text:
\section{Introduction}

The idea of finding parallels between quantum mechanics and financial markets has attracted the attention of scientists and economists for
many years. Early attempts to find those parallels include a quantum model for binomial markets\cite{QuantBin} and the capture of the famous Black-Scholes\cite{BS} model within a quantum physical setting\cite{BSQuantum,QuantumBS}. Others have tried to use a path integral formulation\cite{PathInt,PathInt2,PathInt3} or even quantum game theory\cite{quantumGame} to simulate the pricing of options. More recently, quantum algorithms have been proposed for the pricing of financial derivatives\cite{QComp} and even the explicit concept of quantum economics has been proposed \cite{QMoney}. Similar connections between physical and economic systems have been defining the field of Econophysics \cite{Grass}.

Quantum theory is undoubtedly very successful in treating electronic systems with strong correlations.
Here investigate some of the tools used in quantum theory to study  the correlated structure of financial markets.
Our findings led us to believe that portfolios of
currencies resemble quantum mechanical systems. Also
localization properties of their eigenmodes suggest
a strong and interesting connection between stock markets and quantum
mechanics.

We test these concepts on digital currencies.
These are financial assets deprived of an issuing agent
constructed on a peer-to-peer managed distributed ledger platform called
blockchain. Consensus about the trading of these assets is decentralized,
thus they resemble physical autonomous agents that operate out of
equilibrium but often reach some steady state regimes where financial returns are characterized by some
power law \cite{Mantegna}. For instance,
Bitcoin \cite{Bitcoin}, the most popular digital currency has attracted the
attention of the scientific community despite much criticisms. For example, it has been shown that Bitcoin shares a set of stylized facts
with standard financial instruments and also mimics many natural phenomena\cite{US}.

Since the development of Bitcoin in 2008, many other digital coins appeared
in the market as a result of successive forks of its main code. This has
happened mainly as a tendency for differentiation in order to make the asset
more suitable for specific purposes in a clear case of Darwinian
adaptation \cite{Darwin}. There are over 4000 different digital coins
available today but only a few have a significant market cap that can attract the attention
of investors.

We divide the remaining of the paper as follows. In section \ref{Section:Our_data} we present
the data used in this paper as well as some fundamental background
connecting random matrices, crypto markets, and correlations. We
also describe the notation to be used along the paper. In the following
section (section \ref{Section:Results}) we present a brief theoretical formulation and our main results separated by context  in a few subsections.
Furthermore, we show that these coins have a natural tendency of clustering. We investigate this phenomena studying the minimum spanning tree formed by
connecting these assets according to their spectral properties. Finally, we calculate  the ultrametric ordering of the assets and show that the market tends to value more cryptocurrencies that are significantly distinctive.
Finally our summaries and conclusions are briefly explained in
section \ref{Section:Conclusions}.

\section{Description of Data and Definitions}
\label{Section:Our_data}

The historical series for $M=20$\ digital assets were directly downloaded
from the HitBTC application programming interface (https://api.hitbtc.com)
for $N=10^{5}$\ minutes ending on 2019-08-12. Three currencies with
insufficient historical data were dropped and a portfolio was formed with $%
M=17$\ assets: BTC, ETH, EOS, LTC, BCH, TRX, ETC, XMR, NEO, XEM, IOTA, XLM,
DASH, ZEC, ADA, DOGE, and XTZ. The logarithmic returns for the closing price
of these digital coins were calculated as:

\begin{eqnarray}
	r_{m,n}		 &= \log (p_{m,n+1})-\log (p_{m,n})\nonumber \\
						& \approx  \frac{p_{m,n+1}}{p_{m,n}}-1,
\end{eqnarray}
where $p_{m,n}$ is the $n^{\rm{th}}$ closing price for the $m^{\rm{th}}$
digital asset, with $n=1...N$ spanning the length of the time series ($10^5$ minutes), and $m=1...M$ spanning the number of assets (17). We then computed the
normalized returns that form a matrix $\mathbf{L}$ with elements:

\begin{equation}
	L_{m,n}=\frac{r_{m,n}-\langle r_{m}\rangle }{\sqrt{\left\langle	r_{m}^{2}\right\rangle -\langle r_{m}\rangle ^{2}}},
	\label{Eq:L}
\end{equation}
where, for any observable $O$ in this work, we assign:
\begin{equation}
	\langle O_{m}\rangle =\frac{1}{N}\sum_{n=1}^{N}O_{m,n}.
\end{equation}

The crypto market is composed of only a few major crypto currencies
that dominate the marketshare. Moreover, most of the alternate
cryptocurrencies are constructed on already existing blockchains, which
restricts the size of the matrices that can be analyzed. This creates a major problem for many spectral analyses that are used in this work. Specifically in our
case, there are only $M=17$\ assets in the portfolio, which may not produce
adequate statistics. To circumvent this problem, we constructed an ensemble of
1000 correlation matrices:

\begin{equation}
	\boldsymbol{\Lambda }=\frac{1}{N}\mathbf{L}'\mathbf{L}'^{\rm{T}},
	\label{Eq:correlation}
\end{equation}
with elements related to Eq. \ref{Eq:L}:

\begin{equation}
\Lambda _{ij}=\frac{\langle r_{i}r_{j}\rangle -\langle r_{i}\rangle \langle
	r_{j}\rangle }{\sqrt{\left\langle \left( \Delta r_{i}\right)
		^{2}\right\rangle }\sqrt{\left\langle \left( \Delta r_{j}\right)
		^{2}\right\rangle }},
\end{equation}
where $\mathbf{L}'$ is a randomly resampled matrix from the original matrix $\mathbf{L}$ obtained with replacement taking different windows of $N=100$ continuous closing prices. Also, $\left\langle\left(\Delta r_i\right)^2\right\rangle=\left\langle\left(r_i-\langle r_i\rangle\right)^2\right\rangle=\langle r_i^2\rangle-\langle r_i\rangle^2$.
The dimension of the $\mathbf{L}'$ matrices is 17 $\times$ 100. It is important to note that if the elements of $\mathbf{L}$ were also independent and identically distributed (\textit{i.i.d}) Gaussian random variables, then $\boldsymbol{\Lambda}$ would compose the so-called Wishart ensemble\cite{Wishart}. This is a key concept since the density of eigenvalues for this particular case is analytically known. Therefore, we can use this result to compare corresponding matrices $\boldsymbol{\Lambda}$ with those obtained with experimental data.

\section{Formulation and results: Quantum Analogies and network properties in the context of cryptocurrencies}
\label{Section:Results}
Our main results are presented in this section. For every subsection, we perform a brief theoretical formulation with a subsequent presentation of the numerical results and data analysis.

\subsection{Quantum Mechanics and the concept of Eigenportfolios}

An unobserved quantum system is supposed to have a finite number $N$ of elements in a particular ensemble. A state of this physical system in a Hilbert space is then represented by a ket $\ket{\varphi}$ in Dirac notation. This state can be decomposed in a linear combination kets $\ket{m}$ where $m\in[1;N_{ind}]$:

\begin{equation}
	\ket{\varphi}=\sum_{m=1}^{N_{ind}}p_m\ket{m},
	\label{eq:Upla}
\end{equation}
where $p_m$ is the relative population of the state $\ket{m}$. This coefficients are obviously non-negative and add up to the unity, i.e. $\sum_{m=1}^Np_m=1$. It is important to point out that $N_{ind}$ is the number of elements in the ensemble, not the dimension of the space generated by the eigenvectors of a certain physical observable. There is, actually, a great arbitrariness on the choice of kets $\ket{m}$. For instance, they can freely chosen to be orthogonal or not, or to be the eigenstates of some particular operator or even the eigenstates of two operators simultaneously. Considering the ensemble, if there is only one n-upla $(p_1,\dots,p_N)$ that satisfies Eq. \ref{eq:Upla}, then the ensemble is considered to be pure. Otherwise, if there is more than one n-upla $(p_1,\dots,p_N)$ that satisfies Eq. \ref{eq:Upla}, then the ensemble is considered to be mixed.

Thus, in order to perform a measurement of some observable $\hat{O}$, one must perform averages over the ensemble of such observable. This is given by:

\begin{equation}
	\left\langle\hat{O}\right\rangle = \sum_{m=1}^{N_{ind}}p_m\braket{m|\hat{O}|m}.
\end{equation}

Using the completeness relation $\sum_l\ket{l}\bra{l}=\mathbf{1}$, where $\ket{l}$ are eigenstates of $\hat{O}$, i.e. $\hat{O}\ket{l}=l\ket{l}$, we obtain:

\begin{eqnarray}
		\left\langle\hat{O}\right\rangle &= \sum_{m=1}^{N_{ind}}p_m\braket{m|\hat{O}\mathbf{1}|m}\nonumber\\
			&= \sum_{m=1}^{N_{ind}}\sum_lp_m\braket{m|\hat{O}|l}\braket{l|m}\nonumber\\
			&= \sum_{m=1}^{N_{ind}}\sum_llp_m\braket{m|l}\braket{l|m}\nonumber\\
			&= \sum_{m=1}^{N_{ind}}\sum_llp_m|\braket{m|l}|^2.
\end{eqnarray}

This procedure can be performed twice introducing a new basis:

\begin{eqnarray}
		\left\langle\hat{O}\right\rangle &= \sum_{m=1}^{N_{ind}}p_m\braket{m|\mathbf{1}\hat{O}\mathbf{1}|m}\nonumber\\
			&= \sum_{l,k}\sum_{m-1}^{N_ind}p_m\braket{k|m}\braket{m|l}\braket{l|\hat{O}|k}\nonumber\\
			&= \sum_{l,k}\rho_{kl}O_{lk},
\end{eqnarray}
where $O_{lk}=\braket{l|\hat{O}|k}$ and $\rho_{kl}=\sum_{m=1}^{N_{ind}}p_m\braket{k|m}\braket{m|l}$ are  elements of the hermitian operator $\hat{\rho}$ known as \emph{density operator}:

\begin{equation}
	\hat{\rho}=\hat{\rho}^\dagger=\sum_{m=1}^{N_{ind}}p_m\ket{m}\bra{m}.
\end{equation}

