text:
\section{Introduction}

Why should we use lattice Monte Carlo methods to describe a real system when
there are so many efficient and accurate methods to treat the full problem?
There are at least two good reasons. The first one takes a
pragmatic point of view: For complicated systems a full calculation simply
cannot be done on present-day computers. The second reason rests on the belief
that the physics underlying the properties of real materials is simple and can
be captured in model systems. If we succeed in this there is the additional
benefit of having identified the important general features of the material.

For the doped Fullerides we encounter just such a situation. Even for a
single C$_{60}$ molecule a full QMC calculation is still a challenge, and
simulations of Fullerides, i.e.\ solids made of C$_{60}$ molecules, are
simply out of question. For many properties it is, however, sufficient to
focus on the valence band only, removing all other degrees of freedom from
the Hamiltonian. Important features of the doped Fullerides that
have to be reflected in such a model are the degeneracy of the molecular
orbital that gives rise to the valence band, the filling of the valence
band, and the lattice structure of the solid. All these can be incorporated in
a Hubbard-like Hamiltonian, which can be treated efficiently using lattice
QMC methods.

In the following we will first show how to set up a model Hamiltonian for
the doped Fullerides. Then we discuss Monte Carlo methods for such lattice
Hamiltonians, especially the optimization of Gutzwiller functions both in
variational and fixed-node diffusion Monte Carlo.
Finally we use QMC to investigate the Mott transition in the
doped Fullerides. The interest in these questions comes from the following
situation: Density functional calculations predict that the doped Fullerides
are metals. On the other hand, one finds that the Coulomb repulsion between
electrons on the same C$_{60}$ molecule is very strong. This suggests that
correlations should be dominating, making all doped Fullerides Mott insulators.
Reality falls in between these two extremes: some doped Fullerides are metals
(and even superconductors), while others are insulators. From our QMC
calculations we find that due to the degeneracy of the valence band the
integer-doped Fullerides are close to a Mott transition, and not far into the
Mott insulator regime, as simple theories would suggest. Whether a
given compound is on the metallic or the insulating side of the transition
depends then on the crystal structure (bipartite vs.\ frustrated) and
the filling of the band.

\section{Model Hamiltonian}

\begin{figwindow}[0,r,{\epsfxsize=4cm \epsffile{k3c60_bw.eps}},%
                  {Schematic band structure of A$_3$C$_{60}$.}]
Solid \keyword{C$_{60}$} is characterized by a very weak inter-molecular
interaction. Therefore the discrete molecular levels merely broaden into narrow,
well separated bands (see Fig.~1) \cite{ldabands}. The valence band originates
from the lowest unoccupied molecular orbital, which is a 3-fold degenerate
\keyword{$t_{1u}$ orbital}. Doping the solid with alkali metals does not affect
the band structure close to the Fermi level very much. Only the filling of the
$t_{1u}$ band changes, since each alkali atom donates its valence electron.
To simplify the description of the doped Fullerides we want to focus on the
electrons in the $t_{1u}$ band only. To get rid of the other degrees of freedom
we use the \keyword{L\"owdin downfolding} technique \cite{lowdin}. The basic
idea is to partition the Hilbert space into a subspace that contains the
degrees of freedom that we are interested in (in our case the
`$t_{1u}$-subspace') and the rest of the Hilbert space:
${\cal H}={\cal H}_0 \oplus {\cal H}_1$.
We can then write the Hamiltonian of the system as
\end{figwindow}
\begin{equation}
  H=\left(\begin{array}{cc} H_{00}& 0    \\ 0    &H_{11}\end{array}\right)
   +\left(\begin{array}{cc}  0    &V_{01}\\V_{10}& 0    \end{array}\right) ,
\end{equation}
where $H_{ii}$ is the projection of the Hamiltonian onto subspace ${\cal H}_i$,
while $V_{ij}=H_{ij}$ contain the hybridization matrix elements between the two
subspaces. Writing Green's function $G=(E-H)^{-1}$ in the same way, we
can calculate the projection of $G$ onto ${\cal H}_0$ \cite{invpart}:
\begin{equation}
  G_{00}=\Big(E-\underbrace{[H_{00}+ V_{01}\,(E-H_{11})^{-1}V_{10}]}_{H_{\rm eff}(E)}\Big)^{-1} .
\end{equation}
We see that the physics of the full system is described by an effective
Hamiltonian $H_{\rm eff}(E)$ that operates on the subspace ${\cal H}_0$ only.
This drastic simplification comes, however, at a price: the effective
Hamiltonian is energy dependent. In practice one approximates it with an
energy-independent Hamiltonian $H_{\rm eff}(E_0)$. This works well if we
are only interested in energies close to $E_0$.
In solid C$_{60}$ we have the fortunate situation that the bands
retain the character of the molecular orbitals, since the hybridization
matrix elements are small compared to the energy separations of the orbitals.
In fact we can neglect the other bands
altogether and get the hopping matrix elements $t_{in,\,jn'}$ between the
$t_{1u}$ orbitals $n$ and $n'$ on molecules $i$ and $j$ directly from a
tight-binding parameterization \cite{TBparam,A4C60}. Figure 2 shows the
comparison of the {\it ab initio} $t_{1u}$ band structure with the band
structure obtained from the \keyword{tight-binding} Hamiltonian with only
$t_{1u}$ orbitals.
\begin{figure}
 \centerline{\epsfxsize=9.5cm \epsffile{c60band.eps}}
 \caption[]{Band structure ($t_{1u}$ band) of solid C$_{60}$ (fcc)
            (a) as calculated {\it ab initio} using the
                local density approximation \cite{ldabands} and
            (b) using a tight-binding Hamiltonian with only $t_{1u}$
                orbitals \cite{TBparam}.}
\end{figure}

To get a realistic description of the electrons in the $t_{1u}$ band we have
to include the correlation effects which come from the Coulomb repulsion
of electrons in $t_{1u}$ orbitals on the same molecule. The resulting
Hamiltonian which describes the interplay of the hopping of electrons and their
Coulomb repulsion has the form
\begin{equation}\label{Hamil}
H=\sum_{\langle ij\rangle} \sum_{nn'\sigma} t_{in,jn'}\;
              c^\dagger_{in\sigma} c^{\phantom{\dagger}}_{jn'\sigma}
 +\;U\sum_i\hspace{-0.5ex} \sum_{(n\sigma)<(n'\sigma')}\hspace{-1ex}
       n_{i n\sigma} n_{i n'\sigma'} .
\end{equation}
The \keyword{on-site Coulomb interaction} $U$ can be calculated within density
functional theory \cite{calcU}. It is given by the increase in the energy of
the $t_{1u}$ level per electron that is added to one molecule of the system.
It is important to avoid double counting in the calculation of $U$. While the
relaxation of the occupied orbitals and the polarization of neighboring
molecules has to be included in the calculation, excitations within the
$t_{1u}$ band must be excluded, since they are contained explicitly in the
Hamiltonian (\ref{Hamil}).
The results are consistent with experimental estimates \cite{expU,lof}:
$U\approx 1.2-1.4\;eV$. For comparison, the width of the $t_{1u}$ band
is in the range $W\approx 0.5-0.85\;eV$.

\section{Quantum Monte Carlo}

We now turn to the question of how to calculate the ground state of a
lattice Hamiltonian like (\ref{Hamil}). To simplify the notation most
examples in the present section are for the simple \keyword{Hubbard model}
(only one orbital per site, next neighbor hopping matrix elements $t_{ij}=-t$)
on a 2 dimensional square lattice:
\begin{equation}\label{Hubbard}
  H=-t\;\sum c^\dagger_i c_j + U\sum n_{i\uparrow} n_{i\downarrow} .
\end{equation}
The band width for this model is $W=8\,t$.

We first introduce the Gutzwiller Ansatz as a suitable trial function $\Psi_T$
for the above Hamiltonian. Expectation values for the Gutzwiller function
can be calculated using variational Monte Carlo (VMC). Then we describe the
fixed-node diffusion Monte Carlo (FN-DMC) method that allows us to
calculate more accurate variational estimates of the ground state energy (see
the lecture notes by G.\ Bachelet for a more complete discussion of FN-DMC).
The main emphasis of our discussion will be on the optimization of the trial
function both in variational and fixed-node diffusion Monte Carlo.

\subsection{Variational Monte Carlo}

A good trial function for the Hubbard model has to balance the opposing
tendencies of the hopping term and the interaction term:
Without interaction (i.e.\ for $U=0$) the ground state of the Hamiltonian
(\ref{Hubbard}) is the Slater determinant $\Phi$ that maximizes the
kinetic energy. Without hopping ($t=0$) the interaction is minimized.
Since only doubly occupied sites, i.e.\ sites with $n_{i\uparrow}=1$
and $n_{i\downarrow}=1$, contribute to the Coulomb energy,
the electrons are distributed as uniformly as possible over the lattice
to minimize the number of double occupancies. A good compromise between
these two extremes is to start from the non-interacting wavefunction $\Phi$
but reduce the weight of configurations $R$ with large double occupancies
$D(R)$. This leads (up to normalization) to the \keyword{Gutzwiller
wavefunction} \cite{GWF}:
\begin{equation}\label{GWF}
 \Psi_T(R) =  g^{D(R)}\;\Phi(R) ,
\end{equation}
with $g\in(0,1]$ the Gutzwiller parameter. Figure 3 shows how decreasing the
Gutzwiller factor suppresses the configurations with a large number of double
occupancies.
\begin{figure}
 \centerline{\epsfxsize=4.5cm\epsffile{gwgtp.1.00.eps}\hspace{-0.5cm}
             \epsfxsize=4.5cm\epsffile{gwgtp.0.50.eps}\hspace{-0.5cm}
             \epsfxsize=4.5cm\epsffile{gwgtp.0.30.eps}}
 \caption{Weight of configurations with given number $D$ of double occupancies
          for Gutzwiller wavefunctions $\Psi_T(R)=g^{D(R)}\,\Phi(R)$. Reducing
          the Gutzwiller factor $g$ suppresses configurations with high
          Coulomb energy $E_{\rm Coul}(R)=U\,D(R)$ at the expense of
          increasing the kinetic energy.
          The results shown here are for a Hubbard model with
          $16\times16$ sites and $101+101$ electrons.}
\end{figure}

