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Horse Owner's Guide to Toxic Plants : Identifications, Symptoms, and Treatmen...
Horse Owner's Guide to Toxic Plants : Identifications, Symptoms, and...
Healthy Horse the Natural Way : A Horse Owner's Guide to Using Herbs, Massage, H
Horse Owner's Field Guide to Toxic Plants by A. P. Knight; Sandra Burger
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Horse Owner's Field Guide to Toxic Plants by S. Burger & A. P. Knight MS, MRCVS
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Language: English Publication Year: 2020
Publisher: Skyhorse Publiching ISBN: 9781510741652
Horse Owner's Guide to Toxic Plants is a must-have, exclusive reference book for all horse owners, and the first of its kind on the subject of equines and plants. Keep this book in the medicine cabinet in the barn. Walk around the pastures with the book in hand, especially in late spring or early summer. Or pack it with on a trail ride. It just might save your horse's life. Horse Owner's Guide to Toxic Plants is organized according to types of plants--trees, bushes, shrubs, and vines, ferns and plants, weeds and wildflowers, and grasses and horsetails. Since visuals are very important for correct identification, clear color photographs are shown, including wherever possible a close-up photograph and line drawing to better identify each plant. Horsewoman Sandra McQuinn has researched and compiled information on more than 100 more common but toxic plants that grow in backyards, pastures, and on the range and trail. Also included is advice from a veterinarian on how to recognize the symptoms of poisonings in your horse and what steps you or your own veterinarian should take if you suspect your horse has eaten a toxic plant. Brimming with pertinent information and expert advice, Horse Owner's Guide to Toxic Plants is a must-have for all equine aficionados. No horse owner should be without it, including those who board their horses.
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Q: OneHotEncoding: working in one dataframe, not working in very, very similar dataframe (pyspark) I am applying a OneHotEncoding function to two very similar dataframes. The first dataframe is the following:

When I apply the one hot encoding, everything works fine:

However, when I apply the exact same function to this different, but very similar dataframe:

The following error occurs:

I don't understand why this happens, because dataframe 1 and 2 were both extracted from a previous dataframe (they work as a train and test df for a machine learning application). Both are pyspark.sql dataframes. Can anyone help me?

A: As the error says, you can't sort a list containing None and integers. There is perhaps a null in your column, which causes the line categories.sort() to crash.
If you want to do ML with Spark, I'd suggest using pyspark.ml package, instead of writing your own one-hot encoder. For example, see here.

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text:
\section{Introduction}
Scarce doubts remain that Dark Energy (DE) exists. Not only SNIa data
indicate an accelerated cosmic expansion (Perlmutter et al. 1997,
1998, Riess et al. 1998, Foley et al. 2007); also CMB and deep sample
data show a clear discrepancy between the total density parameter
$\Omega_o,$ approaching unity, and the matter density parameter
$\Omega_{o,m} \sim 0.25$--$0.3~$ (see, {\it e.g.}, Spergel et
al. 2007). DE covers this gap; its state parameter $w\equiv
p_{de}/\rho_{de}$ must approach $-1$ today, so apparently excluding
that DE is made of free particles ($p_{o,de}, ~\rho_{o,de}$: DE
pressure, energy density). The true nature of DE is however still
elusive; a false vacuum and a self--interacting scalar field are among
the most popular hypotheses for it (Wetterich 1988, Ratra \& Peebles
1988).

In this paper we explore some possible consequences of our poor
knowledge of DE nature. In particular we test the risk that other
cosmological parameter estimates are biased by a inadequate
parametrization of the DE component. We shall see that this risk is
real.

Theoretical predictions had an astonishing success in fitting CMB
data. For instance, the SW effect, predicting low--$l$ $C_l$ data, or
primeval compression waves, predicting $C_l$ peaks and deeps, were
clearly detected. There is little doubt that we are exploring the
right range of models.

When we investigate DE nature through CMB data, we must bear in mind
that they were mostly fixed at a redshift $z \sim 1100\, ,$ when the
very DE density should be negligible, and so affects peak and deep
positions indirectly, through the values of $\omega_{o,c}\equiv
\Omega_{o,c} h^2$ and $\omega_{o,b}\equiv \Omega_{o,b} h^2$ (here $
H_o = 100\, h\, $km/s/Mpc is the present Hubble parameter;
$\Omega_{o},~ \Omega_{o,c},~ \Omega_{o,b}$ are the present total, CDM,
baryon density parameters).  Later information on DE state equation,
conveyed by the ISW effect, is seriously affected by cosmic variance
and often relies on the assumption that a single opacity parameter
$\tau$ can account for reionization, assumed to be (almost)
instantaneous.  Accordingly, if we assume dynamical DE (DDE), due to a
scalar field $\phi$ self interacting through a potential $V(\phi),$
CMB data allow to exclude some interaction shape, {\it e.g.}
Ratra--Peebles (1988) potentials with significantly large $\Lambda$
energy scales, but hardly convey much information on potential
parameters.

In spite of that, when we choose a DE potential or a specific scale
dependence of the DE state parameter $w(a),$ we risk to bias the
values of other cosmological parameters, sometimes leading to
premature physical conclusions. An example is the value of the
primeval spectral index for scalar fluctuation $n_s$. Using WMAP3 data
(Spergel et al. 2007) and assuming a $\Lambda$CDM cosmology, the value
$n_s=1$ is ``excluded'' at the 2--$\sigma$ confidence level. On the
contrary, Colombo \& Gervasi (2007) showed that this is no longer true
in a DDE model based on a SUGRA potential (Brax \& Martin 1999, 2001;
Brax, Martin \& Riazuelo 2000), whose likelihood was the same of
$\Lambda$CDM.

The risk that our poor knowledge of DE nature biases parameter
determination is even more serious if DM--DE coupling is allowed.
Coupled DE (CDE) cosmologies were studied by various authors (see,
{\it e.g.}, Wetterich 1995, Amendola 2000, Bento, Bertolami \& Sen
2002, Macci\`o et al. 2004).

While DDE was introduced in the attempt to ease DE {\it fine--tuning}
problems, CDE tries to ease the {\it coincidence} problem. Let us then
parametrise the strength of DM--DE coupling through a parameter
$\beta,$ defined below. When $\beta$ is large enough, DM and DE scale
(quasi) in parallel since a fairly high redshift. In turn this
modifies the rate of cosmic expansion whenever DM and/or DE
contributions to the total energy density are non--negligible, so that
limits on $\beta$ can be set through data.

The range allowed ($\beta < 0.10$--0.12; Mainini, Colombo \& Bonometto
2005, Mainini \& Bonometto 2007, see also Majerotto, Sapone \&
Amendola 2004, Amendola, Campos \& Rosenfeld, 2006), unfortunately, is
so limited that DM and DE are doomed to scale differently, but in a
short redshift interval. Clearly, this spoils the initial motivation
of coupling, but, once the genie is outside the lamp, it is hard to
put him back inside: even though the coupling solves little conceptual
problems, we should verify that no bias arises on the other parameters,
for the neglect of $\beta$'s consistent with data. This is far from
being just a theoretical loophole, the still unknown physics of the
dark components could really imply the presence of a mild DM--DE
coupling, and its discovery could mark a step forwards in the
understanding of their nature.

Here we test this possibility by performing some numerical
experiments. We assume DDE and CDE due to a SUGRA potential and use
MCMC techniques to fit the following parameter set: $\omega_{o,c} $,
$\omega_{o,b} $, $\tau$, $\theta$, $n_s$, $A_s$ and (constant) $w$;
$\theta$ is the angular size of the sound horizon at recombination
(see however below), $n_s$ and $A_s$ are spectral index and amplitude
of scalar waves, no tensor mode is considered.

The plan of the paper is as follows: In Section 2 we discuss how
artificial data are built, outlining the models selected, the DDE
potential used and the sensitivity assumed. In Section 3 we briefly
debate the features of the MCMC algorithm used and illustrate a test
on its efficiency, also outlining the physical reasons why some
variables are more or less efficiently recovered. In Section 4 we
discuss the results of an analysis of DDE artificial data, against the
$w = {\rm const.}$ assumption. In Section 5 we briefly summarize why
and how CDE models are built and do the same of Sec.~4 for CDE
models. This section yields the most significant results of this
work. In Section 6 we draw our conclusions.

\section{Building artificial data}
In order to produce artificial data we use CAMB, or a suitable
extension of it (see below), to derive the angular spectra
$C_l^{(TT)}$, $C_l^{(EE)}$, $C_l^{(TE)}$ for various sets of parameter
values. Artificial data are then worked out from spectra, according to
Perotto et al. (2006)$\, $.

The analysis we report is however mostly based on a single choice of
parameters, WMAP5 inspired (see Komatsu et al., 2008, Spergel et
al. 2007), in association with three different $\beta$'s. Two other
parameter choices will also be used: (i) to test the efficiency of the
MCMC algorithm; (ii) to add results for a still lower $\beta$ value,
so strengthening our conclusions.

