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\section{Introduction}

Parameter estimation is an integral part of physics.  Accurate estimates of physical parameters in quantum mechanical models allows for precision quantum control \cite{khaneja2005optimal, brif_2010_control} which enables practical goals such as quantum computation \cite{nielsen2010quantum} and quantum metrology \cite{caves1981quantum} which in turn can provide probes of fundamental physics such as gravity wave detection \cite{aasi2013enhanced}.

Quantum parameter estimation shares many similarities with its classical counterpart.  But there are many subtle and peculiar differences.  Even in single parameter estimation, {quantum metrology} \cite{Helstrom1976Quantum,caves1981quantum} shows that we can obtain advantages from quantum resources such as squeezed states of light \cite{Lang2013Optimal} and entanglement \cite{giovannetti_2006_quantum}.  With such rich structure, many new subtleties \cite{barndorff2000fisher}, considerations \cite{fujiwara_2008_fibre, knysh_2011_scaling, escher_2011_general} and generalities \cite{Boixo2007Generalized,Tsang2011Fundamental,ferrie_2014_Fisher} can arise, including entirely new approaches to estimation \cite{Higgins2007Entanglement,Hentschel2011Efficient,mahler2013adaptive,ferrie_likelihood-free_2014} and verification \cite{flammia2011direct, da2011practical, magesan_efficient_2012}.

At the other end of the parameter spectrum the quantum state of a physical system is our most complete description of it. Thus estimation of quantum states \cite{paris2004quantum} might be seen as the most ambiguous form of estimation.  There are many approaches to the general problem \cite{hradil1997quantum,blume2010optimal, blume2010hedged,gross2010quantum}, some which specialize for computational efficiency \cite{Gottesman2008Identifying, Cramer2010Efficient,Toth2010Permutationally,LandonCardinal2012Practical} and those which go beyond to estimation of regions \cite{Rehacek2008Tomography, Christandl2011Reliable,Arrazola2013Reliable, BlumeKohout2012Robust,Shang2013Optimal,ferrie_high_2013}.

All of the above mentioned results assume a model.  That is, it was taken as given that a particular parametric distribution generated the data.  But what if this assumption is not correct?  This question has garnered recent interest and classical approaches to \emph{model selection} have been used in a variety of experimental \cite{usami_2003_accuracy,guta_2012_rank} and theoretical \cite{lougovski_2009_characterizing, lin_2011_information, schwarz_2013_error, vanenk_2013_when} works.  Here we supplement these results with a new approach to parameter estimation: \emph{model averaging}.  The technique shares many similarities with model selection---in fact, model selection is a crucial component of model averaging, but goes beyond it.  Although model selection adds an additional layer of security to overconfident estimation, selecting models can be itself a red herring, for the most probable model might only be slightly more probable than others.

The approach considered here combines Bayesian parameter estimation with Bayesian model selection, such that the final estimate of the parameters is the best value of the parameters within each model, averaged over the probability assigned to each model.  We will show that such an approach can reduce the error incurred by first selecting a model---which has some probability of being incorrect---then selecting parameters within that model.  In fact, the numerical experiments presented here show that model average estimation always does better than the estimates from incorrect models and in some scenarios can perform better than even estimates from the correct model.  This is due to the additional hedging afforded by considering multiple models, all of which carry \emph{some} information.

The paper is organized as follows.  In Sec.~\ref{sec:review} we outline the problem and review the model selection techniques used so far.  In Sec.~\ref{sec:Bayes}, we present the full Bayesian approach to model selection and define the \emph{model average estimate} of parameters.  Sec.~\ref{sec:examples} presents two distinct examples where the model average estimate provides an advantage for parameter estimation.  We conclude with a discussion in Sec.~\ref{sec:conclusion}.

\section{General problem and common methods \label{sec:review}}

In Sec. \ref{sec:A} we overview the problem.  In Secs. \ref{sec:AIC} and \ref{sec:BIC} we review the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) which are by far the most commonly used approaches to model selection (and the only used thus far for quantum estimation).  These sections are included for reference and completeness.

\subsection{Problem setup \label{sec:A}}
Let us begin with the base problem of \emph{parameter estimation}.  A physical model prescribes the probabilities for the outcomes of experiments: $\Pr(D|\vec{x};C,M)$.  Here $D$ is some hypothetical or observed data, $\vec{x}$ is a set of real numbers in $\mathbb R^d$, where $d$ is the \emph{dimension} of the model, $C$ is the experimental context\footnote{Experimental context, $C$, here means any additional information necessary to provide a well defined function $\Pr(D|\vec{x};C,M)$.} and $M$ is our model.  For example, we could have the model $M$ be that of qubit which is parameterized by a Bloch vector $\vec{x} = (x,y,z)$.  The experimental context could be a measurement basis, say that of $\sigma_x$.  Then, the quantum mechanical model prescribes $\Pr(\pm|\vec{x};C,M) = (1\pm x)/2$.  In quantum mechanics this is called the \emph{Born rule} and in statistics, the \emph{likelihood function}.

Going from parameters to the probability of data is a deductive process---the model gives us numerical values of $\Pr(D|\vec{x};C,M)$.  The experiment, on the other hand, gives us a particular data set $D$---but what we really want is $\vec{x}$.  This is an example of an \emph{inverse problem}.  What the Bayesian solution provides is $\Pr(\vec{x}|D;C,M)$, the \emph{distribution} of $\vec{x}$ given the data.  Although we lack certainty about $\vec{x}$, we can accurately (read: quantitatively, mathematically) describe our state of knowledge of $\vec{x}$ given we have seen the data $D$.

The formal path forward is through Bayes' rule:
\begin{equation}
\Pr(\vec{x}|D;C,M) = \frac{\Pr(D|\vec{x};C,M)\Pr(\vec{x}|C,M)}{\Pr(D|C,M)}.
\end{equation}
From a chronological point of view relative to $D$, we begin with the \emph{prior} $\Pr(\vec{x}|C,M)$, which encodes the information we have about $\vec{x}$ prior to learning about $D$.  We weight the prior by the likelihood function and normalize by the \emph{marginal likelihood}\footnote{The notation $\mathbb E_x[f(x)]$ means take the expectation of $f(x)$ with respect to the distribution of $x$ (the distribution itself is implicit).}:
\begin{equation}\label{marginal likelihood}
\Pr(D|C,M) = \mathbb E_{\vec{x}|C,M}[\Pr(D|\vec{x};C,M)].
\end{equation}
The distribution produced as result of Bayes rule, $\Pr(\vec{x}|D;C,M)$, is called the \emph{posterior} and represents our knowledge of $\vec{x}$ after the data has been observed.

At this point we could call the problem solved.  This, however, assumes the model is correct.  If the model is suspect, then we have the meta--problem of determining the best model.

\subsection{Akaike Information Criterion (AIC)\label{sec:AIC}}

The most commonly used model selection\footnote{See \cite{burnham_2002_model} for an overview of model selection and the various techniques mentioned here.} technique is the Akaike information criterion (AIC), which arises as follows.  First, we suppose there is some true model, $M=T$, giving a distribution $\Pr(D'|T;C)$.  We quantity the discrepancy between this model and our candidate model via the \emph{Kullback-Leibler divergence}:
\begin{equation}\label{eq:KLD}
{\rm KL}(T\|M) = \mathbb E_{D'|T;C}\left[\log\frac{\Pr(D'|T,C)}{\Pr(D'|\vec{x};M,C)}\right] = \mathbb E_{D'|T;C}\left[\log{\Pr(D'|T,C)}\right] - \mathbb E_{D'|T;C}\left[\log{\Pr(D'|\vec{x};M,C)}\right],
\end{equation}
for some appropriate choice of parameters $\vec{x}$.  The ``best'' model, then, is the one that minimizes ${\rm KL}(T\|M)$, which is equivalent to maximizing the second term in \eqref{eq:KLD} since the first term only depends on the true model.  However, we do not know the true model and we do not know the best set of parameters within our candidate model.  The latter problem is naturally address by collecting data $D$ and producing an estimate of the parameters $\hat{\vec{x}}(D)$, then averaging over possible data sets such that the quantity of interest becomes
\begin{equation}
\mathbb E_{D|T;C}\left[ \mathbb E_{D'|T;C}\left[\log{\Pr(D'|\hat{\vec{x}}(D);M,C)}\right]\right].
\end{equation}
Akaike showed that, independent of the true model (and under some regularity conditions), an unbiased estimator of this quantity is
\begin{equation}\label{eq:AIC}
{\rm AIC}(M) = \max_{\vec{x}} \log\Pr(D|\vec{x};C,M) - d,
\end{equation}
where $d$ is the number of dimension of the model (the number of free parameters).  The preferred model is the one with largest value of AIC$(M)$.  The simple linear penalization with dimension makes it is clear how models with more parameters are penalized.

\subsection{Bayesian Information Criterion (BIC)\label{sec:BIC}}
The Bayesian approach is more general.  Being so, it is less obvious how it might penalize complex models.  Here we show how an asymptotic approximation leads to a form similar to the AIC.
First, we write the marginal likelihood \eqref{marginal likelihood} as the integral expectation
\begin{equation}\label{eq:marginal integral}
\Pr(D|M;C) = \int d\vec{x} \Pr(\vec{x}|M;C)\Pr(D|\vec{x};C,M).
\end{equation}
We will approximate this integral using Laplace's method.  To this end, consider the Taylor expansion of the log of the likelihood function about its peak (note that for brevity, we have dropped the context $C$ and model $M$ from the conditionals):
\begin{equation}
l(\vec{x}) := \log \Pr(D|\vec{x})\approx l(\vec{x}_0) +\nabla^{\rm T}  l(\vec{x}_0) (\vec{x}-\vec{x}_0) +\frac12(\vec{x}-\vec{x}_0)^{\rm T} \nabla \nabla^{\rm T} l(\vec{x_0})(\vec{x}-\vec{x_0}).
\end{equation}
If we assume the number of measurements $N\to\infty$, the law of large numbers gives us
\begin{align}
 \nabla \nabla^{\rm T} l(\vec{x_0}) &= \sum_{j=1}^N  \nabla \nabla^{\rm T} l_j(\vec{x_0}),\\
&\to \sum_{j=1}^N  \mathbb E[\nabla \nabla^{\rm T} l_j(\vec{x_0})],\\
&=-\sum_{j=1}^N I_j(\vec{x}_0),\\
&= - N I(\vec{x}_0),
\end{align}
where $I_j$ is the Fisher information of the $j$'th measurement and $I$ is the arithmetic average of these values.
Then, the integral \eqref{eq:marginal integral} becomes
\begin{align}
\Pr(D|M;C) &= \int d\vec{x} \exp(l(\vec{x}))\Pr(\vec{x}),\\
& =  \exp(l(\vec{x}_0))\Pr(\vec{x}_0)\left(\frac{2\pi}{N}\right)^{\frac d 2}|I(\vec{x}_0)|^{-\frac12}\left(1+O\left(\frac1 N\right)\right).
\end{align}
Now we take the logarithm to obtain
\begin{equation}
\log \Pr(D|M;C) \approx l(\vec{x}_0) - \frac d 2\log N +\frac d 2\log 2\pi+ \log\Pr(\vec{x_0}) +\log |I(\vec{x}_0)|^{-\frac12}.
\end{equation}
If we ignore the terms not changing with $N$, we have a new quantity
\begin{equation}
BIC(M)= \max_{\vec{x}} \log\Pr(D|\vec{x};C,M) - \frac d 2\log N,
\end{equation}
which is the well-known Bayesian information criterion or BIC.  Notice the striking similarity to the AIC \eqref{eq:AIC}.  Being nearly equivalent, the BIC is often considered in addition to the AIC.  Next, we will consider the full solution, which will allow us to obtain more accurate estimates of parameters averaged over the competing models.