If one is interested to study the time evolution of the statistical ensemble, the time derivative of the density operator must be taken:

\begin{equation}
	\frac{\partial\hat{\rho}}{\partial t} = \sum_{m=1}^{N_{ind}}p_m\left(\frac{\partial\ket{m}}{\partial t}\bra{m}+\ket{m}\frac{\partial\bra{m}}{\partial t}\right).
\end{equation}
Substituting $i\hbar\frac{\partial}{\partial t}\rightarrow H$, one obtains the evolution of the density matrix, which is given be a quantum version of the Liouville equation:

\begin{equation}
	i\hbar\frac{\partial\hat{\rho}}{\partial t} = [H,\hat{\rho}].
\end{equation}

In steady state, the density matrix commutes with the Hamiltonian. Therefore, they share a common eigenbasis and we can use it to formulate a quantum description of the crypto market. For this purpose, we apply the Rayleigh-Ritz variational principle to find the ground state of the correlation operator $\boldsymbol{\hat{\Lambda}}$. In order to do so, we expand the correlation matrix in the basis $\ket{n}$ of its eigenstates:

\begin{equation}
	\boldsymbol{\hat{\Lambda}} = \sum_{n=0}^{M-1}\lambda_n\ket{n}\bra{n}.
\end{equation}

Therefore, the elements of the correlation matrix can be written as:

\begin{eqnarray}
		\braket{W|\boldsymbol{\hat{\Lambda}}|W} &= \sum_n\lambda_n\braket{W|n}\braket{n|W}\nonumber\\
			&\geq\lambda\sum_{n=0}^M\braket{W|n}\braket{n|W}\nonumber\\
			&\geq\lambda\braket{W|\left(\sum_{n=0}^M\ket{n}\bra{n}\right)|W}=\lambda\braket{W|W},
\end{eqnarray}
where $\lambda=\min\{\lambda_n\}$ corresponds to the ground state of the system. In order to find ground state, the following difference has to be minimized:

\begin{equation}
	F = \bra{W}\boldsymbol{\hat{\Lambda}}\ket{W}-\lambda\braket{W|W}.
\end{equation}
This is the same expression one would obtain minimizing the volatility $\mathbf{W}^\textrm{T}\boldsymbol{\Lambda}\mathbf{W}$ for a normalized portfolio $\mathbf{W}^\textrm{T}\mathbf{W}=1$.
The extremum of this function is given by:

\begin{equation}
	\boldsymbol{\Lambda}\mathbf{W}=\lambda \mathbf{W}.
	\label{eq:eigenp}
\end{equation}
In order to explore the quantum behavior of the portfolios we will use $\boldsymbol{\hat{\Lambda}}=\boldsymbol{\Lambda}$ as given by Eq. \ref{Eq:correlation}.

The ``\emph{eigenportfolio}'' $\mathbf{W}$ (or \emph{principal component}) is on the eigenbasis $\ket{n}$ of the
correlation matrix, whereas the normalized eigenvalues (or \emph{characteristic roots}), i.e. $\lambda_j'=\lambda
_{j}/\sum_{k=0}^{M-1}\lambda _{k}$, give the explained volatility of the $j^{\rm{th}}$\ portfolio.
This is exactly what one would obtain from a principal component analysis (PCA)\cite{PCA} of the assets.
On the other hand, had the Lagrangian function $F$ included a term that imposes a specific
value to the expected return, one would obtain the so-called Markowitz
Lagrangian used in the modern portfolio theory (MPT)\cite{Markowitz}.

It is interesting to compare the obtained explained volatility
with two limiting cases in order to study the experimental data. One case is obtained from the Wishart ensemble considering the matrix $\mathbf{L}$ previously defined in section \ref{Section:Our_data} and used to construct $\boldsymbol{\Lambda}$. The elements of $\mathbf{L}$ are distributed according to a normal distribution. The Wishart ensemble has been used for the spectral analysis of the density matrix in general quantum systems\cite{Xiao}.
The other limiting case was obtained from matrices $\mathbf{L}$ whose elements are \textit{i.i.d.} random variables drawn from the Cauchy distribution:

\begin{equation}
	f(x;\gamma )=\frac{1}{\pi \gamma }\left[ \frac{\gamma ^{2}}{x^{2}+\gamma ^{2}%
	}\right] ,
\end{equation}
where $\gamma $ is a scale parameter that indicates the half-width at
half-maximum of the distribution. This distribution was particularly chosen
because it is the only known stable pathological distribution on a support $(-\infty,+\infty)$ (both positive and negative returns have to be accounted for) that has fat tails and can be expressed analytically.

The cumulative volatility fraction shown in Fig. \ref{fig:PCA} is defined as:

\begin{equation}
	\phi(j)=\sum_{m=0}^j\lambda_m'=\frac{\sum_{k=0}^j\lambda_k}{\sum_{k=0}^{M-1}\lambda_k},
\end{equation}
where $j$ is the rank of the eigenvalue $\lambda_j$.The figure indicates that the largest eigenvalue explains
approximately 30 \% of the variance. Moreover, the cumulative volatility is
located between those of Gaussian and Cauchy ensembles. Thus, we discard the hypothesis that the
distribution of returns come from a Wiener process. However, the results also indicate that the hypothesis that the
distribution has infinite moments may be discarded. The result indicates that, more likely, the distribution of returns
has long tails, as previously obtained  for Bitcoin\cite{US}.

\begin{figure}[h]
	\centering
	\includegraphics{PCA.pdf}
	\caption{Expected cumulative volatility fraction explained as a function of the rank number
	of eigenvalues for the experimental data, and control series with Gaussian
	and Cauchy distributions with $\gamma=0.1$ (triangle marks) and $\gamma=0.45$ (pentagon marks).}
	\label{fig:PCA}
\end{figure}

\subsection{Random Matrices and Density of States}

Given this initial formulation we now turn our attention to some properties of cryptocurrencies in the context of random matrices, a concept widely used in quantum chaos.
Eugene Wigner has originally proposed in 1955 that the energy levels of heavy nuclei
could be described by the eigenvalues of random matrices. A Wigner matrix
is then defined as a square matrix that is symmetric (but in more general cases
it can also be Hermitian or symplectic), where their elements $%
\{h_{ij}|\forall i\leq j\}$ and $\{h_{ii}\}$ are identically distributed random variables
according to a symmetric distribution with finite first and second moments. Following this condition we can obtain the
joint distribution of its eigenvalues, and integrating all values except
one leads to a universal semicircle law for the the density eigenvalues \cite{Wigner}.

Nonetheless, the semi-circle law does not apply to our matrix of returns since it is non-square. Rather, one can use the Mar\v{c}enko-Pastur
law \cite{MP} to analyze and compare the density of eigenvalues of the $M\times M$
correlation matrices for $N$ returns.
If the elements of $L$ are mutually
uncorrelated \textit{i.i.d.} standard normal random variables, the Mar\v{c}enko-Pastur law states that the density of eigenvalues of $\boldsymbol{\Lambda}$ is given by:

\begin{equation}
	\rho (\lambda )=\frac{N}{2\pi M}\frac{\sqrt{(\lambda -\lambda _{\min
		})(\lambda_{\max} -\lambda)}}{\lambda },
	\label{Eq:Marchenko}
\end{equation}%
where
\begin{equation}
	\lambda _{\max ,\min }=\left( 1\pm \sqrt{\frac{N}{M}}\right) ^{2}.
	\label{eq:Lambdas}
\end{equation}

Thus, it is possible to verify whether the density of eigenvalues of $\boldsymbol{\Lambda}$ follows the law described by Eq. \ref{Eq:Marchenko}. Unlike directly computed by other
authors (see for example \cite{Plerou}), we calculate the
density of eigenvalues of $\boldsymbol{\Lambda}$ using the elegant method of Green's
function for two reasons:

\begin{enumerate}[label=\roman*),font=\itshape]
	\item Our correlation matrix has low dimensionality. Thus, we would run the risk of using insufficient bins for obtaining a meaningful histogram for the density of eigenvalues;
	\item This approach makes the formalism used in quantum mechanics explicit to treat  economic problems found in this new field of Econophysics.
\end{enumerate}

\subsubsection{Green's functions}

The retarded Green's function associated with the correlation matrix $%
\boldsymbol{\Lambda }$ is given by the resolvent:

\begin{equation}
	\mathbf{G}_\eta^{\rm{R}}(\lambda)=\left[(\lambda+i\eta)\mathbf{I}-\boldsymbol{\Lambda}\right]^{-1},
\end{equation}
where $\eta\rightarrow0^+$. Considering $\ket{m}$ as an eigenvector of $\boldsymbol{\Lambda}$ with eigenvalue $\lambda_m$ we have:

\begin{eqnarray}
		\mathbf{G}_\eta^R(\lambda)\ket{m}&=(\lambda+i\eta)^{-1}\left[\mathbf{I}-\frac{\boldsymbol{\Lambda}}{\lambda+i\eta}\right]^{-1}\ket{m}\nonumber\\
			&= (\lambda+i\eta)^{-1}\sum_{j=0}^\infty\frac{1}{(\lambda+i\eta)^j}\boldsymbol{\Lambda^j}\ket{m}\nonumber\\
			&= (\lambda+i\eta)^{-1}\left(\sum_{j=0}^\infty\frac{1}{(\lambda+i\eta)^j}\lambda_m^j\right)\ket{m}\nonumber\\
			&= (\lambda+i\eta)^{-1}\left(1-\frac{\lambda_m}{\lambda+i\eta}\right)^{-1}\ket{m}\nonumber\\
			&= \frac{1}{(\lambda-\lambda_m)+i\eta}\ket{m},
\end{eqnarray}
where we used the geometric series representation of the operator $\left[(\lambda+i\eta)\mathbf{I}-\boldsymbol{\Lambda}\right]^{-1}$ as $(\lambda+i\eta)^{-1}\sum_{j=0}^\infty\boldsymbol{\Lambda}/(\lambda+i\eta)^j$.