To calculate the energy expectation value for the Gutzwiller wavefunction
we have to perform a sum over all configurations $R$:
\begin{equation}\label{Evar}
 E_T = {\langle\Psi_T|H|\Psi_T\rangle \over \langle\Psi_T|\Psi_T\rangle}
     = {\sum_R E_{\rm loc}(R)\;\Psi_T^2(R) \over \sum_R \Psi_T^2(R)} ,
\end{equation}
where we have introduced the local energy for a configuration $R$
\begin{equation}\label{Eloc}
 E_{\rm loc}(R)
 = \sum_{R'} {\langle\Psi_T|R'\rangle\,\langle R'|H|R\rangle
             \over \langle\Psi_T|R\rangle}
 = \sum_{R'}\!'\;t\;{\Psi_T(R')\over\Psi_T(R)} + U\,D(R) .
\end{equation}
Since the number of configurations $R$ grows exponentially with system-size,
the summation in (\ref{Evar}) can be performed only for very small systems.
For larger problems we use \keyword{variational Monte Carlo} \cite{VMC}.
The idea is to perform a random walk in the space of
configurations, with transition probabilities $p(R\to R')$ chosen such
that the configurations $R_{VMC}$ in the random walk have the probability
distribution function $\Psi_T^2(R)$. Then
\begin{equation}\label{Evmc}
 E_{\rm VMC} =
  {\sum_{R_{\rm VMC}} E_{\rm loc}(R_{\rm VMC}) \over \sum_{R_{\rm VMC}} 1}
 \approx
  {\sum_R E_{\rm loc}(R)\;\Psi_T^2(R) \over \sum_R \Psi_T^2(R)}
 = E_T .
\end{equation}
The transition probabilities can be determined from detailed balance
\begin{equation}\label{detailedbalance}
  \Psi_T^2(R)\,p(R\to R') = \Psi_T^2(R')\,p(R'\to R)
\end{equation}
which gives $p(R\to R')={1/N}\;\min[1,\Psi_T^2(R')/\Psi_T^2(R)]$, with
$N$ being the maximum number of possible transitions.
It is sufficient to consider only transitions between configurations that
are connected by the Hamiltonian, i.e.\ transitions in which one electron
hops to a neighboring site. The standard prescription is then to propose a
transition $R\to R'$ with probability $1/N$ and accept it with probability
$\min[1,\Psi_T^2(R')/\Psi_T^2(R)]$. This works well for $U$ not too large.
For strongly correlated systems, however, the random walk will stay for long
times in configurations with a small number of double occupancies $D(R)$, since
most of the proposed moves will increase $D$ and hence be rejected with
probability $\approx 1-g^{D(R')-D(R)}$.

Fortunately there is a way to integrate-out the time the walk stays in a
given configuration. To see how, we first observe that for the local energy
(\ref{Eloc}) the ratio of the wavefunctions for all transitions induced by
the Hamiltonian have to be calculated. This in turn means that we also
know all transition probabilities $p(R\to R')$. We can therefore eliminate
any rejection (i.~e.\ accept with probability one) by proposing moves with
probabilities
\begin{equation}
  \tilde{p}(R\to R') = {p(R\to R')\over\sum_{R'} p(R\to R')}
                     = {p(R\to R')\over 1-p_{\rm stay}(R)} .
\end{equation}
Checking detailed balance (\ref{detailedbalance}) we find that now we are
sampling configurations $\tilde{R}_{VMC}$ from the probability distribution
function $\Psi_T^2(R)\,(1-p_{\rm stay}(R))$. To compensate for this we assign
a weight $w(R)=1/(1-p_{\rm stay}(R))$ to each configuration $R$. The energy
expectation value is then given by
\begin{equation}
 E_T \approx
 {\sum_{\tilde{R}_{VMC}} w(\tilde{R}_{VMC})\,E_{\rm loc}(\tilde{R}_{VMC}) \over
  \sum_{\tilde{R}_{VMC}} w(\tilde{R}_{VMC})} .
\end{equation}
The above method is quite efficient since it ensures that in every Monte Carlo
step a new configuration is created. Instead of staying in a configuration
where $\Psi_T$ is large, this configuration is weighted with the expectation
value of the number of steps the simple Metropolis algorithm would stay there.
This is particularly convenient for simulations of systems with strong
correlations: Instead of having to do longer and longer runs as $U$ is
increased, the above method produces, for a fixed number of Monte Carlo
steps, results with comparable error estimates.

\subsubsection*{Correlated sampling}

We now turn to the problem of optimizing the trial function $\Psi_T$.
A criterion for a good trial function is e.g.\ a low variational
energy. To find the wavefunction that minimizes the variational energy
we could do independent VMC calculations for a set of different trial
functions. It is, however, difficult to compare the energies from these
calculations since each VMC result comes with its own statistical
errors. This problem can be avoided with \keyword{correlated sampling}
\cite{corrsmpl}.
The idea is to use the same random walk for calculating the expectation value
of all the different trial functions. This reduces the {\em relative} errors
and hence makes it easier to find the minimum.

Let us assume we have generated a random walk $R_{VMC}$ using $\Psi_T$ as
a trial function. Using the same random walk, we can then estimate the energy
expectation value (\ref{Evmc}) for a different trial function $\tilde{\Psi}_T$,
by introducing the reweighting factors $\tilde{\Psi}_T^2(R)/\Psi_T^2(R)$:
\begin{equation}\label{corrsmpl}
 \tilde{E}_T \approx
  {\sum_{R_{VMC}} \tilde{E}_{\rm loc}(R)\,\tilde{\Psi}_T^2(R)/\Psi_T^2(R) \over
   \sum_{R_{VMC}}                         \tilde{\Psi}_T^2(R)/\Psi_T^2(R)      }
.
\end{equation}
(Since the random walk $R_{VMC}$ has only a finite number of configurations,
this will only work well as long as the reweighting factors do not deviate
too much from unity. Otherwise a few configurations with large reweighting
factors will dominate. See Fig.~4.)
\begin{figure}
\parbox[b]{6cm}{\epsfxsize=6cm \epsffile{corrvmc.88.epsi}}
\hspace{\fill}
\begin{minipage}[b]{6.0cm}
 \caption{Correlated sampling for the Gutz\-willer parameter $g$. The
          calculations are for a Hubbard model with $8\times8$ sites,
          $28+28$ electrons, and $U=4\,t$.
          The full curve shows the result starting from a calculation
          with $g=1$. The predicted minimum $g_{\rm min}$ is indicated
          by the dotted line. A dashed line gives the correlated sampling
          curve obtained from a calculation using $g_{\rm min}$ in the trial
          function. Both find the same minimum. $E(g)$ becomes unreliable for
          very small $g$ due to reweighting factors much larger than unity.}
 \end{minipage}
\end{figure}
We notice that (also in $\tilde{E}_{\rm loc}$) the new trial function
$\tilde{\Psi}_T$ appears only in ratios with the old trial function.
For Gutzwiller functions (\ref{GWF}) that differ only in the Gutzwiller factor
this means that the Slater determinants cancel, leaving only powers
$(\tilde{g}/g)^{D(R)}$. Since $D(R)$ is {\em integer} we can then rearrange
the sums in (\ref{corrsmpl}) into polynomials in $\tilde{g}/g$. To find the
optimal Gutzwiller parameter we then pick a reasonable $g$, perform a VMC run
for $\Psi_T(g)$ during which we also estimate the coefficients for these
polynomials. We can then calculate $E(\tilde{g})$ by simply evaluating the
ratio of the polynomials. Since there are typically only of the order of some
ten non-vanishing coefficients (cf.\ the distribution of weights in Fig.~3),
this method is very efficient. Figure 4 shows how the method performs in
practice. The idea of rewriting the sum over configurations into a polynomial
can be easily generalized to trial functions with more correlation factors of
the type $r^{c(R)}$, as long as the correlation function $c(R)$ is
integer-valued on the space of configurations.

\subsubsection*{Character of the Slater determinant}

So far we have always constructed the Gutzwiller wavefunction from the
ground state $\Phi$ of the non-interacting Hamiltonian ($U=0$). Alternatively
we could use the Slater determinant $\Phi(U)$ from solving the interacting
problem in the Hartree-Fock approximation. We can even interpolate between
these two extremes by doing a Hartree-Fock calculation with a fictitious
Hubbard interaction $U_0$ to obtain the Slater determinant $\Phi(U_0)$. This
introduces an additional variational parameter in the Gutzwiller wavefunction.
Increasing $U_0$ will change the character of the trial function from
paramagnetic to antiferromagnetic. This transition is also
reflected in the variational energies, as is shown in Figure 5. Clearly, for
small $U$ the paramagnetic state is favorable, while for large $U$ the
antiferromagnetic state gives a lower variational energy. We notice that for
all values of $U$ the optimal $U_0$ is much smaller than $U$.
\begin{figure}
\begin{minipage}[b]{6.1cm}
 \caption{Dependence of variational (VMC) and fixed-node diffusion
          Monte Carlo (FN-DMC) on the trial function. $U_0$ is the Hubbard
          interaction that was used for the Slater determinant in the
          Gutzwiller wavefunction $\Psi_T(R)=g^{D(R)}\;\Phi(U_0)$.
          The Gutzwiller parameter has always been optimized.
          The results shown here are the energies (relative to the atomic
          limit) for a Hamiltonian that describes K$_3$C$_{60}$ (32 sites),
          with $U$ being varied from $1.25$ (lowest curve) to $2.00\,eV$
          (highest curve).}
 \vspace*{1ex}
\end{minipage}
\hspace{\fill}
\parbox[b]{6cm}{\epsfxsize=6cm\epsffile{corrU0.epsi}}
\end{figure}