Recent proposals have used the AIC/BIC on both simulated \cite{lougovski_2009_characterizing, lin_2011_information, schwarz_2013_error, vanenk_2013_when} and experimental data \cite{usami_2003_accuracy,guta_2012_rank}.  In \cite{ vanenk_2013_when}, however, the authors caution its unattended use.  The argument against AIC for quantum states, for example, is simple.  The AIC is derived from a metric which measures their closeness of model in their \emph{predictive} probability---a certainly well-motivated measure.  However, such a measure is only useful if all future measurements will be the same as those used to perform the data analysis.  That is, one can measure copies of a quantum system in some fixed set of bases, estimate the state, then use that estimate to predict the outcome of a measurement in a new basis.  Thus, in quantum theory, one ought to consider a measure on predictive distribution as maximized over all possible future measurements.  As suggested in \cite{ vanenk_2013_when}, such a measure might well be the quantum relative entropy, for example.  Here we avoid these problems by considering the full Bayesian solution, which we describe next.

\section{Bayesian model selection and averaging}\label{sec:Bayes}

\subsection{Model average estimate}

  Within the Bayesian framework, the model selection approach is no different than for parameter estimation.  Rather than focus on the distribution $\Pr(\vec{x}|D;C,M)$, we first consider $\Pr(M|D;C)$.  Using Bayes rule we have
\begin{equation}\label{eq:metaBayes}
\Pr(M|D;C)= \frac{\Pr(D|M;C)\Pr(M|C)}{\Pr(D|C)}.
\end{equation}
Often, practitioners of Bayesian methods go one step further and compare two models---say, $M_1$ and $M_2$---by taking the ratio of these posteriors,
\begin{equation}
\frac{\Pr(M_1|D;C)}{\Pr(M_2|D;C)}= \frac{\Pr(D|M_1;C)\Pr(M_1|C)}{\Pr(D|M_2;C)\Pr(M_2|C)},
\end{equation}
noticing the normalization factor cancels.  This quantity is called the \emph{posterior odds ratio} and first considered by Jeffreys \cite{jeffreys_1998_theory}.  Clearly, if the posterior odds ratio is larger than 1, we favor $M_1$.  The last fraction is called the \emph{prior odds ratio} and the unbiased choice favoring neither model is set this term equal to 1.  This leaves us with
\begin{equation}
\frac{\Pr(M_1|D;C)}{\Pr(M_2|D;C)}= \frac{\Pr(D|M_1;C)}{\Pr(D|M_2;C)},
\end{equation}
which is called the \emph{Bayes factor} \cite{kass_1995_bayes}.  Each quantity in the ratio is marginal likelihood \eqref{marginal likelihood} of its respective model.

For a discrete number of hypothetical models $\{M_k\}$, and assuming one model must be chosen, the optimal strategy is to compute the marginal likelihood if each model and select the one with the highest value.  Model selection of this type has been used in quantum mechanical problems of Hamiltonian finding \cite{wiebe_2014_quantum} and estimating error channels from syndrome measurements \cite{qecc paper}.

Here we will investigate the idea of using a meta-model, which is an average over those in $\{M_k\}$.  Assume that we are interested in some subset of parameters $\vec{y}$ common to all models.  Given we have taken data $D$ and computed each marginal likelihood $\Pr(M_k|D;C)$, we define the model average estimate (MAE) as
\begin{equation}\label{eq:MAE}
\hat{\vec{y}}_{\rm MAE}(D;C) = \mathbb E_{M_k|D;C}[\mathbb E_{\vec{y}|D;C,M_k}[\vec{y}]].
\end{equation}
In words, this is the average (over models) of the average (over parameters within models).  Variants of this approach are referred to as Bayesian model averaging \cite{hoeting_1999_bayesian}.

Before moving to our examples, a few comments are in order.  First, it is not necessary that the models are ``nested'' in the sense that we can order them into supersets.  The only requirement is that the parameters of interest are included in each model.  The other parameters in each model we might call \emph{nuisance parameters}.  Part of the appeal of the Bayesian approach is that these parameters are automatically dealt with and we can focus on those parameters which are of immediate interest.  Of course, the nuisance parameters can be inferred as well.

Let us wax philosophical for a moment.  What is being proposed is to select a meta-model, an average over many different physical models.  This may seem awkward for physical theories---after all, there is only one true model, right?  Not in our view.  Models are human constructs, those Platonic ideals which describe another world, a world we were clever enough to find through our mastery of mathematics and abstraction.  Here, we have dropped the idea that the point is to find the capital-T-Truth.  Rather, we measure our understanding of Nature through our ability to predict and control its behavior.  By averaging physical models, we can show that this idea has merit.

\subsection{Sequential Monte Carlo}\label{sec:SMC}

In practice, the Bayesian update rule and the expectations required in the equations above are analytically and computationally intractable since they involve complicated integrals over multidimensional parameter spaces which may include solutions to equations of motions which are themselves intractable.  To perform the calculations we turn to Monte Carlo techniques.  Our numerical algorithm fits within the subclass of Monte Carlo methods called \emph{sequential Monte Carlo} (SMC) or \emph{particle filtering} \cite{doucet_2000_on}.

The SMC procedure prescribes that we approximate the probability distribution by a weighted sum of Dirac delta-functions,
\begin{equation}
\Pr(\vec{x}) \approx \sum_{j=1}^{n} w_j  \delta(\vec{x} - \vec{x}_j),
\end{equation}
where the weights at each step are iteratively calculated from the previous step via
\begin{equation}\label{eq:smc update}
w_j \mapsto \Pr(D|\vec{x}_j) w_j,
\end{equation}
followed by a normalization step.  The elements of the set $\{\vec{x}_j\}_{j=0}^{n}$ are called \emph{particles}.  Here, $n = {|\{\vec{x}_i\}|}$ is the number of particles and controls the accuracy of the approximation.  Like all Monte Carlo algorithms, the SMC algorithm approximates expectation values, such that
\begin{equation}
\mathbb{E}_{\vec{x}}[f(\vec{x})] \approx \sum_{j=1}^n w_j f(\vec{x}_j).
\end{equation}
In other words, sequential Monte Carlo allows us to efficiently compute multidimensional integrals with respect to the measure defined by the probability distribution.

The resultant posterior probability provides a full specification of our knowledge.  However, in most applications, it is sufficient---and certainly more efficient---to summarize this distribution.   In our context, the optimal single parameter vector to report is the mean of the posterior distribution
\begin{equation}
\hat{\vec{x}} = \mathbb{E}_{\vec{x}}[\vec{x}] = \sum_{j=1}^{n}w_j \vec{x}_j.
\end{equation}
The SMC approximation can also provide efficient calculation and description of \emph{regions} \cite{granade_robust_2012,ferrie_high_2013}.  For our purpose, we also require the SMC approximation to give an accurate and efficient esimate of the marginal likelihood Eq.~\eqref{eq:marginal integral}, which we need to calculate Bayes' rule at the level of models Eq.~\eqref{eq:metaBayes}.  Via the SMC approximation, the integral expectation in the definition of the marginal likelihood, Eq.~\eqref{eq:marginal integral}, is
\begin{equation}
\Pr(D) \approx \sum_{j=1}^n w_j \Pr(D|\vec{x}_j).
\end{equation}
It is not immediate obvious but is easy to see in hindsight that this is exactly the normalization that must be computed already in the SMC algorithm after the weight update, Eq.~\eqref{eq:smc update}, is applied.  By storing this value, we can apply Bayes rule at the meta-level of models Eq.~\eqref{eq:metaBayes}.

An iterative numerical algorithm such as SMC requires care to ensure stability.  Conditions for stability of the algorithm and the specifications of an implementation have been detailed elsewhere \cite{granade_robust_2012, wiebe_hamiltonian_2013}.  The SMC algorithm has now been used in many quantum mechanical parameter estimation problems \cite{chase_2009_singleshot,huszar_adaptive_2011, granade_robust_2012, ferrie_high_2013, wiebe_hamiltonian_2013, wiebe_2014_quantum} and a software implementation (the one used here) is available as a Python package \cite{qinfer,scipy}.

\section{Examples}\label{sec:examples}

\subsection{Rank selection\label{sub:rank}}

We consider first an example similar to Guta, Kypraios and Dryden \cite{guta_2012_rank}: $n$ qubits subjected to random Pauli measurements where the models under consideration are those of differing rank.  Each model will be denoted $M_r$ where $r$ is the rank of the unknown quantum state so that the dimension of model $M_r$ is $d = 2^{n+1}r$. We generate unknown quantum states with fixed rank $r$ as follows \cite{zyczkowski_2001_induced}.  Begin with a matrix $X\in \mathbb C^{2^n \times r}$ where each component $x_{ij}$ is chosen independently according to $\Re(x_{ij})\sim \mathcal N(0,1)$ and $\Im(x_{ij})\sim \mathcal N(0,1)$---standard Normal distributions.  Then define the rank $r$ density operator
\begin{equation}\label{eq:X2rho}
\rho = \frac{X X^\dag}{\Tr(X X^\dag)}.
\end{equation}
If $r= 2^n$, this construction is equivalent to a Hilbert-Schmidt random density matrix.  The model parameters will be the vectorization of the matrix $X$: $\vec{x}= {\rm vec}(X)$.