The parameter sets for the most general case and the (ii) case are
shown in Table~1. In these cases DE is due to a scalar field
self--interacting through a SUGRA potential
\begin{equation}
V(\phi) = (\Lambda^{\alpha+4}/\phi^\alpha) \exp(4\pi\, \phi^2/m_p^2)~,
\label{sugra}
\end{equation}
($m_p:$ Planck mass) which has been shown to fit CMB data at least as
well as $\Lambda$CDM (Colombo \& Gervasi 2007); as outlined in the
Table, we input the value of the energy scale $\Lambda;$ the
corresponding $\alpha$ value is determined by the program itself; the
choice $\Lambda = 1\, $GeV is consistent with Colombo \& Gervasi
(2007) findings and is however scarcely constrained by data. The
meaning of the coupling constant $\beta$ is discussed at the beginning
of Section 5~.

\begin{table}[!hbt]
\begin{center}
\begin{tabular}{ccc}
\hline \hline
& Model A & Model B \\
\hline
$\Omega_o$ & 1 & 1 \\
$10^2 \, \omega_{o,b}$ & 2.273 & 2.4 \\
$\omega_{o,c}$ & 0.1099 & 0.11 \\
$100 \, h$ & 71.9 & 85 \\
$\tau_{opt}$ & 0.087 & 0.15 \\
$\ln(10^{10} \, A_s)$ & 3.1634 & 3.1355  \\
$n_s$ & 0.963 & 1 \\
$\Lambda /$GeV & 1 & 1 \\
\hline
 & 0\, \,   &  \\
$\beta$& 0.05 &  0.02 \\
& 0.10 &    \\
\hline\hline
\end{tabular}
\caption{\textsl{Cosmological parameters for artificial CMB data.}}
\label{tabin}
\end{center}
\vskip -.8truecm
\end{table}

Starting from the spectral components and assuming that cosmic
fluctuations are distributed according to a Gaussian process, we generate {\it
realizations} of the coefficients of the spherical harmonic expansions for the
temperature and E--polarization fields, according to the expressions
\begin{equation}
a_{lm}^{(T)} = \sqrt{C_l^{(TT)}} g_{lm}^{(1)}~,
\label{almt}
\end{equation}
\begin{equation}
a_{lm}^{(E)} = \left[C_l^{(TE)}/C_l^{(TT)}\right] \sqrt{C_l^{(TT)}}
g_{lm}^{(1)} + \sqrt{C_l^{(EE)} -
\left[\left(C_l^{(TE)}\right)^2/C_l^{(TT)} \right] } g_{lm}^{(2)}~,
\label{alme}
\end{equation}
where both $g_{lm}^{(i)},$ for any $l$ and $m$, are casual variables,
distributed in a Gaussian way with null averages and unit variance, so
that the equality $\langle g_{lm}^{(i)} g_{lm}^{(j)} \rangle =
\delta^{ij}$ is approached when the number of realizations increases.
Together with eqs.~(\ref{almt}) and (\ref{alme}) this grants that
$$
\langle a_{lm}^{(T)} a_{l'm'}^{(T)*} \rangle = C_l^{(TT)} \delta_{ll'}
 \delta_{mm'}~,~~
\langle a_{lm}^{(E)} a_{l'm'}^{(E)*} \rangle = C_l^{(EE)} \delta_{ll'}
 \delta_{mm'}~,~~
$$
\begin{equation}
\langle a_{lm}^{(T)} a_{l'm'}^{(E)*} \rangle = C_l^{(TE)} \delta_{ll'}
 \delta_{mm'}~,
\label{aver}
\end{equation}
if averages are taken over an ``infinite'' set of sky realizations.
>From a single realization, we can define estimators of the power as
$$
(2l+1) \hat C_l^{(TT)} = \sum_m a_{lm}^{(T)} a_{lm}^{(T)*}  ~,~~
(2l+1) \hat C_l^{(EE)} = \sum_m a_{lm}^{(E)} a_{lm}^{(E)*} ~,~~
$$
\begin{equation}
(2l+1) \hat C_l^{(TE)} = \sum_m a_{lm}^{(T)} a_{lm}^{(E)*} ~.
\label{sum}
\end{equation}
Taken independently from each other, $ \hat C_l^{(TT)}$ and $ \hat
C_l^{(EE)}$ at a given $l$ are the sum of the squares of $2l +1$
Gaussian random variables, so they are distributed according to a
$\chi^2$ with $2l +1$, which approaches a Gaussian distribution
centered around the fiducial $ C_l^{(TT)}$, $ C_l^{(EE)}$, values, as
$l$ increases.  If we consider $T$ and $E$ simultaneously, the set of
estimators $ \hat C_l^{(TT)}$, $ \hat C_l^{(EE)}$, $ \hat C_l^{(TE)}$
follow a Wishart distribution (see, e.g., Percival \& Brown 2006).

We consider here an idealized full--sky experiment characterized by:
(i) finite resolution, that we shall set through a Full Width Half
Maximum angle $\vartheta_{FWHM}$, where the antenna sensitivity is
reduced to $50\, \%,$ assuming a circularly symmetric Gaussian beam
profile; (ii) background noise due to the apparatus, that we shall
assume to be {\it white}, {\it i.e.} $l$--independent with an assigned
variance~$\sigma^2_N.$

More in detail: for what concerns the Gaussian and circularly
symmetric beam profile, its window function reads
\begin{equation}
_s B_l = e^{-[l(l+1) - s^2] \sigma^2/2}
~,~~{\rm with} ~~~~
\sigma \equiv \vartheta_{FWHM}/\sqrt{8\, \ln 2}~,
\end{equation}
$s$ being the spin of the signal (0 for anisotropy or
$E$--polarization spectra; its value however matters just for the
lowest $l$'s). For what concerns noise, we shall consider the
coefficients $n_{lm}$ such that
\begin{equation}
\langle {a_{lm}^{(R)\, }} n_{l'm'}^{(S)*} \rangle = 0
~,~~~~
\langle {n_{lm}^{(R)\, }} n_{l'm'}^{(S)*} \rangle = N_l^{(RS)} \delta_{ll'}
\delta_{mm'}~,
\end{equation}
with $N_l^{(RS)} = \sigma_N^2 \delta^{RS}$, and $R$ and $S$ stand for
either $T$ or $E$. As the sum of two independent Gaussian random
variables is still Gaussian distributed, the statistics of the
(beam--convolved) CMB +white noise field are given by ${\cal
  C}_l^{(RS)} = C_l^{(RS)}|_0 B_l |^{2} + N_l^{(RS)}$. In an analogous
manner from $\hat C_l^{(RS)}$ we can define $\hat {\cal
  C}_l^{(RS)}$. In the following we will consider both {\it fiducial},
i.e. ${\cal C}_l^{(RS)}$, or {\it realized}, $\hat {\cal C}_l^{(RS)}$,
model data sets.

Under these simplified assumptions, the characteristics of an experiment
are completely defined by the values of $\vartheta_{FWHM}$ and
$\sigma_N^2$.  Here we shall take $\vartheta_{FWHM} \simeq 7.0',$
while $\sigma_T^2 \simeq 3 \times 10^{-4} (\mu {\rm K})^2$ and
$\sigma_P^2 \simeq 6 \times 10^{-4} (\mu {\rm K})^2$. These can be
considered conservative estimates of sensitivity in the forthcoming
Planck experiment.

\section{The MCMC algorithm}
When the number $\cal N$ of the parameters to be determined from a
given data set is large, the whole $\cal N$--dimensional parameter
space cannot be fully explored within a reasonable computing time.
MonteCarlo Markov Chain (MCMC) algorithms are then used, whose
efficiency and reliability have been widely tested.

In this work we used the MCMC engine and statistical tools provided by
the CosmoMC package (Lewis \& Bridle 2002; {\it http://
cosmologist.info/cosmomc}). This tool set allows us to work out a
suitable set of $M$ Markov Chains and analyze their statistical
properties, both in the full $\cal N$--dimensional parameter space,
and in lower dimensional subspaces. Of particular interest are the
{\it marginalized} distributions of each parameter, obtained by
integrating over the distribution of the other ${\cal N}-1$
parameters.

The above algorithms implement the following steps. (i) Let $\zeta_1$
be a point--model in the parameter space. The spectra $C_l$ of such
model are computed and their corresponding likelihood ${\cal L}_1$ is
evaluated according to
\begin{equation}
-\ln {\cal L} = \sum_l \left(l+{1 \over 2} \right) \left[{_d{C}_l|_0B_l|^2+{N}_l
\over C_l |_0B_l|^2+{N}_l}+ \ln \left({ C_l |_0B_l|^2 +{N}_l \over
_d{C}_l|_0B_l|^2 +{N}_l }\right) -1 \right] + {\rm const.} ~,
\end{equation}
where $_dC_l$ stands for either fiducial or realized spectra.
The above expression holds for a single $TT$ or $EE$ spectrum; for its
generalization to 3 spectra and a discussion of the effects of
anisotropic noise, sky cuts, etc. see, e.g. Percival \& Brown (2006).
(ii) The algorithm then randomly selects a different point $\zeta_2$,
in parameter space, according to a suitable {\it selection
  function}. The probability of accepting $\zeta_2$ is given by ${\rm
  min}({\cal L}_2 /{\cal L}_1,1)$. If $\zeta_2$ is accepted, it is
added to the chain, otherwise the multiplicity $N_1$ of $\zeta_1$
increases by 1. (iii) The whole procedure is then iterated starting
either from $\zeta_2$ or from $\zeta_1$ again, until a stopping
condition is met. The resulting chain is defined by $(N_i \zeta_i)$,
where $\zeta_i$ are the points explored and the multiplicity $N_i$ is
the number of times $\zeta_i$ was kept.

