$ and $g_1 = 0$.
This corresponds to one of three special cases of the elliptic
invariants that has been given a special name, this one being the
pseudolemniscate case \cite{Abram}. The pseudolemniscate case has
half-periods $L(\pm 1 + i)/4$ where $L$ is the lemniscate constant
$L/4 = 1.311028\ldots$.

\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=11cm]{Z0_1_a0_-1.eps}
\end{center}
\caption{\textit{Repeated big bang and big crunch scenario without
    torsion.}  Initial values are $A_0= - 1$ and $Z_0 = 1$,
    corresponding to elliptic invariants of $g_2 = -1$ and $g_3 = 0$.
    This is known as the pseudolemniscate case.}
\label{BangCrunch}
\end{figure}

\section{Conclusions}

We have shown that for a Lagrangian that is quadratic in the Riemann
tensor the cosmological equations can be solved analytically in terms
of the elliptic Weierstrass function $\wp(\eta)$.  The model can only
couple to scale-invariant fields, and the only matter considered is
isotropic radiation.  Furthermore, we have shown that these solutions
reduce to standard cosmological solutions in various limits.  This
model is particularly interesting in that it produces many periods of
inflation for a wide range of initial conditions.  But in order for
such a model to be physical it is necessary to break conformal
invariance and introduce mass, which will form the subject of future
research.


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The aim of this study was to determine the reliability of the conditioned pain modulation (CPM) paradigm assessed by an objective electrophysiological method, the nociceptive withdrawal reflex (NWR), and psychophysical measures, using hypothetical sample sizes for future studies as analytical goals. Thirty-four healthy volunteers participated in two identical experimental sessions, separated by 1 to 3 weeks. In each session, the cold pressor test (CPT) was used to induce CPM, and the NWR thresholds, electrical pain detection thresholds and pain intensity ratings after suprathreshold electrical stimulation were assessed before and during CPT. CPM was consistently detected by all methods, and the electrophysiological measures did not introduce additional variation to the assessment. In particular, 99% of the trials resulted in higher NWR thresholds during CPT, with an average increase of 3.4 mA (p<0.001). Similarly, 96% of the trials resulted in higher electrical pain detection thresholds during CPT, with an average increase of 2.2 mA (p<0.001). Pain intensity ratings after suprathreshold electrical stimulation were reduced during CPT in 84% of the trials, displaying an average decrease of 1.5 points in a numeric rating scale (p<0.001). Under these experimental conditions, CPM reliability was acceptable for all assessment methods in terms of sample sizes for potential experiments. The presented results are encouraging with regards to the use of the CPM as an assessment tool in experimental and clinical pain. Trial registration: Clinical Trials.gov NCT01636440.


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How Long Do You Grill Shrimp and Fish – Grill It Right!
Fish and shrimp aren't not only one of the quickest foods you can grill, they can also be the trickiest.
Why? Because two devious misconceptions have become so widespread and popular, they've seduced at least seven out of ten backyard cooks into believing they're the standard rule of thumb for knowing when fish or shrimp are done – turning countless salmon fillets, halibut steaks, and shrimp kebabs into dry, gritty fish jerky.
So, what two cruel, myths are responsible for this seafood sabotage?
You see, while it is true that fish and shrimp are done cooking when these two things happen, food continues to cook for a few minutes after you pull it off the grill.
… which means the times listed below should only be used as an estimate of how long it'll take to cook you meal – not as an exact indicator of when to pull your fish or shrimp off the grill.
To find out how you can easily spot the ideal moment of doneness for pulling your seafood off the grill, check out our tips for grilling fish and shrimp.
And, keep in mind, the times in the table below are for a medium finish. But not all seafood is at its delicious best when it is flaky with a lightly opaque center. Some seafood – such as tuna and oysters are considered to be best served raw, lightly seared, or only lightly smoked.
* This is for tuna that is grilled to medium finish with a barely pink middle. If you prefer your tuna 'Tataki' style, lightly seared (like me), simply sear it for 30 seconds on each side.


A solo guitarist/vocalist with 20 years experience and more than 2,500 performances; in either Acoustic mode or with Electric Guitar and Backing Tracks.
Since 2014 has had the privilege of being the lead singer in the Geoff Harvey Band and the spin off 50's Rock n Roll Band "Johnny and the Spitfires".
A 2000 song repertoire that encompasses beautiful Ballads to Rock, Pop, Country, Swing… 1950's to current Top 40, even Italian Opera to Chinese (Mandarin) songs.
He is consistently the most in-demand entertainer on the Southern Highlands of NSW from all types of Venues, i.e Hotels, Clubs, Resorts, Restaurants, Cafe's, Wineries, as well as Corporate & Private Functions.
and in 2017 Australia's Best Wedding Ceremony Singer.


