text:
\section{Abstract}
In the electronic measurement of the Boltzmann constant based on
Johnson noise thermometry, the ratio of the power spectral densities
of thermal noise across a resistor at the triple point of water,
and pseudo-random noise synthetically
generated by a quantum-accurate voltage-noise source
is constant to within 1 part in a billion for frequencies up to 1 GHz.
Given knowledge of this ratio, and the values of other parameters that are known or measured,
one can determine the Boltzmann constant.
Due, in part, to
mismatch between transmission lines,
the experimental ratio spectrum
varies with frequency.
We model this spectrum
as an even polynomial function of frequency
where the constant term
in the polynomial
determines the Boltzmann constant.
When determining this constant (offset) from experimental data,
the assumed complexity of the ratio spectrum
model and the maximum frequency analyzed (fitting bandwidth)
dramatically affects results.
Here, we
select
the complexity of the model
by cross-validation -- a data-driven statistical learning method.
For each of many fitting bandwidths,
we determine the component of uncertainty
of the offset term
that accounts for random
and systematic effects associated with imperfect knowledge of model
complexity.
We select the fitting bandwidth that minimizes
this uncertainty.
In the most recent measurement of the Boltzmann constant,
results were determined, in part, by application of an earlier version of
the
method described here.
Here, we extend the earlier analysis by considering a broader
range of fitting bandwidths and quantify an additional component of
uncertainty that accounts for imperfect
performance of our fitting bandwidth selection method.
For idealized simulated data
with additive noise
similar
to  experimental data,
our method correctly selects the true complexity
of the ratio spectrum model for all
cases considered.
A new analysis of
data
from the recent experiment yields
evidence for a temporal trend
in the offset parameters.
\\
Keywords:
Boltzmann constant,
cross-validation,
Johnson noise thermometry,
model selection,
resampling methods,
impedance mismatch

\section{Introduction}

There are various experimental methods to determine the Boltzmann
constant
including
acoustic gas
thermometry \cite{M1},\cite{P1},\cite{Pod1}; dielectric constant gas thermometry \cite{G1},\cite{L1}, \cite{Ga1}, \cite{Ga2}, Johnson noise thermometry (JNT)
\cite{B1}, \cite{B2},
\cite{Qu01}, and Doppler broadening \cite{Bo1}, \cite{F1}.
CODATA
(Committee on Data for Science and Technology)
will
determine the
Boltzmann constant as a weighted average of estimates determined
with these methods.
Here, we focus on JNT experiments which utilize
a quantum-accurate voltage-noise source (QVNS).

In JNT, one infers true thermodynamic
temperature based on measurements of the fluctuating voltage and
current noise caused by the random thermal motion of electrons in
all conductors. According to the Nyquist law, the mean square of
the fluctuating voltage noise for frequencies below 1 GHz and
temperature near 300 K can be approximated to better than 1 part
in  billion as $<V^2> = 4 kT R \Delta f$, where $k$ is the Boltzmann
constant, $T$ is the thermodynamic temperature, $R$ is the resistance
of the sensor, and $\Delta f$  is the bandwidth over which the noise
is measured.
Since JNT is a pure electronic
measurement
that is
immune from chemical and mechanical changes in
the material properties of the sensor,
it is an appealing alternative to other forms of
primary gas thermometry that are limited by the non-ideal properties
of real gases.

Recently, interest in JNT has dramatically increased because of its
potential contribution to the ``New SI" (New International System),
in which the unit of thermodynamic temperature, the kelvin, will
be redefined in 2018 by fixing the numerical value of $k$. Although
almost certainly the value of $k$ will be primarily determined by the
values obtained by acoustic gas thermometry, there remains the
possibility of unknown systematic effects that might bias the
results, and therefore an alternative determination using a different
physical technique and different principles is necessary to ensure
that any systematic effects must be small. To redefine the kelvin,
the Consultative Committee on Thermometry (CCT) of the International
Committee for Weights and Measures (CIPM) has required that besides
the acoustic gas thermometry method, there must be another method
that can determine $k$ with a relative uncertainty below 3$\times
10^{-6}$. As of now, JNT is the most likely method to meet this
requirement.

\textcolor{black}{
In JNT with a QVNS,
\cite{Qu01},
according to physical theory,
the Boltzmann
constant is related to the ratio of the power spectral density \textcolor{black}{(PSD)}
of noise produced by
a resistor at the
triple point of water temperature
and
the \textcolor{black}{PSD} of
noise produced
by
a QVNS.
For, frequencies below 1 GHz, this ratio
is constant to within 1 part in $10^{9}$.
The physical model for the
\textcolor{black}{PSD}
for the noise across the resistor is
$S_{\tiny{\mbox{R}}}$
where
\begin{eqnarray}
S_{\tiny{\mbox{R}}} = 4 k T_{\tiny{\mbox{W}}} X_{\tiny{\mbox{R}}} R,
\end{eqnarray}
$T_{\tiny{\mbox{W}}}$ is the temperature of the triple point of water,
$X_{\tiny{\mbox{R}}}$ is the resistance in units of the von Klitzing resistance $R_{\tiny{\mbox{K}}} = \frac{h}{e^2}$
where $e$ is the charge of the electron and $h$ is Planck's constant.
The model for the
PSD of the
noise produced by the QVNS,
$S_{\tiny{\mbox{Q}}}$,
is
\begin{eqnarray}
S_{\tiny{\mbox{Q}}} = D^2 N^2_{\tiny{\mbox{J}}} f_{\tiny{\mbox{s}}} M / K^2_{\tiny{\mbox{J}}},
\end{eqnarray}
where $K_{\tiny{\mbox{J}}} = \frac{2e}{h}$, $f_{\tiny{\mbox{s}}}$ is a clock frequency, $M$ is a bit length
parameter, $D$ is a software input parameter that determines the
amplitude of the QVNS waveform, and $N_{\tiny{\mbox{J}}}$ is the number of junctions
in the Josephson array
in the QVNS.
\textcolor{black}{Assuming that the  Eq. 1 and Eq. 2 models
are valid,
the Boltzmann constant $k$ is}
\begin{eqnarray}
k = h \frac{ D N^2_{\tiny{\mbox{J}}} f_{\tiny{\mbox{s}}} M}
{ 16 T_{\tiny{\mbox{W}}}
X_{\tiny{\mbox{R}}} }
\frac{S_{\tiny{\mbox{R}}}}
{S_{\tiny{\mbox{Q}}}}.
\end{eqnarray}
}

In actual experiments,
transmission lines
that
connect the resistor and the QVNS to preamplifiers
produce a
ratio spectrum that varies with frequency.
Due solely to
impedance mismatch effects,
for the frequencies of interest,
one expects the
ratio spectrum \textcolor{black}{predicted by physical theory}
to be an
even polynomial function of frequency where the
constant term (offset) in the polynomial is the
value $S_{\tiny{\mbox{R}}}/S_{\tiny{\mbox{Q}}}$
provided that dielectric losses are negligible.
The theoretical justification for this polynomial model
is based on low-frequency filter theory where
measurements are modeled
by a ``lumped-parameter approximation."
In particular,
one models the networks
for the resistor and the QVNS
as combination of series and parallel complex impedances
where
the impedance coupling in the resistor network
is somewhat different from that in the QVNS network.
For the ideal case where
all shunt capacitive
impedances are real, there are no dielectric losses.
As a caveat,
in actual experiments,
other effects including electromagnetic
interference
and filtering aliasing also affect
the ratio spectrum.
As discussed in \cite{Qu01},
for the the recent experiment of interest,
dielectric losses and other effects
are small compared to impedance mismatch effects.
As an aside,
impedance mismatch
effects also influence
results in
JNT experiments
that do not utilize a QVNS
\cite{Kamp}, \cite{Bla}, \cite{Whi}.

Based on a fit of the ratio spectrum model to the observed ratio spectrum,
one determines the offset parameter $S_{\tiny{\mbox{R}}}/S_{\tiny{\mbox{Q}}}$.
Given this estimate of $S_{\tiny{\mbox{R}}}/S_{\tiny{\mbox{Q}}}$ and values of other terms
on the right hand sided of Eq. 3 (which are known or measured),
one determines the Boltzmann constant.
However,
the choice
of the order $d$ (complexity) of the polynomial ratio spectrum  model and the upper frequency cutoff for analysis
(fitting bandwidth $f_{\tiny{\mbox{max}}}$)
significantly affects both the estimate and its associated uncertainty.
In JNT, researchers typically select the model complexity and fitting bandwidth based
on scientific judgement informed by graphical analysis of
results.
A common approach is to restrict attention to sufficiently
low fitting bandwidths where curvature in the ratio spectrum is
not too dramatic and
assume that a quadratic spectrum model
is valid
(see \cite{B2} for an example of this approach).

In contrast to a practitioner-dependent subjective approach,
we present a
data-driven
objective
method to select the complexity of the
ratio spectrum model and the fitting bandwidth.
In particular, we select the ratio spectrum model based on
cross-validation
\cite{St1},\cite{St2},\cite{AC},\cite{HTF}.
We note that in addition to cross-validation,
there are other model selection methods
including
those
based on the Akaike Information Criterion (AIC)
\cite{Ak}, the Bayesian Information Criterion (BIC) \cite{S1},
$C_p$ statistics \cite{Mallows}.
However,
cross-validation
is more data-driven and flexible than these other
approaches because
it relies on
fewer modeling assumptions.
Since the selected model
determined by any method is a function of
random data, none perform perfectly.
Hence,
uncertainty due to imperfect
model
selection performance
should be accounted for
in the
uncertainty budget for any parameter
of interest
\cite{BA}, \cite{CH}.
Failure to account for uncertainty in the selected model
generally leads to underestimation of uncertainty.