The whole cycle is repeated until the chains reach a satisfactory {\it
mixing} and a good {\it convergence}. The first requisite essentially
amounts to efficiently exploring the parameter space, by quickly
moving through its whole volume.  In particular, the fact that the
algorithm sometimes accepts points with lower likelihood than the
current point, avoids permanence in local minima, while a careful
choice of parametrization and of the selection function minimize the
time spent exploring degenerate directions.  A good convergence
instead guarantees that the statistical properties of the chains (or
of a suitably defined subset of the chains), correspond to those of
the underlying distribution.  Here we implement the convergence
criterion of Gelman \& Rubin (1992), based on $R$--ratio computation:
convergence and mixing are reached when $R-1 \ll 0.1\, $. Fulfilling
such criterion requires $N \sim 10^5$ points, in the cases considered
here.

\begin{figure}
\epsscale{.60}
\plotone{f1.eps}
\caption{\textsl{Marginalized {\it a posteriori} likelihood
distributions (solid lines), when artificial data derive from a
$\Lambda$CDM cosmology. Vertical lines yield the input parameter
values.  Derived parameter panels are marked by an asterisk. Dotted
lines show the average likelihood distributions. }}
\label{LCDM}
\end{figure}

The algorithm was preliminarily tested by using $\Lambda$CDM as true
cosmology and the set of parameter values shown in Figure~\ref{LCDM}.
Such Figure reports the likelihood distributions found in this case,
both for input parameters (with asterisk) and for several derived
parameters as well. Besides confirming that input values are suitably
recovered, mostly with fairly small errors, Fig.~\ref{LCDM} shows a
broad non--Gaussian distribution for $w$ values, with little skewness
but significant kurtosis. This is a well--known consequence of the
geometrical degeneracy present in CMB spectra, and clearly shows the
difficulty of CMB data to yield results on DE nature. The
non--Gaussian behavior is even more accentuated for some derived
parameter, as $\Omega_{o,c}$, $H_o$ and the Universe age $\tau_o\, .$
We shall recover analogous features in the next plots; here we want to
stress that they do not derive from fitting a partially unsuitable
parameter set.

Figure \ref{LCDM} also shows how errors increase when passing to some
secondary parameter, from primary parameters specifically devised to
break degeneracies. For instance, the errors on $\theta$ and
$\omega_{o,c}$ are $\sim 0.03\, \%$ and $\sim 1.3\, \%$, respectively.
From these parameters, $H_o$ and $\Omega_{o,c}$ are derived, whose
errors are $\sim 15\, \%$.