We label the single qubit Pauli operators $\{\sigma_0,\sigma_1,\sigma_2,\sigma_3\}$ and the multi-qubit Paulis by
\begin{equation}
\sigma_k = \sigma_{k_1}\otimes\sigma_{k_2}\otimes\cdots\otimes\sigma_{k_n},
\end{equation}
where $k = k_1+ 4 k_2 + 4^2 k_3 + \cdots + 4^{n-1} k_n$.  Since each Pauli is idempotent, $\sigma_k^2= \mathbbm 1$, each individual measurement has $2$ possible outcomes which we label $d \in \{+1,-1\}$ for the $+1$ and $-1$ eigenvalues.  Then the likelihood function of a single measurement can be related to the expectation value via: $\Pr(\pm 1|\sigma_k)=(1\pm \langle \sigma_k\rangle)/2$.  Using the properties of the vec operation, we can write this as an explicit function of $\vec{x}$:
\begin{equation}
\Pr(\pm 1|X,\sigma_k) = \frac12\left(1\pm \frac{\Tr(X X^\dag \sigma_k)}{\Tr(X X^\dag)}\right)= \frac12\left(1\pm \frac{\vec{x}\cdot (\sigma_k\otimes \mathbbm{1})\vec{x}}{\vec{x}\cdot \vec{x}}\right) =\Pr(\pm 1|\vec{x},\sigma_k).
\end{equation}

We label the parameter vector within the rank $r$ model $M_r$ by $\vec{x}_r$ and the associated density matrix given by Eq.~\eqref{eq:X2rho} $\rho_r$.  Within each model, there is not a one-to-one correspondence between $\vec{x}_r$ and $\rho_r$---different vectors will yield the same density matrix.  Since we will be interested in obtaining accurate estimates of density matrices as quantified by some norm on the space of density matrices, we will average the models over their $\rho_r$'s rather than their $\vec{x}_r$'s.

Within each model, then, we have the mean density matrix (recall $D$ is data, $C$ is the context---that is, which Paulis were measured)
\begin{equation}
\hat\rho_r(D;C) = \mathbb E_{\vec{x}_r|D;C}\left[\frac{X_r X_r^\dag}{\Tr(X_r X_r^\dag)}\right].
\end{equation}
Explicitly, the MAE in Eq.~\eqref{eq:MAE} is
\begin{equation}
\rho_{\rm MAE}(D;C) = \sum_r \hat\rho_r(D;C) \Pr(r|D;C).
\end{equation}
We assume there is a true density matrix $\rho_{\rm t}$ and we judge each estimate of the true state $\hat \rho$ by its spectral distance to $\rho_{\rm t}$:
\begin{equation}
\|\rho_{\rm t} - \hat\rho\| = \sigma_{\rm max}(\rho_{\rm t}-\hat\rho),
\end{equation}
where $\sigma_{\rm max}$ denotes the largest singular value.  This is the norm induced by the usual Euclidean norm on vectors.

\begin{figure}\centering
  \includegraphics[width=\columnwidth]{rank.pdf}
  \caption{\label{fig:rank}  The performance of Bayesian model selection and the model average estimate for 2 qubits.  Each box represents the data for its labeled rank as the ``true'' model---from left to right, ranks 1 through 4.  The lines represent the median of the data and, where present, the shaded areas are the interquartile ranges.  Each ``measurement'' on the horizontal axis corresponds to 100 experiments of a randomly chosen Pauli measurement.  In the SMC algorithm, $10^4$ particles were used in each model.  For each true rank, 100 simulated states were generated and measured.}
\end{figure}

The data for 2 qubits is presented in Fig.~\ref{fig:rank}.  The important take-away is that the model average estimate does as well, or slightly better than the true model in every case.  Also, we see that it is quite easy to identify rank 1 models (pure states) as well as rank 4 models (full rank states) while it seems difficult to identify states of non-extreme rank.  Notice that it is extremely difficult to distinguish the rank 3 model from the full rank model when the former defines the underlying truth.  However, both models perform well with respect to the error in the estimated parameters and the model average estimate does best, on average.

To further illustrate the difficulty in differentiating high rank states, the probabilities assigned to 3 qubit models is shown in Fig.~\ref{fig:rank3}.  Again, we see that pure states and full rank states are correctly identified, yet it is difficult to correctly distinguish between rank 7 and rank 8 states, in the same way as it was difficult to distinguish rank 3 and rank 4 states for 2 qubits.  We conclude that for the models considered here, it is easiest to correctly identify low rank and full rank states, while it is difficult to correctly identify nearly high rank states.

\begin{figure}\centering
  \includegraphics[width=.75\columnwidth]{rank3.pdf}
  \caption{\label{fig:rank3}  The performance of Bayesian model selection and the model average estimate for 3 qubits.  Each box represents the data for its labeled rank as the ``true'' model.  The lines represent the median of the data and, where present, the shaded areas are the interquartile ranges.  Each ``measurement'' on the horizontal axis corresponds to 100 experiments of a randomly chosen Pauli measurement.  In the SMC algorithm, $10^5$ particles were used in each model.  For each true rank, 10 simulated states were generated and measured.}
\end{figure}

Notice also that models which are far away---in the sense that the ranks differ by relatively large amounts---are quickly ruled out.  In these cases, since the SMC algorithm can be run online (in parallel with the experiment), simulating such models can be stopped to mitigate the computational difficultly in simultaneously simulating many quantum models.  Still, tomography is at one extreme in the spectrum of methods for estimating quantum mechanical parameters---it is the \emph{most complete} description of the physical system.  At the other extreme is summarizing information from experiments into a single number, such as fidelity.

\subsection{Randomized benchmarking\label{sub:rb}}

In the second example, we consider the experimental protocol of randomized benchmarking \cite{magesan_2011_scalable} which has been demonstrated in a variety
of experimental settings
\cite{ryan_randomized_2009,chow_randomized_2009,olmschenk_randomized_2010,brown_single-qubit-gate_2011} to efficiently characterize noise and quantum channels.  The protocol consists of stringing together potentially long sequences of gates which is then undone to determine if the initial state has survived.  In  \cite{magesan_2011_scalable} the approach was shown to give, in expectation, an exponentially decay $A p^m + B$, where $A$ and $B$ encode the errors in preparation and measurement, $p$ is the bare survival probability and $m$ is the length of the sequence.  In the models we consider, $p$ can be related to the average fidelity over a group of gates, but more specialized protocols exists \cite{moussa_2012_practical, magesan_efficient_2012}.

Typically, $p$ is the only parameter of interest since it is directly related to the average fidelity of the device which is then compared to some threshold.  The other parameters are often consider nuisance parameters.  In \cite{granade_2014_accelerated} it was shown that the decay can be interpreted as probabilistic model where the binary outcome of each measurement sequence of length $m$ has probability of survival (labeled $0$)
\begin{equation}
\Pr(0|\vec{x}_0;m,M_0) = A_0 p^m + B_0,
\end{equation}
where the subscripts refer to this as the \emph{zeroth order model}.  In \cite{magesan_2011_scalable}, a hierarchy of models was introduced because the zeroth order model assumes the errors in the gates within the sequence are independent.  By dropping this assumption, a richer set of noise models can be studied \cite{magesan_characterizing_2012}.  Here we will study the zeroth order model and the \emph{first order model},
\begin{equation}
\Pr(0|\vec{x}_1;m,M_1) = A_1 p^m + B_1 + C_1 ( m-1)(q_1 - p^2) p^{m-2},
\end{equation}
where $A_1$ and $B_1$ again encode the preparation and measurement errors, $C_1$ encodes the error on the final gate in the sequence and $q_1-p^2$ is a measure of the gate dependence in the errors.

For the zeroth order model, we take the prior to be a normal
 distribution with a mean vector $(p, A_0, B_0) = (0.95,0.3,0.5)$ and equal diagonal covariances given by a deviation of $\sigma= 0.01$.  Note that the first order model is equal to the zeroth order model when either $C_1=0$ or $q_1 = p^2$.  In order to not make the model so different that it would be trivial to distinguish them, we look at two priors for the first order model which are close to the zeroth order model.  The first is a normal
 distribution with a mean vector $(p, A_1, B_1,C_1,q_1) = (0.95,0.3,0.5,0.03,0.95)=: \mu_{\rm I}$  and equal diagonal covariances given by a deviation of $\sigma= 0.01$ and the second slightly closer with the same covariance matrix but mean vector $(p, A_1, B_1,C_1,q_1) = (0.95,0.3,0.5,0.02,0.92)=:\mu_{\rm II}$.  Note that the difference between these two distribution in the relative entropy divergence is only 0.050, and so we might expect them to behave the same.  Since the both models are close to the zeroth order model, we expect it to be difficult to distinguish them.

\begin{figure}\centering
  \includegraphics[width=1\columnwidth]{rbmodels.pdf}
  \caption{\label{fig:rbmodels}  The performance of Bayesian model selection and the model average estimate for the survival probability in randomized benchmarking experiments.  Each box represents the data for its label as the ``true'' model.  The lines represent the median of the data and, where present, the shaded areas are the interquartile ranges.  Each ``measurement'' on the horizontal axis corresponds to a randomized benchmarking experiment with sequences lengths $\{10,30,50,\ldots, 200\}$ and $1000$ repetitions per sequence length.  In the SMC algorithm, $10^3$ particles were used in for each model. }
\end{figure}

In Fig.~\ref{fig:rbmodels} we simulate the models noting again that, via the priors, they are very close.  This intuition is quantified by the fact that the models are hard to distinguish, regardless of which is true.  On the left in Fig.~\ref{fig:rbmodels}, we see that parameters in the first order model are so close to those in the zeroth order model that it is irrelevant which is chosen, for the purpose of estimating $p$.  However, what is ``close'' can be deceiving as we see in the right of Fig.~\ref{fig:rbmodels}.  Recall that relative entropy from $\mu_{\rm I}$ to $\mu_{\rm II}$ is only 0.050 (which explains why they are so difficult to distinguish).  In this case, the accuracy of the estimates of the parameter $p$ depend crucially on which model is actually correct.
In such cases, the model average estimate can be seen as providing a more conservative estimate of the average gate fidelity by hedging what is at best a 50/50 guess on which model is correct.

\section{Conclusion and discussion}\label{sec:conclusion}

We have introduced a Bayesian model averaging approach to estimating parameters in quantum mechanical models describing data.  In the examples considered, the model average estimate performance as well as the unknown true model in most cases.  In situations where models are difficult to distinguish, the model average estimate can slightly \emph{outperform} the true model.

For the quantum state estimation example (Sec.~\ref{sub:rank}) we considered models of differing rank of the density matrix.  Ranks which differ by large amounts from the true rank are rapidly ruled out---that is, the probability assigned to them quickly approaches zero.  Thus, they contribute nothing to the model average estimate.  On the other hand, ranks which are close to the true rank---especially when the true rank is high---are not so easily distinguished.  This means that first selecting a rank and then performing estimation within that model can lead to overconfident estimates of the state.  By averaging, we can allow those estimates to only contribute with the relative probability that we deem them to be true.

The mechanism for why higher rank states are hard to distinguish is yet unclear.  Although the SMC algorithm and the implementation used here have been extensively studied for a wide range of problems, it is possible that state tomography is an outlier.  That is, some major modification to modeling or the algorithm itself may be required to obtain the best performance.  This resolution would be less interesting than a physical explanation, such as Pauli measurement tomography (which we have used in the example here) is not the optimal scheme to distinguish rank.  These questions are left for future work.

In the example of randomized benchmarking (Sec.~\ref{sub:rb}), we explored a situation where the presence of higher order perturbations were difficult to detect.  The Bayesian model selection approach accurately predicts this by assigning roughly 50/50 probability assignments to the models.  Surprisingly, the ``closeness'' of the models as measured by our ability to distinguish them does not translate into our ability to accurately estimate parameters common to each.  In some cases we can do no more than guess which is correct, yet guessing the wrong model may have disastrous consequences in our ability to accurately infer the parameters of interest.  Again, the model average estimate mitigates the risk of improperly ``guessing'' which model is correct.