Thus, using the closeness relation, one obtains the Green's function written in the eigenbasis of the correlation matrix:

\begin{eqnarray}
		\mathbf{G}_\eta^R(\lambda) &= \mathbf{G}_\eta^R(\lambda)\mathbf{1}\nonumber\\
			&= \sum_{m=0}^{M-1}\left[(\lambda+i\eta)\mathbf{I}-\boldsymbol{\Lambda}\right]^{-1}\ket{m}\bra{m}\nonumber\\
			&= \sum_{m=0}^{M-1}\ket{m}\frac{1}{(\lambda-\lambda_m)+i\eta}\bra{m}\nonumber\\
			&= \sum_{m=0}^{M-1}\ket{m}\mathbf{C}_m,
\end{eqnarray}
where:

\begin{equation}
	\mathbf{C}_{m}=\frac{\bra{m}}{(\lambda -\lambda_m)+i\eta }.
\end{equation}
Therefore, the retarded Green's function can be written as:

\begin{equation}
	\mathbf{G}_{\eta }^{\rm{R}}(\lambda )=\sum_{m=0}^{M-1}\frac{\ket{m}\bra{m}}{(\lambda-\lambda_m) +i\eta}.
\end{equation}

Taking the limit $\eta\rightarrow 0^+$, one obtains:

\begin{equation}
	\lim_{\eta \rightarrow 0^+}\rm{Im}\left\{\bra{n}\mathbf{G}_{\eta }^{\rm{R}}\ket{n}\right\} =-\pi \delta (\lambda -\lambda_{n}).
\end{equation}%
Thus we can calculate the density of states according to:

\begin{eqnarray}
		\rho (\lambda ) &= \frac{1}{M}\sum_{n=0}^{M-1}\delta (\lambda -\lambda _{n})\nonumber\\
					  		  &=  -\frac{1}{\pi M}\lim_{\eta \rightarrow 0}\textrm{Tr}\left\{ \rm{Im}
							\left\{ \mathbf{G}_{\eta }^{\rm{R}}(\lambda )\right\} \right\}.
	\label{Eq:Density}
\end{eqnarray}

Again, we average it over an ensemble of $n_{samp.}=$1000 matrices to get
a mean density of assets $\bar{\rho}(\lambda )=\left\langle \rho
(\lambda )\right\rangle $.

\begin{figure}[h]
	\centering
	\includegraphics{MP.pdf}
	\caption{Measured density of eigenvalues. The shaded area corresponds to the
	region between the expected minimum and maximum eigenvalues from the Mar\v{c}%
	eko-Pastur distribution (Eq. \protect\ref{eq:Lambdas}. The density of
	control series with Gaussian and Cauchy distributions are also shown.}
	\label{fig:MP}
\end{figure}

The density obtained for the series under study in Fig. \ref{fig:MP} resembles that of Gaussian ensembles. However, it occupies a region of eigenvalues slightly different than that expected from the Mar\v{c}enko-Pastur distribution in Eq. \ref
{eq:Lambdas}. The expected theoretical distribution should fit a region between $\lambda _{\min}=0.34$ and $\lambda_{\max}=1.99$. However, our data occupies a region between $\lambda _{\min}=0.03$ and $\lambda _{\max}=11.73$.
A least square fitting with a Cauchy distribution for the elements of the correlation matrix was computed to obtain the density of eigenvalues closest to the experimental data. Our calculation produced a scale parameter $\gamma=0.032$. Also, the observed shift as well as the increase in the density values for the tail obtained experimentally seem to be related to the presence of non-Gaussian returns in the portfolio. Similar analysis of the density using random matrix theory on daily stock prices of the Tokyo Stock Exchange produced similar deviations from the Mar\v{c}enko-Pastur distribution for smaller eigenvalues\cite{Utsugi}. However, the deviations were attributed to different levels of randomness.

Although the elements of a Gaussian ensemble are \textit{i.i.d}, their eigenvalues are not. Rather, any two eigenvalues of a Gaussian matrix are unlikely to be close to each other in value. This is known as \emph{level repulsion}.
We investigated this behavior by calculating the cumulative density of eigenvalues $F(\lambda)=\int_{-\infty}^\lambda\rho(y)dy$ and drawing $10^4$ uniform random values $u\in[0;1]$ such that $\lambda=F'^{-1}(u)$ where $F'^{-1}(u)$ is a linear interpolation for $F(\lambda)^{-1}$. The eigenvalues $\lambda$ were then unfolded. For this we calculated $\eta(\lambda)=\sum_n\theta(\lambda-\lambda_n)$ and averaged $\eta(\lambda)$ over an ensemble of 100 random sets of $\lambda$.  The spacing of these estimated levels were then calculated (only for nearest neighbors) and their histograms are shown in Fig. \ref{fig:Surm} for the experimental data, the Wishart-Gaussian ensemble, and for Wishart-Cauchy ensembles with scale parameters of $\gamma=0.032$ and $\gamma=0.048$. The position of the experimental data in Fig. \ref{fig:Surm} between the benchmark distributions reinforce our hypothesis that some elements of the portfolio have non-Gaussian distributions.

Having studied the density
of eigenvalues and benchmarked it, we will now discuss the quantum localization phenomena applied to
cryptocurrencies.

\begin{figure}[h]
	\centering
	\includegraphics{Surmise2.pdf}
	\caption{Eigenvalue spacing distributions for the experimental data as well as the benchmark distributions.}
	\label{fig:Surm}
\end{figure}

\subsection{Measures of Localization}

Although the portfolio is normalized, its fourth moment is empirically related to the
localization of the eigenfunctions and is commonly known as the \emph{%
inverse participation ratio }\cite{partip1}:

\begin{equation}
	\Delta(\lambda _{m})=\left(\sum_{k=1}^{M}|\braket{e_k|m}|^{4}\right)^{-1},
	\label{eq:particip}
\end{equation}%
where $\ket{m}$ ($m\in[0;M-1]$) are the eigenvectors of $\boldsymbol{\Lambda}$ and $e_{k}$ ($k\in[0;M-1]$) forms a complete canonical orthonormal basis in a Hilbert space with dimension $M$.

It is interesting to consider some cases to illustrate this concept. For instance,
an eigenvector with equal components $\braket{e_k|m}=M^{-\nicefrac{1}{2}}$
has an $\Delta=M$ (the dimension of $\boldsymbol{\Lambda}$), whereas an eigenvector with only one component
different than zero $\braket{e_k|m}=\delta_{mm^{\prime}}$ has $\Delta=1$.
Therefore, the inverse participation ratio gives the number of modes
in a specific eigenvector. Here we explore the concept of normalized participation ratio,
where $\Delta=1$ indicates an \emph{extended state} and $\Delta=M^{-1}$ indicates a \emph{localized state}.

\begin{figure}[h]
	\centering
	\includegraphics{PartRatio.pdf}
	\caption{Expected participation ratio $\langle PR(\protect\lambda)\rangle$
	obtained for: the time series under study (blue), a Gaussian control
	(orange), and a Cauchy control with scale parameter $\protect\gamma=0.0481$
	(purple).}
	\label{fig:Particip}
\end{figure}

In order to obtain $\Delta$ as a continuous function and average it over the whole time series we adopted the
following fitting procedure. First, we construct a function $\varphi(\lambda)$ with Gaussian
functions centered on each eigenvalue:

\begin{equation}
	\varphi (\lambda )=\sum_{m=0}^{M-1}A_{m}\exp \left( -\frac{(\lambda -\lambda_{m})^{2}}{2\sigma ^{2}}\right),
\end{equation}
where $A_{m}$ are constants to be determined. Here, from an \emph{ad hoc} point of
view, we can consider this function to assume the value of the participation
ratio for each eigenvalue:

\begin{equation}
	\varphi (\lambda _{k})=\Delta(\lambda _{k})=\sum_{m=1}^{M}A_{m}\exp \left( -%
	\frac{(\lambda _{k}-\lambda _{m})^{2}}{2\sigma ^{2}}\right).
\end{equation}
This produces a set of equations that can be put in a matrix format:

\begin{equation}
	\mathbf{EA}=\boldsymbol{\Delta},
\end{equation}
where $\mathbf{E}$ has elements given by:

\begin{equation}
	E_{ab} = \exp\left(-\frac{(\lambda_a-\lambda_b)^2}{2\sigma^2}\right),
\end{equation}
and $\boldsymbol{\Delta}$ has elements given by $\Delta(\lambda_a)$ calculated from Eq. \ref{eq:particip}.

This can be solved to find the coefficients $A_{n}$ and construct the
function $\varphi (\lambda)$, which will be taken as $\Delta(\lambda)$. This function is then calculated and averaged
for different regions of the time series to produce an expected
participation ratio $\langle\Delta(\lambda)\rangle $.

We calculated the expected participation ratio for the experimental data and for the Wishart-Gaussian ensemble as shown in Fig. \ref{fig:Particip}. We also applied least squares fitting to find a Wishart-Cauchy distribution whose participation ratio that best fitted that of experimental data. In our case, the scale parameter found was $\gamma=0.048$.
The expected participation ratio for the experimental data indicates the presence of extended states
for small eigenvalues as found for the Wishart-Gaussian ensemble \cite{partip2}. The shift of localization for very small eigenvalues as well as the mild localization found for larger eigenvalues, though, can again be attributed to the presence of elements with non-Gaussian distributions in the portfolio.

\subsection{Correlation Structure}

The structure of the eigenvectors is typically used to analyze the market. We start with a conjoint set of all assets and then the portfolio is divided according to the sign of the
elements of the eigenvector $\ket{n_{\max}}$ corresponding to the largest eigenvalue $\lambda_{\max}$ \cite{Plerou,Coelho}.
Since the $\ket{n_{\max}}$ gives the direction of maximum variability in the data, elements with different signs represent positive or negative contributions to this direction.
Each eigenvector after that is associated with variability in a decreasing manner. They can then successively be accessed to divide the market even further until we reach a completely disjoint set. We applied this strategy to the assets under study and obtained the hierarchical tree structure shown in the inset of Fig. \ref{fig:Cluster}.

\begin{figure}[h]
	\centering
	\includegraphics{cluster.pdf}
	\caption{Number of clusters as a function of the level of partition for the
	real data (blue with dots) and for a trivially connected tree (orange with
	squares). The inset shows a tree diagram for the hierarchical structure of
	the assets under study.}
	\label{fig:Cluster}
\end{figure}

In greater detail, positive elements from the eigenvector $\mathbf{v}_{\max}$ corresponding to the highest eigenvalue form a partition \#1, whereas negative elements form a partition \#2. Within each of these partitions two new sub-partitions are created according to the sign of the elements of the eigenvector $\mathbf{v}_{\max{}-1}$ corresponding to the second highest eigenvalue. Therefore, partition \#3 is created within partition \#1 with the elements of partition \#1 that are positive in $\mathbf{v}_{\max{}-1}$, whereas partition \#4 is also created within partition \#1 but with the elements of partition \#1 that are negative in $\mathbf{v}_{\max{}-1}$. Similarly, partition number \#5 is created within partition \#2 with elements of partition \#2 that are positive in $\mathbf{v}_{\max{}-1}$. Finally, partition number \#6 is also created within partition \#2 with elements of partition \#2 that are negative in $\mathbf{v}_{\max{}-1}$. The same procedure occurs with elements from the following eigenvectors until there are only single elements.