\subsection{Fixed-node diffusion Monte Carlo}

\keyword{Diffusion Monte Carlo} \cite{GFMC} allows us, in principle, to sample
the true ground state of a Hamiltonian. The basic idea is to use a projection
operator that has the lowest eigenstate as a fixed point. For a lattice problem
where the spectrum is bounded $E_n\in[E_0,E_{\rm max}]$, the projection is
given by
\begin{equation}\label{proj}
  |\Psi^{(n+1)}\rangle = [1-\tau(H-E_0)]\;|\Psi^{(n)}\rangle
    \;;\quad |\Psi^{(0)}\rangle=|\Psi_T\rangle .
\end{equation}
If $\tau<2/(E_{\rm max}-E_0)$ and $|\Psi_T\rangle$ has a non-vanishing overlap
with the ground state, the above iteration converges to $|\Psi_0\rangle$. There
is no time-step error involved.
Because of the prohibitively large dimension of the many-body Hilbert space,
the matrix-vector product in (\ref{proj}) cannot be done exactly. Instead, we
rewrite the equation in configuration space
\begin{equation}\label{iter}
  \sum |R'\rangle\langle R'|\Psi^{(n+1)}\rangle
        = \sum_{R,R'} |R'\rangle
          \underbrace{\langle R'|1-\tau(H-E_0)|R\rangle}_{=:F(R',R)}
          \langle R|\Psi^{(n)}\rangle
\end{equation}
and perform the propagation in a stochastic sense: $\Psi^{(n)}$ is
represented by an ensemble of configurations $R$ with weights $w(R)$.
The transition matrix element $F(R',R)$ is rewritten as a transition
probability $p(R\to R')$ times a normalization factor $m(R',R)$. The iteration
(\ref{iter}) is then stochastically performed as follows: For each $R$ we pick
a new configuration $R'$ with probability $p(R\to R')$ and multiply its weight
by $m(R',R)$. Then the new ensemble of configurations $R'$ with their
respective weights represents $\Psi^{(n+1)}$. \keyword{Importance sampling}
decisively improves the efficiency of this process by replacing $F(R',R)$ with
$G(R',R)=\langle\Psi_T|R'\rangle\,F(R',R)/\langle R|\Psi_T\rangle$, so
that transitions from configurations where the trial function is small
to configurations with large trial function are enhanced:
\begin{equation}
  \sum |R'\rangle\langle\Psi_T| R'\rangle\langle R'|\Psi^{(n+1)}\rangle
   = \sum_{R,R'} |R'\rangle\,G(R',R)\,
                 \langle\Psi_T|R\rangle\,\langle R|\Psi^{(n)}\rangle .
\end{equation}
Now the ensemble of configurations represents the product $\Psi_T\,\Psi^{(n)}$.
After a large number $n$ of iterations the ground state energy is then
given by the
\keyword{mixed estimator}
\begin{equation}\label{mixedest}
  E_0 = {\langle\Psi_T|H|\Psi^{(n)}\rangle \over \langle\Psi_T\Psi^{(n)}\rangle}
      \approx {\sum_R E_{\rm loc}(R)\;w(R) \over \sum_R w(R)} .
\end{equation}
As long as the evolution operator has only non-negative matrix elements
$G(R',R)$, all weights $w(R)$ will be positive. If, however, $G$ has
negative matrix elements there will be both configurations with positive and
negative weight. Their contributions to the estimator (\ref{mixedest})
tend to cancel so that eventually the statistical error dominates, rendering
the simulation useless. This is the infamous \keyword{sign problem}.
A straightforward way to get rid of the sign problem is to remove the
offending matrix elements from the Hamiltonian, thus defining a new Hamiltonian
$H_{\rm eff}$ by
\begin{equation}
   \langle R'|H_{\rm eff}| R\rangle = \left\{
     \begin{array}{cc}
                 0           & \mbox{ if $G(R',R)<0$} \\
      \langle R'|H| R\rangle & \mbox{ else}
     \end{array}\right.
\end{equation}
For each off-diagonal element $\langle R'|H| R\rangle$ that has been removed,
a term is added to the diagonal:
\begin{equation}
  \langle R|H_{\rm eff}|R\rangle
       = \langle R|H|R\rangle
       + \sum_{R'} \Psi_T(R')\langle R'|H|R\rangle/\Psi_T(R) .
\end{equation}
This is the \keyword{fixed-node approximation} for lattice Hamiltonians
introduced in Ref.~\cite{FNDMC}. $H_{\rm eff}$ is by construction free of the
sign problem and variational, i.e.\ $E_0^{\rm eff}\ge E_0$. The equality holds
if $\Psi_T(R')/\Psi_T(R)=\Psi_0(R')/\Psi_0(R)$ for all $R$, $R'$ with
$G(R',R)<0$.

Fixed-node diffusion Monte Carlo for a lattice Hamiltonian thus means that
we choose a trial function from which we construct an effective Hamiltonian
and determine its ground state by diffusion Monte Carlo.
Because of the variational property, we want to pick the $\Psi_T$ such that
$E_0^{\rm eff}$ is minimized, i.e. we want to optimize the trial function, or,
equivalently, the effective Hamiltonian. Also here we can use the concept of
correlated sampling. For optimizing the Gutzwiller parameter $g$ we can
even exploit the idea of rewriting the correlated sampling sums into
polynomials in $\tilde{g}/g$, that we already have introduced in VMC.
There is, however, a problem arising from the fact that the weight
of a given configuration $R^{(n)}$ in iteration $n$ is given by the product
$w(R^{(n)})=\prod_{i=1}^n m(R^{(i)},R^{(i-1)})$. Each individual normalization
factor $m(R',R)$ can be written as a finite polynomial, but the order of the
polynomial for $w(R^{(n)})$ increases steadily with the number of iterations.
It is therefore not practical to try to calculate the ever increasing number
of coefficients for the correlated sampling function $E^{(n)}(\tilde{g})$.
But since we still can easily calculate the coefficients for the $m(R',R)$,
we may use them to evaluate $E^{(n)}(\tilde{g})$ in each iteration on a set
of predefined values $\tilde{g}_i$ of the Gutzwiller parameter.
Figure 6 shows an example. It is interesting to note that the Gutzwiller
factor that minimizes $E_{VMC}$ is usually not the optimum Gutzwiller factor
for fixed-node DMC.
\begin{figure}
 \begin{minipage}{5cm}
 \caption{Correlated sampling of the Gutzwiller parameter $g$ in the trial
          function to optimize the effective Hamiltonian in fixed-node
          diffusion Monte Carlo. The results shown are for a Hubbard model
          with $4\times4$ sites, $7+7$ electrons, and $U=4\,t$. The error bars
          are the FN-DMC energies for different values of $g$, the lines
          through the error bars are the corresponding correlated sampling
          curves.}
 \vspace*{3ex}
 \end{minipage}
 \hspace{\fill}
 \parbox{6.5cm}{\epsfxsize=6.5cm\epsffile{dmcs.epsi}}
\end{figure}

As in VMC we can also vary the trial function by changing the character of
the Slater determiant $\Phi(U_0)$. We again find that the change from a
paramagnetic to an antiferromagnetic trial function is reflected in the
fixed-node energies (see Fig.~5), the paramagnetic state being favored
for small $U$, while the antiferromagnetic state gives the lower energy
for large $U$.

We want to use Monte Carlo methods to detect a Mott transition in the doped
Fullerides. For this we anticipate that we need an accuracy of better than
$0.025\,eV$.
To get a feeling for the accuracy of variational and fixed-node diffusion
Monte Carlo, using Gutzwiller trial functions, we compare the results of
the QMC calculations with exact results. Since exact diagonalizations can
only be done for small systems we consider a small cluster of 4 molecules.
The results for different values of the Hubbard interaction $U$ are shown
in Table 1. We find that the FN-DMC error is about an order of magnitude
smaller than the error in VMC. The typical FN-DMC error for our lattice
model is typically some $meV$, which should be sufficient for the
application at hand.
\begin{table}
 {\footnotesize {\it Table 1.}
   Total energy (in $eV$) for a cluster of four C$_{60}$ molecules with $6+6$
   electrons in the $t_{1u}$ band (hopping parameters for K$_3$C$_{60}$).
   The results of variational and diffusion Monte Carlo are compared to the
   exact energy.}

 \vspace{1ex}
 \begin{center}
 \begin{tabular}{d{2}d{4}d{8}@{\hspace{1ex}}d{3}%
                         d{8}@{\hspace{1ex}}d{3}}
  \hline\hline
  \multicolumn{1}{c}{$U$} &
  \multicolumn{1}{c}{$E_{\rm exact}$} &
  \multicolumn{1}{c}{$E_{FN-DMC}$} &
  \multicolumn{1}{c}{$\Delta E$} &
  \multicolumn{1}{c}{$E_{VMC}$} &
  \multicolumn{1}{c}{$\Delta E$} \\
  \hline
  0.25 &  0.8457 &  0.8458(1)& 0.000 &  0.8490(2) & 0.003 \\
  0.50 &  4.1999 &  4.2004(1)& 0.001 &  4.2075(3) & 0.008 \\
  0.75 &  7.4746 &  7.4756(2)& 0.001 &  7.4873(4) & 0.013 \\
  1.00 & 10.6994 & 10.7004(2)& 0.001 & 10.7179(5) & 0.019 \\
  1.25 & 13.8860 & 13.8875(3)& 0.002 & 13.9127(6) & 0.027 \\
  1.50 & 17.0408 & 17.0427(4)& 0.002 & 17.0728(7) & 0.032 \\
  1.75 & 20.1684 & 20.1711(5)& 0.003 & 20.2061(4) & 0.038 \\
  2.00 & 23.2732 & 23.2757(10)&0.003 & 23.3125(6) & 0.039 \\
  \hline\hline
 \end{tabular}
 \end{center}
\end{table}

\section{Mott transition in doped Fullerides}

We now apply the quantum Monte Carlo methods described above to the
Hamiltonian (\ref{Hamil}). Our aim is to understand the
\keyword{Mott transition} in the integer-doped Fullerides A$_n$C$_{60}$.
Here A stands for an alkali metal like K, Rb, or Cs.
The criterion for the metal-insulator transition is the opening of the gap
\begin{equation}\label{gap}
  E_g=E(N+1)-2\,E(N)+E(N-1) .
\end{equation}

Density functional calculations predict that the doped Fullerides
A$_n$C$_{60}$ with $n=1\ldots5$ are metals \cite{ldabands}. Only
A$_6$C$_{60}$ is an insulator with a completely filled $t_{1u}$
band. On the other hand, the strong Coulomb repulsion between
two electrons on the same C$_{60}$ molecule, which is much larger
than the width of the $t_{1u}$ band, suggests that all integer-doped
Fullerides should be Mott insulators. It has therefore been
suggested that experimental samples of, say, the superconductor
K$_3$C$_{60}$ are metallic only because they are non-stoichiometric,
i.e.\ that they actually are K$_{3-\delta}$C$_{60}$ \cite{lof}.