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The Worst Isn't the Last Thing About the World (April 2021)
Happy Easter!!!!
Spring is here and with the successful role out of the vaccines, life is starting to return to some kind of normality. Whilst we need to continue with our vigilance, there is much to be hopeful and thankful for.
Frederick Buechner's famous line, 'the worst isn't the last thing about the world - it's the next to last thing' has been on my mind during preparations for Holy Week and Easter this year. Easter is about resurrection and it teaches us that even in times of deepest loss and tragedy we can have confidence that this isn't the last thing, that life and hope will ultimately triumph. I'm also a firm believer that God also wants us to know resurrection joy and an abundant life now in this life, as well as in the next.
Nicola Slee's marvellous Easter Garden book captures this message in its poetic weaving of Francis Hodgson Burnett's Secrete Garden and Mary Magdalene's encounter with the risen Lord in the Gospels. Resurrection is now as well as then…. it is here as well as there. The book also observes that this Good News of life after death … that the worst thing isn't the last thing… is to be shared and celebrated.
Mary Lennox in The Secret Garden completes her healing not just with the coming of spring but in the sharing of her secret with others who are also in need of healing and new life. There is a working impulse in the garden itself which seems to compel proclamation and invitation. The garden's secret is a secret that demands to be shared. For Mary Magdalene, too, the encounter in the garden is just the beginning. Just as she thought her life was ending in darkness, she finds life and hope. She is asked to not just learn to live again but that the secret she has discovered in the place of burial, like Mary Lennox's, is not a secret to be kept, but a message that demands to be shared. Moving into morning and moving into the light of new creation, we can be confident that in his great love, Christ will wait for us where he has sent us and will go ahead of us and be there to meet us.
I'll end with the full quote from Frederick Buechner that I think really captures something of the message of Easter that we are called to share:
'The worst isn't the last thing about the world. It's the next to the last thing. The last thing is the best. It's the power from on high that comes down into the world, that wells up from the rock-bottom worst of the world like a hidden spring. Can you believe it? The last, best thing is the laughing deep in the hearts of the saints, sometimes our hearts even. Yes. You are terribly loved and forgiven. Yes. You are healed. All is well'.
I wish you a very happy and blessed Eastertide.
With love and best wishes
Fr Richard

redpajama_set_name: RedPajamaCommonCrawl


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Home Government Government: US
IN motor vehicles department still reeling from computer upgrade
$32 million upgrade caused numerous problems with customer data - and department is still cleaning up.
Written by Richard Koman, Contributor on March 2, 2007
The Indiana Bureau of Motor Vehicles has been unable to send out license plate renewal notices in a timely fashion for three months now. The culprit: glitches in the department's computer system, reports the Indianapolis Star.
In one case, the BMV mailed renewal notices to Zoe Burns of Osceola, but the two registrations went to her parents' home even though she hasn't lived there in almost 30 years. "This is the first major problem with receiving registrations," she said. "It's just frustrating."
The bureau's goal is to mail notices 30 to 45 days before renewal deadline but at this point, a BMV spokesman said, the agency did not know how long it would take before it could meet that goal.
The problem stems from a $32 million upgrade to the computer system. The BMV is still cleaning up customer data in the aftermath of the upgrade. In January, 250,000 notices were delayed.
"I can say we've been working very diligently to review data, to get the registrations out to customers as soon as possible," spokesman Greg Cook said. "We're working as hard as we can to make sure the data is accurate."
Cook acknowledged that the agency's computer system had pulled an old address for Burns, rather than her home in the town about 10 miles east of South Bend. "We apologize for that particular situation," he said. "That's one of the things we've been working to clean up, but that obviously escaped us."