After performing this partition composition of cryptocurrencies we progressively remove the links in the formed tree structure from
right to left and the number of disjoint clusters are counted. This result
is illustrated in Fig. \ref{fig:Cluster} and is compared with the trivial case (a 3-coordinated Cayley tree)
where a market is uniformly pairwise clustered. The divergence from the
trivial case in our results indicates that the assets under study tend to
strongly bundle together around the same tendency. This is a characteristic of highly correlated systems, which can also be found in spin glasses\cite{sping}.

The difference between the trivial and the measured partition curves results in a function with the form $N\propto e^{p/p_0}$, where $p_0$ is a characteristic partition of the hierarchical tree. This can be used to quantify the correlation level of the system under study with small values implying high correlations. In our case we found $p_0\approx1.0625$.

\subsubsection{Networks}

We further explore the hierarchical structure of the market by calculating
ultrametric ordering, a concept that is borrowed from the theory of frustrated
disordered systems\cite{ultra,Naylor}. In short, an ultrametric space is a metric space where the triangle inequality is restricted to:

\begin{equation}
	d(x,z) \leq \max\{d(x,y),d(y,z)\},
\end{equation}
for any two points $x$ and $y$, and $d(x,z)$ is a distance function between $x$ and $z$. This implies that there is no intermediate points between $x$ and $z$ and a random walk in an ultrametric space is non-ergodic\cite{spingbook}. This is an appropriate way to describe  hierarchical structures since the concept of ultrametricity is tightly related to the concept of hierarchy. Thus, a hierarchical tree can be used to represent an ultrametric set by calculating the distances between nodes. However, computing the distances between all assets creates a complete graph. This
carries redundant information that can be eliminated if one uses a subdominant ultrametric structure.  The latter can be obtained by calculating the the \emph{minimal spanning tree} (MST) \cite{Mant1,Gorski,Schulz}.

A distance between the assets
can be described by the Euclidean distance between their return vectors:

\begin{eqnarray}
		d_{nm}^E  &= ||\mathbf{L}_m-\mathbf{L}_n||\nonumber\\
							&= \sqrt{||\mathbf{L}_m||^2+||\mathbf{L}_n||^2-2\mathbf{L}_m\cdot\mathbf{L}_n}\nonumber\\
							&= \sqrt{2(1-\Lambda_{nm})}.
\end{eqnarray}
We refer to this metric simply as the Euclidean distance.

Since the structure of the eigenvectors is used to cluster the assets, it is
convenient to also use a \emph{spectral distance}. For this, we create
vectors whose elements are taken from the same entry of different
eigenvectors weighted by the corresponding eigenvalue. The metric is then
the Euclidean distance between these vectors:

\begin{equation}
	d_{nm}^s = \sqrt{\sum_k\lambda_k^2\left[\braket{e_n|k}-\braket{e_m|k}\right]^2}
\end{equation}
We refer to this metric as the spectral distance.

We construct such backbone
of the network choosing links such that the total length of the tree is
minimized. We used Prim's algorithm \cite{Prim} to construct the MST shown
in Figs. \ref{fig:Nets1} and \ref{fig:Nets2}. This algorithm consists of connecting the elements
with the smallest distance, then connect the next set of nodes given that no
loop is produced, and repeat this operation until all nodes are connected.

An agglomerative hierarchical clustering algorithm was also used to create hierarchical clusters (dendrograms)\cite{dendro}. In this algorithm, two clusters with the smallest distance are permanently joined together forming a new one. This new cluster $k$ has a distance to the remaining clusters $m$ given by:

\begin{equation}
	d_{km} = \alpha_i d_{im}+\alpha_j d_{jm}+\beta d_{ij}+\gamma|d_{im}-d_{jm}|.
\end{equation}
Here we use a single linkage strategy with $\alpha_i=\alpha_j=\nicefrac{1}{2}$, $\beta=0$, and $\gamma=-\nicefrac{1}{2}$. The agglomeration process continues until a single cluster is present. The resulting dendrograms using both the Euclidean and the spectral distances are shown in Figs. \ref{fig:Nets1} and \ref{fig:Nets2} respectively.

\begin{figure}[h!]
	\centering
	\includegraphics{dendro1.pdf}
	\caption{Complex network created using the Euclidean distance (top) and the corresponding dendrogram (bottom).}
	\label{fig:Nets1}
\end{figure}

\begin{figure}[h!]
	\centering
	\includegraphics{dendro2.pdf}
	\caption{Complex network created using the spectral distance (top) and the corresponding dendrogram (bottom).}
	\label{fig:Nets2}
\end{figure}

The spanning tree created using the Euclidean distance basically separates the assets in two dissimilar groups, one where BTC is the main hub and another where ETH is the main hub. Its corresponding dendrogram corroborates with this information placing both assets in the bottom of the hierarchy diagram. The dendrogram carries more information. It shows that although EOS, LTC, BCH, TRX, DOGE, and XTZ also form a distinctive hierarchy structure, the remaining assets form a relatively flat correlated structure.

On the other hand, the spanning tree obtained using the spectral distance shows more details of the correlation structure. For instance, it is clear in the spanning tree that DOGE and XTZ are the most dissimilar assets when compared with BTC and ETH. This happens because the eigenvectors carry information about the relationship between
all elements of the correlation matrix, whereas the Euclidean distance is a
binary distance between assets. Yet, the dendrogram obtained using the spectral distance is very similar to that obtained using the Euclidean distance.

The order of appearance of the assets on both dendrograms have a Pearson correlation coefficient of approximately 70 \% with the market capitalization of the assets. This can be regarded as a stylized fact suggesting that coins with large market capitalization tend to appear on the lowest distances in the dendrograms. Thus, the market seems to select those cryptoassets that are significantly distinctive.

\section{Conclusions}
\label{Section:Conclusions}

We developed a formal parallel between financial assets and quantum systems.
One of the main results is the concept of ``eigenportfolios'' that copy the behavior
of the ground state of a quantum system. We then used this methodology to
study portfolios of 17 digital assets. We computed the correlation
matrix for these assets and compared the density of eigenvalues with those
of a Wishart ensemble and a non-square matrix of random variables drawn from
the Cauchy distribution. Our results indicate that digital assets have a
high explained variance that corresponds to an intermediate behavior
between these two control portfolios. Moreover, the eigenportfolios of digital assets
have a density of small eigenvalues similar to that of a Wishart ensemble, but a tail
for bigger eigenvalues that is similar to that found for the Cauchy distribution.

We developed a new tool based on the superposition of Gaussian functions to
perform localization analysis on the eigenvectors of the correlation matrix.
Our results indicate that small eigenvalues correspond to highly localized
states as is similarly expected for the Wishart ensemble. Furthermore, a
mild localization behavior similar to that obtained for the Cauchy ensemble
is obtained for larger eigenvalues.

The correlation structure of the eigenportfolios was also probed with ultrametric ordering.
The concept of the minimum spanning tree was used to investigate the
correlation structure of the market of digital assets. We develop a new
metric, based on the spectral characteristics of the correlation matrix to
explore this behavior and show that the corresponding graph is similar to
that obtained by clustering the market according to the elements of its
eigenvectors. Furthermore, this spectral metric produces minimum spanning
trees that carry information similar to that found in the corresponding dendrograms.

The dendrograms may be useful to design portfolios of cryptocurrencies. For instance,
one could create a diverse portfolio choosing assets that dot not strongly correlate
among themselves. Nonetheless, the dendrograms also show that most of the
cryptocurrencies are very correlated, imposing some difficulties in the design of
adequate investment portfolios. It may be possible to lift these degeneracies by
including a virtual perturbation in the correlation matrix (Eq. \ref{eq:eigenp}).
This can be achieved, for example, by calculating the Markovitz portfolio.

All analyses considered that the correlations between assets are time invariant.
This however may not be the case in real investment scenarios, and a better
description using the Liouville equation may be required.