We have noted in the introduction the numerous approaches to estimation within quantum theory.  This should urge one to ask, are all of these distinct approaches necessary---is there not some unified approach?  Yes!  The Bayesian framework outlined here is remarkably powerful in its generality.  We note that Bayesian ideas have already been put to good use in quantum information theoretic and foundational problems
\cite{Schack2001Quantum,Caves2002Unknown,Caves2002Quantum,Fuchs2009Priors,Fuchs2009QuantumBayesian,Fuchs2010QBism,Fuchs2011Bayesian,Leifer2011Bayesian,Leifer2012Formulating}
as well as for tomographic and parameter estimation problems \cite{Jones1991Principles,Derka1996From, Buzek1998Reconstruction,Teklu2009Bayesian, Gill2009Conciliation, blume2010optimal, Sergeevich2011Characterization,Brivio2010Experimental,Oi2012Quantum} and experimental design \cite{Ferrie2012Adaptive,Ferrie2012How}.  Importantly,  the Bayesian algorithm can provide solutions to these problems \emph{online}, while the experiment is running, with the same software tools \cite{qinfer}.

\begin{acknowledgements}
The author thanks Chris Granade and Robin Blume-Kohout for helpful discussions.  This work was supported in part by National Science Foundation Grant No. PHY-1212445 and by the Canadian Government through the NSERC PDF program.
\end{acknowledgements}

redpajama_set_name: RedPajamaArXiv


I picked up my hydrocodone prescription on April 13, 2012. I never count the pills- didn't think I had to. But when I did count them the following Friday- I only had 46 (I get 120 in each refill) I realized I was short 50 (would have used 28 in the week that I already had them). I got shuffled around from one pharmacist to another for 5 days- when the pharmacist just tossed 20 pills at me, turned her back and refused to discuss my situation any further. I was so humiliated I ended up leaving the store in tears. I can't believe that CVS would support treating customers like this. I have been getting my medications (I am on many meds for a chronic health condition) for over 8 years and even if I was wrong about my pills (I'm not)- they should treat me like a valued customer, not an irritant to be kicked to the curb, or wiped off the bottom of their shoe. And I'm still short 30 pills.
CVS is the worst. I'm in Cedar Hill, Tx and they really do not like white people. I've never in my life spent money in a store and been spoken to so unprofessionally. The "ah-rite" and stupid ghetto talk has helped me find a new pharmacy, one that speaks clear English.


OK, you've tried before. The last few times might not have worked out but your intentions and instincts were right so you should definitely start again. Reading the Bible everyday is worth it.
You need a manageable goal. One chapter a day is a good place to begin. Allow 10-15 minutes per day. It will probably take even less time most days but give yourself the margin.
Let's start with one month in mind. The gospel of John has 21 chapters. Starting today you will complete the entire book in 3 weeks by reading one chapter a day. After that, read the six chapters of Ephesians. To round out the first successful month of your daily Bible reading habit, read the little but powerful book of 2 Thessalonians.
There are 2 things to think about in choosing a Bible. First, I recommend a modern language translation. I use the English Standard Version because it reads well and it's more literal than the popular NIV. Some other version might work better for you. No matter which Bible you choose, I recommend you use the same one each day so you can feel familiar with it.
The second thing to keep in mind is whether to choose a digital or a traditional paper Bible. Both have advantages. A digital Bible is more convenient since it can be stored on your phone. A traditional paper Bible is easier to see "at a glance" if you're following a daily reading plan. I also find a traditional paper Bible easier to keep notes in than the excellent digital options available. Eventually, you will want both at your disposal- I go back and forth between the two depending on the need- but this month you're getting a habit started. Choose the best for you and stick with it.
There won't be a quiz at the end! Too often I have seen believers worry they should know more, or they feel internally pressured to find "deep" revelation every time they read God's word. Stop worrying and start reading. God will speak to us sometimes in dramatic ways and more often in gentle whispers to our conscience. He can handle that part. For now, don't put unrealistic expectations on yourself. Why should you? If you're reading daily, you are doing great!
Our goal right now is to get started and to keep going. So read without overly stressing out if you don't understand a name, geographic reference, or even a concept. Keep reading and God will speak to you in His own way and His own timing.
Finally, feel free to write yourself notes in the Bible or a notebook to keep track of your questions, thoughts, and moments of inspiration. Try to maintain a daily schedule but if you miss a day, start over where you left off. It takes time and consistency to develop a new habit.
Don't worry about next month. Just get started. Start today.
I wake up very early in the morning (4:10-4:15am) and I have ample time to follow this plan to pray and read scripture. Thank you Kie.
I finally finished the first month reading the Bible.
Do you have more information on the second month?


text:
Luca Sisera Roofer
2019-05-06 21:00:00 @Piec' Art Acoustic Jazz Club
Miejsce: Piec' Art Acoustic Jazz Club
Cena biletu: 20
Link do wydarzenia na facebook'u: https://www.facebook.com/events/397082277740297/
Luca Sisera – bass, composition, Michael Jaeger – tenor saxophone, Maurus Twerenbold – trombone, Yves Theiler – piano, Michi Stulz – drums
With their new album Starlex Complex, Luca Sisera Roofer masterfully continue their journey over the hurdles and chasms of contemporary jazz. Starlex Complex follows their critically acclaimed debut album Prospect (Leo Records, 2015) and the live album Moscow Files (Leo Records, 2017). This new work, released on Nils Wogram's label nWog Records, contains nine compositions, including a three-part minisuite.
These open up a musical spectrum in which the ostensibly opposite poles of structure and freedom ethereally imbue each other and blend as a distinctive band sound. Creative Swiss bassist Luca Sisera is a musician considered one of the outstanding instrumentalists on the European scene. As an accomplished sideman, he playfully comes to grips with even the most demanding of jobs across the entire jazz genre, as well as interdisciplinary projects. In 2013, he founded Roofer as his own quintet. Michael Jaeger (saxophone), Maurus Twerenbold (trombone), Yves Theiler (piano) and Michi Stulz (drums) are major musicians from the relatively young Swiss jazz scene. They handle the sometimes highly complex compositions very freely and thus realise their band leader's vision in a congenial way. It is no accident that Sisera named his band Roofer.
So-called "roofers" are climbers who clamber up high structures without safety equipment, and ably cross the hurdles and chasms of urban roof and facade landscapes. Sisera is not one of these extreme athletes, but an extremely agile musician. The qualities with which roofers put their passion into practice characterise not only his compositions, but also his fellow musicians: love of adventure, willingness to take risks, sophisticated techniques, know-how and experience. Sisera's music is refined. It has a challenging edginess without rigidifying in lifeless formulae. Positive restlessness and well-placed contrasts keep it energised. Although the compositions are oriented towards complex forms and rhythmically pointed parameters, they are effortlessly turned into sound that pleases with its warmth and emotion. At certain moments, melodious and tranquil passages lend the music a flowing, hymnic aspect. On the other hand, the fact that each musician can duly draw attention to themselves again in spirited unison passages or interplay contributes to the intense listening experience that this album generates. Luca Sisera wrote the compositions for Starlex Complex while staying at the Nairs Artists' House in Scuol, amid the mountains of Grisons and very close to the soaring peak of Piz Starlex.
This mountain, right on the border between Italy and Switzerland, served the half-Swiss, half-Italian Sisera as inspiration for the album's title. By adding "Complex", he alludes to the complex structures of his music, but also to the building complexes scaled by "real" roofers. The soundscape is congruent: here is music that is genuine and remains adventurous.
Daria Sikora2019-04-09T00:08:33+02:00Kwiecień 9, 2019|
Daria Sikora
Lubi Finlandię (kraj!), planszówki i wschody Słońca, a w wolnych chwilach uaktualnia bazę koncertów KSM.

redpajama_set_name: RedPajamaCommonCrawl


Nice idea. Not sure if the machines should have been helicopters for more realism but good effort.
Nice! You did a great job with the lighting, the bridge...and pretty much everything. Awesome!
Really nice work here! I especially like the extra rays traveling through the bridge. Good luck!
Looks good! Try to distort the far end of the bridge so it's smaller, and the perspective will be better. GL.
Very realistic, I like the ilumination!
PS: You really should make a SBS for this. Would definitely improve your vote.
Now that's what I wish Springville looked like!
Thanks for the congrats... didn't really expect this one to win!
Congratulations on your first place!
i guess it must be a mega bird!
I'm not sure if the bird was necessary either but I think this that the final result is best so far! I hoped that someone would cover the street with water and this is a very neat chop!
A more dramatic sky would definitely add more charm to it so i'll hold my vote until the end but I do like this!
I like it, it shows a nice boat ride.
Nice work on the reflections. Well done!
Tower reflection is out of place (should be beneath original) but otherwise looks good.
@CMKY46, fixed the tower reflection.. thanks!
No, you didn't. See the other reflections and how they're directly below the objects they reflect? The tower reflection needs to move to the right.
@CMKY46.... (*as i facepalm myself*)... I thought you were tallking about the white and red tower down the river (which was off and I fixed)... I didn't even notice the big tower to the left was off too, lol. I will fix it this time... Thanks!
This is a representation of the footage taken near Tiananmen in 1989. Now known as the "tank man" a normal citizen protested for freedom on behalf of millions by blocking the way of a column of tanks. He stood for freedom and is an icon to many people around the world. It still makes the hairs on my neck stand up when I see it!
i love this peice of work, i have two suggestions that really arent vital but wold make this picture just a little better IMO the shadows of the man arent matching with the light source of the tanks at least it seems that way to me and the shadows need to be a liitle more blurry but other than that, awesome image author and best of luck to ya'!
Oh, I guess I remeber that... it was in China, wasn't it?
fix the shadows as suggested and this will be a good entry. GL!
EDIT: Why thanks author, I like my glasses too. Your picture looks good in color.
Did you add the vignette later? The image was too dark already. Try to create depth somehow.
>CMYK,...vignette? yes, sir,...vignette for your clean bold head,....it is easy to create........!
I agree some depth on the image would be good... how about a slight and gradual blur on background figures?
view in high res better..
Really good effort. Well done!
Nice effect, but when it's dark I expect the street lights to be working . Good luck!