\subsubsection*{K$_3$C$_{60}$}

\begin{figwindow}[7,r,%
   {\parbox{3.3cm}{\epsfxsize=3.3cm\epsffile{hop0.eps}
                   \epsfxsize=3.3cm\epsffile{hopp.eps}}},%
   {Degeneracy argument.}]
In a first step we investigate what consequences the degeneracy of the
$t_{1u}$-band has for the Mott transition in K$_3$C$_{60}$. The analysis
is motivated by the following simple argument \cite{Mott,degen}. In the limit
of very large $U$ we can estimate the energies needed to calculate the
gap (\ref{gap}). For half filling, all molecules will have 3 electrons in the
$t_{1u}$ orbital (Fig.~7, top). Hopping is strongly suppressed since it would
increase the energy by $U$. Therefore, to leading order in $t^2/U$, there will
be no kinetic contribution to the total energy $E(N)$. In contrast, the systems
with $N\pm1$ electrons have an extra electron/hole that can hop without
additional cost in Coulomb energy. To estimate the kinetic energy we calculate
the matrix element for the hopping of the extra charge against an
antiferromagnetic background. Denoting the initial state with extra charge on
molecule $i$ by $|1\rangle$, we find that the second moment
$\langle1|H^2|1\rangle$ is given by the number of different possibilities
for a next-neighbor hop times the single electron hopping matrix element $t$
squared. By inserting $\sum_j |j\rangle\langle j|$, where
$|j\rangle$ denotes the state with the extra charge hopped from site $i$ to
site $j$, we find $\langle1|H|j\rangle = \sqrt{3}\,t$, since, with an
antiferromagnetic background and degeneracy 3, there are 3 different ways
an extra charge can hop to a neighboring molecule (Fig.~7, bottom). Thus,
due to the 3-fold degeneracy, {\sl the hopping matrix element is enhanced by a
factor $\sqrt{3}$ compared to the single electron hopping matrix element $t$.}
For a single electron system the kinetic energy is of the order of half
the band width $W/2$. The enhancement of the hopping matrix element in the
many-body case suggests then that the kinetic energy for the extra charge
is correspondingly enhanced. Inserting the energies into (\ref{gap})
we find that for the 3-fold degenerate system our simple argument predicts
a gap
\end{figwindow}
\begin{equation}\label{Egap}
  E_g=U-\sqrt{3}\,W ,
\end{equation}
instead of $E_g=U-W$ in the non-degenerate case.
Extrapolating to intermediate $U,\,$ it appears that the degeneracy
shifts the Mott transition towards larger $U$.

The above argument is, of course, not rigorous. First, it is not clear
whether the result for $E_g$ that was obtained in the limit of large $U$
can be extrapolated to intermediate $U,\,$ where the Mott transition
actually takes place. Also the analogy of the hopping in the many-body case
with the hopping of a single electron is not rigorous, since the hopping of an
extra charge against an antiferromagnetic background creates a string of
flipped spins \cite{Nagaoka}. Nevertheless the argument suggests that orbital
degeneracy might play an important role for the Mott transition.

To test this proposition, we have performed quantum Monte Carlo calculations
for the model Hamiltonian (\ref{Hamil}) with hopping matrix elements
appropriate for K$_3$C$_{60}$ \cite{Mott}. The Coulomb interaction $U$ has been
varied from $U=0\ldots 1.75\,eV$ to study the opening of the gap. Since the
Monte Carlo calculations are for finite systems, we have to extrapolate to
infinite system size.
To improve the extrapolation we correct for finite-size effects: First,
there could be a gap $E_g(U=0)$ already in the spectrum of the non-interacting
system. Further, even for a metallic system of $M$ molecules there will be a
finite-size contribution of $U/M$ to the gap. It comes from the electrostatic
energy of the extra charge, uniformly distributed over all sites. Both
corrections vanish in the limit $M\to\infty$, as they should. The finite-size
corrected gap $\tilde{E}_g=E_g - U/M - E_g(U=0)$ for systems with
$M=$ 4, 8, 16, 32, and 64 molecules is shown in Figure 8. We find that the
gap opens for $U$ between $1.50\,eV$ and $1.75\,eV.\,$ Since for the real
system $U=1.2\ldots1.4\,eV,\,$ K$_3$C$_{60}$ is thus close to a Mott
transition, but still on the metallic side -- even though $U$ is considerably
larger than the band width $W$. This is in contrast to simpler theories that
neglect orbital degeneracy.
\begin{figure}
 \parbox[b]{6cm}{\epsfxsize=6cm\epsffile{Egap3.eps}}
 \hspace{\fill}
 \begin{minipage}[b]{5.5cm}
 \caption{Finite-size corrected gap $\tilde{E}_g=E_g-U/M-E_g(U=0)$ for
          increasing Coulomb interaction $U$ as a function of $1/M$,
          where $M$ is the number of molecules. The calculations are for
          a Hubbard model with hopping matrix elements appropriate for
          K$_3$C$_{60}$. The band width varies between $W=0.58\,eV$ for
          $M=4$ and $W=0.63\,eV$ in the infinite-size limit.}
 \vspace*{4ex}
 \end{minipage}
\end{figure}

\subsubsection*{Doping dependence}

\vspace{0.5ex}
\begin{minipage}{6.5cm}
 The degeneracy argument described above for K$_3$C$_{60}$ can be generalized
 to integer fillings. Away from half filling the enhancement of the hopping
 matrix elements for an extra electron is different from that for an extra
 hole. The effective enhancement for different fillings are given in the
 adjacent table.
\end{minipage}
\hspace{\fill}
\begin{minipage}[t]{5.2cm}
 \begin{tabular}{l@{\hspace{5ex}}c@{$\;\approx\,$}c}
  \hline\hline
  filling & \multicolumn{2}{c}{enhancement}\\
  \hline
  $n=\;3$ & $\sqrt{3}$                  & 1.73\\[0.5ex]
  $n=2,4$ & ${\sqrt{3}+\sqrt{2}\over2}$ & 1.57\\[0.5ex]
  $n=1,5$ & ${\sqrt{2}+   1    \over2}$ & 1.21\\
  \hline\hline
 \end{tabular}
\end{minipage}

\vspace{0.5ex}
We find that the enhancement decreases as we move away from half filling.
Therefore we expect that away from half filling, correlations become
more important, putting the system closer to the Mott transition, or maybe
even pushing it across the transition, making it an insulator. We have
analyzed the \keyword{doping} dependence of the Mott transition for the same
Hamiltonian as used for K$_3$C$_{60}$, changing the filling of the $t_{1u}$
band from $n=1$ to 5 \cite{doping}. This model describes the
Fm${\bar 3}$m-Fullerides A$_n$C$_{60}$ with fcc lattice and orientational
disorder \cite{rmp}. The critical Coulomb interaction $U_c$, at which the
transition from a metal (for $U<U_c$) to an insulator ($U>U_c$) takes place,
is shown in Figure 9 for the different integer fillings. As expected from
the degeneracy argument, $U_c$ decreases away from $n=3$.
We note, however, that $U_c$ is asymmetric around half filling.
This asymmetry is not present in the simple degeneracy argument, where we
implicitly assumed that the lattice is bipartite. In such a
situation we have electron-hole symmetry, which implies symmetry around
half-filling. For frustrated lattices like the fcc lattice electron-hole
symmetry is broken, leading to the asymmetry in $U_c$ that is seen in Fig.~9.
\begin{figure}
 \begin{minipage}[b]{5.5cm}
 \caption[]{Doping dependence of the Mott transition. The error bars indicate
            the estimate of the critical ratio $U_c/W$ for different integer
            fillings of the $t_{1u}$ band. The calculations are for doped
            Fm${\bar 3}$m Fullerides with fcc lattice structure and
            orientational disorder. The shaded region shows the range
            of $U/W$ in which the doped Fullerides are falling.}
  \vspace{5ex}
 \end{minipage}
 \hspace{\fill}
 \parbox[b]{6cm}{\epsfxsize=6cm\epsffile{Mott.eps}}
\end{figure}

\subsubsection*{Lattice dependence}

\begin{figwindow}[1,r,%
 {{\epsfxsize=2cm\epsffile{triangle.eps}}},{\hspace*{\fill}\\Triangle}]
To understand the effect of \keyword{frustration} in terms of the hopping
arguments that we have made so far, we have to consider more than just one
next-neighbor hop.
The simplest system where we encounter frustration is a triangle with hopping
between neighboring sites. In the single electron case we can form a bonding
state with energy $E_{\rm min}=2\,t,\,$ but because of frustration we
cannot form an antibonding state. Instead the maximum eigenenergy is
$E_{\rm max}=t.\;$ Hence frustration leads to an asymmetric 'band' of
width $W=3\,t.$
\end{figwindow}