In cross-validation, one
splits observed data into
training and validation subsets.
One
fits candidate models to training data,
and selects the model that is most consistent
with validation data that are independent of the training
data.
Here (and in most studies) consistency is measured
with a cross-validation statistic equal to
the mean square deviation between predicted and observed values
in validation data.
We stress that, in general,
this mean square deviation depends on both random and systematic
effects.

For each candidate model,
practitioners sometimes
average cross-validation statistics from many
random splits of the data
into training and validation data set
\cite{Pic},
\cite{Sh}, \cite{Xu}.
Here,
from many random splits,
we instead determine
model selection fractions
determined from a five-fold cross-validation
analysis.
Based on these model selection fractions,
we determine
the uncertainty
of
the offset parameter for each fitting bandwidth of interest.
We select
$f_{\tiny{\mbox{max}}}$ by minimizing
this uncertainty.
As far as we know, our
resampling
approach for quantification of uncertainty due to random effects and
imperfect performance of
model selected by
five-fold
cross-validation
is new.
As an aside,
for the case where
models are selected based on
$C_p$
statistics,
Efron \cite{Ef1}
determined
model selection
fractions with a
bootstrap resampling scheme.

In \cite{Qu01},
the complexity of the ratio spectrum
and the fitting bandwidth
were selected
with an earlier version of the method described
here
for the case where
$f_{\tiny{\mbox{max}}}$ was no greater than 600 kHz.
Here, we re-analyze
the data from \cite{Qu01}
but allow
$f_{\tiny{\mbox{max}}}$ to be as large as
1400 kHz.
In this work, we also
quantify an additional component of uncertainty
that accounts for
\textcolor{black}{imperfect performance of our
method for selecting the
fitting bandwidth.}
We stress that this work focuses only
on the uncertainty
of
the offset parameter in ratio spectrum model.
For a discussion of other sources of uncertainty
that affect
the estimate of the Boltzmann constant,
see
$\cite{Qu01}$.
In a simulation study, we show that
our methods
correctly selects
the correct ratio spectrum for
simulated data with additive noise similar to observed data.
Finally,
for experimental data,
we quantify evidence for a possible
linear temporal trend in estimates
for the offset parameter.

\section{Methods}

\subsection{Physical model}
Following \cite{Qu01},
to account for impedance mismatch effects,
we
model the ratio of the
power spectral densities
\textcolor{black}{of resistor noise and QVNS noise},
${r}_{\textcolor{black}{\tiny{\mbox{model}}}}(f)$,
as
a $d$th order even polynomial function of frequency
as follows
\begin{eqnarray}
\textcolor{black}{
{r}_{\textcolor{black}{\tiny{\mbox{model}}}}(f) = \sum_{i=0}^{i_{\tiny{\mbox{max}}}} \alpha_{2j} (\frac{f}{f_0})^{2i},
}
\end{eqnarray}
where
$d = 2 i_{\tiny{\mbox{max}}}$,
and
$f_0$ is a reference frequency (1 MHz in this work).
Throughout this work, as shorthand, we
refer to this model as a $d = 2$ model if $i_{\tiny{\mbox{max}}}=1$,
a $d = 4$ model if $i_{\tiny{\mbox{max}}}=2$, and so on.
The constant term, $a_0$ in the Eq. 4 model
corresponds to
${S_{\tiny{\mbox{R}}}}/{S_{\tiny{\mbox{Q}}}}$
\textcolor{black}{where $S_{\tiny{\mbox{R}}}$ and $S_{\tiny{\mbox{Q}}}$ are predicted by Eq. 1 and Eq 2. respectively.}

\subsection{Experimental data}
\textcolor{black}{
Data was acquired for each of 45 runs
of the experiment
\cite{Qu01}.
Each run occurred on a distinct day
between
June 12, 2014 to September 10, 2014.}
The time to acquire data \textcolor{black} {for each run} varied from 15 h to 20 h.
For each run,
Fourier transforms of
time series corresponding to the
resistor at the
triple point of water temperature and
the QVNS
were determined at a resolution of 1 Hz
for frequencies up to
2 MHz.
\textcolor{black}{Estimates of
mean PSD}
were formed for frequency
blocks of width 1.8 kHz.
For the frequency block with midpoint $f$,
for the $i$th run,
we denote
the \textcolor{black}{mean PSD} estimate
for the resistor \textcolor{black}{noise} and QVNS
\textcolor{black}{noise}
for the $i$th run as
${S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}}(f,i)$
and
${S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}}(f,i)$ respectively
where $i=$ 1,2, $\cdots$ 45.

Following \cite{Qu01},
we define a reference value
$a_{0,\tiny{\mbox{calc}}}$
for the
offset term in our Eq. 4
model as
\begin{eqnarray}
a_{0,\tiny{\mbox{calc}}} = \frac{4 k_{2010} RT }{ S_{\tiny{\mbox{Q}},{\tiny{\mbox{calc}}}}},
\end{eqnarray}
where $k_{2010}$ is the CODATA2010 recommended value of the
Boltzmann constant, $R$ is the measured resistance of the
resistor with traceability to the quantum Hall resistance,
$T$ is the triple point water temperature and $S_{\tiny{\mbox{Q}},\tiny{\mbox{calc}}}$ is the
calculated power spectral
density of \textcolor{black}{QVNS noise}.

\textcolor{black}
{In the recent experiment
the true value of the resistance, $R$,
could have varied from run-to-run.
Hence,
in \cite{Qu01},
$R$ was measured for each run in a
calibration experiment.
Based on these calibration experiments,
$a_{0,\tiny{\mbox{calc}}}$ was determined for each run.}
The difference between the maximum and minimum of the estimates
determined from all 45 runs is
2.36 $\times 10^{-6}$.
For the $i$th run, we denote
the
values $a_0$ and $a_{0,\tiny{\mbox{calc}}}$ as $a_0(i)$ and
$a_{0,\tiny{\mbox{calc}}}(i)$ respectively.
Even though
$a_0(i)$ and
$a_{0,\tiny{\mbox{calc}}}(i)$
vary from run-to-run,
we assume that temporal
variation of their difference,
$a_0(i) -
a_{0,\tiny{\mbox{calc}}}(i)$,
is negligible.
Later in this work, we check the validity of this
key modeling assumption.
The component of uncertainty
of the estimate of
$a_{0,\tiny{\mbox{calc}}}$ for any run
due to imperfect knowledge of
$R$
is approximately 2 $\times 10 ^{-7}$.
The estimated weighted mean value of our estimates,
$\hat{\bar{a}}_{0,\tiny{\mbox{calc}}}$,
is
1.000100961. The weights are determined from
relative data acquisition times for the runs.

Following \cite{Qu01},
for each frequency,
we pool data
from all 45 runs to form
a numerator term
$\sum_{i=1}^{45} S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}(f,i)$
and a denominator term
$\sum_{i=1}^{45} S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}(f,i)$.
From these two terms,
we estimate
one ratio
for each frequency
as
\textcolor{black}{
\begin{eqnarray}
r_{\tiny{\mbox{obs}}}(f) =
\frac{
\sum_{i=1}^{45} S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}(f,i)
}
{
\sum_{i=1}^{45} S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}(f,i)
}
\end{eqnarray}
}
(see Figure 1).
From the Eq. 6 ratio spectrum,
we estimate one residual offset
term
$a_0 -
{\bar{a}}_{0,\tiny{\mbox{calc}}}$
where
${\bar{a}}_{0,\tiny{\mbox{calc}}}$
is the weighted mean of $a_{0,\tiny{\mbox{calc}}}$
values from all runs.

\subsection{Model selection method}
In our cross-validation approach, we select the model that produces
the prediction (determined from the training data) that is most consistent
with the validation data.
Since $a_{0,\tiny{\mbox{calc}}}$ varies from run-to-run,
we correct $S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}$ spectra so that our cross-validation
statistic
is not artificially inflated by
\textcolor{black}{run-to-run
variations} in $a_{0,\tiny{\mbox{calc}}}$.
The corrected ratio spectrum
for the $i$th run is
\textcolor{black}{
\begin{eqnarray}
\textcolor{black}{
{r}_{\tiny{\mbox{cor}}}(f)} =
\frac{
\sum_{i=1}^{45} S_{\tiny{\mbox{R}},\tiny{\mbox{cor}}}(f,i)
}
{
\sum_{i=1}^{45} S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}(f,i)
}
\end{eqnarray}%
}
where
\begin{eqnarray}
S_{\tiny{\mbox{R}},\tiny{\mbox{cor}}}(f,i) =
S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}(f,i) -
(\hat{a}_{0,\tiny{\mbox{calc}}}(i) -
\hat{\bar{a}}_{0,\tiny{\mbox{calc}}} )
S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}(f,i).
\end{eqnarray}
In effect, given that our calibration
experiment measurement of $a_{0,\tiny{\mbox{calc}}}(i)$
has negligible systematic error,
the above correction
returns produces a spectrum where
the values of $a_0$
should be nearly the same for all runs.
We stress that
after selecting the
model \textcolor{black}{based on cross-validation
analysis of corrected spectra (see Eq. 7)},
we estimate
$a_0 - {\bar{a}}_{0,\tiny{\mbox{calc}}}$
from the uncorrected Eq. 6 spectrum.