The point here is that the primary variable is
\begin{equation}
\label{theta}
\theta \equiv r_s(a^*)/D(a^*)~,
\end{equation}
$a^*$ setting the peak of the {\it quasi}--Gaussian last scattering
band (LSB). It is then easy to see that
$$
r_s (a^*) = {c \over H_o\, \Omega_{o,m}^{1/2}} \int^{a^*} {da \over a^2} \,
{c_s(a) \over c}\, {H_o\, \Omega_{o,m}^{1/2} \over  H(a)}~,~~
$$
\begin{equation}
\label{rs} D(a^*) = {c \over H_o\, \Omega_{o,m}^{1/2}} \int_{a^*}
^{a_o} {da \over a^2} {H_o\, \Omega_{o,m}^{1/2} \over H(a)} ~,
~~~~~~~~~~
\end{equation}
so that $\theta$ is apparently independent from $H_o$ and
$\Omega_{o,m}$ as, in the former equation
\begin{equation}
\label{hoh0} {H^2(a) \over H_o^2 ~\Omega_{o,m} } = \left(1+ {a_{eq}
\over a} \right) \left(a_o \over a \right)^3 ~,
\end{equation}
while, in the latter one
\begin{equation}
\label{hoh}
{H^2(a) \over H_o^2 ~\Omega_{o,m} } =
\left(a_o \over a \right)^3 + \left(\Omega_{o,m}^{-1}-1 \right)
g \left(a_o \over a \right)~,
\end{equation}
and $\Omega_{o,m}$ only sets the normalization of the latter term at
the r.h.s., so that $g(1) = 1\, .$ As a matter of fact, these
equations exhibit a mild dependence of $\theta$ on $\omega_{o,m}$ and
$\omega_{o,b}$, as $ a_o/a_{eq} = 2.41 \times 10^4 \omega_{o,m} (T_o/
2.726\, {\rm K})^{-4} [1.681/(1+0.227\, N_\nu)]$ and $(c_s/c)^{-2} =
3[1 + (3/4) (\omega_{o,b}/\omega_{o,m}) (a/a_{eq}) (1+0.227\, N_\nu)]$
(here $T_o$ is the present CMB temperature and $N_\nu$ is number of
neutrino families in the radiative background). Information of
$\Omega_{o,m}$ and, thence, on $H_o$ can be obtained only if the
factor $g(a_o/a)$, yielding the evolution of the ratio between DE and
matter at low redshift, is under control. It is certainly so if a
$\Lambda$CDM model is assumed; but, if we keep $w$ as free parameter,
the uncertainty on it, ranging around 60$\, \%\, ,$ reflect the
difficulty to obtain the secondary parameters $\Omega_{o,m}$
and~$H_o$.

More in general, eq.~(\ref{hoh}) shows that CMB data are sensitive to
a change of $g(a_o/a)$ causing a variation of LSB distance $D^*$.  On
the contrary, $\theta$ does not discriminate between different $w(a)$
yielding the same $D^*$.

Incidentally, all that confirms that it is unnecessary to fix $a^*$
with high precision, or to discuss whether it is a suitable indicator
of the LSB depth. Knowing $a^*$ with $\sim 1\, \%$ approximation is
quite suitable to this analysis.

\section{Dynamical DE vs.~$w={\rm const.}$}
Let us now discuss what happens if DE state equation, in the ``real''
cosmology, cannot be safely approximated by a constant $w\, .$ To
build data, we use then a SUGRA cosmology and our own extension of
CAMB, directly dealing with a SUGRA potential both in the absence and
in the presence of DM--DE coupling. Artificial data worked out for
Model A with $\beta=0$ were then fit to the same parameters as in
Figure \ref{LCDM}. The whole findings are described in Table
\ref{tab1} (second column).

In Figure \ref{dde} we add further information, comparing the value
distributions in fits assuming either a cosmology with $w={\rm
const.}$ or a SUGRA cosmology, then including $\Lambda,$ as parameter,
instead of $w$. The two fits agree well within 1--$\sigma$, among
themselves and with input values. In the Figure we show the fiducial
case.

\begin{figure}
\epsscale{.60}
\plotone{f2.eps}
\caption{\it{Marginalized likelihood distributions on parameter
values. Data built with an uncoupled SUGRA model. The parameter space
for the fit includes either $\log(\Lambda/{\rm GeV})$ (solid lines) or
a constant $w$ (dashed lines). Vertical dotted lines show the input
parameter values.  Derived parameters plots are with asterisk.  }}
\label{dde}
\end{figure}

\begin{table}[!hbt]
\vskip -.2truecm
\begin{center}
\begin{tabular}{cccc}
\hline
\multicolumn{4}{c}{{~~~~~~~~~~~~~~~~~~~~~
\rm Input~model:~{\it SUGRA} ($\Lambda = 1\, $GeV)~with}} \\
{\rm Parameter} \&  & $\beta=0$ & $\beta=0.05$ & $\beta=0.1$
\\
 {\rm Input~value} &
{\rm Av.~value}~$\pm\sigma$ & {\rm Av.~value}~$\pm\sigma$ & {\rm Av.~value}~$\pm\sigma$
\\
\hline
$10^2 \, \omega_{o,b}$  &$2.274\pm0.015$ &$2.274\pm0.015$ &$2.277\pm0.017$\\
$2.273$                 &$2.278\pm0.015$ &$2.275\pm0.015$ &$2.295\pm0.017$\\
                        &$2.278\pm0.015$ &$2.261\pm0.015$ &$2.287\pm0.017$\\
                        &$2.280\pm0.015$ &$2.278\pm0.015$ &$2.282\pm0.017$\\
\hline
$\omega_{o,c}$      &$0.1099\pm0.0013$ &$0.1164\pm0.0014$ &$0.1225\pm0.0016$\\
 $0.1099$           &$0.1083\pm0.0013$ &$0.1166\pm0.0012$ &$0.1225\pm0.0016$\\
                    &$0.1086\pm0.0013$ &$0.1171\pm0.0014$ &$0.1216\pm0.0016$\\
                    &$0.1104\pm0.0013$ &$0.1163\pm0.0014$ &$0.1225\pm0.0015$\\
\hline
$10^2 \, \theta$    &$1.0758\pm0.0003$ &$1.0736\pm0.0003$ &$1.0507\pm0.0003$\\
 $1.072$            &$1.0759\pm0.0003$ &$1.0736\pm0.0003$ &$1.0509\pm0.0003$\\
                    &$1.0760\pm0.0003$ &$1.0737\pm0.0003$ &$1.0507\pm0.0003$\\
                    &$1.0759\pm0.0003$ &$1.0736\pm0.0003$ &$1.0507\pm0.0003$\\
\hline
$\tau_{opt}$        &$0.088\pm0.005$ &$0.087\pm0.005$ &$0.085\pm0.005$ \\
 $0.087$            &$0.087\pm0.005$ &$0.903\pm0.005$ &$0.084\pm0.005$\\
                    &$0.089\pm0.005$ &$0.083\pm0.005$ &$0.087\pm0.005$\\
                    &$0.093\pm0.005$ &$0.079\pm0.005$ &$0.078\pm0.005$\\
\hline
$w$                 &$-0.79-0.12+0.49$ &$-0.75-0.30+0.26$ &$-0.85-0.43+0.38$\\
---                 &$-0.84-0.27+0.25$ &$-0.76-0.30+0.26$ &$-0.96-0.44+0.82$\\
                    &$-0.81-0.26+0.25$ &$-0.79-0.29+0.26$ &$-0.67-0.34+0.37$\\
                    &$-0.87-0.28+0.28$ &$-0.54-0.15+0.16$ &$-0.63-0.24+0.23$\\
\hline
$n_s$               &$0.963\pm0.004$ &$0.962\pm0.004$ &$0.960\pm0.004$ \\
 $0.963$            &$0.966\pm0.004$ &$0.962\pm0.004$ &$0.958\pm0.004$\\
                    &$0.968\pm0.004$ &$0.962\pm0.004$ &$0.963\pm0.004$\\
                    &$0.959\pm0.004$ &$0.961\pm0.004$ &$0.959\pm0.004$\\
\hline
$\ln(10^{10}\, A_s)$ &$3.3168\pm0.0102$&$3.1695\pm0.0101$ &$2.8860\pm0.0101$ \\
 $3.3144$~for~$\beta=0$ \hfill &
$3.3127\pm0.0094$ &$3.1699\pm0.0106$ &$2.8866\pm0.0099$ \\
 $3.1634$~for~$\beta=0.05$ \hfill &
$3.3144\pm0.0103$&$3.1565\pm0.0095$&$2.8885\pm0.0102$ \\
 $2.8902$~for~$\beta=0.10$ \hfill&
$3.3310\pm0.0097$&$3.1486\pm0.0105$ &$2.8736\pm0.0111$ \\
\hline
$100 \, h$          &$74.7-7.2+25.3$  &$70.6-11.3+12.8$ &$66.3-11.7+13.8$ \\
 $71.9$             &$77.3-12.4+13.7$ &$71.0-11.4+12.6$ &$70.2-20.3+14.6$\\
                    &$75.7-12.3+13.3$ &$71.9-11.0+12.6$ &$60.9-11.1+10.5$\\
                    &$78.4-13.6+13.9$ &$61.6-6.1+6.0$   &$59.5-5.7+5.6$\\
\hline
$\Omega_{o,m}$ &$0.255{-0.084}{+0.169}$ &$0.300{-0.100}{+0.095}$
&$0.360{-0.133}{+0.127}$\\
 $0.257$       &$0.235{-0.105}{+0.077}$ &$0.296{-0.096}{+0.096}$
&$0.325{-0.123}{+0.140}$\\
               &$0.245{-0.079}{+0.077}$ &$0.289{-0.093}{+0.088}$
&$0.422{-0.138}{+0.121}$\\
               &$0.233{-0.101}{+0.084}$ &$0.379{-0.074}{+0.073}$
&$0.431{-0.103}{+0.097}$\\
\hline
\end{tabular}
\vskip -.1truecm
\caption{\it Results of an MCMC analysis, seeking the parameters
listed in the first column, on artificial CMB data built with the
parameter values also listed in the first column, but using a SUGRA
cosmology, whose $\Lambda$ and $\beta$ are shown in the header. For
each parameter, the first line yields results for the fiducial case,
the next 3 lines for model realizations.}
\label{tab1}
\end{center}
\end{table}

Let us briefly comment the results in the absence of coupling, when
the fitting parameter set includes $w$ instead of $\Lambda$: (i)
$\omega_{o,b}$ and $\omega_{o,c}$ are recovered without any bias. (ii)
The same holds for $\theta,$ if a numerically refined value of $a^*$
is used; the expression of $a^*$, as above outlined, has a precision
$\sim 1\, \%$. Errors on $a^*$, however, are negligible in comparison
with errors arising from the scarce knowledge of $w(a)$.

As outlined in the previous Section, the main problem to fix
$\Omega_{o,m}$, $\Omega_{o,\Lambda}$, and $H_o$, resides in the
difficulty to determine the state equation of the expansion source
since DE becomes substantially sub--dominant or dominant. This also
makes clear why the formal error in the determination of the above
three parameters is wider when the fit assumes a constant $w:$ varying
$w$ yields an immediate and strong effect on DE contributions and
state equation, extending up to now; on the contrary, only huge
displacements of the energy scale $\Lambda$ cause significant
variations to DE contributions and state equation within the family of
SUGRA cosmologies. In other terms, when $\Lambda$ varies, the part of
the functional space that $w(a)$ covers is not so wide.

Accordingly, the greater error bars on $\Omega_{o,m}$,
$\Omega_{o,\Lambda}$, $H_o$, found when we use $w$ as a parameter, do
not arise because we fit data to a ``wrong'' cosmology, but because
varying $w$ leads to a more effective spanning of the functional space
of $w(a)$.

As a matter of fact, the reliability of the fit must be measured by
comparing the likelihood of the best--fit parameter sets. Likelihood
values, given in the next Section, do not discriminate between the two
fits. Otherwise, a direct insight into such reliability is obtained by
looking at the width of the marginalized {\it a posteriori} likelihood
distributions on primary parameter values. Figure \ref{dde} then
confirms that such distributions, although slightly displaced, have
similar width for all primary parameters.

A general conclusion this discussion allows to draw is to beware from
ever assuming that error estimates on secondary parameters, as
$\Omega_{o,m}$, $\Omega_{o,b}$, and $H_o$, are safe.

\begin{figure}
\epsscale{.55}
\plotone{f3a.eps}
\vskip1.2truecm
\plotone{f3b.eps}
\caption{\it{Marginalized likelihood distributions on parameter
values. Data built with coupled SUGRA models with $\beta = 0.05$,
$\beta = 0.1$ (upper, lower panels). The parameter space for fits
includes $\log(\Lambda/{\rm GeV})$ and $\beta$ (solid lines) or just a
constant $w$ (dashed lines). Vertical dotted lines show the input
parameter values.  Pay attention to the different abscissa units in
the two panel sets. }}
\label{couple}
\end{figure}

\section{Coupled DE vs.~$w={\rm const.}$}

In cosmologies including cold DM and DE, the equation obeyed by