In the many-body case the situation is different. Like in the degeneracy
argument we look at the hopping of an extra electron against a (frustrated)
antiferromagnetic background in the large-$U$ limit. For simplicity we assume
a non-degenerate system, i.e.\ there is one electron per site on the triangle,
plus the extra electron. In this case we have to move the extra charge
{\em twice} around the triangle to come back to the many-body state we started
from. Thus in the large-$U$ limit the many-body problem is an eigenvalue
problem of a $6\times6$ matrix with extreme eigenvalues $\pm2\,t.\;$
In the degeneracy argument we have assumed that the kinetic energy of the
extra charge is given by $W/2$. On the triangle, we find, however, that the
hopping energy is larger than that by a factor $4/3$. This suggests that
for frustrated systems the single electron band width $W$ in (\ref{Egap})
should be multiplied by a prefactor larger than one. We therefore expect that
frustration alone, even without degeneracy, shifts the Mott transition to
larger $U.$

To analyze the effect of frustration on the Mott transition we have determined
the critical $U$ for a hypothetical doped Fulleride A$_4$C$_{60}$ with body
centered tetragonal (bct) structure, a lattice without frustration, having
the same band width ($W=0.6\,eV$) as the fcc-Fullerides, shown
in Figure 9. For $U=1.3\,eV$, we find a gap $E_g\approx0.6\,eV$ for the
Fulleride with bct structure, while the frustrated fcc compound is still
metallic $E_g=0$. This difference is entirely due to the lattice structure.
Using realistic parameters for K$_4$C$_{60}$ \cite{A4C60} that crystallizes
in a bct structure
we find a Mott insulator with gap $E_g\approx 0.7\,eV$, which is in line with
experimental findings: $E_g=0.5\pm0.1\,eV$ \cite{Knupfer}.

\subsubsection*{Conclusion}

We have seen that, due to more efficient hopping, orbital degeneracy increases
the critical $U$ at which the Mott transition takes place. This puts
the integer-doped Fullerides close to a Mott transition. Whether they are on
the metallic or insulating side depends on the filling of the band and the
lattice structure: Since the degeneracy enhancement works best for a half
filled band, systems doped away from half-filling tend to be more insulating.
The effect of frustration, on the other hand, is to make the system more
metallic.

\section*{Acknowledgments}

This work has been supported by the Alexander-von-Humboldt Stiftung under the
Feodor-Lynen-Program and the Max-Planck-Forschungspreis.

redpajama_set_name: RedPajamaArXiv


text:
The National Network for the Education of Care Leavers (NNECL) was first established as a volunteer network in June 2013 by higher education institutions and national organisations committed to the progression and support of care experienced students in further and higher education. Working together we aim to transform the opportunities available by championing the continuous improvement of local practice, multi-agency partnerships and national collaboration.
NNECL became a registered charity in 2018 (Registered Charity No. 1180793) led by a Board of Trustees which is responsible for our strategic objectives, financial security and compliance.
The National Strategy Group (NSG) forms a link between educational providers, their networks and national organisations and agencies. It includes nominated regional representatives from further or higher education and members of national organisations committed to the progression and support of care experienced students.
A world in which care experienced people are empowered and supported to thrive and achieve their full educational potential.
Our mission is to support, connect and empower professionals working with care experienced people in different sectors, with the goal of enabling more care experienced people to access and progress successfully through further and higher education.
Our values shape our organisation and inform everything we do.
Equality: We are working for a fair society which is inclusive and celebrates diversity.
Initiative: We seek out effective educational practice and create opportunities.
Collaboration: We achieve more by working together to build relationships and provide personalised support.
Making a difference: We produce useful, evidence-based work which contributes to systemic change.
Our Strategic Objectives
Inform: Contributing to the creation and dissemination of new knowledge, research and useful information about care experienced learners
Connect: Providing networking opportunities for member organisations and engagement with key stakeholders
Support: Supporting and developing evidence-based effective practice
Champion: Championing the work of our member organisations through advocacy and communications
Sustain: Ensuring the future sustainability of our organisation
Board of Trustees The Board of Trustees is responsible for NNECL's strategic objectives, financial security and compliance.
National Strategy Group (NSG) The NSG is the central forum for communication with NNECL Regional Groups.
NNECL Members
NNECL Regional Networks Regional Networks are central to our work and feed into the National Strategy Group.
NNECL Staff NNECL has a small team of employed staff
Partners and Affiliated Organisations We collaborate with organisations with a shared interest in supporting care experienced students.
Get in touch Please do get in touch to share your activities and events, research, ideas, thoughts and general feedback about our services
Join NNECL NNECL Membership Options
Contact Us We love to hear from our members and network so please do get in touch
Support Us Help NNECL to grow

redpajama_set_name: RedPajamaCommonCrawl


text:
The Huachuca Mountain Ride
…Southern Arizona and Tucson
Eastern Huachucas
"This ride links the trails between Brown Canyo, Carr Canyon, and Miller Canyon. "
Thomas Armstrong
Dogs Leashed
Family Friendly While the whole route is a bit long, the route from the corner of Buffalo Soldier Drive and 92 up to the Brown Canyon Ranch is great for beginners.
The forest service road up to Miller Peak is closed during the winter. There are several signs indicating the wilderness area; this is closed to mounting biking.
This ride ranges from beginner to advanced in both skill and endurance, so you'll want a bit of confidence before heading out on this route. There is singletrack, sand, rocks, and climbing. Get ready for a long climb that averages 7% grade for six miles. There are many places to pause and admire the beautiful views of the San Pedro valley.
There are many bathrooms along the way. To refill your water supplies, there is a gas station on the corner of Ramsey Canyon Road and Hwy 92. All of these trails are popular with pedestrians and horseback riders, so please be courteous and give right of way to your fellow trail users.
There are many trails that head to this ride. This description will start from the corner of Buffalo Soldier Drive and Hwy 92.
The start of the Garden Canyon Linear Park Trail starts on the other side of the concrete wash. Following the singletrack, you'll cross St. Andrews Drive into the concrete wash opening. At the T-intersection, turn right and left at the end of the wash. You'll cross an area of rocks stabilized by cement and head up a steep but small hill.
Right before Cherokee Avenue, there is another steep hill, twice the size of the first one. Crossing Cherokee road, there are three trailheads from which to choose. All paths will end up on the same route.
The left trailhead is for beginners, the middle trailhead is for intermediate, and the right trailhead is for advanced riders. After crossing the wash, follow the wash a short distance and turn right. Any of the singletrack trails will lead you to the southwest corner of the park.
There, look for an entrance to the Garden Canyon Connector trail. After leaving the Garden Canyon Connector trail, you'll be following the fence line on Perimeter Trail Brown-Garden #358. A short distance, 10 meters, after the trail turns away from the fence line, turn right. This trail will, again, turn away from the fence line, take a left at the fork and a right at the next fork. You'll enter the Brown Canyon Ranch. Take the unimproved road to Ramsey Canyon Road.
Take a left at Ramsey Canyon Road (paved). Turn right on S Richards Rd (paved). Veer left on S Astro St (unimproved road) to the gate. There is a pedestrian passage on the right. This trail starts off unchallenging, but quickly turns very rocky and steep. At the top of the hill, turn right onto the driveway (gravel).
The paved road is E Astro St. Continue past the stop and before the highway, turn left onto S Saddle Ln (unimproved). This will take you to E Carr Canyon Rd across from the out-of-business Mesquite Tree restaurant.
Turn right and ride all the way up to the Reef Townsite Campground. On the way down, pay attention to the trailhead sign on the right side at one of the switchbacks indicating the Clark Spring Trail #124. Turn right onto the singletrack.
There are two wilderness signs on this trail. These areas are off-limits to mountain bikers, so follow the trail away from the wilderness areas. From the Upper Miller parking lot, take the forest service road down to the Lower Miller parking lot.
Look for the trailhead sign indicating the Perimeter Trail across from the easternmost entrance into the parking lot. There is a gate on the trail. Sometimes you have to open it. Etiquette dictates closing the gate, as the trail is part of an easement with local land owners who graze livestock in the area.
From the Miller Canyon parking lot, retrace your path to Ramsey Canyon Ranch parking lot. At the Ramsey Canyon Ranch turn off, continue straight and turn right at Brown Canyon Road (unimproved road).
Veer left at the "Keep Right" sign. Take this trail to the Brown Canyon spring where a water trough is located. Turn right, away from the wilderness area.
Coming out of Brown Canyon, you'll be on singletrack following a wash. Turn left at the first Y-intersection followed by two more lefts. Continuing on the Perimeter Trail, Brown-Garden section to the Garden Canyon Connector trail to the Garden Canyon Linear Park Trail crossing both Cherokee Avenue and St. Andrews Drive and bringing you back to your start.
Land Manager: USFS - Coronado National Forest Office
in Eastern Huachucas
in Arizona
4,146 Since Nov 7, 2015
Jul 26, 2015 near Sierra…, AZ
Sep 8, 2015 near Sierra…, AZ
Jul 9, 2020 near Sierra…, AZ
Feb 23, 2018 near Sierra…, AZ
Show 14 More Photos
San Pedro Trail (SPT): Boquillas to Millville (Sky Island Traverse)
9.3 mi 14.9 km • 362' Up 110.19 m Up • 484' Down 147.57 m Down
Huachuc…, AZ
Canelo Hills West
16.6 mi 26.6 km • 777' Up 236.93 m Up • 2,063' Down 628.78 m Down
Sierra…, AZ
AZT - Kentucky Camp to Wilderness Boundary
Corona…, AZ
Kentucky Camp Endurance Race - 29 mile course
Kentucky Camp: Short Course
AZT - Helvetia Road to Coronado National Forest Boundary
Virtual Tour of The Huachuca Mountain Ride


The Alien Bass Station, or ABS for short, is a multi effects pedal that we designed specifically for bass players who are looking to shape and control their sound in both live and studio situations. This unique one of a kind pedal combines three essential effects that all bass players should have: �Limiter/Compressor� � �Amp Generator� � �Gamma Fuzz�.
The Alien Bass Station, or ABS for short, is a multi effects pedal that we designed specifically for bass players who are looking to shape and control their sound in both live and studio situations. This unique one of a kind pedal combines three essential effects that all bass players should have: Limiter/Compressor Amp Generator Gamma Fuzz.