The Buller District Council is carrying out a rolling review of the Buller District Plan (BDP) and has prepared proposed Plan Changes 133-145 (the Proposal).
The Proposal relates to Parts 1-3 of the BDP which contain introductory material and Part 4 which contains the Significant Resource Management Issues, Objectives and Policies for the district. It also addresses Rules 6.2.5., 6.2.6., 6.4.2.2., 6.4.2.4. and 6.4.2.5. which relate to electricity utilities.
Plan Change 133 proposes to replace existing Parts 1-3 with proposed Part 1. Plan Changes 134-144 propose revisions to existing Part 4, as per proposed Part 2. Plan Change 145 proposes to replace the existing rules relating to electricity utilities.
The Council has received applications from the Minister of Education for designations for education purposes, to enable the ongoing operation, maintenance and development of public education, at St Canice's School, Westport and Sacred Heart School, Reefton. These applications have been included in the Proposal.
The Proposal may be inspected at Buller District Council Offices in Westport and Reefton, Buller libraries, the Karamea Information and Resource Centre, the Buller Bay Information and Resource Centre and the Paparoa National Park Visitor Centre & i-SITE, and on Council's website, www.bullerdc.govt.nz. Copies may be obtained from Council offices and the website.
Any person may make a submission on the Proposal. You may do so by sending a written submission to Buller District Council, PO Box 21, Westport 7866, delivering it to the Council office, 6-8 Brougham Street, Westport or emailing it to theplan@bdc.govt.nz.
The submission must be in Form 5 and must state whether or not you wish to be heard in support of your submission. Copies of Form 5 are available from the above locations. Please see links below for relevant documents.
Submissions closed 4.30pm on Friday 8 April 2016.
every person who made a submission has a right of appeal to the Environment Court on the matter/s in their submission.


I started to write this blog post about what Independence Day, the Fourth of July, meant to me. But, I changed my mind. Independence Day only means one thing and it should mean the same thing to all of us. This day, the Fourth of July, Independence Day, marks the birth of the United State of America. Our independence from Great Britain in 1776.
When the Founding Fathers signed the Declaration of Independence, written by Thomas Jefferson, in Philadelphia, they knew that Great Britain would certainly take issue with the American colonies breaking away from their mother country. They knew they were effectively declaring war. They knew that the American colonies did not have the numbers of people or weapons to fight off the British. They had faith that they would, somehow, prevail.
Four days later, the real celebration began. The Continental Congress was still meeting. The Declaration of Independence was read. The Liberty Bell rang. The coat of arms of the King of England was taken down and the celebration began. The United States of America came to life.
What followed was the American Revolutionary War between the 13 colonies and the British Crown. It lasted through approximately 1783 and was a bitter and bloody battle. The French entered the war in 1778 and assisted the Americans. By 1781, the Americans had basically won their freedom. On September 3, 1783, in France, the British recognized that the Americans had won their freedom in the Treaty of Paris.


text:
Why Santander Consumer USA Stock Plummeted 16% Today
The auto and personal loan company surprised the market with its intention to exit the personal lending business.
Jordan Wathen
(TMFValueMagnet)
I think stock investors can benefit by analyzing a company with a credit investors' mentality -- rule out the downside and the upside takes care of itself. Send me an email by clicking here, or tweet me.
Follow @jwthn
What: Shares of Santander Consumer USA (NYSE:SC) dropped more than 16% at the market open today as the company reported third-quarter earnings. Shares have since regained some lost ground, and are now trading down about 12.5%.
So what: Santander shareholders are learning that it's one thing to beat headline earnings, and another thing to meet broad expectations. This quarter, Santander beat analyst expectations on the bottom line, posting quarterly earnings of $0.62 per share compared to a consensus estimate of $0.51 per share.
Ordinarily, this might be the makings of the kind of beat that sends shares soaring, but it's not all about the bottom line. Santander indicated that it may exit the personal lending business in its press release, and subsequently moved its personal lending portfolio to its "held for sale" bucket.
In reclassifying its portfolio, Santander's net charge-off ratio rocketed to 14.4% this quarter, up from 5.3% as of June 30. Notably, its adjusted net charge-off ratio, which excludes the charge for its personal portfolio, rose to 8.7%, higher than its 5.3% ratio last quarter, but mostly in line with its adjusted NCO ratio of 8.4% a year ago.
Moving the personal portfolio to held-for-sale resulted in an adjustment of the loans' carrying value. In the press release, the company noted that it had to carry the portfolio at the "lower of cost or market" value, resulting in the increase in charge-offs this quarter.
Now what: The future for Santander's portfolio is up in the air. The company left it to the imagination, saying only that it was "exploring strategic alternatives" for its personal lending business in its third-quarter presentation.
It did, however, change its 2016 outlook to emphasize that there could be a "timing gap" between when it sells its personal lending portfolio and when it reinvests the capital in car loans, resulting in a drag on its earnings next year. Given the size of Santander's $2.3 billion portfolio, investors should expect to hear much more about its plan in the coming days and weeks.
Santander Consumer USA Holdings Inc.
NYSE:SC
Santander Consumer USA Holdings Inc (SC) Q3 2020 Earnings Call Transcript
Could Auto Loans Be Problematic for Banks Down the Line?
Wells Fargo Is the Canary in the Coal Mine for Subprime Auto Lenders
Why Santander Consumer USA Stock Plummeted 16% Today @themotleyfool #stocks $SC Next Article