\section{Bibliography}
\nocite{*}
\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


text:
New center to address health disparities in inland Southern California
Five-year, $16 million grant from the National Institutes of Health will help launch Center for Health Disparities Research at UC Riverside
The University of California, Riverside, has received a grant of $16 million from the National Institutes of Health, or NIH, to focus on and help reduce health disparities in inland Southern California, particularly among Latino communities that make up about 49% of the region's population.
The five-year grant will allow the School of Medicine to launch the Center for Health Disparities Research at UCR, or HDR@UCR, bringing together environmental scientists, biomedical scientists, and social scientists to study health disparities.
Inland Southern California, currently home to about 4.3 million people, has an acute shortage of primary care physicians, with 35 physicians per 100,000 people. Comprised of Riverside and San Bernardino counties, the region performs poorly compared to other regions in the state in almost all measurable health outcomes — especially in diabetes and coronary heart disease.
Among California's 58 counties, San Bernardino County ranks second worst in diabetes-related deaths; Riverside County is 10th worst in deaths due to coronary heart disease. In San Bernardino County, Latinos have a diabetes-related death rate that is 50% higher than whites. In Riverside County, Latinas have the highest incidence of cervical cancer.
"HDR@UCR will use a community-based approach to assess and improve the health of underserved populations in inland Southern California," said Dr. David Lo, director of the center and senior associate dean for research in the School of Medicine. "We think the knowledge the center produces will inform approaches to address health disparities that Latino communities and marginalized populations experience elsewhere in the country."
Lo, a distinguished professor of biomedical sciences, explained that HDR@UCR would be established in partnership with the College of Humanities, Arts, and Social Sciences and the School of Public Policy, and organized around a set of "cores" to support and train the center's members to do research in health disparities. Colleges from across campus will be involved in the cores that include community engagement and dissemination; investigator development; research infrastructure; recruitment; and administration.
Juliet McMullin, co-director of HDR@UCR and a professor of anthropology, will lead the community engagement and dissemination core. She stressed that collaboration with the community at the start makes the research more robust and the findings more applicable to the communities where they are disseminated.
"The community-engaged approach shifts the research focus from research 'on' to research 'with' people and creates opportunities for biomedical and clinical researchers to frame problems from the perspective of what's relevant and important to the community whose lives are impacted by our research," said McMullin, who chairs the Department of Anthropology.
HDR@UCR will support a number of research projects, including two key projects based in the medically underserved eastern Coachella Valley, a region with only one physician for every 8,407 residents, and a large population of U.S.-born and immigrant Latinos. The first project will focus on the impact of aerosolized particulates on health. The second project will explore the relationship between infant feeding styles and practices in low-income Latino families to infant growth and obesity.
"The complex problems of health disparities require input from multiple perspectives," said Bruce Link, a distinguished professor of public policy and sociology and a co-principal investigator of the NIH grant. "For this reason, HDR@UCR seeks to integrate social and environmental perspectives with biomedical approaches to achieve a more complete understanding of the sources and consequences of health disparities in inland Southern California."
Ann Cheney, an assistant professor in the medical school's Center for Healthy Communities, is co-investigator with Maria Pozar, a community organizer at the Salton Sea, and others on the first project aimed at assessing the impact of aerosolized particulates on health, which will include an investigation, led by Lo, of childhood asthma among Latino populations near the Salton Sea.
"Two health clinics serve the communities at the Salton Sea," Pozar said. "Residents say they wait a long time to be seen. People who have health insurance take the bus farther out, to Indio, or a place where they can be seen and treated in a timelier manner. Residents without health insurance self-medicate or use home remedies."
Cheney and Tanya Nieri, an associate professor of sociology, are the principal investigators on the second project focused on early childhood obesity. This project will take place in Riverside, Orange, and Imperial counties.
"Research shows that intervention in early childhood is more effective in preventing obesity," Nieri said. "Furthermore, we're learning more about how obesity risk begins in early childhood. Existing early childhood interventions, particularly those focused on nutrition, need to incorporate this new knowledge."
HDR@UCR will soon offer grants to UCR researchers interested in working on health-disparity projects. The center will also create interdisciplinary research workgroups that can apply for funding to meet their objectives. These groups will include junior researchers, who, in turn, can apply for pilot grants to help them get established as independent investigators. A community engagement studio is also planned to seek regular feedback on the center and health care priorities; it will serve as a hub for community-engaged proposal development, implementation, and dissemination activities.
Projects of interest to the center include those that examine mental health in Latino communities, study access to good nutrition in those communities, and investigate how living conditions, as well as cultural and environmental factors, contribute to health disparities. The center will also fund "continuity collaboratives" through fellowships to graduate students and postdoctoral scholars interested in taking on research projects that can become vulnerable once students working on them graduate.
"We also hope HDR@UCR will continue to foster and expand an academic environment at UCR that is sensitive to the needs of our community," Lo said. "We plan to hire diverse faculty. Fortunately, a good number of our medical students come from our community; many may want to join our faculty and further strengthen ties to their communities. We expect HDR@UCR will serve as a model not only for other UC medical schools, but also those across the country on how to do community-based and community-informed research."
Research reported in this publication is supported by the National Institute on Minority Health and Health Disparities of the NIH under award number U54MD013368. The content of this news release does not necessarily represent the official views of the NIH.
NIH news release.
College Of Humanities Arts And Social Sciences
David Lo
Juliet McMullin
Ann Cheney
Tanya Nieri
Bruce Link
University||Health||Social Science / Education
Asian American shootings: This is 'not an exception' and other issues that need to be discussed
Gun violence pressures elected officials to make reforms

redpajama_set_name: RedPajamaCommonCrawl


• SelectaAthe high forehead is SelectaAthe sign of intelligence. Absolutely no evidence for this.
• SelectaAthe receeding chin is SelectaAthe sign of SelectaAthe weak character. No truth in that one either.
• Eating green apples causes stomachache. That isn't strictly true; it isn't SelectaAthe fact that apples are green that causes	stomachache, it's possibly because they are so sour to eat they aren't chewed properly and causes SelectaAthe abdominal pains.
• Cobwebs can be used to treat wounds. Probably more likely to cause infection than help, although they might hasten blood clotting. Not to be recommended.
• You can get warts from touching frogs. Unfair on frogs, that one.
The really odd thing is, I suppose, even modem medicine produces its own superstitions.
I've come across several patients who have insisted that their modem capsules only work efficiently if swallowed SelectaAthe right way round. Green end first seems most popular!


Blog Maniac | Page 4 | All Blogging!
With the growing interest in blogging as a means of online promotion and branding, a lot of marketers are starting blogs to promote their opinions, products, books and services.
But a blog is like a website. "Write and they will come" isn't exactly a magic formula to bring in traffic by the boatload.
If you need to promote your website in order to build traffic to it, you need to promote your blog as well.
Here are some ways you can become a well-read and influential blogger.
This should be common sense, but many marketers tend to forget that their readers are real people and that you need to use the principles of online copywriting to make your headlines and copy interesting to your readers.
If you write posts that people enjoy reading, they will reward you by returning to your blog regularly.
Make your posts conversational, pithy and topical. Keep them short and stick to one topic per post.
Write often and regularly so that both readers and search engines visit your blog more often.
But here are the most important rules to follow to get your posts listed for keywords of your choice.
If you publish a blog you should submit your blog and RSS feed to big directories like Yahoo and Dmoz, as well as the numerous blog directories and search engines.
Here is the best list I've found of places to submit your feed or blog, compiled by Luigi Canali De Rossi, who writes under the pseudonym Robin Good.
There are a number of services designed specifically for tracking and connecting blogs. By sending a small ping to each service you let them know you've updated your blog so they can come check you out.
Bookmark the Ping-O-Matic ping results page so you can visit it and quickly ping a number of services with a single click.
I recommend the methods here as the best ways to get links pointing to your blog.
One of the best methods for promoting your website is to write articles and submit them to article directories.
The suggestion for extending this to edit your blog posts into articles and submit them to directories came from the coach at "Explode Blog Traffic" who also has other noteworthy suggestions at his blog.
Creating a buzz about your blog posts and topic in the local and online media will give your marketing a viral component.
Create a controversy around your blog or it's topic.
Distribute bumper stickers or other merchandise with your blog's URL and tagline.
Write a press release about something newsworthy and tie it in with your blog topic.
It may seem strange for a blogger to send out updates by email, but email is still the #1 choice of most people who want to receive news and information.
Using a free service like Feedrner to manage your subscriptions is easy and it allows your subscribers to manage all their subscriptions from one interface.
However, if you want more control over your list and don't mind mailing out the updates yourself, you can use an autoresponder system to capture and follow-up with subscribers.
These tips should give you a good start to building your blog traffic.
Technorati reports that 30,000 – 40,000 new blogs are being created each day.
According to David Sifry, part of the growth of new blogs created each day is due to an increase in spam blogs.
What are spam blogs? They are fake blogs that are created by robots in order to foster link farms, attempted search engine optimization, or drive traffic through to advertising or affiliate sites.
They contain robot-generated posts made up of random words, with the title linking back to the blogger's own pages.
Many bloggers see them as a way of getting their pages indexed quickly by Google and other search engines.
Sifry estimates that about 20% of the aggregate pings Technorati receives are from spam blogs. Most of this fake blog spam comes from hosted services or from specific IP addresses.
Those in the SEO world are well aware of this. There are even services like Blogburner that encourage creation of spammy blogs and spam-pinging to get your sites indexed quickly.
As a blogging evangelist, I wholeheartedly recommend blogging as an SEO tactic. But I also emphasize that you should use your blog for more than just SEO.
At the Spam Squashing Summit, blog services decided to collaborate to report and combat blog-spamming.
Technorati currently claims to catch about 90% of spam and remove it from the index. They also notify the blog hosting operators.
But I believe that they are fighting a losing battle. As I write this there are software and robots being created that will create spam-blogs more efficiently and in ways that will be harder to detect.
The SEO "black hats" are always far ahead of the technology and safeguards that these services can put in place.
Take down a few spam-blogs and hundreds more will arise.
Blogging evangelist and PR guru, Steve Rubel, sums up this dilemma rather well on his Micropersuasion blog.
He believes that its human nature for people to exploit new technologies, and that it's really up to the search engines to help put a stop to these by undercutting the economics of blogspam, much like they did with nofollow and comment spam.
But the trade-off is that such a move would also reduce any impact that blogs have on search results.
Fact: The more you abuse a technology, the less effective it becomes.
Spam blogging will force search engines like Google to change their ranking algorithms and eventually assign less value to links from blogs.
Unless they put in safeguards to prevent robots from taking over, its safe to assume that blogging will become less effective as an SEO tactic over time.
Of course, the spammers will then just have to find new avenues and means to spam the engines.
But why ruin a good thing in the first place? Blogs are much more than just tools for search engine optimization.
A blog can be a great tool for personal branding and building relationships with your website visitors and customers.
Instead of using blogs for spam, focus on building content-rich sites and getting high-value links to them.
Don't restrict yourself to just the SEO benefits of blogging.
Appreciate the value that blogs can add to your marketing and public relations strategy and use them the way they were meant to be used.
Blogging software is really a simple Content Management System (CMS) that easily adds new pages and integrates them into your site's navigational structure and linkage.
But if you're doing it for business and want the targeted traffic to flow your way, keywords in the domain or subdomain are a move in the right direction.
If your primary key phrase is "business blogging" make sure that the word business, or blogging, or both, appear in your blog headers (the H1 or H2 tags) as well as the title of each of your posts.
For example, if you have a blog on Blogger and title your post "Search Engine Optimization For Blogs", Blogger will automatically create a page with your post and name the file "search-engine-optimization-for-blogs.html" or something similar.
Don't overdo this or your posts will end up sounding unnatural and spammy to readers.
Link keywords where they naturally appear in the body text, but again, don't overdo it, or you'll end up with spammy looking pages.
I've seen many people recommend Blogrolling as one method of building links to your blog.
Here is the best list I've found of places to submit your feed or blog.
There's no better food for search engine spiders than fresh content.
Post and update your blog frequently using all the rules outlined above and there's no reason why your blog will not get you top rankings in a short period of time.