As a small business owner, you should consider the ability to be well-organized as one of your most important business skills. It is undoubtedly important for all facets of your business but it is crucial when it comes to accounting.
Of course your focus is on the product or service you offer and making sure that your customers are happy and will come back for more. The problem, when it comes to accounting, is that small business owners often have to do quite a lot of it themselves.
Your tax accountant is a great resource – so use him or her. Don't just wait till tax time rolls around. Talk to your tax accountant about what would make it easier for them to assist you.
My tax accountant helped me set up an easy to use spreadsheet for capturing data, that he can then work with when filing my tax return.
Okay, so with the help of your tax accountant, you've set up the spreadsheet or other method of capturing that all important financial data. But, the system it will only be as good as the data you input. So to save time, input data as soon as you receive it. Don't shuffle it around your desk!
Yes, I know that in the digital age we are all supposed to have paperless offices. However, I believe that it is good to always have hard copy backup. Online data can become corrupted. So I file hard copies of receipts, invoices and other accounting related information. I find that it is easier to file by date but you may prefer to file alphabetically or by project. Whichever way you chose, do it straight away – as per point 2, don't double handle!
Electronic bank statements are another reference point to keep track of incomings and outgoings. I put mine in an online folder which I keep in a portable hard drive. Of course you can access directly from your bank but this can take time.
Note: points three and four are important in case of internet outage. Some people favor using cloud storage but I don't recommend that with potentially sensitive financial information. And again, there is an outage you won't be able to access the information.
I use a financial year desk diary to note transactions. You don't need to write a lot of info – something that will jog your memory is enough. Diary notes are often cited in legal cases along with memos and emails, so in the unlikely or unhappy event that you end up in a dispute with a contractor or supplier you made need to fall back any notation made at the time.


'Under My Skin' চুম্বন HQ স্মারক. Specially requested দ্বারা Beatrix :) Though it's for all of আপনি Huddies out there :). HD Wallpaper and background images in the Huddy club tagged: huddy under my skin house md cuddy kiss make out caps screen captures season 5 5x23.
This Huddy photo might contain ব্যবসা উপযোগী.
yes , looks like he's going to eat her!!!!!!!!


I bet you didn't expect the Equvalence evangelists and denyers to have a battle in your thread.
As for your Nikon choices, sorry I don't know much about the individual N lenses.
Since getting my 5D3 just over a year ago I've slowly built up my Canon FX system without any thought or reference to my 4/3 kit . I just know what I want and need to get the best out of the 5D.
As for Oly, I've not sold any of it, but I know for sure that I'll never buy another Olympus lens, however I just might buy the next E-Mx if it handles better and does a better job with PDAF. Having the ZD150 and ZD300 means I still have a hand in the Olympus 4/3 game and still want to get a better sensor behind my 2 SHG primes.
I hope you find satisfaction with your D800.
Tired of hearing this fallacy about fstop equivalence.
Then understand what Equivalence says.
No, it is not the reason ..
Re: As a photographer ..
Tiger1, I need your help!
Re: Tiger1, I need your help!
Re: true, but . .
Re: Tired of hearing this fallacy about fstop equivalence.
Noise as a function of DOF.


Today's elder population is made up of our parents, grandparents; even brothers, sisters and good friends. People we love and care about. It is so easy to see what needs to be done to help mom and dad out. But do you like to be "told" what to do? Imagine being told that items stacked in your living room are in the way, dangerous, and need to go. These are things that have help memories of your children, when you were married, career awards, school pictures or other milestones.
According to statistics from the National Association of Professional Organizers, the AGS Foundation states that "among older adults living independently, about 75% of falls occur at home. 'Fall hazards' in seniors' homes cause as many as two-thirds of these falls." Eliminating hazards completely is the most affective for making seniors more safe while living at home.
How does this happen? Put yourself in your parents shoes. What if you knew changes needed to be made around the house but you did not have the strength or the mental ability to make them happen?
Aging in Place is the term used by today's elder service providers to make assessments in homes and create more functional and convenient conditions for the resident. This allows our loved ones to be more independent and keep them in their homes and not need a move to assisted living.
Be pro-active. Ask your parents if they have thoughts of what changes might be best for them. Place the decision to make a change with them. And the best tip of all, don't wait until health issues are severe or they are not themselves. Begin with small steps to help them clear clutter around the home.
Set up convenient stations for medicines, check to see if extension or phone cords are where a parent might trip. Help to set up lists to help remember when medicines are to be taken and doctor visits occur.
Consider bring in a professional organizer that specializes in the elder population to help. It is often easier to have a third-party involved than a son or daughter helping mom or dad. Today's organizers work with compassion and know when to comfort while working to meet a goal.
When thinking about the legacy we are leaving, a cluttered home is usually not meant to be part of the inheritance left behind. And most of our parents feel the same way, they are just unsure of how to proceed.
This entry was posted in Clutter Free, Senior Organizing and tagged Aging In Place, AGS Foundation, Chris McKenry, clutter free, dad, elder care, Get It Together LA!. Elder population, mom, parents, retirement, senior moves on October 18, 2011 by Chris McKenry.


Are you or a loved one self-conscious about missing teeth? Dental implants could be the perfect solution to your needs. Implants effectively fill the unwanted gaps in your smile due to missing teeth. Dental implants are designed to blend naturally with your other teeth, producing a beautiful smile.
Many people choose implants to replace a single tooth or several teeth, or to support a full set of dentures. Implants are posts surgically placed into the upper or lower jawbone. They replace the root of one or more missing teeth. Dental implants are made of titanium (a strong, lightweight metal) and other materials that are well accepted by the body.
We take the time to deliver you a natural and durable smile that results in a happier, more confident you.


MHMU - 75 Capped - Custom FFXI Server - Server Xfers!
Re: MHMU - 75 Capped - Custom FFXI Server - Server Xfers!
Awesome server. Everyone is super nice and helpful. Can always find something to get into. Custom game mechanics + gear are a big plus. Admins/GMs are active and helpful, and actually work to fix bugs in a timely manner. It's great!
I am really enjoying my time here. Nice people and admin! Lots of stuff to do.
I've been playing on MHMU for a while now and it's a really great sever! Lots of active players! Definitely would recommend!
Hi guys. Server is stable again. Everything is working like before.


text:
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If you are going to understand the science of psychology, you must first understand science. Science is a process of inquiry – a particular way of thinking. Science is an intellectual process aimed at understanding the natural universe.
Tenacity- is a willingness to accept and maintain ideas as valid knowledge despite contrary evidence and/or lack of supporting evidence.
Intuition- is the direct acquisition of knowledge without intellectual effort or sensory processing.
Authority- is the acceptance of ideas as valid knowledge because some respected source claims they are valid.
Rationalism- is a way of acquiring knowledge through reasoning. The major limitation of rationalism is that the premises must be true, as determined by some other evidence, to arrive at the correct conclusions.
Empiricism- involves gaining knowledge through observation. Empirical observations in science are not limited to direct observations; we can also observe phenomena indirectly through the observation of their impact on other objects, like thermometers.
Each individual scientist, in each research project, must make thoughtful judgments of how best to contribute to science and to humanity.
What distinguishes scientific research from other research is its integration of empirical and rational processes.
Facts are those events that we can observe directly and repeatedly. Most facts observed in psychology are behaviors: verbal and nonverbal behavior, physiological activity, social behavior, and so on. Observation is the empirical process of using one's senses to recognize and record facts. An internal condition is no directly observable fact; we inferred it from the observations of behavior. An inference is an intellectual process in which we derive conclusions from observed facts or from other ideas.
Inferred events, such as gravity, electricity, intelligence, memory, and anxiety, are all rational ideas constructed by the researcher. Such ideas are constructs. Constructs are used by scientists as if they exist in fact and as if they really have a relationship with observable events, used analogically. Confusing a construct for a fact is a logical error know as reification of a construct. A construct relates to observed facts in two ways: we derive it from the observations, and we use it as a basis for predicting future observations.
When we reason from the particular to the general, we are using inductive reasoning, when we use the more abstract and general ideas to return to specifics-that is, to make predictions about future observations-we are using deductive reasoning.
A researcher who begins with empirical observations and then infers constructs is engaged in inductive reasoning. Using constructs as a basis of making predictions about new, specific observations is deductive reasoning. A scientist must use both processes to build and validate conceptual models. We can view the entire scientific research enterprise as a framework within which scientists can carry out inductive and deductive reasoning under the most precise conditions.
A theory is a formalized set of concepts that summarizes and organizes observations and inferences, provides tentative explanations for phenomena, and provides the bases for making predictions. To be scientific, a theory must be testable, that is, it must make specific predictions that scientists can test empirically. Good theories are functional, strong, parsimonious, and valid. Theories are the glue that holds science together and the framework that enables researchers to build on the work of others.
Theories that emphasize induction, called inductive theories, stay close to the empirical data (e.g. B.S Skinner). The more traditional theory, deductive theories, emphasizes deductions from constructs. These deductions are hypotheses, which scientists test empirically through research. Most psychological theories are functional theories that place approximately equal emphasis on induction and deduction.
1. Models are simplified representations of phenomena and have point-to-point correspondence with some of the characteristics of the phenomena.
2. Models provide convenient, manageable, and compact representations of the larger, complex, and mostly unknown reality.
3. Models are incomplete, tentative, and analogical.
4. Models, and manipulations of models, help scientists to organize information, illustrate relationships among parts, create new ideas, and predict new observations.
Scientists judge models and theories primarily by how useful they are in organizing information, explaining phenomena, and generating accurate predictions.
Naturalistic observation requires the researcher to observe the behavior or participants in their natural environment and to not change or limit the environment or the behavior of the participants.
Case-Studies are somewhat more constrained than naturalistic observation, case studies still allow the researcher a good deal of flexibility to shift attention to whatever behaviors seem interesting and relevant.
In Correlational research researchers are interested in quantifying the relationship between two or more variables; they must use precise and consistent procedures for measuring each variable.
Differential research involves comparing two or more groups of participants. We must measure the variables in exactly the same way in each group; that is, the settings and observational procedures must be constrained across groups. The variable that defines the groups is a preexisting variable that is not under the researcher's control (e.g. clinical diagnosis, IQ, gender).
As we move from low to high constraint research, the procedures and findings become more precise. The precision-versus-relevance problem means that researchers should carry out their research at the highest constraint levels possible and then test the findings in natural settings.