In our cross-validation method,
we generate 20 000 random five-way splits of the data.
In each five-way split,
we assign the
pair of spectra,
($S_{\tiny{\mbox{R}},\tiny{\mbox{cor}}}$
and $S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}})$,
from any particular run to one  of the five subsets
by a
resampling
method.
Each of the 45 spectral pairs appears in one and only one
of the five subsets.
We resample spectra according to run to
retain possible correlation structure
within the spectrum for any particular run.
Each simulated five-way split is determined by
a random
permutation of the positive integers from 1 to 45.
The first nine permuted integers corresponds to the runs assigned to the
first subset. The second nine correspond to the runs assigned to the second subset, and so on.
From each random split,
four of the subsets are aggregated to form
training data, and
the other subset forms the
validation data.
Within the training data, we pool all $S_{\tiny{\mbox{R}},\tiny{\mbox{cor}}}$ spectrum and
all
$S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}$ spectrum and form one ratio spectrum.
Similarly, for the validation data, we pool all $S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}$ spectrum and
$S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}$ spectrum and form one ratio spectrum.
We fit each candidate polynomial ratio spectrum model to the training data, and predict
the observed ratio spectrum in the validation data
based on this fit.
We then compute
the (empirical)
mean squared deviation (MSD) between predicted and observed
ratios for the
validation data.
For any random five-way split, there are five
ways of defining the validation. Hence, we compute five MSD values for
each random split.
The cross-validation statistic for
each $d$,
CV($d$),
is the
average of these five MSD values.
For each random five-way split, we select the model
that yields the smallest value of CV($d$).
Based on 20 000 random splits of the 45 spectra,
we estimate
a probability mass function
$\hat{p}(d)$
where
the possible values of $d$ are:
2,4,6,8,10,12 or 14.

\subsection{Uncertainty quantification}
For any choice of $f_{\tiny{\mbox{max}}}$, suppose that
$d$ is known exactly. For this ideal case,
based on a fit of the ratio spectrum model to the
Eq. 6 ratio spectrum,
we could construct a {coverage} interval for
$a_0$ with standard asymptotic methods or with
a parametric bootstrap method \cite{Ef2}.
{For our application,
we approximate the
parametric bootstrap
distribution} of our estimate of $a_0$ as
a Gaussian distribution with mean $\hat{a}_0$ and
variance
$\hat{\sigma}^2_{\hat{a_0}(d),\tiny{\mbox{ran}}}$,
where
$\hat{\sigma}_{\hat{a_0}(d),\tiny{\mbox{ran}}}$
is predicted by asymptotic theory.
To account for
the effect of
uncertainty
in $d$ on
our estimate of
$a_0$, we form a mixture of bootstrap distributions as follows
\begin{eqnarray}
f(x) =  \sum_{d}^{} \hat{p}(d) g( x, \hat{a}_0(d), \hat{\sigma}^2_{\hat{a_0}(d),\tiny{\mbox{ran}}})
,
\end{eqnarray}
where
$g( x, \mu, \sigma^2)$ is the {probability density function} (pdf)
for a Gaussian random variable with expected value $\mu$ and
variance $\sigma^2$.
For any $f_{\tiny{\mbox{max}}}$, we select the $d$
that yields the largest
value of
$\hat{p}(d)$.
Given that the probability density function (pdf) of a
random variable $X$ is $ f(x) = \sum_{i=1}^{n} w_i f_i(x)$,
and the mean and variance of a random variable $Z$
with pdf $f_i(z)$ are
$\mu_i$ and $\sigma^2_i$, the mean
and variance of $X$ are
\begin{eqnarray}
E(X) = \mu =  \sum_{i=1}^{n} w_i \mu_i,
\end{eqnarray}
and
\begin{eqnarray}
VAR(X) =
\sum_{i=1}^{n} w_i \sigma^2_i
+
\sum_{i=1}^{n} w_i  (\mu_i - \mu)^2.
\end{eqnarray}
Hence, the mean
and variance
of a random variable sampled from
the Eq. 9 pdf
are
$\hat{\bar{a}}_0 $
and
$\hat{\sigma}^2_{\tiny{\mbox{tot}}}$
respectively, where
\begin{eqnarray}
\hat{ \bar{a}}_0  =
\sum_{d} \hat{p}(d)  \hat{a}_0(d),
\end{eqnarray}
and
\begin{eqnarray}
\hat{\sigma}^2_{\tiny{\mbox{tot}}}
=
\tilde{\sigma}^2_{\alpha}
+
\tilde{\sigma}^2_{\beta},
\end{eqnarray}
where
\begin{eqnarray}
\tilde{\sigma}^2_{\alpha} = \sum_{d} \hat{p}(d)
\hat{\sigma}^2_{\hat{a}_0(d),\tiny{\mbox{ran}}},
\end{eqnarray}
and
\begin{eqnarray}
\tilde{\sigma}^2_{\beta} = \sum_{d} \hat{p}(d) ( \hat{a}_0(d) - \hat{\bar{a}}_0 ) ^ 2
.
\end{eqnarray}

For each $f_{\tiny{\mbox{max}}}$ value,
we estimate the uncertainty of our estimate of
$a_0$ as
$\hat{\sigma}_{\tiny{\mbox{tot}}}$.
We select
$f_{\tiny{\mbox{max}}}$
by minimizing
$\hat{\sigma}_{\tiny{\mbox{tot}}}$
on grid in frequency space.
For any fitting bandwidth,
$\tilde{\sigma}_{\beta}$
is the weighted-mean-square deviation
of the estimates of $a_0$ from the candidate models
about their weighted mean value where the weights
are the empirically determined selection fractions.
The term
$\tilde{\sigma}_{\alpha}$
is the weighted variance of
the parametric bootstrap sampling distributions for
the candidate models where
the weights
are again the empirically determined selection fractions.
We stress that both
$\tilde{\sigma}_{\alpha}$
and
$\tilde{\sigma}_{\beta}$
are affected by
imperfect knowledge of the ratio spectrum model.

\section{Results}
\subsection{Analysis of Experimental data}

We fit candidate ratio spectrum models to the Eq. 6 observed ratio spectrum by the method of Least Squares (LS).
We determine model selection fractions (Table 1)
and $\hat{\sigma}_{\tiny{\mbox{tot}}}$ (Table 2) for
$f_{\tiny{\mbox{max}}}$ values on an evenly space grid
(with spacing of 25 kHz)
between
200 kHz and 1400 kHz.
In Figure 2,
we show how
selected $d$, $\hat{\sigma}_{\tiny{\mbox{tot}}}$ and
$\hat{a}_0 - \hat{\bar{a}}_{0,\tiny{\mbox{calc}}}$
vary with $f_{\tiny{\mbox{max}}}$.
Our method selects
$(f_{\tiny{\mbox{max}}},d)$ = ( 1250 kHz, 8),
$\hat{\sigma}_{\tiny{\mbox{tot}},*}=$
3.25 $\times 10^{-6}$,
and
$\hat{a}_{0} - \hat{\bar{a}}_{0,\tiny{\mbox{calc}}} = $ 2.36
$\times 10^{-6}$.
In Figure 3, we show results for the values of
$f_{\tiny{\mbox{max}}}$
(
that yield
the five lowest values of $\hat{\sigma}_{\tiny{\mbox{tot}}}$.
For these five fitting bandwidths
(900 kHz, 1150 kHz,
1175 kHz, 1225 kHz and 1250 kHz)
$\hat{\sigma}_{\tiny{\mbox{tot}}}$ values appear to follow no pattern
as a function of frequency, however
visual inspection suggests that the
\textcolor{black}{estimates
of
${a}_{0} - {\bar{a}}_{0,\tiny{\mbox{calc}}}$}
may follow a pattern.
It is not clear if the variations in Figure 2 and 3
are due to
random
or systematic measurement
effects.
To get some insight into this issue, we
study the performance of our method for
idealized simulated data that are free of systematic measurement error.

We simulate
three realizations of
data based on the estimated values of
$a_2,a_4,a_6 $ and $a_8$ in Table 3.
In our simulation, for each run, we set $a_0 - a_{0,\tiny{\mbox{calc}}}$ = 0,
${S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}}(f)$ = 1
and
${S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}}(f)$ equals the sum of the predicted
ratio spectrum and Gaussian white noise.
For each run,
the variance of the noise
is
determined from
fitting
the ratio spectrum model to the experimental ratio spectrum for that run.
For simulated data, the
$d$, $\hat{\sigma}_{\tiny{\mbox{tot}}}$
and $\hat{a}_0 - a_{0,\tiny{\mbox{calc}}}$ spectra
exhibit fluctuations
similar to those in the experimental data (Figures 4,5,6).
Since
variability
in simulated data
(Figures 4,5,6)
is due solely to random effects,
we can not rule out the possibility that
random effects may have produced
the
fluctuations in the
experimental spectra (Figures 2 and 3).
For the third realization of
simulated data (Figure 6), the estimated values of $a_0 - a_{0,\tiny{\mbox{calc}}}$
corresponding to the $f_{\tiny{\mbox{max}}}$ values that yield
the five lowest values of $\hat{\sigma}_{\tiny{\mbox{tot}}}$
form two clusters in $f_{\tiny{\mbox{max}}}$ space which are separated by
approximately 300 kHz (Figure 7).
This pattern is similar
to that
observed for the experimental data (Figures 3).
As a caveat,
for the experimental data, we can not rule
out the possibility that systematic measurement error could
cause or enhance observed
fluctuations.

Our method correctly selects the $d$=8
model for each of three independent realizations of simulation data (Table 4).
In a second study, we simulate
three realizations of
data according to a $d$=6 polynomial model
based on  the fit to experimental
data for $f_{\tiny{\mbox{max}}} = $ 900 kHz.
Our methods correctly selects the $d$=6
for each of the three realizations.