the stress--energy tensors of the dark components
\begin{equation}
\label{conti0}
T^{(c)~\mu}_{~~~~\nu;\mu} + T^{(de)~\mu}_{~~~\, ~~\nu;\mu} = 0~,
\end{equation}
yields
\begin{equation}
{d \over d\tau} (\rho_c + \rho_{de}) = -3 (\rho_c + p_c +
\rho_{de} + p_{de}) {\dot a \over a} ~, \label{conti}
\end{equation}
if their pressure and energy densities are $p_{c}$, $p_{de}$ and
$\rho_{c},$ $\rho_{de};$ $\tau$ is the conformal time and dots
indicate differentiation in respect to $\tau.$ Eqs.~(\ref{conti0}) and
(\ref{conti}) state that no force, apart gravity, acts between
standard model particles and the dark components. The
eq.~(\ref{conti0}) is fulfilled if DM and DE separately satisfy the
eqs.
\begin{equation}
T^{(de)~\mu}_{~~~\, ~~\nu;\mu} = C T^{(c)} \phi_{,\nu}~,~~~~~~~~
T^{(c)~\mu}_{~~~~\nu;\mu} =- C T^{(c)} \phi_{,\nu}~,
\end{equation}
where $T^{(de),(c)}$ are traces of the stress--energy tensors. $C$ can
be an arbitrary constant or, {\it e.g.}, a function of $\phi$ itself;
when $C=0$, the two dark components are uncoupled and so are the cases
we considered up to here.

It is however known (Wetterich 1995, Amendola 2000, Amendola \&
Quercellini 2003) that self consistent theories can be built with
\begin{equation}
C \equiv 4 \sqrt{\pi \over 3} { \beta \over m_p} \neq 0~,
\end{equation}
so that $\beta $ is used to parametrize the strength of DM--DE
coupling.

By using MCMC techniques, we explored cosmologies with $\beta = 0.05$
and 0.1 (Model A); we also report some results for $\beta = 0.02$ (Model
B). We aim to show that, when $\beta$ is excluded from the parameter
budget, the values MCMC provide for some parameters can be
significantly biased, even though $\beta $ is small.

\begin{figure}
\epsscale{.60}
\plotone{f4.eps}
\caption{\it Anisotropy spectra comparison. The 3 values of $\beta$
considered are clearly distinguished thanks to their different input
normalization and to the line type indicated inside the upper frame.
The dotted lines (hardly visible at low $l$'s in the upper panel) are
the spectra of the corresponding best--fit model when assuming no
coupling and $w = const.\, $. In the lower panel the relative
differences between input and best--fit models are compared with WMAP5
error~size.  }
\label{Cla}
\end{figure}
\begin{figure}
\epsscale{.60}
\plotone{f5.eps}
\caption{\it The comparison made in the upper panel of the previous
Figure is extended to ET and E--polarization spectra. Model differences
are hardly visible at very low $l$ and on the $l$ values where the
ET spectrum changes sign. }
\label{Clb}
\end{figure}

\begin{figure}
\epsscale{.50}
\plotone{f6a.eps}
\vskip0.5truecm
\plotone{f6b.eps}
\vskip0.5truecm
\plotone{f6c.eps}
\caption{\it Luminosity distance vs.~redshift in models with $\beta =
$0, 0.05, 0.10~(solid lines).  Each model is compared with the
corresponding best--fit constant--$w$ model (dashed line) and
with a SCDM model (dotted line) with equal $\Omega_b~.$
}
\label{hubdia}
\end{figure}
\begin{figure}
\plotone{f7.eps}
\caption{\it Transfer functions for the models A. The dotted lines
yield the transfer function of the models with w=const., yielding
the best--fit for CMB spectra. }
\label{trans}
\end{figure}

In Table \ref{tab1} (3rd--4th columns) we report the results of
fitting the parameter set including constant $w$, in place of
$\Lambda$ and $\beta$. The Table allows an easy comparison with the
uncoupled case, when all parameters unrelated to DE are nicely
recovered. On the contrary, already for $\beta = 0.05$, the input
$\omega_{o,c}$ value is formally $4.5~\sigma$'s away from best--fit,
in the fiducial case, and more than 5~$\sigma$'s in some realization.
The effect is stronger for $\beta = 0.1$, yielding a discrepancy $\sim
8$ $\sigma$'s. That coupling affects the detection of $\omega_{o,c}$
is not casual: in coupled models a continuous exchange of energy
between DM and DE occurs.

Several parameters exhibit a non--Gaussian distribution, however.
This is visible in Figure \ref{couple}, where we also provide a
comparison between likelihood distributions when (i) the fit includes
just $w$ or, instead, (ii) the parameter space includes $\Lambda$ and
$\beta$.

The comparison allows to appreciate that, in the (i) case,
$\omega_{o,c}$ is apparently much better determined than in the (ii)
case. Appreciable discrepancies concern also the $\theta$ parameter and
they reflect onto the derived parameters $\Omega_{o,b}$,
$\Omega_{o,m}$ and $H_o$, whose distribution however appears
significantly non--Gaussian.

These results deserve to be accompanied by a comparison between the
likelihood values in the different cosmologies. The following table
shows
$\chi^2_{\rm eff} \equiv -2 \, {\rm ln}
({\cal L}) $ for the fiducial cases only:
$$
\left|
\matrix{
& & {\rm constant~} w & \Lambda~\&~\beta \cr
{\bf }~~ & & ----- & ----- \cr
{\bf }~~ &\beta = 0 \hfill & 0.175  & 0.887 \cr
{\bf }~~ &\beta = 0.05 \hfill & 0.214 & 0.332 \cr
{\bf }~~ &\beta = 0.10 \hfill & 0.778 & 0.251 }
\right|
$$
The likelihood values for realizations are systematically smaller, as
expected, but confirm the lack of significance shown here. Given that
coupled models have 1 additional parameter over the $ w = const$
model, differences $\Delta \chi^2_{\rm eff} < \sim 1$ indicate that
both models are an equally good fit of data. The
conclusion is that spectral differences, between input and best--fit
models,
lay systematically below the error size. As a matter of fact, we are
apparently meeting a case of degeneracy.

This statistical observation is corroborated by a direct insight into
angular spectra, provided by Figures \ref{Cla} and \ref{Clb}.  We show
the behaviors of the $C_l$ spectra for the Model A, with $\beta=0$,
$\beta=0.05$, $\beta=0.1$, compared with the $C_l$ for the
best--fitting ($w={\rm const.}$) model. Differences are so small to be
hardly visible. Figure \ref{Cla} refers just to anisotropy. In its
lower panel the $\Delta C_l/C_l$ ratio is compared with WMAP5
1--$\sigma$ error size ($\Delta C_l$ is the difference between the
spectra of the input and best--fit models). Notice that shifts
by 1 or 2 units along the abscissa,
at large $l$ values,
would still badly cut--off the apparent
ratios. Clearly, degeneracy can be removed only if the error size is
reduced by a factor $\sim 10$ or more, in the region between the first
deep and the second acoustic peak.

A further example we wish to add concerns a still smaller coupling
intensity, $\beta = 0.02$ (Model B, Table \ref{tab02}). At this
coupling level, the MCMC meet all input parameter values within a
couple of $\sigma$'s. A closer inspection of plots similar to Figure
\ref{couple}, not reported here, shows that the probability of
realizations yielding $\omega_{o,c}$ formally more than 3--$\sigma$'s
away from the true value, is still $> 8 \, \%:$ the genie is still not
completely back inside the lamp.

\begin{table
\begin{center}
\begin{tabular}{cc}
\hline \hline
\multicolumn{2}{c}{{\rm Input~model:~coupled {\it SUGRA} ($\Lambda = 1\, $GeV,~~$\beta=0.02$)}} \\
\hline \hline {\rm Parameter} \& {\rm Input~value} & {\rm
b.f.~value}~$\pm\sigma$
\\
\hline \hline
$10^2 \, \omega_{o,b} = 2.400$               & $2.400\pm0.016$ \\
                                                   & $2.424\pm0.016$ \\
                                                   & $2.423\pm0.017$ \\
                                                   & $2.391\pm0.016$ \\
\hline
$\omega_{o,c} = 0.1100$              & $0.1127\pm0.0014$ \\
                                                   & $0.1120\pm0.0013$ \\
                                                   & $0.1121\pm0.0013$ \\
                                                   & $0.1130\pm0.0014$ \\
\hline
$10^2 \, \theta$                               & $1.11135\pm0.00032$ \\
                                                   & $1.11174\pm0.00031$ \\
                                                   & $1.11170\pm0.00032$ \\
                                                   & $1.11108\pm0.00032$ \\
\hline
$\tau = 0.1500$              & $0.1515\pm0.0059$ \\
                                                   & $0.1413\pm0.0067$ \\
                                                   & $0.1412\pm0.0061$ \\
                                                   & $0.1510\pm0.0061$ \\
\hline
$w$ (at $z=0$)                         & $-0.70-0.16+0.16$ \\
                     &            $-0.65-0.17+0.17$ \\
                                                   & $-0.67-0.17+0.16$ \\
                                                   & $-0.63-0.14+0.13$ \\
\hline
$n_s = 1.0000$              & $0.9998\pm0.0042$ \\
                                                   & $0.9994\pm0.0039$ \\
                                                   & $0.9990\pm0.0041$ \\
                                                   & $0.9976\pm0.0041$ \\
\hline
$\ln{(10^{10} \, A_s)} = 3.136$               & $3.138\pm0.011$ \\
                                                   & $3.119\pm0.013$ \\
                                                   & $3.119\pm0.012$ \\
                                                   & $3.139\pm0.012$ \\
\hline
$100 \, h = 85$                      & $79-9\phantom{0}+10$ \\
                                                   & $77-10+10$ \\
                                                   & $77-10+10$ \\
                                                   & $75-8\phantom{0}+8\phantom{0}$ \\
\hline
$\Omega_{o,m} = 0.185$               & $0.254-0.057+0.058$ \\
                                                   & $0.294-0.062+0.062$ \\
                                                   & $0.268-0.059+0.059$ \\
                                                   & $0.219-0.054+0.054$ \\
\hline\hline
\end{tabular}
\caption{\textsl{As previous Table, with different input values of
cosmological parameters and $\beta$ as small as 0.02}}
\label{tab02}
\end{center}
\end{table}

\section{Other observables}
The degeneracy observed in CMB spectra could be broken off through
different observables. We plan to deepen this aspect in a forthcoming
work, by building detailed data sets accounting from the dependence on
cosmology of the expansion rate and growth factor.

A first insight into the actual situations can be however gained