text:
COUNT EVERY VOTE!
HPAE congratulates victorious pro-labor candidates while calling for Every Vote to be Counted
After one of the most extraordinary elections in American history, HPAE sends out congratulations to the large slate of candidates that the union endorsed who are the declared victors in national, state and local races in this election cycle.
HPAE President Debbie White, RN, is standing with allies to demand that every vote be counted in the remaining outstanding races, including in the race for President of the United States.
White, who is also an American Federation of Teachers (AFT) Vice President, said, "The AFT passed a resolution demanding that every vote be counted. Our vote is our voice and a sacred right upon which freedom depends. We see no choice: To be true to ourselves and the values we hold dear, we must rise to the defense of democracy."
HPAE is proud to congratulate Cory Booker, who won re-election to the U.S. Senate, Andy Kim, re-elected to the U.S. House Representatives for District 3, and Donald Norcross, who was also re-elected to the House of Representatives for District One. HPAE also wants to congratulate the following declared winners and those leading by a wide margin in their districts:
Frank Pallone, Jr., District 6
Tom Malinowski, District 7
Albio Sires, District 8
Bill Pascrell, Jr., District 9
Donald Payne, Jr., District 10
Rebecca "Mikie" Sherrill, District 11
Bonnie Watson Coleman, District 12
We remain hopeful for Amy Kennedy for the House of Representatives for District Two. In Monmouth County, freeholder candidates Michael Penna and Moira Nelson are leading in early vote count. Monica Townsend is in good shape in the early vote count for the Middlesex Borough Council. and, Rupande Mehta is polling well in NJ State Senate District 25.
For more information, please contact: Michael Allen: (646) 436-7556, mallen@hpae.org
Related Campaigns:
Election Center 2020


Ithan Elementary School is currently on a level one lockdown due to a possible bear sighting in a nearby woods.
BRYN MAWR, Pa. (WPVI) -- Ithan Elementary School is currently on a level one lockdown due to a possible bear sighting in a nearby woods.
It happened Tuesday morning on the 600 block of Clyde Road.
A level one lockdown means that all exterior doors are kept shut with the students and teachers inside the school.
Everyone is safe, and there are no injuries reported.


text:
Muddled politics undoes terrific acting in 'Elah'
By Daniel M. Kimmel Telegram & Gazette Reviewer
Paul Haggis has written some powerful scripts for Clint Eastwood (�Million Dollar Baby,� �Letters from Iwo Jima�) but when he�s writing and directing himself, as he did in the Oscar-winning �Crash,� he tends to wear his heart on his sleeve. With �In the Valley of Elah� he has an interesting story of a criminal investigation that gets tied up in a muddled statement against the war in Iraq.
Hank Deerfield (Tommy Lee Jones) is awaiting the return of his son from duty in Iraq and is informed that his son seems to have gone AWOL. Hank can�t believe it. He is quickly and tragically proved correct. His son is dead. The investigation by both civilian and military authorities into what happened � along with Hank�s own prying � takes up the bulk of the film.
There are many pluses, starting with Jones� performance. He evinces a quiet sorrow and anger as Hank. The character isn�t given to big emotional scenes. We learn has many reasons not to just leave the matter to others, ranging from guilt over both his sons dying in uniform, to the fact that he is a veteran himself who did police work in the service. Now he�s feeling helpless, and going back to work, even unofficially, gives him purpose again.
Then there�s Charlize Theron as Detective Emily Sanders. This is a character part, like �Monster� and �North Country,� not a glamour role. Her byplay with Jones is effective. On the one hand she�s being given a tough time by both the other cops and the military, while on the other hand she realizes that Hank�s �interference� is actually proving helpful.
In many ways this is reminiscent of �Missing,� the 1982 film about an older man and young woman trying to solve the mystery of an American man who has �disappeared� in a South American country under suspicious circumstances. The difference is that that film was directed by Costa-Gavras, who�s an old hand at weaving together political statements and intense drama. When Haggis tries it here, it clunks as loudly as the clumsy title. Even the Biblically literate may not immediately get the allusion to the fight between David and Goliath, and it�s even more of a stretch figuring out what it has to do with the present story.
Susan Sarandon has a couple of good scenes as Hank�s wife, but is basically a footnote to the story of Hank and the detective pursuing the investigation. When we get an answer as to what happened, it gets awkwardly tied to the war in Iraq so that a STATEMENT can be made. There are statements to be made on the subject, but this isn�t it.
�In the Valley of Elah� is one of those near misses that have enough things going for it � such as the performances of Jones and Theron � that you may be willing to forgive the film its flaws. Being forgiving, however, is not the same thing as not noticing them.


text:
"Make PPE in America Act" Mandates a Shift to U.S.-Based PPE Supply Chain
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Article provided by US Meltblown
Restoring America's capacity to manufacture PPE, everything from face masks and surgical wear to medical supplies is critical to keeping the nation's hospitals functioning in times of crisis. The "Make PPE in America Act" will require a wide range of federal agencies–including Homeland Security, Health and Human Services, and the Veterans Administration–to purchase American-made PPE. The bill also requires federal agencies to issue long-term contracts to U.S. manufacturers.
Covid-19 exposed the lack of domestic production of PPE (personal protective equipment), which makes the U.S. supply chain extremely vulnerable. The new "Make PPE in America Act," part of the just-signed Infrastructure Bill, is an admission of this vulnerability and addresses the fact that the United States requires a robust, secure, and wholly domestic PPE supply chain to safeguard public health and national security.
Beginning 90 days from the Infrastructure Bill signature, and to ensure sustainment and expansion of PPE manufacturing in the U.S., the new act requires that any contract for procurement shall:
Be issued for a duration of 3 years to incentivize investment in the production and the materials and components in the United States.
Be for Personal Protective Equipment that: Is grown, reprocessed, or produced in the United States, and when assembled outside the U.S., contains only materials and components that are grown, reprocessed, reused, or produced in the United States.
Please note that this is NOT the same "Made In America" or "Made in USA" provision per the FTC guidelines which allows percentages of products to be sourced with resources from overseas. In the strongest sense, this new "Make PPE in America Act" is a mandate that the ingredients must be 100% made in the United States. This seismic change is needed to ensure the supply chain physically moves to and will now be controlled within the United States. "This is the first step in a long-term strategy that is critically needed to permanently onshore PPE production to ensure our nation is prepared for the next health security crisis," said NCTO (National Council of Textile Organizations) President and CEO Kim Glas. "This infrastructure package will help incentivize the reshoring of PPE production by guaranteeing long-term federal contracts and expanding Berry Amendment rules to more federal agencies' purchases of PPE products, important priories of the U.S. textile industry."
"We at US Meltblown have done our part by establishing a reliable, domestic source for this vitally important PPE material," said US Meltblown Founder and CEO Robert Sires. "We are asking others to do their part by purchasing PPE products from companies here in the United States, thereby supporting the economy and better protecting American citizens."
US Meltblown built its business around this strategy. When the pandemic hit and the realization of how little Made In America PPE was available, US Meltblown opened its doors to begin making non-woven fabric for PPE needs. Enabling you to meet the requirements of the "Make PPE in America Act".
Visit US Meltblown and read their latest press release on the steps that US Meltblown has taken to meet these requirements.
By Guest Contributor on 11/24/2021 / In The News, News / Leave a comment


text:
Tag: cowboys game
How to play the 'armor games'
The Cowboy Game has become a fixture of the annual Dallas Cowboys game, and it's not just because the Cowboys are a team that has won a Super Bowl and a ring.The game has also been a huge hit at the Cowboys' home games in Arlington.But is the game...
Why the Cowboys are playing "Hhentai Games" on the internet
This week, we're going to be taking a look at a new, popular game in the internet gaming industry: the "Hentai Games".This game, which has been around for years and is known as "Hetalia", has spawned many different sub-cultures around the world.Hetalians have traditionally been depicted as young, beautiful...


text:
var common = require("../common-tap")
var test = require("tap").test
var path = require("path")

// ignore-scripts/package.json has scripts that always exit with non-zero error
// codes. The "install" script is omitted so that npm tries to run node-gyp,
// which should also fail.
var pkg = path.resolve(__dirname, "ignore-scripts")

test("ignore-scripts: install using the option", function (t) {
  createChild(["install", "--ignore-scripts"], function (err, code) {
    t.ifError(err, "install with scripts ignored finished successfully")
    t.equal(code, 0, "npm install exited with code")
    t.end()
  })
})

test("ignore-scripts: install NOT using the option", function (t) {
  createChild(["install"], function (err, code) {
    t.ifError(err, "install with scripts successful")
    t.notEqual(code, 0, "npm install exited with code")
    t.end()
  })
})

var scripts = [
  "prepublish", "publish", "postpublish",
  "preinstall", "install", "postinstall",
  "preuninstall", "uninstall", "postuninstall",
  "pretest", "test", "posttest",
  "prestop", "stop", "poststop",
  "prestart", "start", "poststart",
  "prerestart", "restart", "postrestart"
]

scripts.forEach(function (script) {
  test("ignore-scripts: run-script "+script+" using the option", function (t) {
    createChild(["--ignore-scripts", "run-script", script], function (err, code) {
      t.ifError(err, "run-script " + script + " with ignore-scripts successful")
      t.equal(code, 0, "npm run-script exited with code")
      t.end()
    })
  })
})

scripts.forEach(function (script) {
  test("ignore-scripts: run-script "+script+" NOT using the option", function (t) {
    createChild(["run-script", script], function (err, code) {
      t.ifError(err, "run-script " + script + " finished successfully")
      t.notEqual(code, 0, "npm run-script exited with code")
      t.end()
    })
  })
})

function createChild (args, cb) {
  var env = {
    HOME: process.env.HOME,
    Path: process.env.PATH,
    PATH: process.env.PATH,
    "npm_config_loglevel": "silent"
  }