In \cite{Qu01},
our method selected
$f_{\tiny{\mbox{max}}}=$ 575 kHz and $d=4$
when $f_{\tiny{\mbox{max}}}$ was constrained to be less than
600 kHz.
For these selected values,
our current analysis yields
$\hat{a}_0 - \hat{\bar{a}}_{0,\tiny{\mbox{calc}}} = $ 1.81
$\times 10^{-6}$
and
$\hat{\sigma}_{\tiny{\mbox{tot}}}=$ 3.58
$\times 10^{-6}$.
In this study,
when $f_{\tiny{\mbox{max}}}$ is allowed to be as large as 1400 kHz,
our method selects
$f_{\tiny{\mbox{max}}}$ = 1250 Hz and $d=8$,
and
$\hat{a}_0 - \bar{\hat{a}}_{0,\tiny{\mbox{calc}}} = $ 2.36
$\times 10^{-6}$
and
$\hat{\sigma}_{\tiny{\mbox{tot}},*}=$ 3.25
$\times 10^{-6}$.
The difference between
the two results,
0.55
$\times 10^{-6}$,
is small compared to the
uncertainty of either result.

We expect imperfections in our fitting
bandwidth selection method for various reasons.
First,
we conduct a grid search with a resolution of 25 kHz
rather than a search over a continuum of frequencies.
Second, there are
surely
fluctuations in
$\hat{\sigma}_{\tiny{\mbox{tot}}}$
due to random effects that vary with fitting bandwidth.
Third,
different values of
$f_{\tiny{\mbox{max}}}$ can yield very similar values of
$\hat{\sigma}_{\tiny{\mbox{tot}}}$ but somewhat different values of
$\hat{a}_0 - \hat{\bar{a}}_{0,\tiny{\mbox{calc}}}$.
Therefore, it is reasonable to
determine an additional component of uncertainty, $\hat{\sigma}_{f_{\tiny{\mbox{max}}}}$,
that accounts for uncertainty due to imperfect
\textcolor{black}{performance of our method to
select $f_{\tiny{\mbox{max}}}$.}
Here we equate
$\hat{\sigma}_{f_{\tiny{\mbox{max}}}}$
to the estimated standard deviation of
estimates of
$a_0  -{\bar{a}}_{0,\tiny{\mbox{calc}}}$
corresponding to the
five $f_{\tiny{\mbox{max}}}$ values that yielded
the lowest $\hat{\sigma}_{\tiny{\mbox{tot}}}$ values (Figures 3 and 7).
For the three realizations of simulated spectra, the corresponding
$\hat{\sigma}_{f_{\tiny{\mbox{max}}}}$
values {are}
0.39 $\times 10^{-6}$,
0.45 $\times 10^{-6}$,
and
1.83
 $\times 10^{-6}$.
For the experimental data
$\hat{\sigma}_{f_{\tiny{\mbox{max}}}}= $ 0.56
$\times 10^{-6}$.
For both simulated and experimental data, our update for
the total uncertainty of estimated  $a_0$
is
$\hat{\sigma}_{\tiny{\mbox{tot}},\mbox{final}}$ where
\begin{eqnarray}
\hat{\sigma}_{\tiny{\mbox{tot}},\mbox{final}}  =
\sqrt{
\hat{\sigma^2}_{\tiny{\mbox{tot}},*}  +
\hat{\sigma^2}_{f_{\tiny{\mbox{max}}}} }.
\end{eqnarray}
For the simulated data,
$\hat{\sigma}_{\tiny{\mbox{tot}},\mbox{final}}$
is
2.69 $\times 10^{-6}$,
3.08 $\times 10^{-6}$,
and
3.42
$\times 10^{-6}$.
For the experimental data,
$\hat{\sigma}_{\tiny{\mbox{tot}},\mbox{final}}= $
3.29
$\times 10^{-6}$.
As a caveat, the choice to quantify
$\hat{\sigma}_{f_{\tiny{\mbox{max}}}}$ as the standard deviation
of the estimates corresponding to $f_{\tiny{\mbox{max}}}$ values that
yield the five lowest values is
based on scientific judgement.
For instance,
if we determine
$\hat{\sigma^2}_{f_{\tiny{\mbox{max}}}} $ based on the
the $f_{\tiny{\mbox{max}}}$ values that yield the ten lowest
rather the five lowest
values $\hat{\sigma}_{\tiny{\mbox{tot}}}$,
for the three simulation cases and the observed data
we get
$\hat{\sigma}_{f_{\tiny{\mbox{max}}}}  =$
0.55 $\times 10^{-6}$,
1.08 $\times 10^{-6}$,
1.42 $\times 10^{-6}$,
and
0.73 $\times 10^{-6}$ respectively.

\subsection{Stability analysis}
From the corrected Eq.7 spectra,
we estimate
$a_0 - \bar{a}_{0,\tiny{\mbox{calc}}}$
for each of the 45 runs
by
fitting our selected ratio spectrum model
($d=$ 8 and $f_{\tiny{\mbox{max}}}=$ 1250 kHz)
to the data from each
run
by the method of LS
(Figure 8).
Ideally, on average, these
estimates should not \textcolor{black}{vary} from run-to-run assuming that
our Eq. 8 correction model based on calibration
data is valid.
From these estimates, we determine the
slope and intercept
parameters for a linear trend
model by the method of Weighted Least Squares (WLS)
where we minimize
\begin{eqnarray}
\chi^2_{\tiny{\mbox{obs}}}
=
\sum_{i=1}^{45} w_i ( y_i - \hat{y}_i )^2.
\end{eqnarray}
Above, for the $i$th run,
$y_i$ and $\hat{y}_i$
are the estimated and predicted (according to the trend model)
values of
$a_{0} - {\bar{a}}_{0,\tiny{\mbox{calc}}}$,
and
$w_i$ is the
inverse of the squared
asymptotic uncertainty of
associated with our estimate
determined by the LS fit to data from the  $i$th run.
We determine the uncertainty of the trend model
parameters with a nonparametric bootstrap method (see Appendix 1)
following \cite{DH}
(Table 5).
We repeat the bootstrap procedure but set
$\hat{y_i}$ to a constant.
This analysis yields an estimate of the null distribution
of the slope estimate
corresponding to the hypothesis that there is no trend.
The fraction of bootstrap slope estimates with magnitude greater than
or equal to the magnitude of the estimated slope determined
from the observed data is the bootstrap $p$-value
\cite{Ef2}
corresponding to a two-tailed test of the null hypothesis.
For the $f_{\tiny{\mbox{max}}}$ values that yield
the five lowest values of $\hat{\sigma}_{tot}$,
our bootstrap analysis provides strong evidence that
$a_{0} - {\bar{a}}_{0,\tiny{\mbox{calc}}}$ varies with time.
At the value of $f_{\tiny{\mbox{max}}} = $ 575 kHz,
there is a moderate amount of evidence for a trend.

For each $f_{\tiny{\mbox{max}}}$ choice,
we test
the hypothesis that the linear trend is consistent
with observations based on the value of
$\chi^2_{\tiny{\mbox{obs}}}$.
If the observed data are consistent with the
trend model,
a resulting $p$-value
from this test
is realization of a random variable
with a distribution that is approximately uniform between 0 and 1.
Hence, the large $p$-values reported column 7 of Table 5 suggest that
the asymptotic uncertainties
determined by the LS method
for each run may be inflated.
As a check, we estimate the slope uncertainty with a
parametric bootstrap method where we simulate
bootstrap replications of the observed data by adding
Gaussian noise to the estimated trend with standard deviations equal to the
asymptotic uncertainties determined by the
LS method.
In contrast to the method from
\cite{DH},
the
parametric bootstrap method yields larger slope uncertainties.
For instance, for the 1250 kHz and 575 kHz cases, the parametric
bootstrap slope uncertainty estimates are larger than the
corresponding Table 5 estimates by 30 $\%$ and
23 $\%$ respectively.
\textcolor{black}{That is, the parametric bootstrap method estimates
are inflated with respect to the estimates determined with the
method from $\cite{DH}$.}

\textcolor{black}{This inflation}
could result due to
heteroscedasticity
(frequency dependent additive measurement error variances).
This follows from the well-known fact that when
models are fit to heteroscedastic data, the variance of
parameter estimates determined by the LS method
are larger than the variance of parameter estimates determined
by the ideal WLS method.
Based on fits of selected models to data pooled from all runs,
we test the hypothesis that the variance of the additive noise
in the ratio spectrum is independent of frequency.
Based on
the
Breush-Pagan method \cite{BP}, the $p$-values
corresponding to the test of this hypothesis are
0.723, 0.064, 0.006, 0.001, 0.001 and 0.001 for
fitting bandwidths of 575 kHz,
900 kHz,
1150 kHz,
1175 kHz,
1225 kHz,
and 1250 kHz respectively.
Hence, the evidence for heteroscedasticity is
very
strong for the larger fitting bandwidths.

For a fitting bandwidth of 1250 kHz,
the variation of the estimated trend
over the duration of the experiment
is
$18.2 \times 10^{-6}$.
In contrast,
the uncertainty of
our estimate
of
$a_{0} - \bar{a}_{0,\tiny{\mbox{calc}}}$
determined under the assumption that there is no trend
is only
3.29
$\times 10^{-6}$ (Table 4).
The  evidence for a linear trend at particular fitting bandwidths above 900 kHz
is strong (p-values are 0.012 or less) (column 5 in Table 5).
In contrast, the evidence (from hypothesis testing) for a linear trend at 575 kHz
(the selected fitting bandwidth in \cite{Qu01})
is not as strong since
the p-value is 0.049.
However, the larger p-value at 575 kHz may be due to more random variability
in the estimated offset parameters rather than lack of a deterministic trend
in the offset parameters.
This hypothesis is supported by the
observation that the uncertainty of the estimated slope parameter
due to random effects generally increases as the fitting bandwidth
is reduced, and
that fact that
all of the slope parameter
estimates for cases
shown in Table 5 are negative
and vary from
-0.440 $\times 10^{-6}$ / day
to
-0.164 $\times 10^{-6}$ / day.
Together,
these observations strongly suggest a
deterministic trend in measured offset parameters at a fitting bandwidth of 575 kHz.
Currently, experimental efforts are underway to understand the physical source
of this (possible) temporal trend.