text:
GreaterGroton.com Aims to Amplify Citizen Voices
The Town of Groton has launched a new community engagement platform, GreaterGroton.com. Everyone who lives in, works in or visits Groton is invited to use this tool to share views on what is happening in our community.
GreaterGroton.com is a discussion forum for current issues and ongoing projects. On the site, users can participate in polls and surveys, pinpoint areas of concern on a map, and offer comments and ideas for Town of Groton staff to review. Built-in monitoring tools prevent the loudest voices in the room from taking over the conversations. The platform is designed to complement all other current forms of public outreach and input.
A great time to register is now. The Town's Long-Term Recovery Committee is using this platform to collect public input on how to spend the $8+ million received through the American Rescue Plan Act. A key element of this strategy is an upcoming budget simulation tool to allow users to conduct a virtual allocation of funds to a series of spending categories such as infrastructure, social services and COVID-adaptation.
The platform is hosted by Bang The Table (bangthetable.com), a team of community engagement specialists who have worked with hundreds of communities over the past 14 years.
An ongoing marketing campaign will promote the platform to Town residents, employees and visitors.
Good Fortune Smiled on New Bookstore Owner
A delayed flight in mid-June proved serendipitous for Colleen Lynch. Lynch, who lived in Sandy Hook, Newtown, but spent summers in Groton's Eastern Point neighborhood with her family while growing up, was flying out of Providence to visit friends in Kansas when her flight was delayed until the next day. ...Continue Reading
History Remembered: Groton's skating rink gone, but memories roll on
Groton's Galaxy Roller Rink, the only roller skating facility in southeastern Connecticut, closed just over three and a half years ago. The recent announcement of the sale of the building that housed the rink, and the strong probability that it will be torn down, brought a considerable amount of disappointmen...Continue Reading
Via Emilia in Mystic is one of the best restaurants in the region
Here's the truth. We had such a good meal the first time we dined at Via Emilia that we went back for a second visit nine days later. And when I say we had a good meal, it was the food first and foremost, but also the ambience, service, an...Continue Reading


and slept on the bunk directly above mine.
Basically, he was way cooler than me.
how we actually became such close friends.
and we just sat in the back with Alina and talked the whole time.
it was speeding down the freeway at night blasting techno.
ping pong and how we would always compete to see who was the best.
I remember driving up to Mt. Hood and getting stuck in the snow without chains.
we were laughing so hard that we couldn't sleep.
laugh uncontrollably, and it still happens to this day.
He's really mellow and doesn't get stressed out easily.
Through all the time we've spent together, it's fascinating to see how he's changed.
He's become more stable, more of a man.
he's become less afraid to show people who he really is.
with our spiritual growth that we've experienced.
for the sake of fun and entertainment.
You are awesome and I'm super blessed to have you as a friend.
ahead of you and your future is looking very promising.
Awesome :) Joey really is growing up to be an awesome man who truly loves the Lord.
Great job on the card dude!
So sweet, Artem! I'm glad I don't live at home anymore because your little giggles at 3:00 in the morning were ridiculous!
erroneous. I heard it loud and clear.


In this video we go for a trip with my friends on Honda CB650F (me), Yamaha XSR900 and Honda Africa Twin. We went to Artenra to visit one special place - the restaurant in the cave.
I appreciate my friend Ondrej Vymetalik who rents motorcycles here in Gran Canaria http://www.canaryride.com and helps me to do my video tests. Thank you!
This looks like a video game.. Is this real?
@JF Motorcycles Thank u for showing me this video. I will keep trying, Thank youuuuuuu!
Hahaha, speed and passion are always together.
I've been asking my parents to buy me a motorcycle, but they've always turned me down.


There are many benefits to being a member of AMPS. The best way to learn about these is to explore the website - read the About page and look at Membership Benefits for a list of advantages.
If you work as one of these, or a closely related profession, you are eligible. Depending on your years of experience, you'll automatically be allocated a Membership Category after applying.
Sponsors are existing AMPS members who know you professionally and are willing to recommend you as a member. Check the Directory to find people.
If you are a sound student applying, you only need your course leader to sponsor you.
If you are unable to secure the number of Full Member sponsors stipulated in the above categories, Council may nevertheless consider your application if it is accompanied by a verified CV and one or more internet links or email addresses for an appropriate person, e.g. senior technician, director, producer or employer, with whom you have worked. Council will consider the application on an individual basis, and its decision shall be final.
In each case you should ask the people involved if they are happy to sponsor you and then provide their email addresses, so they can be contacted directly.
You will need to upload a copy of your CV. It should include accurate dates for all work. We recommend you don't include your postal address as this CV will be part of your online profile and may become publicly viewable.
You'll upload this when you fill out your application.
You are ready to go now, simply go to our Membership Application and complete your details.


text:
Jay-Z sends $40K Rolex watches to Meek Mill, Swizz Beatz & his VIP guests ahead of his Shawn Carter Foundation Gala
2019-11-06 2019-11-07 AdminEntertainment
The father of three and husband of crooner Beyonce has sent his VIP guests a $40,000 Rolex Daytona watch and…
Beyonce poses with husband Jay-Z in new photos shared to her Instagram at Tyler Perry Studios opening in Atlanta
2019-10-07 AdminEntertainment
The American singer , Beyoncé Giselle Knowles-Carter looked stunning in a glittering gold gown with husband Jay-Z at her side…
Taylor Swift tops World's Highest-Paid Women In Music 2019(See full list)
The "Me!" singer Taylor Swift has topped the Forbes' list for highest-paid women in music after earning a whopping $185…
Coachella 2019: Ariana Grande takes home $8 million, Double Beyonce's Fee
The choice for this year fell on "God Is A Woman" crooner, Ariana Grande and the choice of choosing her…
Beyonce, Jay Z And Their Kids Dropped A Live Coachella Album Along With The "Homecoming" Netflix Documentary
A Film by Beyoncé," premiered on Netflix early on Wednesday and she also released "Homecoming: The Live Album" on her…
Beyonce's Twins Have Different Personalities – Tina Knowles
2019-02-12 2019-02-12 Folami DavidEntertainment
It was a day to remember when Beyonce and Jay Z welcomed their twins, the world waited for it and…
Beyonce parades her cleavage as she presents in a spotted jumpsuit and jewels in new attractive photos
Pop Queen, Beyonce looked exquisite as ever in these new new sexy photos she posted on Instagram. In the photos,…
Beyonce flaunts her hot legs in Instagram photo shoot looking skimpy silver ensemble
The mother of three Beyonce flaunts her hot legs on display. the pop queen layered a matching bodysuit underneath a…
Pop Diva, Beyonce performs in six different outfits at Nelson Mandela charity concert in South Africa
Pop diva, Beyonce perform at the Nelson Mandela charity concert on Sunday along side with her husband Jay-Z in six…
Beyoncé pens letter of gratitude to Nelson Mandela-You made it possible to reject Impossibilities'
2018-11-29 AdminForeign News
South African daily paper Sowetan has published a letter written by Beyoncé and routed to the late Nelson Mandela. The…
Beyoncé and Jay–Z paid tribute to black athletes and black power for Halloween
Beyonce and Jay-Z go on sports route for their couples costume on Halloween as Jay-Z dressed as Tommie Smith while…
Beyoncé And former Destiny Child bandmate Kelly Rowland Connects At City of Hope Gala
The mother of three Beyonce performed at this year's City of Hope gala in Los Angeles earlier this week along…
Beyonce stage performance with Jay-Z on last ten shows of on the their Run Tour II
Beyonce took to her Instagram page to share these staggering photographs from her stage execution with Jay-Z in front of…
Full List of 2018 MTV VMAs nominees : Cardi B, Beyonce Lead
Last year's 2017 VMAs were hosted by Katy Perry. Kendrick Lamar began off the show with a red hot ninja-filled…
Beyoncé Speculation She's Pregnant With Baby four,conceals her stomach in baggy T-shirt she relaxes on a yacht with Jay-Z
The 36-year-old mother-of-three Beyoncé, who people speculate might be pregnant with her 4th child, concealed her figure in a loose…
Family photos of Beyonce and Jay-Z on holiday with their daughter Blue Ivy
The 36-year-old whiz Beyonce and her husband Jay-Z who are as of now on a joint tour took some time…
Beyoncé and JAY-Z still Crazy In Love -the Internet Reacts
After a mind-boggling beginning of their On The Run Tour II a week ago, Beyoncé and JAY-Z steamed up our…
Beyoncé Bought a Church, former church of Christ,Now it is a church of Beyoncé
Pop superstar Beyonce Knowles the new owner of a stone structured, 7,500 sq. ft house of God in The Big…