  if (process.platform === "win32")
    env.npm_config_cache = "%APPDATA%\\npm-cache"

  return common.npm(args, {
    cwd: pkg,
    stdio: "inherit",
    env: env
  }, cb)
}

redpajama_set_name: RedPajamaGithub


Leaving Certificate in five subjects i.e. Grade O6 or H7 in five subjects. The five subjects must include Mathematics*, and either English or Irish.
Quality and Qualifications Ireland (QQI) operates within the National Framework of Qualifications, and has awards (formerly FETAC awards) placed at Level 5 (Certificate) or Level 6 (Advanced Certificate) of the Framework.
Mature students (23yrs on the 1st January on year of entry to the Course) and holders of the Leaving Certificate Applied with one year's relevant industrial experience may apply as Special Category Applicants through the CAO. They may be required to undertake an Institute interview.
There is a formal structured work placement over the summer at the end of Year 1. Students will have a formal, organised work placement in a good quality hotel or restaurant under the guidance of an experienced hospitality professional. The placement will be matched to the student's area of interest and skill level. The work placement is a formal component of the programme and is awarded academic marks and credits.
Helpful subjects are English, Mathematics, Business Subject(s), Home Economics, and a European Language.
Hospitality Studies is a broad programme of learning which provides an introduction to all of the operations areas in the hospitality sector. Students get an opportunity to study and practice the areas of restaurant service, bar service operations, front office, rooms division, accommodation, event organisation, introduction to culinary skills, along with a range of business subjects.
The combination of practical skills and theoretical subjects gives the student the opportunity to identify their area of preference in the sector and to subsequently develop a valuable career in their chosen field.
The Higher Certificate in Arts in Hospitality Studies is designed to meet the skills requirements of students who wish to pursue careers within the hospitality sector. Graduates typically work in contact with the customer in hotels, restaurants or bar operations or associated areas such as conferences and events. The strong element of practical learning involved in this course is appealing to many candidates.
Practical classes, formal lectures, guest lectures, site visits and group projects are all used to ensure students receive a fully rounded study environment. A formal work placement allows the student to put into practice the skills which they have learned while in college, under the guidance of an experienced hospitality professional, and students are awarded academic marks for this important component of their course.
The Tourism and Hospitality buildings are of the best modern standard and include modern Demonstration and Production Kitchens, IT Laboratories, a Demonstration Theatre, Training Restaurants, a Training Bar, Training Reception and fully equipped classrooms. In addition students have easy access to the wider Institute facilities such as an excellent Library, IT facilities, sports and recreation facilities and other student supports, such as a large range of student clubs and societies.
Administration and support facilities are offered in an environment where students have direct access to an experienced and qualified lecturing team.
There is a formal structured work placement over the summer at the end of Year 1. Students will have a formal, organised work placement in a good quality hotel or restaurant under the guidance of an experienced hospitality professional.
The Placement will be matched to the student's area of interest and skill level. The work placement is a formal component of the programme and is awarded academic marks and credits.
What is the difference between Hospitality Studies and Hospitality Management?
Hospitality Studies focuses on the day-to-day operations within the hospitality sector, where positions require a hands-on customer centred focus.
Hospitality Management focuses on the successful operation and profitable management of the overall business and its resources.
The facilities in the Department of Tourism and Hospitality are of the highest European standard. The Building is run with the leading standards relating to both hygiene and the environment in mind at all times.
The Department is located within its own building on the campus and provides excellent facilities to enhance student learning including a range of Kitchens, Classrooms, Labs and other training facilities.
The work placement sounds exciting. Is it based in Ireland or can you be placed abroad?
The work placement takes place in a quality hospitality establishment in Ireland and it is supported by a Department of Tourism & Hospitality staff member together with a workplace mentor. However, on qualification, graduates possess a skillset which they can use to gain employment in many different roles abroad.
Having graduated from CIT with her Higher Certificate in Hospitality Studies, Louise decided to progress and pursue a degree in Hospitality Management in the Department of Tourism & Hospitality. During her time in college, Louise represented CIT at the final of the National Skills Restaurant Service Competition.
Louise is currently the Restaurant Supervisor in the 5 Star Park Hotel in Kenmare, where she works daily with the Brennan brothers of televisions 'At Your Service'.
For the student who is prepared to work hard and who brings flair and passion to hospitality, the opportunities are endless. Hotels, restaurants, bars, events and work place catering are all areas which are an ideal career choice for graduates. Many of our graduates travel overseas to gain experience and to enhance their skills or go on to embark on further studies in the area of hospitality.


Maps like this make me just want to go back to the simple days of the Nokia phone - Pheonixmaster1 Reaally glad I have S!Micaiah and pulled S!Palla to fodder her Pegasus Carrot.
That's a pretty good strategy~ I generally only play when my Stamina naturally recharges until the last day when I use all the Lances. Which ends up being more than expected since I have to get the ones from Ranking up, too. I used to unload them all at night but that became a biiiiit stressful so I've gotten in the habit of using them up in the morning.
Congrats! You ever planning on feeding her that nice DD4? Nice +10 B!Celica! Walhart is's a common Grail project so it's cool to see you got him done!


PlantRun can provide highly accurate maintenance KPI's in real-time for improved maintenance effectiveness or performance.
This is achieved by recording all downtime events or stoppages to one second accuracy. Any downtime period can have multiple reasons and comments assigned to it. In this way any breakdown and sequence of actions to rectify it can be measured and reported.
As an example, referencing the diagram below, PlantRun records whenever a machine stops. If the stoppage is requires attention from an engineer the machine operator can request assistance using the engineer call button on the PlantRun Outstation at the machine, or a call might be automatically generated after a preset down time.
In either case this call can be sent via a SMS text to mobile phone, email or public address message or andon board. PlantRun takes account of the number of engineers on shift and can prioritise machines to minimise engineer calls.
The period between the fault start (far left) and engineer call is MODT. When an engineer logs on at the machine the wait time is recorded - MWT. This allows tracking of engineer response times. If there is time lost in logistics such as awaiting parts this can be sub assigned as MLDT.
When the fault is repaired the engineer logs off from the machine to give MTTM. Any idle time until a machine operator logs on to the machine to begin production is recorded as MIT.
This allows reliability and maintainability KPI's to be reported, tracked and trended to enable improved maintenance performance and effectiveness. It is also possible to report on engineer call rate per machine or shift, which can often highlight problematic issues.
Below is an example of PlantRun Response Time Tracking for an engineer callout to a machine breakdown.
Continuous condition monitoring of a wide range of parameters affecting equipment maintenance intervals such as hours run, number of cycles or operations, total throughput, time spent under load etc. is also possible.
PlantRun can calculate when a pre-determined level of any monitored parameter has been passed. The system then alerts that maintenance is required via an on screen message, report generation, email or SMS text message. This allows maintenance to be optimised based on actual equipment work load or usage.
Condition monitoring parameters can also be graphed against process data to detect changes over time that might indicate problems associated with specific machines allowing planned repair rather than breakdown maintenance.


text:
Rams Earn Split at George Mason to Begin Conference Play
Rhode Island (5-19, 1-1) 0 0 1 0 2 0 3 6 9 5
George Mason (10-14, 1-1) 2 0 0 0 0 1 1 4 9 2
George Mason (10-13, 1-0) 0 0 4 0 1 0 X 5 3 0
Photo Credit: Mike Scott
2B: Erica Robles
2B: Adriana Erickson
HR: Adriana Erickson
HR: Rachel Kuhlman
HR: Sydnee Wells
Rhode Island scored three runs in the seventh inning to knock off George Mason and earn a doubleheader split in Atlantic 10 action Saturday afternoon.
Game 1: George Mason 5, Rhode Island 2
A four-run rally in the bottom of the third inning was enough to spur George Mason to victory in the first game. The Patriots () had just one hit in the inning, but that hit was a two-out grand slam by Sydnee Wells. Two walks and an error loaded the bases for the big hit.
Game 2: Rhode Island 6, George Mason 4
With the score tied 3-3 heading into the final inning, Rhode Island scored three times in its final at bat to take a 6-3 lead. Erica Robles and Kylie Shivery had back-to-back RBI singles and a groundout by Erika Yeager drove in an insurance run for the Rams. In the bottom of the seventh, George Mason score one run and had the potential tying runs on the corners before sophomore Sarah Gunderson induced an infield pop up to end the game and secure the victory.
Sophomore Caileigh Holland singled three times and scored three runs in the second game.
Sophomore Erica Robles doubled, singled twice and drove in three runs. She now has a five-game hitting streak and has her batting average up to a team-best .353.
Senior Kylie Shivery extended her own hitting streak to seven by picking up hits in both games. She also drove in three runs,
Junior Adriana Toro had two hits and two runs scored on the day.
Senior Rachel Kuhlman had a solo home run in the first game.
Sophomore Erika Yeager had three hits and one RBI on the day, while freshman Abby Fenbert walked and scored two runs.
Sophomore Sarah Gunderson picked up her first victory of the season, going the distance in the second game. She allowed just two earned runs while striking out six batters.
2 – Pitchers Becca Rogers and Sarah Gunderson combined to allow just two earned runs in 14 innings of work Saturday. Rogers and Gunderson each pitched a complete game.
Rhode Island and George Mason close out the series with a single game Sunday at noon.


Non-natural and non-organic farming was introduced only recently during the 20th century in order to increase corporate profits by reducing costs of production with toxic chemical fertilizers, synthetic pesticides, hormones, antibiotics, industrial solvents, and monopolization of the food supply via patents on genetically modified seeds and other proprietary technologies.
Previously no entity could patent seeds since all seeds were originally created by Nature and, thus part of public domain. Now securing a patent is possible by artificially manipulating the DNA of the seed or any life form, thus securing exclusive rights to use that seed or animal commercially with the unacceptable potential of monopolizing the entire global food supply.