If there is
a linear temporal trend in the offset parameters at a fitting bandwidth of 575 kHz,
with slope similar to what we estimate from data,
the reported uncertainty for the Boltzmann constant reported in
\cite{Qu01} is optimistic because the trend was not accounted for
in the uncertainty budget.
To account for the effect of a linear trend on results, one must
estimate the associated systematic
error due to the trend at some particular time.
Unfortunately,
we have no empirical method to
do this.
As a further complication,
if there is a trend, it may not be exactly linear.

\section{Summary}
For electronic measurements of the Boltzmann constant
by JNT, we
presented a data-driven method
to select the complexity of
a ratio spectrum  model
with
a cross-validation
method.
For each candidate fitting bandwidth,
we quantified
the
uncertainty of
the offset parameter in the spectral ratio model
in a way that
accounts for random effects as well as systematic
effects associated with imperfect knowledge of model
complexity.
We selected the fitting bandwidth that minimizes
this uncertainty.
We also quantified an additional component of uncertainty
that accounts for imperfect
knowledge of the selected fitting bandwidth.
With our method, we re-analyzed data from a recent experiment by considering a broader
range of fitting bandwidths and found evidence for a temporal linear trend
in offset paramaters.
For idealized simulated data
free of systematic error with additive noise
similar
to  experimental data,
our method correctly selected the true complexity
of the ratio spectrum model for all
cases considered.
In the future, we plan to study
how well our methods work for other experimental and simulated JNT data sets
with variable signal-to-noise ratios and investigate how
robust our method is to systematic measurement errors.
We expect our method to find broad
metrological applications including
selection of optimal virial equation models
in gas thermometry experiments,
and selection of line-width models in Doppler broadening thermometry experiments.

{\bf Acknowledgements.}
Contributions of staff from NIST, an agency of the US government,
are not subject to copyright in the US.
JNT research at NIM is supported by grants NSFC (61372041 and 61001034).
Jifeng Qu acknowledges Samuel P. Benz, Alessio Pollarolo, Horst Rogalla,
Weston L. Tew of the NIST and Rod White of MSL, New Zealand for
their help with
the JNT measurements analyzed in this work.
We also thank Tim Hesterberg of Google for
helpful discussions.

\section{Appendix 1: nonparametric bootstrap resampling method}
We denote the estimate of
$a_0 - \bar{a}_{0,\tiny{\mbox{calc}}}$
from the $i$th run as
$y_i$,
and the data acquisition time for the $i$th run as $t_i$.
Our linear trend model
is
\begin{eqnarray}
y = X \beta + \epsilon,
\end{eqnarray}
where the observed data is $y=(y_1,y_2 \cdots y_{45})^T$,
$\epsilon$
is an additive noise
term,
and
the matrix
$X$ is
 \[ \left( \begin{array}{cc}
X_{1~1} & X_{1~2}\\
X_{2~1} & X_{2~2}\\
. & . \\
. & . \\
. & . \\
X_{45~1} & X_{45~2} \end{array} \right)
=
  \left( \begin{array}{cc}
1 & 0   \\
1 & t_2 - t_1  \\
. & .  \\
. & .  \\
. & .  \\
1 & t_{45} - t_1  \end{array} \right),\]
and ${\beta} = {( \beta_0 , \beta_1 )}^{T}$ where
the $\beta_0$ is the intercept parameter and $\beta_1$ is the slope parameter.
Above, we model
the $i$th component of
$\epsilon$ as a realization of a random variable with
expected value 0 and variance $ \kappa V_i$
where $V_i$ is known but $\kappa$ is unknown.
Following \cite{DH},
the predicted value
in a linear regression model is $\hat{y}= X \hat{\beta}$
where the estimated model parameters  $\hat{\beta}$
are
\begin{eqnarray}
\hat{\beta} = ( X^T W X )^{-1} X^T W y,
\end{eqnarray}
where $W$ is a diagonal weight matrix.
Here, we set the $j$th component of $W$
to $w_j =  \frac{1}{V_j}$ where
$V_j$ is the
estimated asymptotic variance of $y_i$ determined by the method of LS.
Following \cite{DH}, we form a modified residual
\begin{eqnarray}
r_i = \frac{  y_i - \hat{y}_i } {  \sqrt{V_i( 1 - h_i) } },
\end{eqnarray}
where $h_i$ is the i$th$ diagonal element of the
hat matrix $H = X( X^T W X)^{-1}X^T W$. This transformation ensures that
the modified residuals are realizations of random variables with
nearly the same variance.
The $i$th component of
a bootstrap replication of the
observed data is
\begin{eqnarray}
y^{*}_i = \hat{\beta}_0 + \hat{\beta}_1 (t_i - t_1) + \sqrt{V_i}  {e^{*}_i},
\end{eqnarray}
where $i =1,2, \cdots 45$ and
$(e^{*}_1, e^{*}_2, \cdots e^{*}_{45}) $
is sampled
with replacement
from  $(r_1 - \bar{r}, r_2 - \bar{r}, \cdots r_{45} - \bar{r})$
where $\bar{r}$ is the mean modified residual.
From each of 50 000 bootstrap replications of the observed data,
we determine a slope and intercept parameter.
The bootstrap estimate of the uncertainty of the
slope and intercept parameters are the estimated standard
deviations of the slope and intercept parameters determined
from  these estimates.

\section{Appendix 2: Summary of model selection and uncertainty quantification method}

\noindent
1. Based on a calibration data estimate of $a_{0,\tiny{\mbox{calc}}}$ for each run, correct
$S_{\tiny{\mbox{R}},\tiny{\mbox{obs}}}$ spectra per Eq. 8.
\\

\noindent
2. Set fitting bandwidth to $f_{\tiny{\mbox{max}}}$ = 200 kHz.
\\

\noindent
3. Set resampling counter to $n_{\tiny\mbox{resamp}}=$ 1.
\\

\noindent
4. Randomly split
$S_{\tiny{\mbox{R}},cor}$ and $S_{\tiny{\mbox{Q}},\tiny{\mbox{obs}}}$ spectral pairs
from each of 45 runs
into five subsets.
Select $d$ by five-fold cross-validation
and
update appropriate model selection fraction estimate.
\\

\noindent
5. Increase $n_{\tiny\mbox{resamp}}$ by 1.
\\

\noindent
6.  If $n_{\tiny\mbox{resamp}} < $ 20 000, go to 4.
\\

\noindent
7.  If $n_{\tiny\mbox{resamp}} = $ 20 000,
select the polynomial model with largest associated selection fraction.
Calculate estimate of residual offset and its uncertainty
$\hat{\sigma}_{\tiny{\mbox{tot}},\mbox{final}}$ (Eq. 16) from pooled uncorrected spectrum (see Eq. 6).
\\

\noindent
8. Increase $f_{\tiny{\mbox{max}}}$ by 25 kHz
and go to 3 if $f_{\tiny{\mbox{max}}} < $ 1400 kHz.
\\

\noindent
9. Select
$f_{\tiny{\mbox{max}}}$
by minimizing
$\hat{\sigma}_{\tiny{\mbox{tot}}}$. Denote the minimum value as
$\hat{\sigma}_{\tiny{\mbox{tot}},*}$.
\\

\noindent
10. Assign component of uncertainty associated with imperfect
performance of method to select $f_{\tiny{\mbox{max}}}$ as
$\hat{\sigma}_{f_{\tiny{\mbox{max}}}}$ to estimated
standard deviation of
offset estimates
corresponding to $f_{\tiny{\mbox{max}}}$ values that yield
the five lowest values of
$\hat{\sigma}_{\tiny{\mbox{tot}}}$.
Our final estimate of the uncertainty of the offset is
$\hat{\sigma}_{\tiny{\mbox{tot}},\mbox{final}} = \sqrt{
\hat{\sigma^2}_{\tiny{\mbox{tot}},*} +
\hat{\sigma^2}_{f_{\tiny{\mbox{max}}}}}$.
\\

For completeness, we note that
simulations and analyses were
done with
software scripts
developed in the public domain R \cite{RR} language and environment.
Please contact Kevin Coakley regarding any software-related questions.

\section{References}

redpajama_set_name: RedPajamaArXiv


Our sister publication, Canadian Architect, is now accepting entries for the annual Awards of Excellence. Celebrating 51 years, Canadian Architect has since 1967 sponsored an annual national awards program recognizing projects in the design stage. Each year, submissions are due in September, judging takes place in October and the winning schemes are published in a special issue every December. Student Awards of Excellence are also awarded for final-year projects by Canadian architecture students.
Meanwhile, submissions to our own Best of Canada Awards are still being accepted, with the May 11 deadline fast approaching!


text:
fairytale – trzeci singel zespołu Kalafina, wydany 24 grudnia 2008 roku. Album zawiera piosenki śpiewane przez Wakana, Keiko oraz Hikaru. Tytułowy utwór został wykorzystany jako motyw przewodni w szóstej części filmu anime Kara no kyōkai.

Singel osiągnął 9 pozycję w rankingu Oricon, sprzedano  egzemplarzy.

Lista utworów
Wszystkie utwory zostały skomponowane i napisane przez Yuki Kajiura.