text:
Mueller should go public now about the President, or go home
Anti-Trump media has created a permanent crisis news cycle based on the Mueller probe that has people at each other's throats – If Mueller has the goods on Trump he should say so, or announce there's no there there.
Posted by William A. Jacobson Wednesday, August 1, 2018 at 09:30pm 68 Comments
Robert Mueller did not start Trump Derangement Syndrome. That started before the 2016 election, but went ballistic when Trump won.
#TheResistance movement immediately went into crisis attack mode, trying to intimidate Electors and to delegitimize the election result.
At every stage the media has played a critical role in arguing that Trump colluded with the Russians to steal the election.
The Steele Dossier, perhaps the most successful opposition disinformation project in memory, served to provide fodder for the evidence-free accusations against Trump. The dossier was a collusive effort between the Clinton campaign and DNC, on the one hand, and Russian sources who supposedly fed information to Steele.
With the connivance of the Obama intelligence and law enforcement apparatus, the dossier helped perpetuate the collusion narrative in the endless media news cycles. Leaks about otherwise casual and non-substantive "contacts" between Trump campaign officials or supporters and Russians were a weekly news mania. That hysteria created the public crisis atmosphere in which Jeff Sessions recused himself because of his "contacts" with Russians, even though there is zero evidence Sessions did anything wrong.
But the Steele dossier lacked media legs because the key allegations in the document were unsubstantiated. That's where Mueller comes in.
Since Mueller was appointed in May 2017, after James Comey was fired as FBI Director, we have been in a perpetual 3-5 day "scoop" news cycle based on the Mueller probe.
For over a year barely a week goes by that some publication doesn't publish a "scoop" about what Mueller is thinking, who his team is talking to, what they might do or might not do, and so on. The Mueller probe is the media gift that keeps giving, usually based on anonymous sources.
Just as each breathless and frequently demonstrably inaccurate media firestorm has died down — Wait, another Big Scoop. Let's start a new news cycle. It never ends, and will not end so long as Mueller is investigating Trump, whether Trump is a "subject" or a "target" or something else.
The nation has suffered this media-driven Mueller probe gaslighting to the point that there is an increasing likelihood of serious violence.
You see it everywhere. #TheResistance, prodded daily by media "scoop" hysteria, is ready to fight — literally — the grave threat Trump the supposed "traitor" presents.
There is anger all around. I've never sensed what I sense now. Things are coming apart, and I blame the permanent crisis news cycle in substantial part.
Mueller is not to blame for the media. But he can't ignore how his investigation is being exploited. Mueller has had over a year to investigate Trump. The FBI and intelligence services have been investigating Trump for over two years. If there is a there there, they should know it by now. So far, nothing has been publicly revealed.
This is not the usual criminal investigation, where time is not of the essence. And the investigation of Trump is qualitatively different than the investigation of others.
If Mueller has the goods on the President, he should tell the nation now what those goods are.
If Mueller has nothing on the President, he should say so now to put an end to the media madness that is driving the nation to fratricide.
68	68 Comments media bias, Robert Mueller, Trump Derangement Syndrome, Trump Russia
media bias, Robert Mueller, Trump Derangement Syndrome, Trump Russia
Matt_SE | August 1, 2018 at 9:41 pm
What makes you think that the Democrats don't want chaos? Isn't that the moment when most of our liberties are lost, sometimes permanently? When there's a "crisis?"
Barry | August 1, 2018 at 9:43 pm
"…he should say so now to put an end to the media madness…"
Mueller and his merry band of crooks like the media madness. That's part of their "job".
Bucky Barkingham in reply to Barry. | August 2, 2018 at 7:37 am
All of Müeller's Leftist lawyers will continue to draw big pay checks as long as this "investigation" is ongoing. I expect it will continue until Jan 20 2025.
4th armored div in reply to Bucky Barkingham. | August 2, 2018 at 9:02 am
all you hear from the msm AND smith (FNC) is that mueller, comey
etc are REPUBLICANS what they do not say is that is that they are NeverTrumpers DeepState with agendas!
Jackie in reply to Bucky Barkingham. | August 8, 2018 at 5:58 am
They all worked for law firms and drew large salaries. It's about power and the ability to screw with people they hate.
regulus arcturus | August 1, 2018 at 9:52 pm
Muller was illegitimate from inception. He has no intention of closing up shop without scalps, and has every intent of getting the largest scalp – Trump's.
It is becoming increasingly clear that Muller is out to squeeze Trump associates and force them to fabricate "evidence" out of whole cloth, thereby committing prosecutorial crimes.
Trump should take no mercy on Muller's entire goon squad, and imprison them all once the full scope of spygate/deep state corruption is revealed.
Muller needs to spend the rest of his natural life in prison, along with Brennan, Clapper, and others.
V.Lombardi in reply to regulus arcturus. | August 2, 2018 at 6:09 am
Yes the illegitimacy of Mueller is not debatable and began day one. Plus Mueller likes to win no matter how dirty he needs to be. I favor harsh retribution against Mueller, Rosenstein, Sessions, and other key participants.
Colonel Travis | August 1, 2018 at 9:53 pm
Just curious why you think it's more awful now vs., say, 6 months ago or a year ago? Not saying you're wrong, Prof. I'm just saying I don't know what you're sensing. Maybe it's because I've unplugged myself from all TV news and don't read the constant BS over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over and over from leftist activists pretending to be journalists.
I like to think I know what's going on in America in a general sense, but I'm willing to concede that perhaps I may not.
Tom Servo in reply to Colonel Travis. | August 1, 2018 at 11:33 pm
It's bad, but from what I remember 1967 and 1968 were a lot worse.
kenoshamarge in reply to Tom Servo. | August 2, 2018 at 11:19 am
I would tend to agree except back then there wasn't the constant social media mobs to make things worse.
Let one of the twitidiots read a headline or hear a talking point and they are outraged, vile and near insane. I've never seen anything quite like it and I've been watching politics a very long time.
Skankywoman | August 1, 2018 at 10:17 pm
My favorite site. New here. I absolutely love love this site and glad to be a part of it finally. I will be posting from New Jersey, that sick State. In NJ if anyone is interested, we have Dereal (real name no kidding) from Plainfield and nj.com posted this news:
"A Plainfield man was arrested Saturday on a felony charge accusing him of making threats on social media targeting U.S. Rep. Chris Smith.
Dereal Finklin, 43, is charged with making terroristic threats and is being held at the Monmouth County Correctional Institute in Freehold."
Later on in the article does it state finally state that Rep. Chris Smith is a republican.
I've made comments about this and my comments are banned from NJ.com. I'll share those here if you will entertain them. I'd like to be a NJ contributor when I can. Anyway, here it is: (I stole the this from Gateway Pundit.)
Just repeating what President Obama said and nj.com red boxes {meaning they won't or disabled my comments} it. Why? Not lies.
** Obama: "They Bring a Knife…We Bring a Gun"
** Obama to His Followers: "Get in Their Faces!"
** Obama on ACORN Mobs: "I don't want to quell anger. I think people are right to be angry! I'm angry!"
** Obama to His Mercenary Army: "Hit Back Twice As Hard"
** Obama on the private sector: "We talk to these folks… so I know whose *** to kick."
** Obama to voters: Republican victory would mean "hand to hand combat"
** Obama to lib supporters: "It's time to Fight for it."
** Obama to Latino supporters: "Punish your enemies."
** Obama to supporters: "I'm itching for a fight."
Obama to UAW mob: "Fight for me!"
TheFineReport.com in reply to Skankywoman. | August 1, 2018 at 10:30 pm
Talk about treasonous scum…
"We cannot continue to rely only on our military in order to achieve the national security objectives that we've set. We've got to have a civilian national security force that's just as powerful, just as strong, just as well-funded."
– Beta Barry
What a pathetic, sick f–k.
https://www.youtube.com/watch?v=Tt2yGzHfy7s
Skankywoman in reply to TheFineReport.com. | August 1, 2018 at 10:39 pm
That statement was particularly troubling, scary and an eye into the soul of an evil man.
TheFineReport.com in reply to Skankywoman. | August 2, 2018 at 3:46 am
Obama wasn't Dereal thing.
locomotivebreath1901 in reply to Skankywoman. | August 2, 2018 at 12:57 pm
Leftists always, eventually, resort to violence, threats of violence, or glorification of violence to advance their wicked agenda. Always.
One more thought on this specific topic and may have been made before, if so, excuse me. Remember when MSM, particularly when Morning Joe (MSNBC) gave Trump such a soft platform on its show? Basically propping up Trump? I do, cause I switched channels all the time to see who what was saying what. I knew, while I was skanking myself up for work, what Morning Joe and his ugly on the inside sidekick were doing … they wanted MAGA Trump to win and thought that witch Hillary would win against MAGA Trump. SAD for Morning Joe … Didn't work out like you thought. Ha.
Morning Joe still not over it how it BACKFIRED. Ha.
Morning Joke.
assemblerhead | August 1, 2018 at 11:01 pm
Prof, he can't end the probe.
The libs/progs/establishment will either punish him severely or kill him if he doesn't setup an impeachment of Trump.
That is the same story for all the prosecutors on his staff.
That is why they are now trying to force Cohen ( Trumps old personal lawyer ) to manufacture the evidence they need.
Cohen is deliberately destroying his creditably in the courts. ( the tapes Cohen released )
What good is forged evidence coming from someone who has no creditably?
lc in reply to assemblerhead. | August 2, 2018 at 9:46 am
Interesting theory on Cohen destroying his credibility…….
He is between a rock and hard place. That would be clever.
georgfelis | August 1, 2018 at 11:18 pm
When determining somebody's goals, it is far more effective to look at their actions than to listen to their words (in the long run)
*IF* Mueller's goals were as stated, to search for any evidence of foreign governmental assaults on the US election system, he would be working with the various states to check on evidence of hacking attack from outside, working with both main parties to examine their servers with a neutral, secure team of intrusion analysts, and tracking any international hacking groups to see if they had been snooping around. The end result would be a much more secure election system with voter validation at the voting end all the way to the final counts.
That's not what is happening.
Instead, we have a case of an investigative team being handed two points (Russians hacked the election, and Trump conspired with them), and attempting to draw a somewhat squiggly, crooked, odd-looking line between them.
That is not an investigation. That is a frame job. And if we had President Hillary, the frame would have been perfect and the message unmistakable: "Don't get in the way of a Clinton or you'll be sorry."
V.Lombardi in reply to georgfelis. | August 2, 2018 at 6:15 am
Anyone who does not realize it is a frame job has a judgement problem.
navyvet | August 1, 2018 at 11:38 pm
No, the probe will continue through the mid-terms. And the frequency of the "scoops" will intensify as the election approaches. All to serve the greater political good, you understand.
If the left does not take the House and/or Senate, expect Mueller's Merry Band to continue as long as Trump is in the White House.
It's leverage the left can't afford to give up.
oldgoat36 | August 1, 2018 at 11:51 pm
Mueller has been tainted from the start. Comey set this whole thing up because of being butt hurt over being fired, over Hillary not being elected. Mueller knew about the Russian payments to Hillary through Bill's speaking fees and "donations" to the Clinton Foundation of millions of dollars, which Putin spoke about, yet allowed the sale to go through. The ties between Mueller and Comey run deep.
This is a cover up of a lot of criminal behavior by the prior administration, and Rosenstein – who was also heavily involved – along with Mueller are put in charge of this so called investigation to find a crime to pin on Trump, which isn't how the whole thing is supposed to work. And Sessions recusing himself so quickly and handing it over to Rosenstein who should have been recused for his actions and roles in the FISA deal to spy on Trump's campaign, yeah, I smell a bunch of crap with this all this.
Mueller is a rat, and he has one job, on real job, and that is to effect a coup against the sitting President while passing the crimes of the prior administration onto Trump.
Milhouse in reply to oldgoat36. | August 2, 2018 at 1:23 am
What are you talking about? Rosenstein spent the 0bama years as a US Attorney in Maryland. How could he have been involved with any of this stuff?
elle in reply to Milhouse. | August 2, 2018 at 2:27 am
Milhouse in reply to elle. | August 2, 2018 at 3:19 pm
Shut your filthy disgusting mouth. You have no right to fling accusations you know to be false. Unless you're so stupid that you don't know what a bot is, and are just using it as a random insult, which you also have no right to do.
Observer in reply to Milhouse. | August 2, 2018 at 6:25 am
Rosenstein, along with Andrew McCabe, supervised the investigation into the Russian bribery scheme tied to the decision approved by Hillary's State Dept. to allow Russia to purchase Uranium One. That investigation began in 2009 when Mueller was FBI director, and ended in late 2015, when Comey was director. The connections between Rosenstein and the other major players in this saga are long and deep.
https://www.dailywire.com/news/22398/report-robert-mueller-was-fbi-director-when-agency-ryan-saavedra
http://thehill.com/policy/national-security/355749-fbi-uncovered-russian-bribery-plot-before-obama-administration
SDN in reply to Observer. | August 2, 2018 at 11:42 am
http://www.nationalreview.com/article/452972/uranium-one-deal-obama-administration-doj-hillary-clinton-racketeering
Don't forget this one.
Observer in reply to SDN. | August 2, 2018 at 1:17 pm
Yes, for those who were previously unaware of Rod Rosenstein's key role in the Obama-era Russian bribery/uranium scam, this article is helpful in filling in some of the details. It explains why the DOJ/FBI investigation was centered in Maryland (that's where Russia's state energy company had its U.S. arm headquartered), and it also shows how the crooked Clintons cashed in (to the tune of $145 million in "donations" to the Clinton Foundation, according to Newsweek) by selling then-SOS Hillary's influence in getting the Uranium One deal approved, despite the deal being clearly contrary to the U.S.'s national security interests.
We know what the Clintons got for selling out our country (lots and lots of cash). We still don't know what people like Rod Rosenstein got for their work in hiding the evidence from congress and the American people. But hopefully someday all of these corrupt actors will be exposed for what they've done.
V.Lombardi in reply to Milhouse. | August 2, 2018 at 7:03 am
This is not your personal forum to interrogate other posters, especially after you have been caught in several major inaccuracies. Oldgoat did not mention the Obama years, you dnd. Consider trying to understand the history of RR, and crimes committed in Maryland, especially, try to understand what RR has done in the Trump years.