Individuals are more and more turning to non-public medical insurance coverage as an alternative choice to state well being care. As noted above, ready periods sometimes will not apply in case you are switching insurance policies or insurers to avoid the loss of cowl brought on by an insurer altering your policy. The concept that customers should have choice within the services they receive has been promoted by authorities and personal medical insurance firms for some years, with nice success. This battle is particularly interesting as it lies on the confluence of two philosophies on health care risk coverage.
Germans are supplied three sorts of social security insurance coverage dealing with the bodily standing of an individual and which are co-financed by employer and worker: medical insurance, accident insurance coverage, and long-time period care insurance coverage. Earlier than taking out the insurance coverage coverage, please read fastidiously the documents beneath which are integral parts of the insurance coverage coverage. The non-public well being care business says business kickbacks to medical doctors and some non-public hospitals are encouraging inflated costs.
Accident, illness, the start of a child – the NHS is there, and the care will usually be not solely good but supplied by exactly the identical advisor you would probably have seen, had you decided to say on personal medical insurance, and possibly in the same hospital too. The Medicare Levy Surcharge is a tax on people who earn over a specific amount and haven't got personal medical insurance hospital cowl.
Your health fund might have you to acquire the Medicare merchandise numbers your physician shall be using to provide you an correct quote. In nations in Asia, the Center East, and North Africa, government initiatives are providing incentives to private payors to help reduce general healthcare spending whereas enhancing access to care. In some instances you could be required to purchase non-public medical insurance as a part of your visa circumstances.
You might have to pay an extra while you declare in your hospital cover.
Medical insurance could be very difficult, and many people are overwhelmed and irritated with the process. Individual personal health insurance plans purchased on the Well being Insurance coverage Market and any new plan from Unity meet the necessities of the Inexpensive Care Act (ACA). If the intent of the private medical insurance rebate is to take strain off public hospitals, then there is no such thing as a policy justification for applying the rebate to junk policies," he said. It strikes me that I would be most comfortable seeing the decisions on what know-how to make use of and how you can apply it made on scientific and public well being grounds slightly than on insurance coverage grounds.
We discover that insurance does induce individuals to choose out of the general public sector in favor of the higher-high quality private sector, thereby reducing total public expenditures on well being care. Collect the required supporting documentation (e.g., EOB, pertinent pages from your advantages booklet, therapy plan, take a look at outcomes, letters of support). The thought of sitting down around a desk with physicians and hospital directors is a very tough idea for individuals in the insurance culture.
One of the upshots of all of this need to explain companies so as to predict how many can be covered is that insurers keep away from soft" providers, these which might be tough to define. Most non-public health insurers have a complete hospital cowl possibility. In case of any change in your health or household standing, you possibly can change the scope of your insurance and add further coverages anytime. "There are individuals leaving non-public health insurance every day; there are people downgrading their stage of canopy; there's too many sufferers who, when they go to make use of their insurance, discover out they do not have the cover they thought they'd," Dr Gannon advised 7.30.
It signifies that an individual who takes out hospital cowl at age forty for the primary time pays 20 per cent extra on their premium than someone who buys the same hospital cowl at age 30. After ten years of steady cover any LHC will cease to use. It is not obligatory to have private medical health insurance cowl. They didn't pay any lifetime health cover loading. The principle profit of making use of the private health sector in the UK will not be necessarily the quality of remedy, but rather avoiding the potentially lengthy ready instances and, depending on the region you reside in , the restricted availability of specialists who settle for NHS sufferers.
Quite a few problematic insurance coverage coverage and rating actions outcome from these employer and employee trade-offs and cost pressures.


text:
Initiative to End Gender-Based Violence in Immigrant and Refugee Communities
OCASI's Initiative to End Gender-Based Violence in Immigrant and Refugee Communities provides resources, education and leadership to the settlement sector and the broader community on gender-based violence prevention and survivor support.
We facilitate resource development, public education campaigns, professional development and training, online courses, community-building, knowledge-sharing, advocacy, and use of the arts in order to prevent and respond to gender-based violence within and against immigrant and refugee communities.
Our work builds on decades of expertise, as OCASI has been engaged in gender-based violence prevention work since 2002. All of our work is grounded in an anti-oppressive, anti-racist and intersectional feminist framework.
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Use of this Website constitutes acceptance of the Terms & Conditions and Privacy Statement.


text:
Why So Many Bars Are Named After Cocks
Londoners once loved an ale whose key ingredient was a rooster.
by Kathleen Crowther January 29, 2019
Famous Londoners once sipped rooster-infused beverages on these premises. Courtesy of Ye Olde Cock Tavern
On February 2, 1663, after a long day of business meetings, the celebrated diarist Samuel Pepys and his colleague and friend John Creed "turned into a house and drank a cup of Cock ale." If the scenario of two coworkers sharing a drink at the end of the day seems familiar, the beverage Pepys and Creed enjoyed does not. The key ingredient in cock ale, which was popular in 17th- and 18th-century England, was a rooster.
Pepys was a great fan of the stuff and frequented several "cock ale houses" in London, including ones on Fleet Street, Bow Street and Threadneedle Street. Cock ale, like other kinds of ale and beer in this period, was also prepared at home by women, and contemporary cookbooks include numerous recipes. Hannah Woolley's The Accomplish'd Lady's Delight (1670) called for placing a boiled cock in eight gallons of ale, along with raisins, dates, nutmeg, mace, and sack (fortified wine).
While people seem to have genuinely liked the taste of cock ale, it was particularly valued for more medicinal qualities. Depending on who made it and where, cock ale was seen as a warm and nourishing elixir that could alleviate tuberculosis, or a "provocative" drink, a kind of early Viagra. The drink was so renowned for these properties that the modern popularity of bar and tavern names such as The Cock Tavern, The Cock and Bottle, and The Famous Cock can be traced back to cock ale.
The perceived healing powers of cock ale are part of a long history of using chicken as medicine. In Ornithology, a massive work published in 1600, the Italian naturalist Ulisse Aldrovandi declared that "there is almost no internal or external disease that is not remedied" by chicken. Many chicken medicines—such as dissolving chicken dung in vinegar or wine for stomach pains, or placing the plucked anus of a live chicken on plague buboes—seem bizarre to modern readers. But one is very familiar: chicken soup. For more than a thousand years, physicians have touted the healing properties of chicken soup. Chicken broth was believed to be easily digestible. It heated and fortified the body.
Roosters rule bar and tavern signage. Jim Linwood/CC BY 2.0
Cock ale that was produced at home by women was lauded for these nourishing and healing qualities. English men and women thought it ideal for invalids, especially those suffering from consumption (tuberculosis), while recipe books described cock ale as a "restorative Drink, which contributes much to the Invigorating of Nature" and "very pleasant."
But when Samuel Pepys and his peers visited cock ale houses, they were generally not trying to cure tuberculosis. In commercial establishments, the invigorating properties of cock ale took on sexual connotations.
In Richard Ames's ribald poem The Bacchanalian Sessions (1693), the god Bacchus stages a disputation between drinks—including various wines, beers, and ales, as well as coffee, tea, and chocolate. Each beverage explains why it's best. Cock Ale's argument is that it is the drink of choice for lovers. It claims to be:
… belov'd by the Sparks of the Town,
And their Mistresses too, who 'fore Wine me prefer,
When they meet at a House very near Temple bar
The "House very near Temple bar" was Samuel Pepys' favorite Cock Ale House on Fleet Street, and according to Ames, it was also a popular site for assignations.
An anonymous satirical pamphlet from 1674, The Women's Petition Against Coffee, also portrays cock ale as an aphrodisiac. In the petition, "several Thousands of Buxome Good-Women" complain that drinking coffee makes men impotent (they "fall down flat before us") and call for a return to "Lusty nappy Beer, Cock-Ale, Cordial Canaries, Restoring Malago's, and Back-recruiting Chocholet."
Another view of the bar shows the golden rooster above the entrance. MikeStnly/CC BY-SA 4.0
The notion that cock ale was sexually stimulating is linked to its healing reputation, since both relied on cock ale as a "Restorer of decay'd Nature." But it also comes from cocks' reputation as hyper-masculine birds. In his Ornithology of 1678, Francis Willughby describes the cock as "a most salacious bird" prone to "the immoderate use of Venery," and also notes that cocks are "very couragious and high spirited birds, that will rather die than yield." This latter quality made cock fighting a popular sport, and taverns were common venues. Cocks were renowned for their sexual and fighting prowess; the qualities that made drinking their flesh an aphrodisiac also made them great sporting animals.
The Cock Ale House on Fleet Street where Samuel Pepys spent so many happy hours still exists. The current pub, Ye Olde Cock Tavern, is across the street from the original building, and a golden cock hangs over the door. Cock ale is no longer on the menu. Neither is it served at The Cock Tavern, The Cock and Bottle, or The Famous Cock. But the large number of pubs with cock in their names and roosters on their signs demonstrate that this long-forgotten beverage has left its mark on London.
A New, Up-Close Look at an Old, Near-Earth Asteroid
The spacecraft OSIRIS-REx gives us a startlingly clear view of space rock that probably won't hit us.
aphrodisiacschickensbarsalcoholfood
To Evade Pre-Prohibition Drinking Laws, New Yorkers Created the World's Worst Sandwich
It was everywhere at the turn of the 20th century. It was also inedible.
Darrell Hartman June 3, 2019
Remembering the Clandestine 'Aunty Bars' of Prohibition-Era Bombay
Grabbing a drink once meant moonshine in a neighbor's living room.
Abbey Perreault September 3, 2018
Do You Order the Second-Cheapest Wine?
Help us investigate a popular ordering strategy.
Alex Mayyasi April 16, 2018
The 'Six O'Clock Swill' Was an Hour of Drunken Anarchy
How Australia and New Zealand's restrictive alcohol laws fostered a culture of binge drinking.
Natasha Frost April 4, 2018
Meet Piano Pat and the Sip 'n Dip Mermaids
Jellied Eels
No traditional East Ender meal is complete without pie, mashed potatoes, and gelatinous river creatures.
Amaro di Sant'Antimo
At an abbey in the Tuscan countryside, monks specialize in a curative, flower-based liqueur.
Hot Springs Beer at Superior Bathhouse Brewery
This Arkansas town is known for its gangster history, its healing waters, and now its brews.
George Washington's Whiskey
Taste the white whiskey that the United States' first president once distilled and enjoyed at Mount Vernon.
The Perils and Pleasures of Bartending in Antarctica
At the South Pole, the freezer is just a hole in the wall to the ice outside.