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EUSTACE MULLINS SECRETS OF THE FEDERAL RESERVE PDF
Eustace Clarence Mullins (born in Virginia) was an American political writer, author and biographer. A friend of American poet and artist Ezra Pound and. Eustace Mullins is a veteran of the United States Air Force, with thirty-eight .. work called "Secrets of the Temple–the Federal Reserve". The record of the Federal Reserve System proves that it double- crossed the farmers of America at a secret meeting on May 18, , when it raised the rate to 7.
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Search the history of over billion web pages on the Internet. This money power in their hands enabled them to create two world wars, and two depressions, and to bring on the present world crisis, leading to the death of our Con- stitution and the end of our liberties.
What I expected to be a week's labor turned into a lengthy research job of nineteen months, for I discovered, in my initial inquiry, that there existed not one narrative account of the origins and activities of this powerful organization. Consequently, the majority of my information was gathered piecemeal from a vast number of periodicals, ranging from popular magazines such as the Saturday Evening Post to the exclusive bankers 3 magazine, The Economist.
The standard works on the Federal Eeserve System, almost entirely abstruse and technical works on economics, I found of little practical value.
Even in the matter of acceptances, the usual textbooks contained no information upon -such an important item in Am erica's economic history as the changeover from the open- book system of credit to the acceptance system, which has wrought such vast changes in our practice of commerce, and for this in- formation I found only one souree, a few pamphlets published by the American Acceptance Council from to It is, then, little Wonder that the student with a Master's Degree in Eco- nomics from one of the better universities will see here for the first time material which should have been before him in his ele- mentary courses.
The birthplace of the Federal Reserve Act, J ekyl Island, is now operated as a public park by the State of Georgia, but the tourist will find no plaque there commemorating the event. This is not so much an oversight on the part of the park officials as it is a triumph for the more than adequate publicists of the Federal Reserve Board, who have perpetuated the comfortable fiction that the Act was born in the halls of Congress, the.
It is the thhe hope that this and many similar fictions will not long survive the federa, of this work. I wish, to thank my fellow-members of the staff of the Library of Congress, whose very kind suggestions, assistance, and co- operation have " made this book possible. I particularly wish to thank Mr. Luther Evans, Librarian of Congress, Col. They had been tipped off that some very highly-placed people were coming over to Hoboken from New York City to board a train and go away on a secret mission.
What the mission might be, or who the personages involved, none of them knew, hat they were certain that an extremely important event was in the making.
Senator Nelson Aldrich entered the station. Here Was their proof. The reporters gathered around him. He was always good copy, although he was noted for his brusqueness and the difficulty secrdts getting a story from him. This was due to his tieup with the powerful Rubber Trust and the Hte Trust.
As one of the coali- tion of five Republican Senators then ruling the Senate, Aldrieh had used his elective position to enact a series of tariffs and laws favorable to his own interests, and bad been denounced many times for his callous disregard of his oath of office as he devoted his power to the program of international financier.
Aldrich had recently returned from Europe with mullins National Monetary Commission, of which he was head. This was a Com- mission appointed by Congress in response to mullind feeling against big bankers after the artificial Panic of T. The commission had eustave charged to make a thorough study of financial practices before formulating banking and currency reform legislation for Congress It was pointed out at the time that such legislation seemed unlikely to offer genuine reform sdcrets the leadership of a man with Aldrich reesrve known sympathies and employment but Congress was blithely im- pervious to this criticism.
Senator Aldrich and the Thw Monetary Commission had spent nearly two years touring Europe at the American taxpayer's expense.
He and his entourage had dissipated more than three hun- dred thousand dollars of public money, although they had been wined and dined by all the important European financiers and seemed to live off the land wherever they travelled. Since his return to this country, Senator Aldrich had made no effort to report to Congress the mullisn of his trip, nor had he a's yet offered any ideas as to banking reform.
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The srcrets waited for him to provide a cure for the recurring financial panics which had upset business and small for- tunes continually since the Civil "War. He had not come to any defi- nite plan for such a cure.
Piatt Swcrets, professional econ- omist and Assistant Secretary of jullins Treasury, who had. They were followed by Aldrich 's resrve secretary, — 5 — Shelton, and reporters "with, a – number of pieces of luggage. Evidently they were going away for an extended time. The crowd of reporters, representing most of the great New York dailies, were convinced that the secret mission must sercets some connection with the proposed finan- cial reform, and clustered aggressively around Aldrieh, demanding a story.
Aldrieh was accustomed to dealing with reporters, and euetace past them without answering any of the questions shouted at him, nor did his companions so much as look up at the newsmen. They en- tered Aldrieh 5 s private ear at the end of the train, and the shades were immediately drawn over the windows. The reporters were left to speculate with each other on the possible destination of the legis- lators. Their curiosity was increased when they saw coming into the station two more hankers, followed by a group of porters.
Here was Frank Vanderlip, a stocky, genial man who had risen from working as a farmhand to become President of the National City Bank of New York, the most powerful bank in this country, representing the Rocke- feller oil interests and the railroad systems owned by the banking house of Kuhn, Loeb Company.
Davison, senior part- ner of J. Morgan Company, and Charles D. These three financiers were dominant in the small group of New York Bankers which had been accused of controlling the entire money and credit of the United States. In response to the reporter's question, Mr. Vanderlip de- clared that they were only going away for a quiet weekend in the country. These men controlled the oil, railroads, communications, and heavy industry of this country.
Men as resedve as these had no reason to hide their comings and goings, and in the past they kullins been openly scornful of public opinion and public interest. No large new enterprise could be undertaken without coming to one or more of these men, and they saw tc it that their advice and aid were well recompensed.
They elected Congressmen, appointed Judges, and bought and sold newspapers and publishing houses whenever they needed a job done.
One of their number had once earned a' sort of fame by exclaiming "The public be damned! The reporters had the same luck with these bankers that they had — 6 — had with. Aldrieh, and watched their story disappear into Aldrich's private ear.
The next figure to appear was hte so well known to them. This was Paul Moritz "Warburg, a German immigrant who had "been in this country less than eight years, hut who had so availed himself of the privileges of this land of opportunity that he was already a partner in the hanking house of Kuhn, Loeh Company, New York, at a salary of secreys hundred thousand dollars a year.
His family house of M. Warburg Company, of Hamburg and Amsterdam, was the chief German representative of the great European hanking family, the Rothschilds. Liberal amounts of Rothschild funds had enabled Jacob Schiff to purchase a partnership in Kuhn, Loeb Company and less than twenty years later achieve an unchallenged domination over the large railway systems of the United States.
Paul Warburg had not devoted much attention to business since he arrived in this country. Instead, he had spent much of his time writing and lecturing on the subject of monetary reform. This seemed to be in direct conflict with his personal interests and the interests of his employers, for a genuine monetary reform would scerets reduce their profits and power, but his work along these lines brought him an increased salary and even more time to advocate banking legislation which would set up a central hank in the United States similar to those of Europe.
Morgan, when he demonstrated his ability to carry out orders. This was a money panic which had been called by Morgan to wipe out the competition of the Heinze-Morse group in the banking, ship- ping, and iron industries. Strong's appearance as companion of War- burg was no accident, for the J.
Morgan interests and Kuhn, Loeb interests had formed an alliance inknown as the Northern Se- curities Company which dominated the country ever since. Roosevelt was successful in doing this, and the Morgan-Kuhn-Loeb alliance was able to work out a' more complicated and less vulnerable system. For this work, Roosevelt was given the name of "trust-buster.
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Morgan and Company having become international screts inwhen J. Morgan and Anthony Drexel went to London and concluded an agreement with N. Rothschild Company that J. Morgan Company would henceforth act as their agent.
Thus Drexel Company of Philadelphia, J. Morgan had been chosen for this high honor beeause of the affair of the Hall carbines during the civil war, when he swindled — 7 — Warburg and Secdets were silent as the others, and the reporters watched the train leave the station without so much as a quote from any of the bankers. They returned to their papers with nothing more than a few paragraphs on the mysterious departure of the financiers from New York, but not a single metropolitan daily carried the story.
The city editors wisely ignored the event. This was an article by E. Forbes in Frank Leslie's magazine, a feature in praise of Paul "Warburg which incidentally told a story called " Jekyl Island", giving the first reve- lation of what happened in November, Bit by bit, Forbes' ac- count was enlarged upon during the next thirty years, in statements and biographies of the principal characters, until the entire story had come out.
Aldrich's private car, which had left Hoboken Station with drawn shades, had taken the financiers to Jekyl Island, Georgia, to the Jekyl Island Hunt Club, a very exclusive club owned by J.
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Morgan and a small group of influential New York bankers. The club was very isolated, and was used as a comfortable retreat far from the cares of the New York money market.
Fedfral advantageous location made it much in demand for pursuits other than hunting, and on such oc- casions members of the club were informed that they should not appear there for resere certain number of days. When Aldrieh 's group left New York, the club's members had been notified that the club would be occupied for the next two weeks. The Aldrieh group was not interested at this time in hunting.
They had eusttace to Jekyl Island to get a lot of work done, and they wanted to do that work in absolute secrecy. For that reason, the eusttace tomary attendants at the club were given two week vacations, and new servants brought in for this occasion. The Aldrieh group felt that it was imperative that their seceets be eustacd secret, and allowed no visitors during the next two weeks. They were so anxious to rfserve any knowledge of their mission leaking out that they never used last names, calling each other by their first names only, such as Henry Ben, and Paul.
Why all this secrecy? Why this thousand-mile trip in a closed railway ear to a remote hunting club? At stake waa the future control of the money and credit of the United States. If any monetary reform was passed by Congress which was not written by and for the New York bankers, their power would be ended. As the most technieally-inf ormed of the bankers, Paul Warburg was charged with doing most of the drafting of the plan.
Rexerve Nelson Aldrieh was there to see that it came out in a form which could be eustafe through Congress, and the other bankers were there to offer sugges- tions and help on banking problems. The t Jekyl Island group remained at the club for nine days, work- ing steadily to complete their job, for Congress was already complain- ing that the National Monetary Commission seemed to have no solu- tion ready. Despite the common interests of all present, the work did not proceed without frietion.
Senator Aldrieh considered himself the leader of the group, and, as a dictatorial type, could not help ordering everyone about. Aldrieh also felt somewhat out of place as the only member who was not a professional banker.
He knew very little about the technical aspects of financial operations, previously having been content to see to it that the country's laws took reservf of his business for him. Paul "Warburg felt that every question demanded a lecture, and he never lost an opportunity to go into a long discourse or to im- press the others with the extent of his technical knowledge of banking.
This often seemed a waste of time, and drew many barbed remarks from Aldrieh, so that it sometimes required all the diplomacy of Henry P. Davison to keep them at their work.
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People said making clothes inside out was not proper. I disagreed, because clothes that are inside out are as beautiful as a cathedral. Online media is increasingly influential in fashion. I still appreciate individuality. Style is much more interesting than fashion, really. It is difficult to talk about fashion in the abstract, without a human body before my eyes, without drawings, without a choice of fabric – without a practical or visual reality. Success isn't about the end result, it's about what you learn along the way.
Delete the negative; accentuate the positive! You're only as good as your last collection, which is an enormous pressure. I love to design things that people can actually buy. I'm staggered by what a boot costs today. I want people to be afraid of the women I dress. My dresses are very reasonably priced, for dresses that are cut on the body.
There are always protests, whether you do something good or bad. Even if you do something beneficial, people say you do it because it's advertising. Sometimes incompetence is useful. It helps you keep an open mind. Fashion is a very stressful place to work because of the demands of doing the shows – no one expects a writer to produce two books a year on the dot – but it's also a very toxic place to work. It's really easy to get colors right. It's really hard to get black – and neutrals – right. Black is certainly a color but it's also an illusion. Sometimes incompetence is useful. It helps you keep an open mind.