Milhouse in reply to V.Lombardi. | August 2, 2018 at 3:17 pm
you have been caught in several major inaccuracies.
You filthy liar. Name one.
I'm still waiting for your apology and acknowledgment that every word I wrote about aliens and conscription was the exact truth, and you had no right to accuse me of lying.
Oldgoat did not mention the Obama years, you dnd.
Liar. Oldgoat's exact words are right up there, where everyone can see them: "This is a cover up of a lot of criminal behavior by the prior administration, and Rosenstein – who was also heavily involved". Rosenstein could not have been involved in any behavior by the prior administration.
elle in reply to Milhouse. | August 2, 2018 at 7:03 pm
"This is a cover up of a lot of criminal behavior by the prior administration, and Rosenstein – who was also heavily involved"
Hmmm getting even more suspicious since you were unable to comprehend the meaning of "and" before spouting off. It should have been clear once pointed out to you. I know bots have trouble with that sort of thing.
Close The Fed in reply to Milhouse. | August 2, 2018 at 9:23 am
Duh, Milhouse, Rosenstein signed the last application for the renewal of the FISA warrant. Look at the FISA warrant applications. His big fat signature is right there.
Milhouse in reply to Close The Fed. | August 2, 2018 at 3:17 pm
Which had what to do with the prior administration?
regulus arcturus in reply to Milhouse. | August 2, 2018 at 9:43 pm
It continued their malfeasance.
Read up, imbecile
https://themarketswork.com/2018/08/02/revisiting-the-page-fisa-applications-james-wolfe-indictment/
Olinser | August 2, 2018 at 12:00 am
At this point Mueller has NOTHING, but will never, EVER voluntarily end his investigation. The entire investigation was predicated on the projection of the Democrats who ASSUMED that an exhaustive investigation of Trump would yield enough crimes to put him away forever – because that's exactly what would happen if they actually did an investigation of Hillary, Obama, or any of dozens of Democrats in office. But to their shock – they found NOTHING.
At this point Mueller's sole goal is to goad Trump into firing him so the Democrats can scream about 'obstruction'.
Why do you think they did that bullshit raid on Cohen's office? Rosenstein gave the game away when he was caught saying that he 'expected' to be fired.
They WANT Trump to fire Mueller and Rosenstein. They have nothing else.
Tom Servo in reply to Olinser. | August 2, 2018 at 9:15 am
Trump needs to see his supporters stay in control of the House, and expand their margin in the Senate in November. Any move before the election risks that, so I believe he's stuck for now. But if he comes out of that election in stronger shape politically, then he'll be able to fire Rosenstein and Mueller the next day.
There is one possible early exit – if the Manafort Trial goes as badly for the prosecution as it looks like it's going, that may give Trump the political backing to go ahead and end it all early.
SAFVet | August 2, 2018 at 1:10 am
The Mueller investigation has one overriding purpose – to continue to provide "active investigation" coverage to the weasels in the DOJ and FBI who have been trying to overthrow a legitimate election. E.g. congressional testimony of Strozk, McCabe, etc. With the Mueller investigation active, they can claim that they can't answer the congressional or other questions due to "investigation". Neat, but diabolical, strategy… All the rest is chaff and countermeasures…
gad-fly | August 2, 2018 at 1:58 am
If Mueller didn't have case against Trump before today, he has one after he ordered Sessions to shut down the investigation. The lies keep spewing from his Twitter, his mouth and Rudy's mouth.
How difficult is it for a rule-of-law conservative law professor continue to not recognize that Trump can only talk about himself and repeat "No Collusion." Turn your investigative skills onto the man's past and you will need a staff of hundreds just to stay with his lies and his dishonesty. And ask why he says he has not done deals with Russians when we know that negotiations for a Trump Tower in Moscow continued into the campaign.
And how much money did he borrow from Russian Oligarchs for golf course purchases and how many Florida and NYC buildings are financed through Russian money-launderers.
If Donald continues to own his businesses, in violation of he constitution, the American economy will will move toward the genius kleptocracy that Putin installed in Russia – starting with Mnuchin's proposal to lower taxes (again in less than a year) on Donald's authority.
elle in reply to gad-fly. | August 2, 2018 at 2:34 am
blah…blah…blah..
Where were you on Uranium One.
TheFineReport.com in reply to elle. | August 2, 2018 at 3:51 am
Probably in on it.
JohnSmith100 in reply to gad-fly. | August 2, 2018 at 9:22 am
After Obama, Trump is so refreshing 🙂 It is long past time to clean up, and clean out both the FBI and DOJ. People involved in systematic disruption of Trump's presidency should be charged and spend some time in jail.
regulus arcturus in reply to gad-fly. | August 2, 2018 at 9:41 pm
Hilarious.
Please provide evidence showing Trump ordered Sessions to "shut down" the illegal investigation.
JBourque | August 2, 2018 at 2:05 am
In the end, it comes down to Trump choosing whether to fire an FBI director, or to speak about his law enforcement preferences without actually ordering people to prosecute or not prosecute specific individuals, constitutes obstruction of justice because the FBI and DOJ ought to be independent from the executive branch, which would also make them almost fully independent from the legislative and judicial branches as well.
If that is the world people want to live in, be my guest. I see problems with this approach, but Mueller is now the ultimate champion of this vision of law enforcement independence. If it means law enforcement can and should depose a President, let's have that debate in public. There's no need to nibble at the edges.
inspectorudy | August 2, 2018 at 2:30 am
Think about this for one moment. Mueller has the power to go after anyone no matter if it has anything to do with this investigation and can use that acquired information to then threaten that person that he will go after his children if he doesn't cooperate. Is this America? WTF has happened to the people who protect and serve?
JohnSmith100 in reply to inspectorudy. | August 2, 2018 at 9:25 am
Bureaucracies always evolve to serve bureaucrats interests before serving any other purpose.
elle | August 2, 2018 at 2:31 am
Desperate men require desperate measures. Hillary said it best, "If Trump wins, we all hang from nooses."
They do this because they can't afford not to do it.
No, she didn't. It's a stupid lie, apparently invented by some nobody rumormonger called Bill Still, and spread by gullible paranoid freaks who will believe anything about someone they don't like, no matter how unlikely, and without demanding any evidence at all.
Romey | August 2, 2018 at 3:16 am
This pseudo investigation will not end until, at the very minimum, after the mid-term elections. The dinosaur media need all the selective "outrage" they can gin up. I have read that the negative/positive ratio for Trump coverage is 90/10. I am not surprised.
TheFineReport.com in reply to Romey. | August 2, 2018 at 3:52 am
We have a psuedo AG.
Cleetus | August 2, 2018 at 5:28 am
If I remember correctly, Mueller was tasked with investigating Russian interference with the 2016 election. This investigation has raised the following questions in my mind.
1. If Russian interference in the 2016 election was to be investigated, then why has no effort been made to investigate the efforts of Hillary Clinton being pursued? It was Clinton who paid for the Trump dossier, it was Clinton who took money from Russians and others illegally, it was the Clinton campaign who appeared to violate so many other lases…. It would seem that focusing solely upon Trump's behavior would be a dereliction of duty and a reason to terminate Mueller.
2. Congress started a ten month investigation of Trump and Mueller has been at it for well over a year for a combined total of 2 years. If nothing has been found after 2 years, then what causes us to think that there is anything there to find?
3. Since nothing concerning the Russians and Trump working together has been found, then what is the justification to expand the probe to include so many other areas? Increasingly this is becoming an investigation in search of a crime.
4. Since the Mueller instigation was founded on fabricated "evidence" then what justification is there to continue? The Trump Dossier was opposition research created and paid for by the Democrats. Information coming from various wire taps were obtained (apparently) by using a dishonest FISA application and, even then, nothing incriminating was found. If the premise behind the investigation has been found to be fabricated, if nothing has been found after two years, and nothing appears to be on the orizon, then what justification is there to continue?
Edward | August 2, 2018 at 6:13 am
The minuscule investment the Russians made in trying to gin up some chaos in or from the 2016 election has paid off far beyond their wildest dreams – thanks to the Democrats and MSM (but I repeat myself). I disagree with the idea that the Russians "interfered with" the election because I believe that terminology infers some degree of success and they most certainly didn't effect any difference in the electoral outcome. And they would not have had any effect on the new administration but for the efforts of the MSM and their political arm, the Democrat Party.
RodFC | August 2, 2018 at 8:23 am
My suspicion is that Trump is waiting for the Manafort trial to fizzle.
After that he will order a Special prosecutor to investigate the handling of the Mueller investigation, and all sorts of other things.
( Including the immunity of Tony Podesta. ). Either that or outright
fire Mueller.
I have heard speculation that Manafort is planning on calling Rod Rosenstein as his first witness, suppose that is so. Imagine that the judge gives Manafort a bit of latitude in questioning.
Tom Servo in reply to RodFC. | August 2, 2018 at 9:22 am
The Manafort trial so far is bizarre, to put it mildly. Tax evasion cases are usually fairly dry and mathematical – the prosecution brings in the income statements, the bank statements, and the tax statements, and says "here's the income earned, here's the income declared, here's the actual tax paid (if any), and here's what should have been paid." Usually all very precise and cut and dried.
But instead in this trial there is all of this sensationalism, Look at the suits he bought! Look at the houses he built!!! Okay, well prosecutor, you've got to prove beyond a reasonable doubt that he didn't pay taxes on that income, go ahead, prove it. That's your job.
If a prosecutor can provide proof of income on which taxes were not paid, then there's no purpose to making someone testify as to what a Pergola is. (that happened yesterday) And on the other hand, if he CAN'T provide legal proof of income, then all of this lifestyle stuff is incompetent showboating that should result in an acquittal.
I'm starting to suspect that Mueller has no actual, court admissible evidence of the crimes he has alleged.
Close The Fed in reply to Tom Servo. | August 2, 2018 at 9:30 am
Tom Servo, I agree with you. All this testimony about irrelevant matters certainly makes it appear no admissible evidence exists to prove Mueller's case.
The Packetman in reply to Close The Fed. | August 2, 2018 at 1:11 pm
And apparently, the judge is keeping prosecutors on a tight leash.
Edward in reply to Tom Servo. | August 2, 2018 at 3:38 pm
All of that is an effort to influence the Jurors against Manafort, nothing more, nothing less. The Judge reined the prosecution in some on that, prohibiting the further use of the term "oligarch", etc. Mueller's Democrats have a history of dirty prosecution, I expect they will keep the Judge on his toes to catch all they try.
Milhouse in reply to Tom Servo. | August 2, 2018 at 3:52 pm
That is incorrect. The lifestyle stuff is evidence of undeclared income. The prosecution can't provide direct proof of the income, because it was (allegedly) earned overseas, and obviously the Ukranian government did not file W9 forms with the IRS! But if they can show that he's spending all this money overseas, which isn't coming from his declared bank accounts and can't be accounted for by his declared income, then they can ask the jury to infer that he had undeclared income of approximately the amount they allege.
unommin | August 2, 2018 at 9:28 am
What happens if M clears Trump? If the partisan witchhunt by democrats actually results in no related charges. What happens then.
Close The Fed in reply to unommin. | August 2, 2018 at 9:33 am
Re: Unommin:
I think the question not relevant because Mueller has been squeezing Manafort and Cohen so hard for them to flip, that it's clear he's desperate. I don't think Mueller has it in him to admit Trump is clean…. even if Trump is clean.
So Mueller gets fired one way or the other, because I don't see Mueller letting go of this as hard as he is still pushing.
I must say, the Cohen tape was such a nothingburger, if I were Mueller, I'd be embarrassed to have sunk to that level. How unprofessional and inept!!
lc | August 2, 2018 at 9:50 am
What do you think of this- Judge Napolitano says Manafort was exonerated 8 years ago- may call Rosenstein as witness:
https://www.thegatewaypundit.com/2018/08/judge-napolitano-doubles-down-says-paul-manafort-was-exonerated-8-years-ago-may-call-rosenstein-as-first-witness-video/
Milhouse in reply to lc. | August 2, 2018 at 4:00 pm
It's very unlikely to be true. What does "exonerated" mean? He was certainly not tried and found not guilty. It could mean there was an official finding that he'd done no wrong, but if that were so he wouldn't be on trial now. The fact that they're trying him means there was never any such official finding, but at most a determination that it wasn't in the public interest to proceed against him at that time, or that there was insufficient evidence to proceed at that time. Such a finding would get him nowhere at all.
MSO | August 2, 2018 at 10:02 am
The Mueller investigation reinforces my belief that plea-bargains violate the basic principles of justice and ought to be completely eliminated.
The Mueller can openly extort defendants such as Cohen and Manafort with the encouragement and approval of many within the justice system and our legislators is simply astounding.
When we consider that somewhere upward of 80% of all court cases are resolved through the plea mechanism, the totality of the abuse suffered by the victims is incalculable.
The real purpose of plea-bargains seems to be to allow our government to poke at its citizens with wild abandon and still convict them for made-up, distorted and questionable offenses that jury trials would never permit.
Milhouse in reply to MSO. | August 2, 2018 at 4:01 pm
Yes, many people plead guilty to crimes they never committed, because they don't fancy taking their chances in front of a jury on more serious crimes which they also never committed.
Conan | August 2, 2018 at 10:59 am
Try and picture a world In Democrat land where the Mueller probe is finished and they have nothing. The Russia collusion story and special council were launched to give reason to the Left for opposing Trump in unprecedented ways and for the Democrat Leadership to avoid the blame for rigging the primary for a losing candidate that brought about Trump to the Left.
I see the Mueller probe going on forever because the whole structure of the Democrat party is now dependent on this narrative. It can't end without ending this narrative and then what? We talk about Issues? They treat the Trump Presidency legitimately? They will do anything to not face that day.
Dean V | August 3, 2018 at 4:12 pm
This will be an intergenerational vendetta. Long after we are dead, Robert Mueller VII will be investigating Donald Trump VII.
PODKen | August 3, 2018 at 6:32 pm
Two years is long enough for Mueller to do his job. We need to see the results … now.