Dysk pierwszy (CD)

Dysk drugi (DVD)

Przypisy

Linki zewnętrzne
 Profil singla na Oricon

Single Kalafiny
Single wydane w roku 2008

redpajama_set_name: RedPajamaWikipedia


text:
var mdw = require('./mdw.js');

const routes = [
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    method: 'get',
    path: '/api/status',
    version: undefined,
    before: [mdw.m2xClientMdw],
    handler: require('./routes/get_status.js').handler
  },
  {
    method: 'get',
    path: '/api/toilets',
    version: undefined,
    before: [mdw.m2xClientMdw],
    handler: require('./routes/get_toilets.js').handler
  },
  {
    method: 'get',
    path: /^[^(api)].*$/,
    version: undefined,
    handler: require('./routes/get_assets.js').handler
  }
];

function pushToChain(chain, routes) {
  if (Array.isArray(routes))
    chain.push.apply(chain, routes);
  else if (routes instanceof Function)
    chain.push(routes);
}

function loadRoutes(server, log) {
  var chain;
  routes.forEach(function (route) {
    chain = [];
    if (route.before) pushToChain(chain, route.before);
    pushToChain(chain, route.handler);

    server[route.method]({path: route.path, version: route.version}, chain);
    var msg = 'successfully loaded route: ' + route.method.toUpperCase() + ' ' + route.path;
    if (route.version) msg += ' [' + route.version + ']';
    log.info(msg);
  });
}
module.exports.loadRoutes = loadRoutes;

redpajama_set_name: RedPajamaGithub


Widespread poverty and extreme violence hinder access to quality education as well as other basic services and opportunities. Poverty and violence are compounded by under-resourced public schools, with inadequate infrastructure, overcrowding, and many safety concerns. We invest in public schools throughout the region, through initiatives including: After-school programs, Mental Health Committees, Restorative Practices, Mindfulness, and Extreme Makeovers. We provide kids from marginalized communities with opportunities that enable them to stay in school and away from violence. Our goal is to create safe, healthy, dynamic, and stimulating environments that respond to students' interests (i.e. sports, arts, academics, leadership and service, science, and technology) and develop core life skills in children and youth. These programs also integrate and empower communities, strengthening the social fabric by mobilizing students, teachers, parents, and volunteers, as partners in development.
Latin America is home not only to extreme rates of violence, poverty, and trauma, but also dramatic gender disparities, high rates of teen pregnancy, and limited access to healthcare services that are often low-quality. At Glasswing, we believe that we all have the potential to improve our communities' public health outcomes. We invest in health throughout the region to enhance the quality of healthcare in clinics, hospitals, and communities, and providing children, youth, and adults with services that will improve their overall physical, mental, and emotional health. We implement Girls' Clubs, aimed at shifting gender paradigms, building girls and young women's confidence and other key social skills, providing comprehensive reproductive health education, as well as developing their financial and entrepreneurial capabilities. We also partnering with local companies, government, and communities to improve the quality of maternal child, nutrition, and community health services in rural communities. We train healthcare professionals and first responders in basic and advanced life support, as well as trauma-informed care. We also implement Sanando Heridas (Healing Wounds), a hospital-based violence prevention program, aimed at breaking the cycle of violence by educating survivors of violence about the physiological and emotional consequences of trauma, and providing them with the tools to manage them.
Due to the relatively low rate of economic growth in the region in the last decade, employment opportunities are scarce, and income generation is difficult, particularly for young people between the ages of 16 to 29. As a result, it is estimated that one in four young people neither studies nor works. This lack of economic opportunity, coupled with the extreme rates of violence, extortion, and the resulting lack of mobility, thousands of young people are displaced from their communities and forced to migrate. Workforce development programs build young people's life skills and enhance their employability, better preparing them to integrate into the formal economy. Through our programs – Jóvenes Constructores, Mujeres con Futuro, Jóvenes Emprendedores Sociales – we work with youth to believe in their own potential, reintegrate into the school system, participate in community service projects, and acquire the skills they need to access living wage jobs. Aside from the technical training, we also provide ongoing socio-emotional support to help them manage the multiple and complex challenges they face.
Public space is a vital component of a prosperous city. Well-designed and managed public spaces are a key asset for a city's functionality and have a positive impact on its economy, health, climate, safety, integration, and connectivity. Working in some of the most violent regions in the world, the high rates of homicide and crime, increase citizens' fear particularly in public transportation and public spaces, which contribute to low levels of civic participation, coupled with extreme social and political polarization and distrust. Through our public space revitalization programs, we empower citizens to actively participate in the creation, revitalization, and maintenance of public parks, schools, and health facilities.


text:
<?php

namespace Magento\Checkout\Test\Unit\Model\Session;

use Magento\Framework\TestFramework\Unit\Helper\ObjectManager as ObjectManagerHelper;

class SuccessValidatorTest extends \PHPUnit_Framework_TestCase
{
    /** @var ObjectManagerHelper */
    protected $objectManagerHelper;

    protected function setUp()
    {
        $this->objectManagerHelper = new ObjectManagerHelper($this);
    }

    public function testIsValid()
    {
        $checkoutSession = $this->getMockBuilder(
            '\Magento\Checkout\Model\Session'
        )->disableOriginalConstructor()->getMock();
        $this->assertFalse($this->createSuccessValidator($checkoutSession)->isValid($checkoutSession));
    }

    public function testIsValidWithNotEmptyGetLastSuccessQuoteId()
    {
        $checkoutSession = $this->getMockBuilder(
            'Magento\Checkout\Model\Session'
        )->disableOriginalConstructor()->getMock();

        $checkoutSession->expects(
            $this->at(0)
        )->method(
            '__call'
        )->with(
            'getLastSuccessQuoteId'
        )->will(
            $this->returnValue(1)
        );

        $checkoutSession->expects($this->at(1))->method('__call')->with('getLastQuoteId')->will($this->returnValue(0));

        $this->assertFalse($this->createSuccessValidator($checkoutSession)->isValid($checkoutSession));
    }

    public function testIsValidWithEmptyQuoteAndOrder()
    {
        $checkoutSession = $this->getMockBuilder(
            'Magento\Checkout\Model\Session'
        )->disableOriginalConstructor()->getMock();
        $checkoutSession->expects(
            $this->at(0)
        )->method(
            '__call'
        )->with(
            'getLastSuccessQuoteId'
        )->will(
            $this->returnValue(1)
        );

        $checkoutSession->expects($this->at(1))->method('__call')->with('getLastQuoteId')->will($this->returnValue(1));

        $checkoutSession->expects($this->at(2))->method('__call')->with('getLastOrderId')->will($this->returnValue(0));

        $this->assertFalse($this->createSuccessValidator($checkoutSession)->isValid($checkoutSession));
    }

    public function testIsValidTrue()
    {
        $checkoutSession = $this->getMockBuilder(
            'Magento\Checkout\Model\Session'
        )->disableOriginalConstructor()->getMock();
        $checkoutSession->expects(
            $this->at(0)
        )->method(
            '__call'
        )->with(
            'getLastSuccessQuoteId'
        )->will(
            $this->returnValue(1)
        );

        $checkoutSession->expects($this->at(1))->method('__call')->with('getLastQuoteId')->will($this->returnValue(1));

        $checkoutSession->expects($this->at(2))->method('__call')->with('getLastOrderId')->will($this->returnValue(1));

        $this->assertTrue($this->createSuccessValidator($checkoutSession)->isValid($checkoutSession));
    }

    protected function createSuccessValidator(\PHPUnit_Framework_MockObject_MockObject $checkoutSession)
    {
        return $this->objectManagerHelper->getObject(
            'Magento\Checkout\Model\Session\SuccessValidator', ['checkoutSession' => $checkoutSession]
        );
    }
}


This entry was posted in Health, Ingredients, Lifestyle and tagged Cache in Aspen, Chris Lanter, cooking with marijuana, I'll never go there to eat, why Chris has a stupid grin on his face, why Chris has to wear sunglasses inside by mycookinglifebypatty. Bookmark the permalink.
They did not make drugs legal. They decriminalized marijuana. Alcohol is already a cash cow, so I don't see the difference. Good parenting will help keep your kiddos safe, not overreaching laws. But, I do agree that the recent decriminalization in Colorado has resulted in a tidal wave of stupid. Yet, at the same time, even here is good ol' Tennessee, you can drop a few hundred for a course on how to make noodles for Chrissakes. Modern cuisine and those that market it are the 21st century PT Barnums. The insecure and plain stoopid will pony up the dough, for sure.
Well said! And I think you are spot on.
Good article Patty. I can't agree more about it all is a public relations campaign. Someone has to be making a lot of money off making drugs legal.
Yes and thank you Jack. I am going to pull that string and find out more about it.
Way to go Patty. Glad your back.