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The Federal Reserve's Expanding Regulatory Umbrella
Hester Peirce
Former Senior Research Fellow
Luce Scholar, FinTech, Henry Luce Foundation
The Federal Reserve's performance as a regulator in the years leading up to the 2007–08 crisis earned it widespread criticism. In the wake of the crisis, its fate as a regulator was uncertain as Congress considered regulatory reforms. Some reform proposals would have substantially diminished the Federal Reserve's regulatory role, but the financial reform ultimately signed into law in July 2010—Dodd- Frank—instead increased the Federal Reserve's regulatory power.
While the Federal Reserve, the nation's century- old central bank, is primarily known for its monetary policy responsibilities, it also exercises substantial regulatory powers. The Federal Reserve System consists of the seven-member Board of Governors (Board), supported by a staff of 2,400, and twelve regional Federal Reserve Banks, with their own boards of directors and a combined staff of more than 15,500.[1] The governors are presidentially nominated and Senate-confirmed and fill staggered fourteen-year terms. Few appointees serve a full term. From among the governors, the president nominates and the Senate confirms a chairman and two vice-chairmen to serve four-year terms. Dodd- Frank added the second vice-chairman position to oversee the Board's supervision and regulation functions. The Federal Open Market Committee, which comprises the Board and certain Federal Reserve Bank presidents, makes monetary policy decisions.
As will be discussed below, the Board supervises and regulates an increasing number of companies. In its regulatory capacity, the Board writes prudential rules, imposes reporting and record-keeping obligations, approves or disapproves activities, conducts examinations, and brings enforcement actions. The Board delegates some of these responsibilities—particularly examinations—to the regional Reserve Banks.
The Board supervises and regulates state-chartered commercial banks that are members of the Federal Reserve System. Dodd-Frank did not alter the Board's authority over these banks, of which there were 828 at the end of 2011.[2] Nationally chartered banks continue to be primarily regulated by a separate agency, the Office of the Comptroller of the Currency (OCC). The Federal Deposit Insurance Corporation (FDIC) is the principal federal regulator for state banks that are not members of the Federal Reserve System.
BANK HOLDING COMPANIES
The Federal Reserve Board supervises and regulates all US bank holding companies, including financial holding companies. There were 5,341 bank holding companies—companies that own or control one or more banks—at the end of 2011.[3] Dodd-Frank enhanced the Board's authority over bank holding companies.
1. Dodd-Frank requires the Board to subject bank holding companies with more than $50 billion in assets to "more stringent" prudential standards than apply to other bank holding companies.[4] These standards must include risk-based capital requirements, leverage limits, liquidity requirements, risk-management requirements, resolution plan and credit exposure report requirements, and limits on credit exposure to other companies. The Board also may impose contingent capital requirements, enhanced public disclosures, short- term debt limits, and other prudential standards.
2. Dodd-Frank expands the Board's authority over the whole holding company structure, including subsidiaries—even subsidiaries that have another regulator. Dodd-Frank broadened the Board's ability to write rules for, impose reporting obligations on, examine the activities and financial health of, and bring enforcement actions against subsidiaries, including entities regulated by the Securities and Exchange Commission (SEC) or the Commodity Futures Trading Commission (CFTC) and state-regulated entities.[5] The Board must attempt to avoid duplicating the primary regulator's work.[6] Dodd-Frank requires the Board to examine activities of unregulated subsidiaries.[7] Dodd-Frank's requirement that holding companies serve as a source of strength for their depository subsidiaries gives the Board additional regulatory power over bank holding companies.[8]
SAVINGS AND LOAN HOLDING COMPANIES
Dodd-Frank eliminated the Office of Thrift Supervision and split its regulatory authority among the Board, the OCC, and the FDIC. Regulatory authority over savings and loan (thrift) holding companies and their non-depository subsidiaries went to the Board.[9] The Board's regulatory approach to savings and loan holding companies is patterned on its supervision of bank holding companies, and savings and loan holding companies must serve as a source of strength for their thrift subsidiaries. As of mid-2011, there were 427 savings and loan holding companies.[10]
SECURITIES HOLDING COMPANIES
Prior to Dodd-Frank, an investment bank holding company that owned or controlled a broker or dealer and was not affiliated with a bank could apply to the SEC for comprehensive consolidated supervision in order to satisfy foreign regulatory requirements. Dodd-Frank gives the Board consolidated supervision authority for securities holding companies—companies that own or control one or more SEC-registered brokers or dealers.[11] A securities holding company regulated by the Board will "be supervised and regulated as if it were a bank holding company."[12] To date, there are no securities holding companies supervised by the Board.
DESIGNATED NONBANK FINANCIAL COMPANIES
Dodd-Frank gives the Board regulatory authority over nonbank financial companies designated by the Financial Stability Oversight Council (FSOC). The FSOC is authorized to designate domestic and foreign companies "predominantly engaged in financial activities" such as insurance and investment activities that "could pose a threat to the financial stability of the United States."[13] Dodd-Frank directs the Board to determine by rule what it means to be predominantly engaged in financial activities.[14] Although no entity has yet been designated, several are under consideration.
Designated nonbank financial companies will be subject to heightened prudential regulatory standards, which are likely to be similar to those applicable to large bank holding companies.[15] Dodd-Frank gives the Board authority to regulate the financial activities of nondepository subsidiaries of designated nonbank financial companies.[16]
TARP-RECIPIENT BANK HOLDING COMPANIES
Dodd-Frank included a provision to ensure that the Board retains regulatory authority over bank holding companies with more than $50 billion in assets as of January 1, 2010, that participated in the Capital Purchase Program under the Troubled Asset Relief Program.[17] Even if they cease to be bank holding companies, Dodd-Frank directs the Board to treat them like designated nonbank financial companies. To date, there are no companies in this category.
DESIGNATED FINANCIAL MARKET UTILITIES AND ACTIVITIES
Dodd-Frank also empowers the FSOC to designate "financial market utilities" and payment, clearing, and settlement activities that it "determines are, or are likely to become, systemically important."[18] Designated financial market utilities and financial institutions engaging in designated activities are subject to enhanced regulation by the Board. With respect to financial market utilities or financial institutions regulated by the SEC or the CFTC, the Board plays a backup regulatory, examination, and enforcement role.[19] The FSOC has designated eight systemically important financial market utilities. The Board serves as primary regulator for CLS Bank International—which operates a cash settlement system for foreign exchange transactions—and The Clearing House Payments Company—which operates the Clearing House Interbank Payments System, known as CHIPS. The FSOC has not designated any payment, clearing, or settlement activities.
INTERNATIONAL BANKING ACTIVITIES
Dodd-Frank did not alter the Board's supervisory authority over Edge Act and agreement corporations, which are chartered by the Board and states respectively to engage in international banking transactions. As of the end of 2011, there were 48 Edge Act/agreement corporations.[20 ]Dodd-Frank also did not affect the Board's oversight of domestic banks' foreign operations.
US OPERATIONS OF FOREIGN BANKS
Prior to Dodd-Frank, the Board had authority over the US operations of foreign banking organizations—of which there were more than 200 as of September 30, 2012.[21] Dodd-Frank enhanced the Board's authority to impose prudential regulations on large foreign banking organizations.[22] A recent Board proposal includes heightened prudential standards for large foreign banking organizations and a requirement that certain foreign banking organizations establish separately capitalized intermediate holding companies, which would contain all US subsidiaries.[23]
Dodd-Frank expanded the Board's discretionary authority with a nebulous mandate to consider risk to the financial system in different contexts, such as merger and acquisition approvals and divestitures.[24]
CONSUMER FINANCIAL PROTECTION
Prior to Dodd-Frank, the Board was the regulator primarily charged with promulgating consumer financial protection regulations, but it shared examination and enforcement responsibilities. Dodd-Frank transferred most of the Board's consumer financial protection responsibilities to the Bureau of Consumer Financial Protection.[25] The Bureau, although technically housed within and funded by the Federal Reserve System, is independent from the Board.[26] Consumer regulation is, therefore, one area in which the Board lost regulatory authority under Dodd-Frank.
Dodd-Frank did not—as some policy analysts pro- posed or expected—decrease the Federal Reserve Board's regulatory powers. To the contrary, it gave the Board heightened regulatory authority over certain entities it previously oversaw, and new regulatory authority over entities it did not previously regulate. The Board has demonstrated an intent to exercise this authority aggressively and an interest in gaining new authority. The magnitude of the Board's new powers is indicated by the fact that it has employed 964 employees on Dodd-Frank implementation, which exceeds the staff commitment made by any other regulator.[27] Legislators and other policymakers should continue to evaluate whether the increasingly Federal Reserve-centric allocation of regulatory power and the Board's broad rulemaking discretion is the optimal regulatory structure for the diverse financial services sector.
An Introduction to US Monetary Policy
Is It Time To End the Federal Reserve?
Lawrence H. White, James Broughel
The CFPB Has a Partial Epiphany