through an inspection of Hubble diagrams and transfer functions.

In Figure \ref{hubdia} we show the redshift dependence of the
luminosity distances for models with $\beta=0$, 0.05, 0.1 and compare
them with the corresponding best--fit models with constant $w$, as
well as with SCDM models with the same value of $\Omega_b$.  These
plots clearly indicate that a fit with SNIa data would hardly allow
any discriminatory signal: discrepancies from constant--$w$ model
increase with $\beta$; but, even for the $\beta = 0.10$ case, they
hardly exceed $\sim 10\, \%$ of the difference from SCDM.

In Figure \ref{trans} we then exhibit the transfer functions $T(k)$
(multiplied by $k^{1.5}$ to improve the visibility of details) for
models A.

In the cases $\beta = 0$ and $\beta = 0.05$, we notice slight
displacements for the BAO system and the slope. The actual setting of
BAO's is however subject to non--linear effects and residual
theoretical uncertainties are wider than the shifts in the plots.  The
change of slope is also easily compensated by a shift of $n_s$ by
$\sim 0.01$, widely within expected observational errors.  Notice then
that the relative position of the input and best--fit functions is
opposite in the two cases. Accordingly, in the intermediate case
$\beta = 0.033$, not shown in the plot, the overlap is almost exact
and the observed scale dependence of the growth factor, at low
redshift, does not break the degeneracy at all.

The situation is different when $\beta > 0.05$ is considered. For
$\beta = 0.1$, the BAO displacement is indeed relevant; to compensate
for the change of slope, we would then require a shift of $n_s$
greater than 0.1$\, $.

A numerical analysis can therefore determine at which value, probably
intermediate between 0.05 and 0.1, the CMB spectra degeneracy is
broken.

\section{Conclusions}
The nature of the dark cosmic components is unclear. DE could be a
self--interacting field, yielding a scale dependent state parameter
$w(a)\, .$ Which bias does then arise on cosmological parameter
estimates, if performed by assuming $w = {\rm const.}\, $?  This
question regards also parameters which do not describe DE; their
estimate could be biased because the {\it true} model is not directly
explored. A first conclusion of this work is that such bias exists
but, in the cases we treated, yields acceptable displacements, within
1--$\sigma$.

Suppose however that future data allow to exclude $n_s = 1$, within
3--$\sigma$'s, when we assume $w = {\rm const.}\, $. Setting $n_s < 1$
discriminates among inflationary potentials. It would be however
legitimate to assess that, at that stage, such conclusions would still
be premature.

Our analysis was then extended to the case of DM--DE coupling. The
idea that DM and DE have related origins or arise from the same field
has been widely pursued (see, {\it e.g.}  Kamenshchik, Moschella \&
Pasquier 2001, Bento, Bertolami \@ Sen 2002, 2004; Mainini \&
Bonometto 2004; for a review, see~Cop\-eland, Sami \& Tsujikawa
2006). Coupling causes DM--DE energy exchanges and this option was
first explored in the attempt to ease the {\it coincidence} problem.

Unfortunately, when a DM--DE coupling, strong enough to this aim, is
added to models, predictions disagree with data. This does not forbid,
however, that the physics of the dark components includes a weaker
coupling or that a stronger coupling is compensated by other features
(see, {\it e.g.}, La Vacca et al. 2008).

In this work we pointed out that a significant degeneracy exists, so
that we can find an excellent fit of CMB data for coupled DE
cosmologies just by using constant--$w$ uncoupled cosmologies. The fit
is so good that even likelihood estimates do not allow to distinguish
between the ``true'' cosmology and the best--fit constant--$w$ model,
at the present or foreseeable sensitivity levels. {\it Unfortunately,
however, the values obtained for several parameters are then widely
different from input ones.}

In fact, if we ignore the coupling degree of freedom, when data are
analyzed, we can find biased values for some primary parameter as
$\omega_{o,c}$, for which input values lay $\sim 5$--$\sigma$'s away
from what is ``detected''.  Also $\Omega_{o,m} $ and $H_o$, which are
secondary parameters, are significantly biased. In particular, with a
coupling as low as $\beta = 0.05$, we found model realisations
yielding $H_o$ estimate $\sim 2$--$\sigma$'s away from the input
value. If we keep to the fiducial case, however, the probability to
find $H_o \geq $ its input value is 36.5$\, \%$ for $\beta = 0.05$ and
26.5$\, \%$ for $\beta = 0.1~.$ This outlines the tendency to find
smaller values than ``true'' ones.

As a matter of fact, however, because of the uncertainty induced by
our ignorance on DE state equation, the width of errors on secondary
parameter significantly exceeds the width for primary ones, and a
5--$\sigma$ discrepancy is partially hidden by such ignorance. This
agrees with the fact that data analysis shows a significant increase
of errors on secondary parameters when the set of models inspected
passes from $\Lambda$CDM to generic--$w$ cosmologies.  For instance,
in the very WMAP5 analysis, the error on $H_0$ increases by a huge
factor $\sim 6$, when one abandons the safety of $\Lambda$CDM to
explore generic constant--$w$ models. A general warning is then that
errors obtained assuming $\Lambda$CDM are to be taken with some
reserve.

An important question is whether the bias persists when different
observables, besides CMB, are used. A preliminary inspection shows
that SNIa data would hardly provide any discrimination. On the
contrary an analysis of fluctuation growth can be discriminatory if
$\beta >\sim 0.07$--0.08~.

An even more discriminatory signal could be found in the $z$
dependence of the growth factor is suitably analyzed.  Observational
projects aiming at performing a tomography of weak lensing, like
DUNE--EUCLID (see, {\it e.g.}, Refre\-gier et al. 2006, 2008),
therefore, can be expected to reduce this degeneracy~case.

\vskip .3truecm

\noindent
ACKNOWLEDGMENTS. LPLC is supported by NASA grant NNX07AH59G and JPL--Planck
subcontract no. 1290790.

\vfill\eject

redpajama_set_name: RedPajamaArXiv


Delilah Dawson, who also publishes under the name Lila Bowen, is the New York Times bestselling author of the Blud series, as well as a prolific writer of many other fantasy, young adult, Star Wars, and media tie-in books. Kevin Hearne is the author of the popular fantasy series The Iron Druid Chronicles, of which the ninth and final book, Scourged, released early last year. Together, these two authors have created the outrageously hilarious and irreverently fun Kingdom of Pell. Filled with puns, plays on old fantasy tropes, and witty banter, the Pell series appeals to fans of both Terry Pratchett and Monty Python. No Country for Old Gnomes, follow-up to Kill the Farm Boy, opens upon a violent conflict between the clean, cardigan-wearing gnomes and the hairy-footed violent halflings. After a firebomb destroys the childhood gnome-home of twin brothers Onni and Offi, forcing the pair to retreat and plot revenge, it begins the start of their adventure. A colorful cast of characters such as an adventurous halfling, a gryphon with peculiar appetites, a metal man, and a young ovitaur keep the laughs coming.
In conversation with Delilah and Kevin is fellow author Stephen Blackmoore. Stephen is the Los Angeles-based writer of the Eric Carter series of books, including noir/urban fantasy titles Dead Things, Broken Souls, and Hungry Ghosts.
This event is free and seating is first come, first serve. To get a book signed during one of our events, a copy of the event book must be purchased through Mysterious Galaxy. Event purchases through Mysterious Galaxy not only keeps our bookstore doors open, but also makes author signings possible.


11 pad goalie shirt with protection on the clavicle, ribs, wrists, deltoids and high sternum/chest.
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The unique Zoombang® viscoelastic polymer is a semi-solid plastic like material that is extremely soft at rest and will conform to any shape. However it will instantly change characteristics and behave as a solid when impact is applied.
Zoombang is being used for a vast arrays of applications outside of the sports world as well.
The unique ability for these polymers to react in direct proportion to the energy applied sets it apart from any other form of added protection for athletes. An additional benefit is that our polymer, being fluid-like at rest, easily conforms to the individual player's anatomy and helps fill voids between the athlete and traditional hard shell equipment. The result is an overall equipment fit that was previously impossibly to achieve. Zoombang® will not freeze, dry out, or melt.
Zoombang® has been approved by the NHL as a supplier for the professional teams in the US and Canada. A majority of NHL teams use Zoombang® Protective Gear™ as an integral part of their equipment.
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Zoombang merchandise may be returned within 30 days of purchase for size exchange only. Shipping charges will be charged to ship the new item.


THE CALIFORNIA QUARTERLY . Editor Thomas McGRATH, etc.
vols 1/2-3/2, 1952-1954. Poems, short stories, articles, plays & graphics.
CHOICE . A Magazine of Poetry and Photography & later Graphics .
Ed John LOGAN & Aaron SISKIND . Chicago. Nos 1-8 (1960's) .
DOWN HERE. A Magazine of prose, poetry, theatre, art & criticism from The East Village. USA. Ed M PERKINS.
Vol.1/2. Spring 1967 (Story by T Berrigan; V H Cruz interviewed by E Oatman; Poems by J Ceely, G Kimball, A Planz, C Bukowski, J Tyack, etc.
EPOS. USA. Ed W TULLOS & E THORNE.
FIREWEED. Verse, short stories, graphics. Ed G & K GREEN. Columbus. U.S.A. Nos 1-6. Winter 1976-Winter 1977. Contributors include A Waldman, C Bukowski, C Berge, J Merrill etc. with illustrations by S Sturgill.
No 2 is limited to 400 numbered copies signed by the Editors.
INTREPID . 1964-1969. ED A DE LOACH .
Staple bound covers in original wraps of varying colours.
NORTHWEST REVIEW. U.S.A. Fiction, Poetry, Reviews & Photographs.