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Jeffris Family Foundation Grant
Archaeology Gallery
The Peter Dougherty Pier
Peter Dougherty Society Corporate Affairs
Peter Dougherty's Mission
Log Cabin Day 2019
Invest in History! Donors were crucial to the acquisition of the Peter Dougherty Historic Home Site located in the Village of Old Mission on the Old Mission Peninsula in Northern Michigan. Donors are also crucial for the successful continued stewardship of this historic site. Your charitable contribution to "Peter Dougherty Society" helps restore and preserve this National Historic Register site and tell the many stories about inspirational people who lived and worked at Old Mission and to demonstrate how their lives contributed to the growth of our multiethnic farming community.
The Peter Dougherty Society will use gifts to renovate, restore and preserve this important piece of Old Mission history. The Society also plans to create a place of adventure, fun and excitement. The educational programs and family-based activities that are planned when this historic landmark is restored, will, we hope, instill in our visitors a sense of enthusiasm and inquiry leading to a lifelong appreciation of our community's history.
To make a gift by check to The Peter Dougherty Historic Home Site, click here to print a Donor Form in MS Word or click on the "Donate" link at the bottom of the page to donate by credit card or Paypal.
Peter Dougherty Society is a non-profit 501(c)(3) organization.
PO Box 101, Old Mission, MI 49673
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TV 7 & 4 and ABC 29 & 8 broadcast 528 times a 30-second pubic service announcement for the "Dougherty House Jeffris Fundraising Campaign" from March through August 2015 – a value pf $13,500. Thank you for your support of our fundraising!
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SAN FRANCISCO / Devil in the details for cabbie No. 666 / He has heckuva time -- taxi panel won't retire his medallion
News // Bay Area & State
Steve Rubenstein, Chronicle Staff Writer
July 25, 2007 Updated: Jan. 15, 2012 2:53 p.m.
SAN FRANCISCO, CA - JULY 24: Thomas George-Williams a driver for Green Cab debates with the San Francisco Taxicab Commission about retiring the number 666 at the bi-monthly meeting at City Hall on July 24, 2007 San Francisco, California. The commission was considering retiring the number at the owners request due to the association of the number with things satanic. (Photo by David Paulm Morris/ The Chronicle)David Paul Morris
The devil gets to keep riding around in a San Francisco cab, the San Francisco taxi commission decreed on Tuesday.
After nearly half an hour of discussion and debate, the commission brought the weight of government to the question of whether to grant a request by a San Francisco cab driver seeking to retire Medallion No. 666 because of the number's association with Satan.
The debate was the best show to play City Hall in some time. It featured commissioners bickering good-naturedly with one another, the head of the cab drivers union arguing before the board with red horns on his head and several other cabbies pleading for common sense, a quality not always found in the stone building at Civic Center.
At issue was the request of veteran driver Michael Byrne, who said he has had bad luck and misfortune since being assigned the supposedly cursed number last year.
Commission President Paul Gillespie said he favored granting the request, "and hopefully we can do this quickly so we never have to deal with this again."
But with the underworld, the Book of Revelation and the Mark of the Beast at stake, quickness was not to be. Six cabbies had something to say during public comment.
"How dare you take Lucifer's number away," said Thomas George-Williams, president of the cab drivers union, who was sporting the red horns. "This is a serious issue."
A cabbie named Tom warned the commission that it was "opening a can of worms" and would soon be deluged with requests to retire other numbers. A cabbie named Barry pointed out that 666 was the address of SS Peter and Paul's Church on Filbert Street, an outfit not thought to be in Satan's pocket. A cabbie named Grasshopper said it was a "bad idea to get into mysticism and voodoo."
And then the commissioners batted the issue about, and it was clear that Gillespie was the lone voice favoring the retirement of the number. Others seemed worried about opening the can of worms, too -- the phrase itself being spoken by at least three commissioners.
"Where does it end?" said Vice President Patricia Breslin. "I lived at an address of 666 and I did not go over to the dark side."
Commissioner Malcolm Heinecke said he might approve the request if the commission decided to charge a "significant fee." Commissioner Ton Oneto pointed out that the number had been around for at least 30 years and San Francisco has somehow survived.
And then the clerk called for a formal vote, and the commission voted 5-1 to grant sympathy to the devil and keep No. 666 on the books. Only Gillespie -- who said he had once driven cab No. 666 himself and was versed with its implications -- voted to kick the number out.
Byrne himself did not show up to get the bad news -- and could not be reached for comment afterward.
When it was all over, the keenest minds at City Hall observed that the commission had discussed the matter for exactly 24 minutes (2 plus 4 equals 6) on the 24th of the month (2 plus 4 equals 6) in a meeting that began at half past 6 o'clock.
Steve Rubenstein
Chronicle staff writer Steve Rubenstein first joined The Chronicle reporting staff in 1976. He has been a metro reporter, a columnist, a reviewer and a feature writer. He left the staff in 2009 to teach elementary school and returned to the staff in 2015. He is married, has a son and a daughter and lives in San Francisco. He is a cyclist and a harmonica player, occasionally at the same time.
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text:
Family: Fabaceae Lindl.
Genus: Dalea L.
Dalea pogonathera A.Gray
This species is accepted, and its native range is Arizona to Texas and N. Mexico.
Accepted Infraspecifics
According to International Legume Database and Information Service
[ILDIS]
International Legume Database and Information Service
Perennial, Not climbing, Herb
Arizona, Mexico Northeast, Mexico Northwest, New Mexico, Texas
Dalea pogonathera var. walkerae (Tharp & F.A.Barkley) B.L.Turner
Includes 1 Accepted Infraspecifics
Parosela pogonathera (A.Gray) A.Heller
Dalea pogonathera A.Gray appears in other Kew resources:
Wright, C. [1352], New Mexico K000846402
Wright, C. [125], New Mexico K000846404
Wright, C. [79], New Mexico K000846403
Torrey [s.n.], Mexico K000082161 syntype
Vasey, G.R. [s.n.], Texas K000846405
First published in Mem. Amer. Acad. Arts, n.s., 4(1): 31 (1849)
Villaseñor, J.L. (2016). Checklist of the native vascular plants of Mexico Revista Mexicana de Biodiversidad 87: 559-902.
Allred, K.W. (2012). Flora Neomexicana, ed. 2, 1: 1-599. Range Science Herbarium, Las Cruces, New Mexico.
Govaerts, R. (2000). World Checklist of Seed Plants Database in ACCESS D: 1-30141.
Isely, D. (1998). Native and Naturalized Leguminosae (Fabaceae) of the United States: 1-1007. Monte L. Bean Life Science Museum. Brigham Young University, Provo, Utah.
International Legume Database and Information Service (ILDIS) V10.39 Nov 2011
http://creativecommons.org/licenses/by/3.0