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Home / Covington
Sheriff's Deputy, Former Teacher & Covington Officer, Returns to Schools
Kevin Sumner spent four years at Covington Independent Public Schools as a teacher and then sixteen years as a Covington Police Officer.
After retiring from the police department in 2013, he joined the Kenton County Sheriff's Office in December as a deputy and will now use his career skills in education and law enforcement together.
Sumner is the sheriff's department's school resource officer for Covington's elementary schools.
"It's good to have a positive interaction with the kids and to be a good role model and to undo any negative stereotypes of law enforcement that some of the kids may have," Sumner said Thursday at John G. Carlisle Elementary School.
His experience as a teacher sets him apart from other school resource officers because he has a better understanding of classroom management and other issues facing educators during the day.
"It gives me the opportunity when I'm in the schools to have a better idea of where I fit in without being a distraction," Sumner said.
He will spend one day a week at each of the district's elementary schools.
John G. principal Joy Collins said that so far Sumner has spent time answering questions from children about his profession. He was a stop at a recent career fair the school hosted for its kids. "We want him to be a good role model and to connect with kids about law enforcement," Collins said.
"We believe Sumner's interactions with our students as a role model will go a long way in establishing positive relationships with police officers,'' Superintendent Alvin Garrison said.
Garrison joined Sumner and Kenton Co. Sheriff Chuck Korzenborn for lunch at the school on Thursday.
The Kenton County Sheriff's Office provides school resource officers to the school district where officers have been placed in the middle and high schools for years. In January, the district added an officer at the elementary level.
In addition to spending one day a week at each school and serving as a role model, Sumner will help the schools maintain a safe environment, work with teachers on lessons showing how specific subjects are needed to be a police officer (he recently used an example of car accident reconstruction and the math it requires), review emergency plans, and eat lunch with students.
Story & photos by Michael Monks, editor & publisher of The River City News