text:
Data is the key to tackling gender inequality head-on
More data is required to contribute to a meaningful policy dialogue on gender inequality and provide a solid base for new perspectives. Source: AFP
Breaking the data-on-glass ceiling
Data from the World Bank shows that up to 80% of countries regularly produce sex-disaggregated statistics on mortality, labor force participation, education, and training. But less than one-third of countries disaggregate statistics by sex on informal employment, entrepreneurship such as the ownership and management of a small-to-medium business, and unpaid work, or collect data about violence against women. More and better data is required to contribute to a meaningful policy dialogue on gender equality and provide a solid evidence base for development policy.
But closing gender inequality data gaps goes beyond data collection. Greater efforts are also needed to make the existing country data more accessible to international policymakers and to development practitioners alike, to make lasting changes for future generations – and not just around the time of year that International Women's Day rolls around.
"This year's International Women's Day focuses on #ChooseToChallenge – indeed, we must constantly push the boundaries and aspire towards a more equitable future for all," muses Alexandra Roza, the vice president of Customer Solutions for Asia Pacific and Japan regions at Tableau Software. Tableau is a data visualization firm under global enterprise technology giant, Salesforce.
And despite recent improvements, there is still a noticeable discrepancy between the genders in the workplace, and it is getting more pronounced even in forward-looking industries like the technology scene. "Despite progress in the field, there remains a lack of representation for women in ICT: accounting for just 35% of the cohort in Singapore universities, and 30% of the local Infocomm (information communications) workforce in 2019," says Roza. They also do not have enough visibility in senior leadership or board level roles to support executive decision-making."
At the heart of a lot of these gender inequality concerns are data. Or more accurately, the lack thereof of gender-specific data, which makes it oftentimes difficult to properly ascertain if situations are truly as lopsided as they sometimes appear.
"More needs to be done to level the playing field. At Tableau, we believe that data can be harnessed as a powerful resource to challenge the status quo," affirms Roza. "Data can reveal insights, ignite conversations, and drive change. It is important for us to leverage this asset on both personal and organizational levels to address inequities and empower women."
How to tackle the sticky gender bias in AI?
But what pivotal role can data actually play when it comes to gender inequality in an enterprise setting? "For instance, data plays an important role to highlight gender leadership imbalance; around 70% of people believe men and women are paid equally, but the truth is that women still earn less than their male counterparts even in developed countries," exclaims Tableau's Roza, singling out how a lack of data transparency can affect both perceptions and decision-making.
"This is where data visualizations like the Economic Empowerment of Women, Gender Inequality and the number of women in CEO roles go a long way to change public perception and educate people about prevailing gender issues at the workplace."
Big Data Data

redpajama_set_name: RedPajamaCommonCrawl


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ALINE Racks Up PGA Tour Player Support
Footwear Insole Helps Performance, Reduces Fatigue
ALINE, creators of a new class of golf equipment that replaces your shoes insoles, announced that PGA Tour Professionals, including Ken Duke, Kevin Kisner, Adam Hadwin, Kevin Na, D.A. Points and over 40 more have worn their patented Foot Suspension System this year.
Each week, more and more players on the PGA Tour are discovering the advantages of wearing ALINE. PGA Tour Rep. Mark Gerent stated, "in my 15 years working on tour this is the broadest adoption of a new product I've ever seen." To date more than 100 Tour players, caddies and industry professionals have worked with the ALINE technical staff. They've all recognized the benefits of wearing ALINE on the course and off.
So far this season, three victories have been achieved and over $5 million have been earned by players with ALINEs under their feet. ALINE Golf is engineered with the World's First Foot Suspension System, designed to help improve performance and comfort on the golf course.
Golf Tips editor Vic Williams has put Aline into play over the years and loves how it keeps him feeling fresh even during long walking rounds. "They put factory insoles to shame," he says. "If you want a healthier back and better swing mechanics, take care of your feet. ALINE does that."
Founded in 2005 by a team dedicated to improving performance and health from the ground up, ALINE patented technology optimizes a golfer's performance by properly aligning the back, hips, knees and ankle. This helps reduce lower body fatigue and improves swing mechanics, resulting in maximization of ground force reaction for more distance and accuracy. Proven by 10 PGA Tour wins, Olympic Gold Medals, over 100 X Games medals and doctors across the country, ALINEs are designed for performance in sports and life. ALINE makes similar equipment for skiing, snowboarding, hiking, cycling, gym workouts, running, walking and general fitness activities. The company's motto describes the produce well: "ALINE…what's inside counts."
www.ALINE.com


Winx is a retired champion Australian Thoroughbred racehorse. Between May 2015 and her retirement in April 2019, she won 33 consecutive races including 25 Group 1s, at distances ranging from 1300 metres to 2200 metres. In the World's Best Racehorse Rankings, she was the second-ranked filly or mare in 2015, improving in 2016 to become both the world's top-ranked filly or mare and the world's top-ranked turf horse. She retained this ranking in 2017 and in 2018 was co-ranked as the best horse in the world. In 2017 she was inducted into the Australian Racing Hall of Fame, only the third horse to earn this honour while still in training. She is the leading money-earner in history.


She has three children. Her boyfriend Warren Smith has a son.
Melinda Jane Messenger was born on 23 February 1971 in Swindon.
Her parents divorced when she was five. The Independent carried a detailed article, including an account about the difficulty between Melinda Messenger's parents.
Melinda Messenger worked as an air stewardess and then had a managerial role in a marketing company before she was selected to model for a double glazing company, which led to The Daily Star featuring her on a centre page spread in 1997.
Melinda Messenger then became a Page 3 girl with The Sun.
After modelling, Melinda Messenger moved into TV including presenting her own Channel 5 chat show, Melinda's Big Night In.
In January 2009, Melinda Messenger entered Dancing on Ice partnering Fred Palascak.
Melinda and Fred survived a skate-off in the women celebrities' first week competing in Dancing on Ice.
They went on to survive two more skate-offs, but in week seven of Dancing on Ice, Melinda Messenger and Fred Palascak could not see off the strength of Jessica Taylor and Pavel Aubrecht.
Like fellow Dancing on Ice competitor Jeremy Edwards, Melinda Messenger's previous TV experience has included being a housemate on Celebrity Big Brother, in which she came third behind Les Dennis and Mark Owen.
Around the time of Dancing on Ice, Melinda Messenger was co-presenting Cowboy Builders with Dominic Littlewood.
Melinda Messenger and her husband Wayne Roberts married in Bali on 26 November 1998. They have three children. She is the MD of his electronics company.
In December 2008, it was reported that Melinda Messenger had rekindled her romance with estranged husband Wayne Roberts.
Nevertheless, they broke up again in 2012.
She subsequently started going out with Warren Smith.


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Asia Pacific, Deal Makers, News, The Rich
Former Malaysia Prime Minister Mahathir Becomes PM Again at the Age of 92
Former Malaysia prime minister Mahathir Mohamad from 1981 to 2003, has been elected as the Malaysia 7th prime minister at the age of 92. The general election took place on the 9th of May 2018, with PH and its ally Parti Warisan Sabah led by Mahathir, winning 121 seats in the 222-seat federal Parliament against 76 seats from Barisan Nasional (BN) coalition. the 61 years ruling party since Malaysia become independent in 1957.
" Former Malaysia Prime Minister Mahathir Becomes PM Again at the Age of 92 "
The now 2-time prime minister Mahathir Mohamad was Malaysia's prime minister from 1981 to 2003 for 22 years until 2003. At age 92, he is also the world's oldest elected prime minister. In 2016, he joined the opposition party after the alleged 1MDB billion dollar scandal linked to the now-former Prime Minister Nijab Razak.
Source: New Straits Times, Daily Sabah, SCMP
Producer of Wolf of Wall Street to Pay $60 Million to US Government for Using Malaysia State Funds
Malaysia Names New Central Bank Chief
Saudi Arabia Dismisses its Oil Minister Ali al-Naimi
Previous ArticleChairman of China Insurer Anbang Group Wu Xiaohui Jailed for 18 YearsNext ArticleRolls-Royce Releases The Cullinan – First Ever SUV Priced at $325,000
Malaysian Police Seizes $270 Million of Luxury Goods from Ex-Prime Minister Najib Razak Producer of Wolf of Wall Street to Pay $60 Million to US Government for Using Malaysia State Funds Malaysia Names New Central Bank Chief Saudi Arabia Dismisses its Oil Minister Ali al-Naimi


We've arrived at the Artisa gallery and headquarters of Aruba Art Fair where we've come for a painting workshop with local artist Vanessa Paulina.
We find Vanessa busy painting a mural on the walls of a local shop, which is yet to be finished. A string of Indian beads like those that would have been traded by the first inhabitants of Aruba, is ornamented with African masks, Indian faces and the head of the Spanish queen who funded Christopher Columbus to adventure here. Vanessa tells me how the beads represent a circle of life that connects us all, from the native Indians, the colonists and traders, to the artists of today.
She's a well known artist on Aruba, with paintings on exhibition in the Historical Museum at Fort Zoutman and plenty of experience of community street-art projects, from her time studying and living in the Netherlands. The mural has been commissioned by the Ministry of Culture and as we walk around we realise that it's only the latest in a street-art gallery that covers the buildings of San Nicholaas. This may be the Caribbean, but it's an unexpected contrast to the white sand beaches and palm leaf beach umbrellas that you'll find elsewhere on the island.
By comparison with the bustling shopping malls of Oranjestad, packed with cruise visitors, San Nicholaas feels sleepy and somewhat down-at-heel. When the oil refinery closed in 2009, people and jobs moved away from the town and there was little to bring tourists here unless they were driving to the popular Baby Beach nearby. But since the Aruba Art Fair took place in September 2016, there's a new reason to visit this quiet corner of Aruba, and that's the Street Art.
Art Fair organiser, Tito Bolivar, told me how he'd come up with the idea after a trip to Colombia when he'd seen so much amazing art on the streets of Bogota. "I came back to the island and thought – why not here?" he told me, and in less than a year the project took shape, with the first Aruba Art Fair being held in September 2016.
One of the first international street-artists that Tito invited to be part of the project was Bordalo II from Portugal, who is known for recycling rubbish to create his large-scale "Trash Animal" pieces. To create the iguana that we saw clinging to the side of the building in San Nicholaas, the team drove around the island, picking over car wrecks, scrap metal and rubbish washed up on the beach.
Next on board with the project was Leon Keer of the Netherlands who is known for his surrealist pieces. In a disused building next to the old customs house, he painted the 3D cardboard 'Pan' box, which would normally contain a well known brand of cornmeal from nearby Venezuela. The custom house doorways on either side of it are a reference to the large numbers of Venezuelans who arrive on Aruba for economic reasons, since the mainland is only 500 miles away – watch the video here.
As we circled the side streets around the gallery we found striking murals covering the buildings wherever we looked. In the parking lot, was a piece by Bond Truluv of Germany, which he painted when he arrived as a 'tryout' piece, and then went on to create a large dolphin, next to the "Daddy Cool" mural by Amsterdam Streetart. My favourite murals were the colourful carnival-like faces of a man and woman by Guache from Colombia which covered the entire height of a building.
As Tito gave me an impromptu tour, he told me how his initial idea for an art fair expanded to eventually include seven different art-related projects. Before the main art fair, there was a culinary competition with a twist, in which six teams from Aruba's cookery schools, each headed by an executive chef, were tasked to create a new desert inspired by canvases from local artists. There was an auction dinner and a fashion show to showcase the work of local and international designers, as well as video interviews of local artists filmed by Conocemi, an Aruban TV show.
During the art fair itself, Tito was able to enlist the support of Aruba's Ministries of Culture and Tourism as well as sponsorship from Aruba's banks and business community, so that the artists themselves could sell their artwork in outdoor galleries without any charge. Several empty buildings were loaned so that Aruban art organisations could hold their own exhibitions as part of the show and provide a space for more established contemporary artists.
Tito's mother and co-organiser Diana Croe showed me the mosaic benches around the town that had been created as part of a community project with different groups contributing the designs. The work is planned to continue with more benches and canvas sun shades which will be painted in bright colours.
Despite the success of the Aruba Art Fair, which is now established as a regular event, Tito has plenty more plans in the pipeline. His hope is to use the Art Fair and other projects to infuse art into the local community on Aruba, and he told me "I'm not an artist myself, but I feel it's important to make a change. I see a lot of talent, and beautiful art, I want to start tapping into that talent and pushing those artists forward." Next on the agenda is to establish a website and mobile app for the Artisa (standing for Art Is Aruba) organisation which will give information about the artists and artisans on Aruba, so that they can be more easily found.
With so much creative energy on Aruba it seems sure that this year's Aruba Art Fair will be even bigger and better. Last year the Aruba Art Fair was held in mid September 2016, so look out for announcements of the next date on the Aruba Art Fair website and social channels: Twitter| Instagram | Facebook. For an alternative taste of the Caribbean on Aruba, head to San Nicholas for a walk around the streets to see all the murals and call in at the Artisa HQ and gallery at Theaterstraat 20, San Nicolaas, Aruba.
San Nicholaas is around 30 mins drive from Oranjestad at the south-east end of the island and buses run several times an hour. A morning seeing the street-art could happily be combined with lunch at the quirky Charlie's Bar, and a relaxing afternoon on nearby Baby Beach.