SATIS . Ed Matthew MEAD. Nos 1-5. 1961-1962 . All published. Newcastle upon Tyne. 5 issues in original wraps containing contributions by A Cluysenaar, A Hollo, G Turnbull, R Weber, D Carroll, L Eigner, J H Prynne, C Bukowski, M Mead, J Heath-Stubbs, M Shayer, etc.) Together with another Satis publication : Max Holzer-Amfortiade. Etc.
SAN FRANCISCO BARK. Thorp Springs Press.
Edited by T HEAD & P FOREMAN.
civil liberties & individual rights.
Ed R MILLER, G HITCHCOCK, June MCKEEN.
Nos 1-13 all published in this format 1958-1962.
VENTURE . A Writers Workshop Quarterly. NY. Ed J J FRIEDMAN .
THE WORMWOOD REVIEW. Ed. Marvin MALONE . USA.
schools, moods & manners that reflect the temper & depth of the human scene".


Several thousand "gilets jaunes" protesters have marched through Paris and other French cities on Saturday on the 12th weekend of action against the government despite opinion polls pointing to a recovery in Emmanuel Macron's popularity.
The protests – named after the fluorescent jackets French motorists are required to carry in their cars – began in November over plans to raise fuel taxes, before developing into a broader revolt against the government that mobilised tens of thousands of demonstrators nationwide each Saturday.
As in previous weeks, protesters carried French flags and held signs attacking the French president as being out of touch or calling for referendums tabled by citizens.
Protesters injured in previous weeks of violence were put at the front of the protests, some of whom wore eyepatches with a target sign on them.
The government warned on Friday that police would not hesitate to use flashballs in the event of violence by demonstrators after it was authorised by France's highest administrative court. Flashball riot control guns are banned in much of Europe.
"It's true that this intermediate weapon can hurt, but faced with rioters, the police need it to defend themselves against those who attack them," said the interior minister, Christophe Castaner.
A Harris Interactive poll of 1,000 people on Friday showed Macron gaining four percentage points since December, taking him to a 35% approval rating.


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Libyan PM kidnapped by armed men from a hotel in Tripoli: Reports
Guards at the Corinthia Hotel said gunmen had taken Ali Zeidan from the hotel but there were no shots fired or clashes during the incident.
Tripoli: Gunmen from a former rebel faction seized Libyan Prime Minister Ali Zeidan from a Tripoli hotel on Thursday, the government said.
"The head of the government Ali Zeidan was taken at dawn this morning by gunmen to an unknown place for unknown reasons," the statement said.
Guards at the Corinthia Hotel said gunmen had taken Zeidan from the hotel but there were no shots fired or clashes during the incident.
One guard described it as an "arrest" while another told Reuters the men were militants.
Government officials could not immediately be reached to give more details.
Al-Arabiya television channel quoted Libya's justice minister as saying that Zeidan had been "kidnapped" and showed what it said were video stills of Zeidan frowning and wearing a grey shirt undone at the collar surrounded by several men in civilian clothes pressing closely around him.
Two years after a revolution toppled Libya's Colonel Muammar Gaddafi, the fragile central government has been struggling to contain rival tribal militias and Islamist militants who control parts of the country.
Last weekend, the US military captured a top al Qaeda suspect in Tripoli in a raid that angered Islamist militant groups, including one blamed for the 2012 attack on the US consulate, in Benghazi.
The US State Department was looking into the reports of the incident and was "in close touch with senior US and Libyan officials on the ground," spokeswoman Jen Psaki said.
ali zeidan
People are Using FaceApp's Aging Filter to Compare Selfies with Photos of their Parents

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SA68 news, reviews and local events in SA68 areas including Begelly, Broadmoor, Carew, and communities in SA68. Are these places the most relevant to this postcode? Let us know!
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I think I will sleep well tonight knowing I have defeated the horde.
Well done. A few dozen rounds atta do 'em. Fave.
@grizzlydex they are 357 and 38 shells.
The world will know that a free beard stood against trimming implements, that few stood against many, and before this battle was over, even a razor can bleed.
Nice... flipped back through the week. Great story and glad it had a happy ending!
@yogibeard That is probably the best comment I have gotten so far.


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Early Voting Report: Votes Switched From Trump to Hillary in Texas
"She voted straight Republican and the vote had changed to Clinton!"
Residents of at least two cities in Texas are complaining that they voted for Donald Trump only to see the voting machine switch their ballot to Hillary Clinton.
Early voting for the 2016 presidential election started yesterday for people in some areas who have been given the opportunity to avoid the long lines on November 8.
However, in Amarillo, a woman was shocked to see her ballot flip from Republican to Democrat.
"Gary and I went to early vote today," wrote Lisa Houlette on Facebook. "I voted a straight Republican ticket and as I scrolled to submit my ballot I noticed that the Republican straight ticket was highlighted, however, the Clinton/Kaine box was also highlighted!"
"I tried to go back and change and could not get it to work. I asked for help from one of the workers and she couldn't get it to go back either. It took a second election person to get the machine to where I could correct the vote to a straight ticket," she added.
Meanwhile, in Arlington, Texas, another voter reported a similar experience.
"I had a family member that voted this morning and she voted straight Republican," wrote Shandy Clark. "She checked before she submitted and the vote had changed to Clinton! She reported it and made sure her vote was changed back. They commented that It had been happening."
Social media forums are also ablaze with concerns about votes being switched.
"Multiple reports on my Facebook, Periscope, Snapchat, and Twitter from my friends in Texas, and all of them had their vote switched to Clinton automatically," one post on The Donald Reddit is headlined.
The reports are alarming, especially given the fact that the media, Hillary Clinton's campaign and even President Obama himself have all attempted to dismiss Donald Trump's concerns about vote rigging as a baseless conspiracy theory.
Facebook: https://www.facebook.com/paul.j.watson.71
Paul Joseph Watson is the editor at large of Infowars.com and Prison Planet.com.
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Top Wireless Charging Technologies: What is the best wireless charging technology?
Most consumers are now aware that wireless charging exists, but what they do not know is that every wireless charging technology has different capabilities and acts very differently. Sure, they will all charge your device in the end, but exactly how they charge your device varies by technology, and different wireless charging technologies work better for different types of devices.
Best wireless charging technologies for different devices:
Magnetic Induction/Resonance Wireless Charging
Inductive/resonance charging tends to be better for larger devices, such as smartphones or electric toothbrushes, because it uses an electromagnetic field to transfer the energy between the device and the charging station – usually a pad or mat. The magnetic field is generated by the transmitter coil and then converted into an electrical current by the receiver to charge your electronics. Inductive charging tends to work well for large, flat electronic devices because they can fit the induction coils required to create a charge.
Depending on the type of technology integrated within the device, an inductive wireless charging pad can be purchased on Amazon, or encountered in places like Starbucks and even available inside some Ikea furniture! Induction can be a good solution for many larger devices where precise placement is less of a hassle, such as electric vehicles, tablets and similar devices.
Ikea inductive wireless charging pad (Photo credit: ikea.com)
Radio Frequency Wireless Charging
While inductive/resonance wireless charging works better for larger, flatter devices; RF wireless charging is best for wearables and other small devices because they are not restricted to the size and shape of the coils in the same way as inductive charging. Radio frequency wireless charging technology utilizes radio frequencies also transmitted through a wireless charger and picked up by a receiver within the device (not a coil) that is then converted into DC voltage. This way, the transmitter and receiver are not restricted by measurements for effective wireless power transfer and do not necessitate alignment of the transmitter and receiver for effective charging.
What is the Best Wireless Charging Technologies?
Pros and Cons of Inductive Wireless Charging Technology
Inductive charging is the best wireless charging technology for flat-shaped devices: Inductive charging works well for large, flat electronic devices because they can fit the induction coils required to create a charge. Depending on the type of technology integrated within the device, an inductive wireless charging pad can be purchased on Amazon, or encountered in places like Starbucks and even available inside some Ikea furniture! Induction can also be a great solution for many larger devices where precise placement is less of a hassle, such as electric vehicles, tablets and similar devices.
Availability: There are several types of wireless charging pads available on the market, and can be found anywhere from Starbucks to Ikea furniture (provided that your smartphone has a compatible wireless charging receiver).
Coil is limited in size & shape: This coil has physical limitations in size and shape in order for effective wireless charging to take place. Meaning, it can only be integrated into large, flat devices that have the empty real-estate to integrate a coil, such as a smartphone.