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Q: Grails BigDecimal constraints not working I am using Grails version 2.3.3, and groovy version 2.1.8.
I am using an online tutorial to help learn Grails web dev, and I have created a domain class with the following constraints
package racetrack

class Race {

static constraints = {
    name(blank:false, maxSize:50)
    city(blank:false)
    state(inList:["GA", "NC", "SC", "VA"])
    startDate()
    distance(min: 0.0)
    cost(min: new BigDecimal(0.0), max: new BigDecimal(100.0))
    maxRunners(min:0, max:100000)
}

String name
Date startDate
String city
String state
BigDecimal distance
BigDecimal cost
Integer maxRunners

}

I'm using scaffolding so I have full CRUD functionality. The problem is, when I go to create a new Race, the app allows me to input values like "-1" in both the distance and cost fields, and values like "200" for the cost field. I noticed that the Integer field maxRunners was working correctly, as it displays a warning message if I try to put in -1 maxRunners. I changed the cost field to be of type Integer, and then the constraints started working.
Why is this happening? I copy and pasted the code from the tutorial into my text file and the constraints to not work for BigDecimal type fields.

A: According to the docs for the min and max constraints, the parameter must be

a class that implements java.lang.Comparable. The type of the value must be the same as the property.

so I can't see any reason why your definition shouldn't work. As a workaround, you could try replacing this
cost(min: new BigDecimal(0.0), max: new BigDecimal(100.0))

with
cost(range: 0..100)

and you could replace this constraint:
distance(min: 0.0)

with a custom validator, e.g.
distance validator: {
    it >= 0.0
}

I've just noticed the following oddity which appears before the 2 problematic constraints
startDate()

Perhaps replacing it with either:
startDate(nullable: true)

or
startDate(nullable: false)

might fix the problem?

A: Doesn't Groovy use java.math.BigDecimal by default? Could you change new BigDecimal(0.0) to simply 0.0 and new BigDecimal(100.00) to 100.00 like this:
cost(min: 0.0, max: 100.0)

Here is the documentation that states:

To support the 'least surprising' approach, groovy literals with decimal points are instantiated as java.math.BigDecimal types rather than binary floating point types (Float, Double).