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When it comes to installation, repair or replacement for any kind of siding, including fiber and vinyl siding in Little Falls NJ, American Eagle Exteriors offers premium quality services. We're capable of offering a wide selection of brands, including CertainTeed siding, and our experts will have the ability to help you decide what the ideal option will be. You can stop worrying about whether or not you've got the right kind of siding installed with the assistance of the experienced contractors at American Eagle Exteriors.
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At Andalem, we have a fundamental conviction that it is by collaborating on a global scale that we can overcome our challenges as one global community. We cultivated a ecosystem approach to deploy global transformative technologies and a digital mindset to create leapfrog opportunities for Africa.
Our strategic public/private partnerships and our vast network enables us to establish multi-stakeholder consortium projects that fast track sustainable solutions to the communities we are serving.
Defining the right amount of deliverable and review processes.
Copyright © 2016 Andalem. All Rights Reserved.


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CLEVELAND ELECTRIC ILLUMINATING CO.
The CLEVELAND ELECTRIC ILLUMINATING CO., now (2020) one of ten electric utility companies owned by Akron-based FirstEnergy Corp., was organized on 29 Sept. 1892 as the Cleveland General Electric Co.—the product of a merger between Brush Electric Light & Power Co. and the Cleveland Electric Light Co. The former, founded by inventor and electric light pioneer CHAS. F. BRUSH and others on 16 Mar. 1881, used Brush arc lamps to light PUBLIC SQUARE and several streets and stores. The Cleveland Electric Light Co., established on 21 June 1884, bought a power-generating station on Johnson St. (now Johnson Ct.) between Bank (now W. 6th) and Water (now W. 9th) streets and used the power to supply its Edison incandescent lights in several downtown stores. The new Cleveland General Electric Co. adopted the name of Cleveland Electric Illuminating Co. (CEI) on 21 July 1894. In 1895 the company built a generating plant on Canal Rd., considered "the most modern in the world." With offices in the CUYAHOGA BLDG., by 1910 it had 31,000 customers in a service area that included E. CLEVELAND, EUCLID, CLEVELAND HTS., LAKEWOOD and almost all of Cleveland. In 1911 CEI opened its Lake Shore steam generating plant at E. 70th St., and in Mar. 1913 the company moved into the new 15-story Illuminating Bldg. at 75 Public Square, which served as its headquarters until the move into another new Illuminating Bldg. at 55 Public Square in Feb. 1958. In the early 1940s, CEI began promoting Cleveland as "the best location in the nation" in hopes of attracting new industries to the area. In 1946 it purchased the Cleveland Light & Power Co., organized in 1893. CEI customers numbered 370,000 in 1946.
In Sept. 1967 CEI became a charter member of the Central Area Power Coordination Group (CAPCO), which included Toledo Edison, Ohio Edison, the Duquesne Light Co., and the Pennsylvania Power Co. CAPCO members pooled financial resources to build generating facilities.
The 1970s were a difficult period for the company, marked by clashes with consumer groups over rate increases and environmental groups over the dangers of pollution and nuclear power. A long dispute with the City of Cleveland over relations with the city's municipal light plant culminated in an antitrust suit against CEI filed by the city in 1975, a suit that the city eventually lost. In 1974 CEI began construction of the Perry Nuclear Power Plant near North Perry, OH, and in 1978 service began from the Davis-Besse Nuclear Power Station in Oak Harbor, OH (now owned by Energy Harbor, an independent power producer formerly known as FirstEnergy Solutions). CEI became affiliated with Toledo Edison in April 1986 with the formation of Centerior Energy Corp. That relationship lasted until 1997 when Centerior merged with Ohio Edison to form FirstEnergy Corp. Cleveland Electric Illuminating Co. currently serves more than 750,000 electric utility customers in five Northeast Ohio counties.
Updated by Christopher Roy 5 June 2020
View image in Digital Cleveland Starts Here®
Finding aid for the Centerior Energy Corporation Records, WHRS.
Finding aid for the Centerior Energy Corporation Photographs, WRHS.
http://www.firstenergycorp.com/corporate/Corporate_Profile/Company_History.html


In this animated tale from Disney, Joaquin Phoenix (yes, really) voices a young hunter named Kenai in prehistoric North America. After he kills a bear, the boy actually turns into a bear himself and ends up being hunted by his own brother. Sounds tragic, but it's actually a sweet story about the relationship between Kenai and an orphaned bear cub named Koda (voiced by Jeremy Suarez). Comic relief comes by way of a pair of moose voiced by Rick Moranis and Doug Thomas in their McKenzie brothers/Canadian dude mode. In the sequel, an old female friend of Kenai's (voiced by Patrick Dempsey this time) needs his help on a quest, much to Koda's consternation.


Keep Nature Close To Your Heart.
Decorate wood leaves with included markers.
Leaves feature a hole in the stem for stringing.
Finish with wood beads and hemp cord.
A beautiful way to keep nature close to your heart. Includes 2-7/8" x 1-1/16" wood leaves with hole in the stem for stringing, wood beads, hemp cord and assorted markers.
We really liked this product. We ordered enough for 48 children to do the craft but only received 47 leaf cut outs thankfully we only had 45 children attend the program.
This is a pretty good project. They do warn you about the markers on wood being a little messy and they are messy. Maybe putting permanent markers in would be a good idea. We had kids and dads doing the project together and they all had a hard time threading the beads and leaf onto the hemp cord. Not a huge problem but something to look out for. Overall a good craft.


Dr. Brian Lovato is a visiting assistant professor at Augustana College with experience in teaching, research, and labor organizing. His research focuses on social movements, identity politics, and critical Marxist theory. His first book, Democracy, Dialectics, and Difference, was released by Routledge in 2016 and argues for a renewal of the Marxist tradition grounded in radical democracy and Hegelian thought. His current research in the area of comparative political theory argues that all liberalism is racial liberalism and that no attempts to salvage its universalist core can successfully generate an anti-racist politics. He turns to the Black Radical Tradition and theorist-practitioners of decolonization in order to propose an alternative. Articles on this and other subjects have been published in or are forthcoming in PS, Rethinking Marxism, The Review Journal of Political Philosophy, and Political Parties, Interest Groups and Organizations that Shaped America: An Encyclopedia and Document Collection. As a founding editor of Abolition: A Journal of Insurgent Politics, he has worked to publish scholarship that bridges the divide between academic and activist scholars. He plans on using the resources provided by the Latino Scholarship Fund to attend the Latino Caucus meetings, panels and events at the 2018 meeting of the American Political Science Association.


He called it the "organic braid" and it was really basic except that it magically secured itself at the end—no elastic, ribbon or knotting required. It is good to braid it close to the end, unless the hair is permed. Now, hold the Take a few strands of hair and tie it around the rest of the hair. Tie your braid off. At the end of your braid, use a small elastic hair tie to tie it off. Elastic hair ties that are slightly smaller in circumference than a dime and are.
If you try this back-combing technique on a large braid you will end up For this one you will need a small elastic band, preferably one that. Without a fastener at the end of your braid, it's likely to unravel in seconds. When working with smaller braids on the sides of you head, spray the area you'll be. I find it useful to turn my head over my shoulder as the braid grows. Be careful not to catch any hair from the main ponytail as you braid, and tie off the end with a.