text:
Disabled Peoples' International (DPI) ist eine internationale Nichtregierungsorganisation mit Sitz in Ottawa und mit regionalen Niederlassungen in Asien-Pazifik, dem Mittleren Osten, Europa, Afrika, Lateinamerika und Nordamerika und der Karibik.

Es ist ein Netzwerk von nationalen Organisationen oder Vereinigungen von Menschen mit Behinderungen, gegründet im Jahr 1981, um die Menschenrechte von Menschen mit Behinderungen durch eine volle Teilhabe, Angleichung der Chancen und Entwicklungsmöglichkeiten zu fördern. DPI unterstützt Organisationen in über 120 Nationen bei den alltäglichen Problemen.

Die Ziele sind:
 Förderung der Menschenrechte von Menschen mit Behinderungen;
 Förderung der wirtschaftlichen und sozialen Integration von Menschen mit Behinderungen;
 Entwicklung und Unterstützung von Organisationen von Menschen mit Behinderungen.

DPI hat einen Sonderstatus als Berater bei den Vereinten Nationen und arbeitet mit vielen internationalen Organisationen und Regierungen der Welt zusammen.

1992 initiierte der Verband den europäischen Protesttag zur Gleichstellung von Menschen mit Behinderungen, der seither jährlich am 5. Mai begangen wird, 2011 beispielsweise unter dem Motto "Inklusion beginnt im Kopf".

Der deutsche Zweig des Verbandes ist die Interessenvertretung Selbstbestimmt Leben.

Literatur

 Handbuch Armut und soziale Ausgrenzung. VS Verlag für Sozialwissenschaften, 2008, ISBN 978-3-531-15220-2, S. 402.

Weblinks
 Offizielle Website

Einzelnachweise

Behindertenorganisation
Selbsthilfeorganisation
Interessenverband (Gesundheitswesen)
Internationale Organisation
Menschenrechtsorganisation
Gegründet 1981
Organisation (Ottawa)

redpajama_set_name: RedPajamaWikipedia


text:
Kim Clavel is a Canadian professional boxing who held the WBC female light flyweight title until February of 2022, where she lost a unification title bout against Jessica Nery Plata.

Professional career
Clavel made her professional debut on December 16, 2017, scoring a four-round unanimous decision (UD) against Yoseline Martinez Jose at Place Bell in Laval, Quebec.

After compiling a record of 11–0 (2 KO), Clavel faced Esmeralda Gaona Sagahon for the vacant WBC-NABF female light flyweight title on December 7, 2019 at the Bell Centre in Montreal. Clavel won her first professional title via UD, with all three judges scoring the bout 100–90.

In 2021 she was a competitor in the Quebec edition of Big Brother Célébrités.

On September 6th 2022 it was announced that Kim Clavel and Jessica Nery Plata would be squaring off for a world female junior flyweight title unification fight on December 1.  The 10-round bout will take place at the Place Bell in Laval, Canada.

Professional boxing record

References

External links

Year of birth missing (living people)
Date of birth missing (living people)
Living people
Canadian women boxers
Boxers from Montreal
Light-flyweight boxers
Big Brother Canada contestants


Pearl, cultured freshwater (dyed), berry, 7x6mm-10x7mm top-drilled rice, D- grade, Mohs hardness 2-1/2 to 4. Sold per 15" to 16" strand.
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RECM and Calibre Limited is a long-term investment company with access to permanent capital, providing a closed-end vehicle for investors in South Africa. The company's history stems back to 2009 through a joint venture partnership between fund manager Regarding Capital Management and private equity firm Calibre Capital. Today, RECM and Calibre shares are for sale on the Johannesburg Stock Exchange (JSE).
The group aims to buy assets where size, regulations, liquidity and complexity act as a deterrent to most buyers, acquiring minority stakes and partnering with management teams in private businesses. The group currently has core investments in mining, engineering, retail, gaming and food and beverage companies. Assets are valued at over R500 million.
Ordinary shares are held by the executive directors of the company, whilst investors are given the opportunity to subscribe for preference shares. RECM and Calibre share price has performed well on the JSE of late, with a forecast for future growth.
RECM and Calibre's investment strategy involves investing in listed or unlisted operating businesses, either onshore or offshore, and investment in various types of securities. The group adheres to a patient investment strategy and does not plan to pay dividends until investments are found which satisfy the board's criteria. The business measures its performance mainly through Net Asset Value (NAV) per share, which has grown by around 97% since RECM and Calibre shares were listed in 2010.
In the gaming sector, the group's main investment, Goldrush, performed well during the 2016 financial year, with revenue increasing by 20% and net profits almost doubling. Investments in mining, which include Transhex, West Coast Resources, and Sentula Mining, have weighed on the group's financial data due to the difficult trade conditions within the mining industry.
The group owns a 28.3% stake in premier hunting and outdoor equipment retailer Outdoor Investment Holdings, which increased both revenues and operating profit by 10%. The group's 11.3% stake in poultry producer Sovereign Foods has been hampered by a competitor trying to negatively influence the market perceptions of the company, with an aim to either buy it out or hinder operations. The company aims to navigate tough conditions in the poultry industry by increasing production at lower cost. Meanwhile, the investment in unlisted wine and spirits producer KWV has produced solid profits.
The group has yet already caught the attention of JSE investors, holding strong cash resources and well set to expand its portfolio of investments. The group is well diversified and adheres to a cautious acquisition and investment strategy, which should encourage similarly cautious investors to buy RECM and Calibre shares. The live online stocks chart shows that RECM and Calibre share price has grown fromaround R10 per share in 2011, to R23 by October 2016, highlighting investor confidence in this well-managed company.
Truffle Asset Management (Pty) Ltd., Regarding Capital Management (Pty) Ltd, Kagiso Asset Management (Pty) Ltd and Allan Gray (Pty) Ltd.
We have made it simple to buy JSE listed firm shares online. The easiest way to buy RECM and Calibre Group shares or stocks is to; start by submitting the 'BUY THIS SHARE' form. Next, one of our experienced and certified stock brokers will personally get in contact with you to discuss your custom stock request. Finally, a stock advisor will confirm the amount of shares you are looking to invest in RECM and Calibre Group and assist you with the setup and management of your stock portfolio account.
Then, Indicate the amount you are looking to invest in RECM and Calibre Group.


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Charice Pempengco Verified Contact Details ( Phone Number, Social Profiles) | Profile Info
Author Celebs StaffPosted on November 13, 2017 November 13, 2017 Leave a comment
Charice Pempengco aka Jake Zyrus Verified Contact Details ( Phone Number, Social Profiles) | Age, Wiki Profile Info- Jake Zyrus is a Filipino Pop Singer who is famous by the stage name Charice. Her 2010 self-titled debut album propelled her to fame, with the hit single "Pyramid" peaking at number 56 on the Billboard Hot 100 charts. Her mother is Racquel. In 2012, he began judging the Philippine X Factor. She was dubbed by Oprah Winfrey as "the most talented girl in the world. Jake has also played the role of Sunshine Corazon on three episodes of Fox's hit series Glee from 2010 to 2011. She came out as transgender in 2016 and changed her name from Charice to Jake in 2017. She has got relationship Alyssa Quijano from 2013 to 2017.
Profile Info :
Name: Charmaine Clarice Relucio Pempengco
Nick Name: Jake Zyrus
Date of Birth: 10 May 1992
Birth Place: Cabuyao, Philippines
Sun Sign: Taurus
Profession: Singer
Nationality: Filipina
Instagram Jake Zyrus
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YouTube charice
Email Id themadunion@icloud.com
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