Also, you could try forcing it by using the G suffix like this:
cost(min: 0.0G, max: 100.0G)

redpajama_set_name: RedPajamaStackExchange


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Courtesy of Law Co. EMA
Tornado rips through Lawrence County
By Ben T.N. Mause Staff Writer
A strong EF-1 tornado ripped through Lawrence County on Thursday, Jan. 12 morning around 8:09 a.m. The twister caused extreme damage along its bouncing path through the county and beyond. According to the Lawrence County Emergency Management Agency, the tornado produced 104 mph winds. It traveled over 30 miles with a maximum width of 325 yards.
"The weather service went ahead… [and] issued a statement that it was a stronger EF-1," said EMA Director Chris Waldrep. "It basically had a long track where it skipped across the county from west to east in a northeastern direction. It would just kind of sit down in different places.
"It was definitely not a long track tornado that we see in the springtime. [Those] get on the ground and just stay on the ground for a long period of time."
A few minutes prior to 8:00 a.m., the National Weather Service issued a tornado warning for the area. Residents were urged to find shelter. Tornado sirens rang across the county.
At approximately 8:09 a.m., the storm hit. Piercing rain caused temporary flooding and wind gusts of over 60 miles per hour hit across the county. The tornado dropped on County Road 177. It caused tremendous damage: massive trees uprooted and flung across fields, a building caved in, and five greenhouses demolished. The barbed wire fences along the road were strewn with tin siding ripped from barns, and debris rested in tree tops.
The twister picked up and jumped to the new travel ball fields by H.A. Alexander Park. A chain link fence surrounding a ballfield was torn down; a set of 30-foot bleachers sat in the middle of the infield, upside down. The metal bleachers flew 50 yards.
At Lawrence Medical Center, part of the roof was ripped off and tossed to the ground. The same occurred at the Relax Inn and other buildings and residences along the storm's track. It dropped again in East Lawrence, snapping grown trees like toothpicks along County Roads 170, 214, 352, and 460.
The storm resulted in several power outages. Some were temporary, but others resulted from downed power lines and twisted power poles. Joe Wheeler EMC worked through the weekend to restore power to some residents in the county.
"As compared to the rest of the state down south, our damage wasn't near as devastating as those tornadoes there," said Waldrep. "But we did have homes that were severely damaged in the county. We had structures like Relax Inn, who lost their roof; the hospital, which had their roof peeled back on it; many downed trees; downed power lines; snapped telephone poles. That all had to be cleaned up and had to be taken care of."
While the county experienced severe damage, Waldrep believes most residents can quickly bounce back.
"We've been through this so many times," said Waldrep. "This county is so resilient. The people in this county know – they spring into action as soon as something happens. You have neighbors helping neighbors. You have people who volunteer their time and their skills to help the people that are in need. So I don't foresee it being a real long process as far as recovery; especially not as long as you're going to see down south."
But for some, recovery will be difficult. Dana Peeden's mom, Elaine LouAllen, owned a home on County Road 177; it was one of the first places the twister dropped. The shop behind the house was destroyed. The tin walls and roof were tossed along the roadway and into the treetops.
"It was horrible because my dad – that was his pride and joy," said Peeden. "I'm glad that he wasn't here to see that."
Peeden and family spent the weekend working to remove her father's antiques from the rubble.
"We made a dent, but we still have a long way to go," Peeden said.
A short way from Elaine LouAllen's home, the tornado hit LouAllen Farms, owned by Peeden's uncle, Larry LouAllen. Five greenhouses were demolished – the remaining two damaged – row covers were swept away, and the tractor barn and house suffered damage.
"It makes you want to sit down and cry," said LouAllen.
All told, the destruction amounted to approximately $260,000 in property loss.
"If we don't have any [insurance] coverage – on the green houses especially – we probably will not build back," said LouAllen.
LouAllen and others were working inside the greenhouses when they received the tornado alert on their phones.
"The girls went in the basement, and I was outside," said LouAllen. "The temperature dropped; it seemed like 10 or 15 degrees in one second."
The wind picked up, and LouAllen made it to the basement right before the storm hit.
In the wake of destruction, the community stopped to pick up the pieces. The tornado passed, and neighbors arrived at debris-strewn properties with chainsaws and trucks. Peeden said people she didn't know showed up to help her family dig through the shop.
"It's like a big community," said Peeden. "Everybody loves everybody."
On Sunday, a neighbor visited each house in the area to provide the volunteers with food.
"This made my day [Sunday] because we were hungry," said Peeden. "And this couple that was down [her mom's] road had grilled out hamburgers and hotdogs and had them in coolers. And they were going around to everyone's house and asking if they were hungry. And they fed us."
LouAllen said that over 50 people worked to begin cleaning up the farm.
"Thursday afternoon folks came; Friday and Saturday we had probably 25 people each day helping," said LouAllen. "It's been a lot of volunteer help. We really appreciate that."
With the destruction and tragedy in Autauga County, Peeden expressed relief that Lawrence escaped further harm.
"We're very grateful that no one was killed," said Peeden.
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Allied: Moulton unites in wake of overdoses
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This time - Type-N female. One of the most critical components in DIY calibration standard is the connector used to build it. The market is flooded with all kinds of connectors but most of them are of really shoddy quality (sorry to bash on China but that's where all the junk comes from). After playing with and testing different connectors, my conclusion is that one is shooting in the dark ordering connectors from China to use for DIY cal standards. Very rare there will be good enough connector from China, even for 60 MHz VNA cal standard. It is unbelievable the amount of sub-standard junk they make!
The best way to go about is to find high-quality brand name connectors on the surplus market. Ebay is also a good source but it takes time and patience to find what you need.
I've mentioned before that having a few sets of cal standard -different connector type and gender is very useful! I needed a good set of female Type-N OPEN and SHORT (I have a commercial LOAD).
One can buy on eBay a used female Type-N to female-SMA adapter of REALLY high quality for about $10/pc - I am talking about Amphenol 131-445 / HP-Agilent #1250-1404. Even at $30 this adapter is still a bargain. It is actually a bulkhead female Type-N used for commercial VNAs, Spectrum analyzer and other lab equipment. The body is machined from stainless steel, the pin receptacle is gold-plated copper-beryllium and it is using very interesting dielectric.
The center dielectric is made of a small plastic disc with 6 dead holes - 3 on each side of the disc. In each set the holes are at 120 degrees and the two sets are offset by 60 degrees from each other. As a result - the center pin receptacle is supported only by 6 very little plastic spokes. The holes are fairly large leaving mostly air around the center. This is as close as it gets to DIY air dielectric while still have strong mechanical support for the pin receptacle. I think the reason for the "dead holes" is to stop dust and contaminants getting inside.
For the OPEN I just cut the center pin flush to the dielectric. The dielectric disc has a brass sleeve in the center. A dab of solder fixes the pin receptacle to the sleeve. The disc is not made from teflon and soldering time and temperature should be minimal. One can easily measure the distance to the reference plane and calculate the offset. The stray capacitance and losses are minimal due to the dielectric's construction.
The SHORT is made by soldering a "washer" of tin-plated brass to the center pin. When the back shell (the gold plated part) of the connector is screwed in place it presses onto the outer part of the washer and makes the electrical connection to the connector's body. I left the rest of the center pin intact - it goes inside the teflon dielectric of the back SMA part for additional mechanical support.