(Slow) Performance: One of the reasons that wireless charging has not been fully integrated is that it can still be slower and less efficient than a traditional charger. In addition, the heat generated in certain types of wireless charging technologies is generally higher in comparison with the conventional way of charging.
Precise Placement: Inductive charging requires the exact alignment of two coils (both the charging and receiving coil), in order to charge the device and sustain the charging process. This means that in order for there to be effective wireless power transfer, the user must place the device precisely in a certain point, otherwise power may be wasted and the device may be heated.
Pros and Cons of Radio Frequency Wireless Charging Technology
Multiple Device Wirelessly Charging: Everyone in today's electronic world has multiple devices that need to be charged daily. So how can we charge all of our devices simultaneously, with minimum clutter? This is where wireless charging stations come in handy. Because RF wireless charging does not require precise placement, a multiple devices charging station can help keep all of your gadgets in one place and hiding the unaesthetic clutter of cords. So you can reduce the amount of cables and discard international power adapters. In today's 'connected world,' multiple device wireless charging is becoming more of a necessity than anything. With so many smartphone, wearables, and other tech gadgets that require recharging devices, wireless charging is inevitable.
Integration: One of the best advantages of certain wireless charging technologies is the ability to integrate into any device size or shape. This can come in handy for factory workers, IoT healthcare, or anyone else who will be using smart devices for to streamline their work. With a tiny wireless charging receiver module just like Humavox's Thunderlink wireless charging can be implemented into the smallest of electronic devices, such as hearing aids, smartwatches, and more, in order to make wireless charging convenient for all.
Drop & Charge: Unlike induction, RF wireless charging provides users a drop & charge user experience. Meaning, that no matter how they place their device within a certain area, it will effectively charge. Allowing electronic devices to recharge exactly where you place them, regardless of how you placed them.
Mobility: Though the signal transmitted between your smartphone and the charging station is wireless, it is still necessary to plug the charging station to the wall. Therefore, devices currently available on the market are not portable, and therefore do not allow you to charge 'on-the-go.' Even far-field wireless charging RF technologies, while claiming to be able to charge from long distances, are still limited to a certain extent in size and efficiency. Humavox charging stations also require a plug, but come with a portable battery that can be charged on-the-go until there is enough energy to sustain its power.
Lack of Standardization in the Market: Competing technologies and lack of standardization in the wireless charging market means that devices will not work with just any type of charging station – each requires their own. At the end of the day, you aren't interested in knowing what technology is charging your device, you just want it to work.
Standardization for the Top Wireless Charging Technologies
Wireless charging may not yet be mainstream, but we've come a long way. For example, two major alliances currently exist – Qi Wireless Charging Standard and AirFuel Alliance (formed with the merging between PMA and A4WP). These two groups, are attempting to standardize the wireless charging space in order to make wireless charging accessible for all. Understanding the discrepancies between the different technologies, AirFuel Alliance (with a membership of close to 200 companies) has created the Uncoupled Power Working Group (UPG) for all technologies which are not induction. Their ultimate goal is to facilitate collaboration between the different wireless charging technologies, so that end-users won't even know, which technology they're using to wirelessly charge.
One RF wireless charging technology company aimed at such devices is Humavox, currently the Vice Chair of the Uncoupled Power Working Group (UPG) under the AirFuel Alliance. Humavox's top wireless charging technology, ETERNA®, is a flexible hardware platform based on near-field radio frequency (RF) technology with the ultimate goal of making charging simple, seamless and intuitive for users. Unlike induction, ETERNA does not require precise placement or alignment of the receiver and transmitter is not required for efficient wireless power transfer. The technology and its small wireless charging receiver enables integration of wireless charging into the tiniest of devices, making it most suitable for small electronics, such as wearables and IoT devices. It is implemented with a charging station that can be in the form of any container such as a cupholder, drawer, box and more. For example, by simply tossing your Humavox-enabled fitness band into a wireless charging station, charging begins.
Other Top Wireless Charging Technologies
There are several other types of wireless charging technologies being tested on the market, though they are not yet up to par with the industry standards. For example, infrared wireless charging technology uses an infrared transmitter (that would ideally be integrated into a light fixture), to beam light energy into a receiver while converting it to electric energy. The devices will, ideally, charge as long as they're in line of sight from the transmitter. Another example is, ultrasound wireless charging technology, which relies on ultrasonic transduction to take power from the nearest electricity and convert it into ultrasonic waves. The waves are then beamed into the device carrying the receiver.
Wireless charging hasn't exactly become standard, but it is constantly improving. At Humavox, we have created a new and exciting way for RF wireless charging that lets users simply drop their wearable into a charging station, blending wireless power into all your different life environments. Soon we will charge without even noticing!
ד"ר צבי וורטר נ' מכבי
ד"ר צבי וורטר
MWC 2015: Showcasing the Future of Mobility and Connectivity
Consumers' demand for mobility has driven hyper connectivity in our digital world and is one of the largest driving forces of the Internet of Things. At this year's Mobile World Congress in Barcelona, connectivity...
Wearable of the Month: Pivothead Smart Eyewear
Our wearable of the month for January goes to Pivothead, the smart (or shall we say, AWESOME), sunglasses! About Pivothead Pivothead is a connected set of sunglasses with an integrated camera that let you...


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WesScholar
Home > Theses and Dissertations > Masters Theses > 75
Shamanic Rituals as Sites of Religio-Cultural Revival: A Statistical Analysis of the Demographic and Cultural Differences of Attendees at Shamanic Ceremonies in Buryatia, Russia
Eric Michael Stephen, Wesleyan UniversityFollow
Advisor(s)
Lisa C. Dierker; Justine B. Quijada; Jennifer Rose
During the summer of 2012, anthropologist of religion Justine Quijada and colleagues collected ethnographic and survey data at five shamanic ceremonies led by a religious organization in Buryatia named Tengeri. The goal of this interdisciplinary research was to examine—through both quantitative and qualitative lenses—the ways in which these rituals provide a space for individuals in Buryatia to engage with the elements of traditional Buryat religion and culture that had been suppressed during the Soviet period. This work represents the first attempt to place these various methodological approaches in conversation with one another to provide a more holistic understanding as to why individuals choose to attend Tengeri's ceremonies. In line with the ethnographic fieldwork analyzed by Quijada, it was found that individuals who attend these ceremonies report behavior patterns consistent with traditional Buryat culture—such as Buryat language use and past shamanic practice—at much higher rates than the population of Buryatia more broadly. Additionally, significant cultural differences were identified between individuals who attended Tengeri's small ceremonies and those who attended the organization's large ceremony on Olkhon Island. Moreover, statistical analyses revealed a striking contrast with regard to attendance choice between self-reported ethnicity and one's connection to Buryat culture. As such, the data mining techniques and empirical analyses used in this work not only bolster the ethnographic hypotheses developed by Quijada and colleagues but also identify areas for future academic research.
Stephen, Eric Michael, "Shamanic Rituals as Sites of Religio-Cultural Revival: A Statistical Analysis of the Demographic and Cultural Differences of Attendees at Shamanic Ceremonies in Buryatia, Russia" (2014). Masters Theses. 75.
https://wesscholar.wesleyan.edu/etd_mas_theses/75
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Bo'az Mo'av (: בועז מואב; žil 3. dubna 1938 – 16. ledna 2002) byl izraelský politik a poslanec Knesetu za strany Rac, Ja'ad-Hnutí za lidská práva a opět Rac .

Biografie
Narodil se v Tel Avivu. Zde navštěvoval střední školu. Absolvoval Telavivskou univerzitu a University of Pennsylvania, kde obdržel doktorát z makrobiologie. Přednášel na Telavivské univerzitě.

Politická dráha
Byl členem hnutí ha-N'oar ha-oved a strany Mapaj. Patřil mezi zakladatele hnutí Rac. Byl jeho místopředsedou. Zasedal ve vedení ekologické organizace Malraz.

V izraelském parlamentu zasedl po volbách v roce 1973, do nichž šel za stranu Rac. V průběhu funkčního období tato strana fúzovala a vytvořila formaci Ja'ad-Hnutí za lidská práva. Pak se ale Bo'az Mo'av vrátil do samostatného poslaneckého klubu Rac. Byl členem parlamentního výboru pro ústavu, právo a spravedlnost a výboru pro záležitosti vnitra a životního prostředí. Ve volbách v roce 1977 mandát neobhájil.

Odkazy

Reference

Externí odkazy
  Kneset – Bo'az Mo'av

Narození v roce 1938
Úmrtí v roce 2002
Izraelští Židé
Sabrové
Absolventi Telavivské univerzity
Vyučující na Telavivské univerzitě
Členové Knesetu
Muži

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