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The 7th of Aban is one of the most important days in the history of the country; The day after the efforts of the greatest Achaemenid king named Cyrus the Great. According to Moj News Agency, the name of Cyrus the Great or Cyrus the Great, the greatest Achaemenid king, is so brilliant in the history of Iran that thousands of years after his death, traces of it can still be seen in the minds of many Iranians. This name is so ingrained in the soil of this land that a day has been set aside to honor him; A day that has no place in the calendar and is recorded only in the memory and minds of the inhabitants of this land.
What's happening in Iran in Cyrus the great day
Today, November 27, is the anniversary of the founding of the transition and the first Achaemenid emperor, Cyrus the Great, or Cyrus the Great, who relied on vast areas of Asia for thirty years from 559 to 529 BC. Everyone who lives in this land is well acquainted with the name of Achaemenid Cyrus; However, many have only heard his name and know little about his way of life and governance. Under the pretext of this day, we want to take a look at the life of this king.
On this day, the 7th of Aban of the year ١١٩٩ Persian equal ٥٣٩ BC, Cyrus the Great entered Babylon. The people of Babylon thought that with the rule of Cyrus the Great they would face plunder, murder, and encroachment on their lives, property, and wives, and then they would be ruled by a tyrant and oppressor, but not only did Cyrus the Great and his soldiers not do so, but he commanded freedom and Gave equality.
According to Herodotus, Cyrus was of royal descent, and other Greek writers, except Katzias, considered Astana, the daughter of Astyages, to be Cyrus' mother, and reported that Cyrus was the wife of Cambyses I and Mandana. Some modern historians consider this narration to be valid, but others believe that the narration had political roots and its purpose was to make the founder of the Achaemenid Empire a semi-material man to reconcile the Medes with the rule of the Persians. They do not believe in Cyrus and consider it a myth.
Explore the rest of Iranian events
Iran is home to different types of events just like Nowruz, Yalda night and etc. These events are the true representative of the rare Iranian history and culture which are belonging to the rare Persian territory. This is why exploring Iranian events could be a great guide to those who wants to travel and discover. the land of beauties, Iran.


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